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Purpose: Accurately evaluating fluid flow behaviors and determining permeability for deforming porous media is time-consuming and remains challenging. This paper aims to propose a novel machine-learning method for the rapid estimation of permeability of porous media at different deformation stages constrained by hydro-mechanical coupling analysis. Design/methodology/approach: A convolutional neural network (CNN) is proposed in this paper, which is guided by the results of finite element coupling analysis of equilibrium equation for mechanical deformation and Boltzmann equation for fluid dynamics during the hydro-mechanical coupling process [denoted as Finite element lattice Boltzmann model (FELBM) in this paper]. The FELBM ensures the Lattice Boltzmann analysis of coupled fluid flow with an unstructured mesh, which varies with the corresponding nodal displacement resulting from mechanical deformation. It provides reliable label data for permeability estimation at different stages using CNN. Findings: The proposed CNN can rapidly and accurately estimate the permeability of deformable porous media, significantly reducing processing time. The application studies demonstrate high accuracy in predicting the permeability of deformable porous media for both the test and validation sets. The corresponding correlation coefficients (R2) is 0.93 for the validation set, and the R2 for the test set A and test set B are 0.93 and 0.94, respectively. Originality/value: This study proposes an innovative approach with the CNN to rapidly estimate permeability in porous media under dynamic deformations, guided by FELBM coupling analysis. The fast and accurate performance of CNN underscores its promising potential for future applications. [ABSTRACT FROM AUTHOR]

Purpose: This study aims to computational numerical simulations to clarify and explore the influences of periodic cellular lattice (PCL) morphological parameters – such as lattice structure topology (simple cubic, body-centered cubic, z-reinforced body-centered cubic [BCCZ], face-centered cubic and z-reinforced face-centered cubic [FCCZ] lattice structures) and porosity value () – on the thermal-hydraulic characteristics of the novel trussed fin-and-elliptical tube heat exchanger (FETHX), which has led to a deeper understanding of the superior heat transfer enhancement ability of the PCL structure. Design/methodology/approach: A three-dimensional computational fluid dynamics (CFD) model is proposed in this paper to provide better understanding of the fluid flow and heat transfer behavior of the PCL structures in the trussed FETHXs associated with different structure topologies and high-porosities. The flow governing equations of the trussed FETHX are solved by the CFD software ANSYS CFX® and use the Menter SST turbulence model to accurately predict flow characteristics in the fluid flow region. Findings: The thermal-hydraulic performance benchmarks analysis – such as field synergy performance and performance evaluation criteria – conducted during this research successfully identified demonstrates that if the high porosity of all PCL structures decrease to 92%, the best thermal-hydraulic performance is provided. Overall, according to the obtained outcomes, the trussed FETHX with the advantages of using BCCZ lattice structure at 92% porosity presents good thermal-hydraulic performance enhancement among all the investigated PCL structures. Originality/value: To the best of the authors' knowledge, this paper is one of the first in the literature that provides thorough thermal-hydraulic characteristics of a novel trussed FETHX with high-porosity PCL structures. [ABSTRACT FROM AUTHOR]

Purpose: This study aims to introduce a novel machine learning feature vector (MLFV) method to bring machine learning to overcome the time-consuming computational fluid dynamics (CFD) simulations for rapidly predicting turbulent flow characteristics with acceptable accuracy. Design/methodology/approach: In this method, CFD snapshots are encoded in a tensor as the input training data. Then, the MLFV learns the relationship between data with a rod filter, which is named feature vector, to learn features by defining functions on it. To demonstrate the accuracy of the MLFV, this method is used to predict the velocity, temperature and turbulent kinetic energy fields of turbulent flow passing over an innovative nature-inspired Dolphin turbulator based on only ten CFD data. Findings: The results indicate that MLFV and CFD contours alongside scatter plots have a good agreement between predicted and solved data with R2 ≃ 1. Also, the error percentage contours and histograms reveal the high precisions of predictions with MAPE = 7.90E-02, 1.45E-02, 7.32E-02 and NRMSE = 1.30E-04, 1.61E-03, 4.54E-05 for prediction velocity, temperature, turbulent kinetic energy fields at Re = 20,000, respectively. Practical implications: The method can have state-of-the-art applications in a wide range of CFD simulations with the ability to train based on small data, which is practical and logical regarding the number of required tests. Originality/value: The paper introduces a novel, innovative and super-fast method named MLFV to address the time-consuming challenges associated with the traditional CFD approach to predict the physics of turbulent heat and fluid flow in real time with the superiority of training based on small data with acceptable accuracy. [ABSTRACT FROM AUTHOR]

Purpose: The purpose of this paper is to study the two-dimensional micropolar fluid flow with conjugate heat transfer and mass transpiration. The considered nanofluid has graphene nanoparticles. Design/methodology/approach: Governing nonlinear partial differential equations are converted to nonlinear ordinary differential equations by similarity transformation. Then, to analyze the flow, the authors derive the dual solutions to the flow problem. Biot number and radiation effect are included in the energy equation. The momentum equation was solved by using boundary conditions, and the temperature equation solved by using hypergeometric series solutions. Nusselt numbers and skin friction coefficients are calculated as functions of the Reynolds number. Further, the problem is governed by other parameters, namely, the magnetic parameter, radiation parameter, Prandtl number and mass transpiration. Graphene nanofluids have shown promising thermal conductivity enhancements due to the high thermal conductivity of graphene and have a wide range of applications affecting the thermal boundary layer and serve as coolants and thermal management systems in electronics or as heat transfer fluids in various industrial processes. Findings: Results show that increasing the magnetic field decreases the momentum and increases thermal radiation. The heat source/sink parameter increases the thermal boundary layer. Increasing the volume fraction decreases the velocity profile and increases the temperature. Increasing the Eringen parameter increases the momentum of the fluid flow. Applications are found in the extrusion of polymer sheets, films and sheets, the manufacturing of plastic wires, the fabrication of fibers and the growth of crystals, among others. Heat sources/sinks are commonly used in electronic devices to transfer the heat generated by high-power semiconductor devices such as power transistors and optoelectronics such as lasers and light-emitting diodes to a fluid medium, thermal radiation on the fluid flow used in spectroscopy to study the properties of materials and also used in thermal imaging to capture and display the infrared radiation emitted by objects. Originality/value: Micropolar fluid flow across stretching/shrinking surfaces is examined. Biot number and radiation effects are included in the energy equation. An increase in the volume fraction decreases the momentum boundary layer thickness. Nusselt numbers and skin friction coefficients are presented versus Reynolds numbers. A dual solution is obtained for a shrinking surface. [ABSTRACT FROM AUTHOR]

Purpose: Cilia serves numerous biological functions in the human body. Malfunctioning of nonmotile or motile cilia will have different kinds of consequences for human health. More specifically, the directed and rhythmic beat of motile cilia facilitates the unidirectional flow of fluids that are crucial in both homeostasis and the development of ciliated tissues. In cilia-dependent hydrodynamic flows, tapering geometries look a lot like the structure of biological pathways and vessels, like airways and lymphatic vessels. In this paper, the Carreau fluid model through the cilia-assisted tapered channel (asymmetric) under the influence of induced magnetic field and convective heat transfer is investigated. Design/methodology/approach: Lubrication theory is a key player in the mathematical formulation of momentum, magnetic field and energy equations. The formulated nonlinear and coupled differential equations are solved with the aid of the homotopy perturbation method (HPM). The graphical results are illustrated with the help of the computational software "Mathematica." Findings: The impact of diverse emerging physical parameters on velocity, induced magnetic field, pressure rise, current density and temperature profiles is presented graphically. It is observed that the cilia length parameter supported the velocity and current density profiles, while the Hartman number and Weissenberg number were opposed. A promising effect of emerging parameters on streamlines is also perceived. Originality/value: The study provides novel aspects of cilia-driven induced magnetohydrodynamics flow of Carreau fluid under the influence of induced magnetic field and convective heat transfer through the asymmetric tapered channel. [ABSTRACT FROM AUTHOR]

Purpose: Flow control has a great potential to contribute to a sustainable society through mitigation of environmental burden. However, the high dimensional and nonlinear nature of fluid flows poses challenges in designing efficient control laws using the control theory. This paper aims to propose a hybrid method (i.e. machine learning and control theory) for feedback control of fluid flows, by which the flow is mapped to the latent space in such a way that the linear control theory can be applied therein. Design/methodology/approach: The authors propose a partially nonlinear linear system extraction autoencoder (pn-LEAE), which consists of convolutional neural networks-based autoencoder (CNN-AE) and a custom layer to extract low-dimensional latent dynamics from fluid velocity field data. This pn-LEAE is designed to extract a linear dynamical system so that the modern control theory can easily be applied, while a nonlinear compression is done with the autoencoder (AE) part so that the latent dynamics conform to that linear system. The key technique is to train this pn-LEAE with the ground truths at two consecutive time instants, whereby the AE part retains its capability as the AE, and the weights in the linear dynamical system are trained simultaneously. Findings: The authors demonstrate the effectiveness of the linear system extracted by the pn-LEAE, as well as the designed control law's effectiveness for a flow around a circular cylinder at the Reynolds number of ReD = 100. When the control law derived in the latent space was applied to the direct numerical simulation, the lift fluctuations were suppressed over 50%. Originality/value: To the best of the authors' knowledge, this is the first attempt using CNN-AE for linearization of fluid flows involving transient development to design a feedback control law. [ABSTRACT FROM AUTHOR]

Purpose: The purpose of this paper is to design a simple and accurate a-posteriori Lagrangian-based error estimator is developed for the class of backward differentiation formula (BDF) algorithms with variable time step size, and the adaptive time-stepping in BDF algorithms is demonstrated for efficient time-dependent simulations in fluid flow and heat transfer. Design/methodology/approach: The Lagrange interpolation polynomial is used to predict the time derivative, and then the accurate primary result is obtained by the Gauss integral, which is applied to evaluate the local error. Not only the generalized formula of the proposed error estimator is presented but also the specific expression for the widely applied BDF1/2/3 is illustrated. Two essential executable MATLAB functions to implement the proposed error estimator are appended for practical applications. Then, the adaptive time-stepping is demonstrated based on the newly proposed error estimator for BDF algorithms. Findings: The validation tests show that the newly proposed error estimator is accurate such that the effectivity index is always close to unity for both linear and nonlinear problems, and it avoids under/overestimation of the exact local error. The applications for fluid dynamics and coupled fluid flow and heat transfer problems depict the advantage of adaptive time-stepping based on the proposed error estimator for time-dependent simulations. Originality/value: In contrast to existing error estimators for BDF algorithms, the present work is more accurate for the local error estimation, and it can be readily extended to practical applications in engineering with a few changes to existing codes, contributing to efficient time-dependent simulations in fluid flow and heat transfer. [ABSTRACT FROM AUTHOR]

Purpose: This paper aims to study the effect of concentric hot circular cylinder inside egg-cavity porous-copper nanofluid on natural convection phenomena. Design/methodology/approach: The finite element method–based Galerkin approach is applied to solve numerically the set of governing equations with appropriate boundary conditions. Findings: The effects of different range parameters, such as Darcy number (10–3 = Da = 10–1), Rayleigh number (103 = Ra = 106), nanoparticle volume fraction (0 = ϑ = 0.06) and eccentricity (−0.3 = e = 0.1) on the fluid flow represent by stream function and heat transfer represent by temperature distribution, local and average Nusselt numbers. Research limitations/implications: A comparison between oval shape and concentric circular concentric cylinder was investigated. Originality/value: In the current numerical study, heat transfer by natural convection was identified inside the new design of egg-shaped cavity as a result of the presence of a circular inside it supported by a porous medium filled with a nanofluid. After reviewing previous studies and considering the importance of heat transfer by free convection inside tubes for many applications, to the best of the authors' knowledge, the current work is the first study that deals with a study and comparison between the common shape (concentric circular tubes) and the new shape (egg-shaped cavity). [ABSTRACT FROM AUTHOR]

Purpose: This paper aims to study a non-Newtonian micropolar fluid flow over a bidirectional flexible surface for multiple exact solutions of momentum boundary layer and thermal transport phenomenon subject to wall mass flux, second-order slip and thermal jump conditions. Design/methodology/approach: The coupled equations are transformed into ordinary differential equations using similarity variables. Analytical and numerical techniques are used to solve the coupled equations for single, dual or multiple solutions. Findings: The results show that the stretching flow, shrinking flow, the wall drag, thermal profile and temperature gradient manifest large changes when treated for special effects of the standard parameters. The role of critical numbers is definitive in locating the domains for the existence of exact solutions. The nondimensional parameters, such as mass transfer parameter, bidirectional moving parameter, plate deformation strength parameter, velocity slips, material parameter, thermal jump and Prandtl number, are considered, and their physical effects are presented graphically. The presence of governing parameters exhibits special effects on the flow, microrotation and temperature distributions, and various exact solutions are obtained for the special parametric cases. Originality/value: The originality and value of this work lie in its exploration of non-Newtonian micropolar fluid flow over a bidirectional flexible surface, highlighting the multiple exact solutions for momentum boundary layers and thermal transport under various physical conditions. The study provides insights into the effects of key parameters on flow and thermal behavior, contributing to the understanding of complex fluid dynamics. [ABSTRACT FROM AUTHOR]

Purpose: The purpose of this paper is the examination of fluid flow around NACA0012 airfoil, with the aim of the numerical validation between the experimental results in the wind tunnel and the Lattice Boltzmann method (LBM) analysis, for the medium Reynolds number (Re = 191,000). The LBM–large Eddy simulation (LES) method described in this paper opens up opportunities for faster computational fluid dynamics (CFD) analysis, because of the LBM scalability on high performance computing architectures, more specifically general purpose graphics processing units (GPGPUs), pertaining at the same time the high resolution LES approach. Design/methodology/approach: Process starts with data collection in open-circuit wind tunnel experiment. Furthermore, the pressure coefficient, as a comparative variable, has been used with varying angle of attack (2°, 4°, 6° and 8°) for both experiment and LBM analysis. To numerically reproduce the experimental results, the LBM coupled with the LES turbulence model, the generalized wall function (GWF) and the cumulant collision operator with D3Q27 velocity set has been used. Also, a mesh independence study has been provided to ensure result congruence. Findings: The proposed LBM methodology is capable of highly accurate predictions when compared with experimental data. Besides, the special significance of this work is the possibility of experimental and CFD comparison for the same domain dimensions. Originality/value: Considering the quality of results, root-mean-square error (RMSE) shows good correlations both for airfoil's upper and lower surface. More precisely, maximal RMSE for the upper surface is 0.105, whereas 0.089 for the lower surface, regarding all angles of attack. [ABSTRACT FROM AUTHOR]

Purpose: The main purpose of this paper was to investigate Lattice Boltzmann (LB) models for the bulk incompressible flow past immersed bodies and to find the set of boundary conditions (BCs) that can be considered suitable for modeling the borders of the numerical simulation domain in such a way as to avoid any effect of these BC on the flow trail that is formed behind the body. Design/methodology/approach: Three different models of the Lattice Boltzmann equation (LBE) and six different sets of BCs are tested. In addition to the classical LBE based on the Bhatnagar–Gross–Krook (BGK) single relaxation time collision model, a moments-based model and a model with two relaxation times were investigated. Findings: The flow pattern and its macroscopic effects on the aerodynamic coefficients appear to be very dependent on the set of BC models used for the borders of the numerical domain. The imposition of pressure at the exit results in pressure perturbations, giving rise to sound waves that propagate back into the simulation domain, producing perturbations on the upwind flow. In the same way, the free-slip BC for the lateral bords appears to affect the trail of vortices behind the body in this range of Reynolds number (Re = 1,000). Originality/value: The paper investigates incompressible flow past immersed bodies and presents the set of BCs that can be considered suitable for modeling the borders of the numerical simulation domain in such a way as to avoid any effect of these BCs on the flow trail that is formed behind the body. [ABSTRACT FROM AUTHOR]

Purpose: Maintaining the turbine blade's temperature within the safety limit is challenging in high-pressure turbines. This paper aims to numerically present the conjugate heat transfer analysis of a novel approach to mini-channel embedded film-cooled flat plate. Design/methodology/approach: Numerical simulations were performed at a steady state using SST k – ω turbulence model. Impingement and film cooling are classical approaches generally adopted for turbine blade analysis. The existing film cooling techniques were compared with the proposed design, where a mini-channel was constructed inside the solid plate. The impact of the blowing ratio (M), Biot number (Bi) and temperature ratio (TR) on overall cooling performance was also studied. Findings: Overall cooling effectiveness was always shown to be higher for mini-channel embedded film-cooled plates. The effectiveness increases with increasing the blowing ratio from M = 0.3 to 0.7, then decreases with increasing blowing ratio (M = 1 and 1.4) due to lift-off conditions. The mini-channel embedded plate resulted in an approximately 21% increase in area-weighted average overall effectiveness at a blowing ratio of 0.7 and Bi = 1.605. The lower uniform temperature was also found for all blowing ratios at a low Biot number, where conduction heat transfer significantly impacts total cooling effectiveness. Originality/value: To the best of the authors' knowledge, this study presents a novel approach to improve the cooling performances of a film-cooled flat plate with better cooling uniformity by using embedded mini-channels. Despite the widespread application of microchannels and mini-channels in thermal and fluid flow analysis, the application of mini-channels for blade cooling is not explored in detail. [ABSTRACT FROM AUTHOR]

Purpose: The purpose of this study is to investigate the effects of the shear-thinning viscoelastic behavior of the surrounding matrix on droplet deformation by weakly compressible smoothed particle hydrodynamics (WC-SPH). Also, the effect of the presence of another droplet is examined. Design/methodology/approach: A modified consistent weakly compressible SPH method is proposed. After code verification, a complete parameter study is performed for a drop under the simple shear flow of a Giesekus liquid. The investigated parameters are 0.048≤Ca ≤ 14.4, 0.1≤c ≤ 10, 0.04≤De ≤ 10, 0≤α ≤ 1 and 0.12≤Re ≤ 12. Findings: It is demonstrated that the rheological behavior of the surrounding fluid could dramatically affect the droplet deformation. It is shown that the droplet deformation is increased by increasing Re and Ca. In contrast, the droplet deformation is decreased by increasing a, De and polymer content. Also, it is indicated the presence of another droplet could drastically affect the flow field, and the primary stress difference (N1) is resonated between two droplets. Originality/value: The main originality of this paper is to introduce a new consistent WC-SPH algorithm. The proposed method is very versatile for tackling the shear-thinning viscoelastic multiphase problems. Furthermore, a complete parameter study is performed for a drop under the simple shear flow of Giesekus liquid. Another novelty of the current paper is studying the effect of the presence of a second droplet. To the best of the authors' knowledge, this is performed for the first time. [ABSTRACT FROM AUTHOR]

Purpose: During thermal laser processes, heat transfer and fluid flow in the melt pool are primary driven by complex physical phenomena that take place at liquid/vapor interface. Hence, the choice and setting of front description methods must be done carefully. Therefore, the purpose of this paper is to investigate to what extent front description methods may bias physical representativeness of numerical models of laser powder bed fusion (LPBF) process at melt pool scale. Design/methodology/approach: Two multiphysical LPBF models are confronted: a Level-Set (LS) front capturing model based on a C++ code and a front tracking model, developed with COMSOL Multiphysics® and based on Arbitrary Lagrangian–Eulerian (ALE) method. To do so, two minimal test cases of increasing complexity are defined. They are simplified to the largest degree, but they integrate multiphysics phenomena that are still relevant to LPBF process. Findings: LS and ALE methods provide very similar descriptions of thermo-hydrodynamic phenomena that occur during LPBF, providing LS interface thickness is correctly calibrated and laser heat source is implemented with a modified continuum surface force formulation. With these calibrations, thermal predictions are identical. However, the velocity field in the LS model is systematically underestimated compared to the ALE approach, but the consequences on the predicted melt pool dimensions are minor. Originality/value: This study fulfils the need for comprehensive methodology bases for modeling and calibrating multiphysical models of LPBF at melt pool scale. This paper also provides with reference data that may be used by any researcher willing to verify their own numerical method. [ABSTRACT FROM AUTHOR]

Purpose: The subject of the fractional calculus theory has gained considerable popularity and importance due to their attractive applications in widespread fields of physics and engineering. The purpose of this paper is to present results on the numerical simulation for time-fractional partial differential equations arising in transonic multiphase flows, which are described by the Tricomi and the Keldysh equations of Robin functions types. Design/methodology/approach: Those resulting mathematical models are solved by using the reproducing kernel method, which provide appropriate solutions in term of infinite series formula. Convergence analysis, error estimations and error bounds under some hypotheses, which provide the theoretical basis of the proposed method are also discussed. Findings: The dynamical properties of these numerical solutions are discussed and the profiles of several representative numerical solutions are illustrated. Finally, the prospects of the gained results and the method are discussed through academic validations. Originality/value: In this paper and for the first time: the authors presented results on the numerical simulation for classes of time-fractional PDEs such as those found in the transonic multiphase flows. The authors applied the reproducing kernel method systematically for the numerical solutions of time-fractional Tricomi and Keldysh equations subject to Robin functions types. [ABSTRACT FROM AUTHOR]

Purpose: The aim of this paper is to investigate the conjugate forced convection in a semi-cylindrical cavity with air flow. Isotherms, streamlines, Bejan number and local entropy generation number are obtained for the semi-cylindrical cavity. Local Nusselt number, the temperature and the skin friction along the interface wall are calculated with different Reynolds numbers and geometric configurations. Design/methodology/approach: The governing differential equations discretized by finite volume method are solved using SIMPLE algorithm. In this study, collocated grid, where all flow variables are stored at the same location, is used. Alternating direction implicit method and tri-diagonal matrix algorithm are used to solve linear algebraic equation systems. Findings: The effects of Reynolds numbers, inlet and exit cross-section, the locations of exit section on fluid flow are also numerically investigated. It has been observed that since the secondary vortices developed near the exit cross-section negatively affect heat transfer, the temperature value is higher at this region. Better cooling inside cavity is provided in the cases of higher Re number, larger inlet and exit cross-section. The minimum average Nu numbers are computed for the location of L = 0.40 and the minimum total entropy generation numbers are founded in the case of L = 0.20. Originality/value: This study provides insight into proper cooling and entropy generation inside the semi-cylindrical cavity for different conditions. [ABSTRACT FROM AUTHOR]

Purpose: The purpose of this paper is to present a new discretisation scheme, based on equation-coupled approach and high-order five-point integrated radial basis function (IRBF) approximations, for solving the first biharmonic equation, and its applications in fluid dynamics. Design/methodology/approach: The first biharmonic equation, which can be defined in a rectangular or non-rectangular domain, is replaced by two Poisson equations. The field variables are approximated on overlapping local regions of only five grid points, where the IRBF approximations are constructed to include nodal values of not only the field variables but also their second-order derivatives and higher-order ones along the grid lines. In computing the Dirichlet boundary condition for an intermediate variable, the integration constants are used to incorporate the boundary values of the first-order derivative into the boundary IRBF approximation. Findings: These proposed IRBF approximations on the stencil and on the boundary enable the boundary values of the derivative to be exactly imposed, and the IRBF solution to be much more accurate and not influenced much by the RBF width. The error is reduced at a rate that is much greater than four. In fluid dynamics applications, the method is able to capture well the structure of steady highly non-linear fluid flows using relatively coarse grids. Originality/value: The main contribution of this study lies in the development of an effective high-order five-point stencil based on IRBFs for solving the first biharmonic equation in a coupled set of two Poisson equations. A fast rate of convergence (up to 11) is achieved. [ABSTRACT FROM AUTHOR]

Purpose The purpose of this paper is to theoretically study the problem of the unsteady boundary layer flow past a permeable curved stretching/shrinking surface in the presence of a uniform magnetic field. The governing nonlinear partial differential equations are converted into ordinary differential equations by similarity transformation, which are then solved numerically.Design/methodology/approach The transformed system of ordinary differential equations was solved using a fourth-order Runge-Kutta integration scheme. Results for the reduced skin friction coefficient and velocity profiles are presented through graphs and tables for several sets of values of the governing parameters. The effects of these parameters on the flow characteristics are thoroughly examined.Findings Results show that for the both cases of stretching and shrinking surfaces, multiple solutions exist for a certain range of the curvature, mass suction, unsteadiness, stretching/shrinking parameters and magnetic field parameter.Originality/value The paper describes how multiple (dual) solutions for the flow reversals are obtained. It is shown that the solutions exist up to a critical value of the shrinking parameter, beyond which the boundary layer separates from the surface and the solution based upon the boundary layer approximations is not possible. [ABSTRACT FROM AUTHOR]

Purpose: The purpose of this paper, computational fluid dynamics (CFD) work, is to promote turbulent thermal convection in a heated circular tube using a passive scheme of a slotted twisted sheet. Design/methodology/approach: The inventive design uses square-cut and conjugate triangular perforations to diversify the twisted tape for better thermal convection. The current novel passive scheme methodology is accomplished by carving the same square cuts and slitting various sizes of equilateral triangle perforations (side length varies between 8 and 16 mm). The re-normalisation group turbulence model and the semi-implicit method for pressure-linked equation method examine the turbulent thermal convection aspects of all simulations at different Reynolds numbers (6,000, 10,000 and 14,000). Findings: The analyses of simulations exhibit that the placement of a twisted tape with triangle perforations and equidistant square cuts can effectually promote thermal convection in a circular tube. A larger-sized triangle perforation can increase the thermal convection enhancement and thermal performance factor, but an enlarged perforation may decrease the thermal convection enhancement and thermal performance factor. As a result, compared with the smooth circular tube, the circular tube with the slotted twisted sheet slit by a 10 mm equilateral triangle brings about the maximum improvement ratio of the mean Nusselt number of about 2.8 at Re = 6,000. Under weighing the friction through the circular tube, the tube with the slotted twisted sheet slit by a 10 mm equilateral triangle gains the best thermal performance factor of about 1.36 at Re = 6,000. Research limitations/implications: The working fluid is water and its physical features are assumed to be constant. In addition, the fluid is considered a steady flow in this CFD work. Practical implications: These CFD predictions will benefit the development of heat exchanger tubes equipped with a slotted twisted sheet to acquire preferable thermal convection enhancement. Social implications: Higher thermal performance achieved by placing a slotted twisted tape in a heated tube will benefit society in lower energy consumption, machinery maintenance costs and impact on the environment. Originality/value: This study combined triangle perforations and square cuts on the twisted sheet. This combination can induce the fluid flow across the sheet to disturb the swirling flow and then promote the fluid mixing to increase thermal convection. Therefore, this modified tape can be a profitable passive device for designing a heat exchanger. [ABSTRACT FROM AUTHOR]

Purpose: The classical integer derivative diffusionmodels for fluid flow within a channel of parallel walls, for heat transfer within a rectangular fin and for impulsive acceleration of a quiescent Newtonian fluid within a circular pipe are initially generalized by introducing fractional derivatives. The purpose of this paper is to represent solutions as steady and transient parts. Afterward, making use of separation of variables, a fractional Sturm–Liouville eigenvalue task is posed whose eigenvalues and eigenfunctions enable us to write down the transient solution in the Fourier series involving also Mittag–Leffler function. An alternative solution based on the Laplace transform method is also provided. Design/methodology/approach: In this work, an analytical formulation is presented concerning the transient and passage to steady state in fluid flow and heat transfer within the diffusion fractional models. Findings: From the closed-form solutions, it is clear to visualize the start-up process of physical diffusion phenomena in fractional order models. In particular, impacts of fractional derivative in different time regimes are clarified, namely, the early time zone of acceleration, the transition zone and the late time regime of deceleration. Originality/value: With the newly developing field of fractional calculus, the classical heat and mass transfer analysis has been modified to account for the fractional order derivative concept. [ABSTRACT FROM AUTHOR]

Purpose The purpose of this paper is to solve unsteady compressible Navier–Stokes equations without the commonly used dual-time loop. The authors would like to use an adaptive time-stepping (ATS)-based local error control instead of CFL-based time-stepping technique. Also, an all-speed flow algorithm is implemented with simple low dissipation AUSM convective scheme, which can be computed without preconditioning which in general destroys the time accuracy.Design/methodology/approach In transient flow computations, the time-step is generally determined from the CFL condition. In this paper, the authors demonstrate the usefulness of ATS based on local time-stepping previously used extensively in ordinary differential equations (ODE) integration. This method is implemented in an implicit framework to ensure the numerical domain of dependence always contains the physical domain of dependence.Findings In this paper, the authors limit their focus to capture the unsteady physics for three cases: Sod's shock-tube problem, Stokes' second problem and a circular cylinder. The use of ATS with local truncation error control enables the solver to use the maximum allowable time-step, for the prescribed tolerance of error. The algorithm is also capable of converging very rapidly to the steady state (if there is any) after the initial transient phase. The authors present here only the first-order time-stepping scheme. An algorithmic comparison is made between the proposed adaptive time-stepping method and the commonly used dual time-stepping approach that indicates the former will be more efficient.Originality/value The original method of ATS based on local error control is used extensively in ODE integration, whereas, this method is not so popular in the computational fluid dynamics (CFD) community. In this paper, the authors investigate its use in the unsteady CFD computations. The authors hope that it would provide CFD researchers with an algorithm based on an adaptive time-stepping approach for unsteady calculations. [ABSTRACT FROM AUTHOR]

Purpose: Thus, the purposes of this study are to study the limits of applicability of the self-similar solution to the problem of fluid flow, heat and mass transfer in conical gaps with small conicity angles, to substantiate the impossibility of using a self-similar formulation of the problem in the case of large conicity angles and to substantiate the absence of the need to take into account the radial thermal conductivity in the energy equation in its self-similar formulation for the conicity angles up to 4°. Design/methodology/approach: In the present work, an in-depth and extended analysis of the features of fluid flow and heat transfer in a conical gap at small angles of conicity up to 4° is performed. The Couette-type flow arising, in this case, was modeled using a self-similar formulation of the problem. A detailed analysis of fluid flow calculations using a self-similar system of equations showed that they provide the best agreement with experiments than other known approaches. It is confirmed that the self-similar system of flow and heat transfer equations is applicable only to small angles of conicity up to 4°, whereas, at large angles of conicity, this approach becomes unreasonable and leads to significantly inaccurate results. The heat transfer process in a conical gap with small angles of conicity can be modeled using the self-similar energy equation in the boundary layer approximation. It was shown that taking into account the radial thermal conductivity in the self-similar energy equation at small conicity angles up to 4° leads to maximum deviations of the Nusselt number up to 1.5% compared with the energy equation in the boundary layer approximation without taking into account the radial thermal conductivity. Findings: It is confirmed that the self-similar system of fluid flow equations is applicable only for small conicity angles up to 4°. The inclusion of radial thermal conductivity in the model unnecessarily complicates the mathematical formulation of the problem and at small conicity angles up to 4° leads to insignificant deviations of the Nusselt number (maximum 1.5%). Heat transfer in a conical gap with small conicity angles up to 4° can be modeled using the self-similar energy equation in the boundary layer approximation. Originality/value: This paper investigates the question of the validity of taking into account the radial heat conduction in the energy equation. [ABSTRACT FROM AUTHOR]

Purpose – The purpose of this paper is to point out a paradox in variational theory for viscous flows. Chien (1984) claimed that a variational principle of maximum power loses for viscous fluids was established, however, it violated the well-known Helmholtz’s principle. Design/methodology/approach – Restricted variables are introduced in the derivation, the first order and the second order of variation of the restricted variables are zero. Findings – An approximate variational principle of minimum power loses is established, which agrees with the Helmholtz’s principle, and the paradox is solved. Research limitations/implications – This paper focusses on incompressible viscose flows, and the theory can be extended to compressible one and other viscose flows. It is still difficult to obtain a variational formulation for Navier-Stokes equations. Practical implications – The variational principle of minimum power loses can be directly used for numerical methods and analytical analysis. Originality/value – It is proved that Chien’s variational principle is a minimum principle. [ABSTRACT FROM AUTHOR]

Purpose: The purpose of this paper is to investigate micropolar magnetohydrodynamics (MHD) fluid flow passing over a vertical plate. Three different base fluids have been used that include water, ethylene glycol and ethylene glycol/water (50%–50%). Also, a nanoparticle was used in all of the base fluids. The effects of natural convection heat transfer and magnetic field have been taken into account. Design/methodology/approach: The main purpose of solving the governing equations is to scrutinize the effects of the magnetic parameter, the nanoparticle volume fraction, micropolar parameter and nanoparticles shape factor on velocity, temperature and microrotation profiles, the skin friction coefficient and the Nusselt number. These surveys have been considered for three base fluids simultaneously. Findings: The results indicate that for water-based fluids, the temperature profile of lamina-shaped nanoparticles is 38.09% higher than brick-shaped nanoparticles. Originality/value: This paper provides micropolar MHD fluid flow analysis considering natural convection heat transfer and magnetic field in three different base fluids. The aim of assessments is the diagnosis of some parameter effects, such as magnetic parameter and nanoparticle volume fraction, on velocity, temperature and microrotation profiles and components. Also, the use of mixed base fluids presented as a novelty in this paper. [ABSTRACT FROM AUTHOR]

Purpose: The purpose of this paper is to formulate and analyse a convergent numerical scheme and apply it to investigate the coupled problem of fluid flow with heat and mass transfer in a porous channel with variable transport properties. Design/methodology/approach: This paper derives the model by assuming a fully developed Brinkman flow with temperature-dependent viscosity and incorporating viscous dissipation, variable transport properties and nonlinear heat and mass sources. For the numerical formulation, the nonlinear sources are treated in semi-implicit manner, whereas the non-constant transport properties are treated by lagging in time leading to decoupled diagonally dominant systems. The consistency, stability and convergence results are derived. The method of manufactured solutions is adopted to numerically verify the theoretical results. The scheme is then applied to investigate the impact of relevant parameters, such as the viscosity parameter, on the flow. Findings: Based on the numerical findings, the proposed scheme was found to be unconditionally stable and convergent with first- and second-order accuracy in time and space, respectively. Physical results showed that the flow parameters have influence on the flow fields, particularly, the flow is enhanced by increasing porosity and viscosity parameters and the concentration decreases with increasing diffusivity, whereas both the temperature and Nusselt number decrease with increasing thermal conductivity. Practical implications: Numerically, the proposed numerical scheme can be applied without concerns on time steps size restrictions. Non-physical solutions cannot be computed. Physically, the flow can be increased by increasing the viscosity parameters. Pollutants with higher diffusivity will have their concentration decreased faster than those of lower diffusivity. The fluid temperature would decrease faster if its thermal conductivity is higher. Originality/value: A fully coupled fluid flow with heat and mass transfer problem having nonlinear properties and nonlinear fractional sources and sink terms, presumably, has not been investigated in a general form as done in this study. The detailed numerical analysis of this particular scheme for the identified general model has also not been considered in the past, to the best of the author's knowledge. [ABSTRACT FROM AUTHOR]

Purpose: The dynamic stability of nano-tubes is an important issue in engineering applications. Dynamic stability of anti-symmetric coupled-carbon nanotubes (C-CNTs)-systems in thermal environment is presented in this paper. In this system, the top and bottom CNTs are subjected to axial harmonic load and action of the viscous fluid, respectively. Design/methodology/approach: The coupling and surrounding mediums of the CNTs are simulated by visco-Pasternak foundation containing the spring, shear and damper coefficients. Based on the Timoshenko beam theory and Hamilton's principle, the coupled motion equations are derived considering size effects using Eringen's nonlocal theory. Using the exact solution in conjunction with Bolotin's method, the dynamic instability region (DIR) of the coupled structure is obtained. The effects of various parameters such as small scale parameter, Knudsen number, fluid velocity, static load factor, temperature change, surrounding medium and nanotubes aspect ratio are shown on the DIR of the coupled system. Findings: Results indicate that considering parameters such as small scale effects, static load factor, Knudsen number and fluid velocity shifts the DIR of C-CNTs to a lower frequency zone. Originality/value: To the best of our knowledge, analyses of anti-symmetric coupled CNTs have not received enough attentions so far. In order to optimize the nanostructures designing, the main purpose of the present paper is to investigate nonlocal dynamic stability of CNTs subjected to axial harmonic load coupled with CNTs conveying fluid. [ABSTRACT FROM AUTHOR]

Purpose: The purpose of the paper was the application of computational fluid dynamics (CFD) techniques in fluid flow using Maxwell's equation for partial slip modelling, estimating the flow parameters, and selecting tangential momentum accommodation coefficient (TMAC) for tight rock samples in permeability calculations. Design/methodology/approach: The paper presents a numerical analysis of fluid flow in a low-porosity rock sample by using CFD. Modelling results allowed to determine mass flow rates in a rock sample and to calculate permeability values using a modified Darcy's equation. Three-dimensional (3D) geometrical model of rock sample generated using computed X-ray tomography was used in the analysis. Steady-state calculations were carried out for defined boundary conditions in the form of pressure drop. The simulations were applied taking into account the slip phenomenon described by Maxwell's slip model and TMAC. Findings: Values of permeability were calculated for different values of TMAC, which vary from 0 to 1. Results in the form of gas mass flow rates were compared with the measured value of permeability for rock sample, which confirmed the high accuracy of the presented model. Practical implications: Calculations of fluid flow in porous media using CFD can be used to determine rock samples' permeability. In slip flow regime, Maxwell's slip model can be applied and the empirical value of TMAC can be properly estimated. Originality/value: This paper presents the usage of CFD, Maxwell's equation for partial slip modelling, in fluid flow mechanism for tight rock samples. 3D geometric models were generated using created pre-processor (poROSE software) and applied in the raw form for simulation. [ABSTRACT FROM AUTHOR]

Purpose: This paper aims to numerically study the laminar natural convection in a thermosyphon filled with liquid gallium exposed to a constant magnetic field. The left wall of the thermosyphon is at an uniformed hot temperature, whereas the right wall is at a uniform cold temperature. The top and bottom walls are considered to be adiabatic. All walls are electrically insulated. The effects of Hartmann number, in a wide range of Rayleigh number and aspect ratio combinations, on the natural convection throughout the thermosyphon, are investigated and discussed. Furthermore, different forces that influence the natural flow structure are studied. Design/methodology/approach: A Fortran code is developed based on the finite volume method to solve the two-dimensional unsteady governing equations. Findings: Imposing a magnetic field improves the stability of the fluid flow and thus reduces the Nusselt number. For a given Hartmann and Rayleigh number, there is an optimum aspect ratio for which the average velocity becomes maximum. Research limitations/implications: This paper is a two-dimensional investigation. Originality/value: To the best of the authors' knowledge, the effect of the magnetic field on natural convection of liquid gallium in the considered thermosyphon has not been studied numerically in detail. The results of this paper would be helpful in considering the application of the low Prandtl number's liquid metals in thermosyphon MHD generators and certain cooling devices. [ABSTRACT FROM AUTHOR]

Purpose: Two-dimensional incompressible fluid flows around a rectangular shape placed over a larger rectangular shape at low Reynolds numbers (Re) have been numerically analyzed in the present work. The vortex shedding is investigated at different arrangements of the two shapes allowing the investigation of three possible configurations. The calculations are carried out for several values of Re ranging from 1 to 200. The effect of the obstacle geometry on the vortex shedding is analyzed for crawling, steady and unsteady regimes. The analysis of the flow evolution shows that with increasing Re beyond a certain critical value, the flow becomes unstable and undergoes a bifurcation. This paper aims to observe that the transition of the unsteady regime is performed by a Hopf bifurcation. The critical Re beyond which the flow becomes unsteady is determined for each configuration. A special attention is paid to compute the drag and lift forces acting on the rectangular shapes, which allowed determining; the best configuration in terms of both drag and lift. The unsteady periodic wake is characterized by the Strouhal number, which varies with the Re and the obstacle geometry. Hence, the values of vortex shedding frequencies are calculated in this work. Design/methodology/approach: The dimensionless Navier–Stokes equations were numerically solved using the following numerical technique based on the finite volume method. The temporal discretization of the time derivative is performed by an Euler backward second-order implicit scheme. Non-linear terms are evaluated explicitly; while, viscous terms are treated implicitly. The strong velocity–pressure coupling present in the continuity and the momentum equations are handled by implementing the projection method. Findings: The present paper aims to numerically study the effect of the obstacle geometry on the vortex shedding and on the drag and lift forces to analyze the flow structure around three configurations at crawling, steady and unsteady regimes. Originality/value: A special attention is paid to compute the drag and lift forces acting on the rectangular shapes, which allowed determining; the best shapes configuration in terms of both drag and lift. [ABSTRACT FROM AUTHOR]

Purpose: This paper aims to develop a numerical study of the steady natural convection in an inclined square porous cavity filled by a nanofluid with sinusoidal temperature distribution on the side walls and adiabatic conditions on the upper and lower walls. Design/methodology/approach: Governing equations transformed in terms of the dimensionless variables using the Darcy–Boussinesq approximation have been solved numerically using a central finite-difference scheme. The Gaus-Siedel iteration technique was used for the system of discretized equations. The two-phase nanofluid model including the Brownian diffusion and thermophoresis effects has been considered for simulation of nanofluid transport inside the cavity. Findings: The numerical results of streamlines, isotherms and isoconcentrations are investigated and the effect of different important parameters, such as inclination angle of the cavity, amplitude ratio of the sinusoidal temperature or phase deviation, is discussed. The results obtained for no inclination of the cavity are compared and successfully validated with previous reported results of the literature. The important findings of the study are focused on the changes made by the inclination angle and the periodic thermal boundary conditions, on the heat and fluid flow. Originality/value: The originality of the present study is given by the mathematical model presented for an inclined cavity, the numerical solution with new results for inclined cavity and the applications for design of solar energy devices such as solar collectors in which the boundary conditions vary with time because of changes in weather conditions. [ABSTRACT FROM AUTHOR]

Purpose: This paper aims to numerically analyze the effect of non-gray gas radiation on mixed convection in a horizontal circular duct with isothermal partial heating from the sidewall. The influence of heater location on heat transfer, fluid flow and entropy generation is given and discussed in this study. Design/methodology/approach: The numerical computation of heat transfer and fluid flow has been developed by the commercial finite element software COMSOL Multiphysics. Radiation code is developed based on the T10 Ray-Tracing method, and the radiative properties of the medium are computed based on the statistical narrow band correlated-k model. Findings: The obtained results depicted that the radiation considerably contributes to the temperature homogenization of the gas. The findings highlight the impact of the heater location on swirling flow. It is also shown that the laterally heating process provides better energy efficiency than heating from the top of the enclosure. Originality/value: This study is performed to improve heat transfer and to minimize entropy generation. Therefore, it is conceivable to improve the model design of industrial applications. [ABSTRACT FROM AUTHOR]

Purpose: This paper aims to use the Lattice Boltzmann method (LBM) to numerically simulate the natural convection heat transfer of Cu-water nanofluid in an L-shaped enclosure with curved boundaries. Design/methodology/approach: LBM on three different models of curved L-shape cavity using staircase approach is applied to perform a comparative investigation for the effects of curved boundary on fluid flow and heat transfer. The staircase approximation is a straightforward and efficient approach to simulating curved boundaries in LBM. Findings: The effect of curved boundary on natural convection in different parameter ranges of Rayleigh number and nanoparticle volume fraction is investigated. The curved L-shape results are also compared to the rectangular L-shape results that were also achieved in this study. The curved boundary LBM simulation is also validated with existing studies, which shows great accuracy in this study. The results show that the top curved boundary in curved L-shape models causes a notable increase in the Nusselt number values. Originality/value: Based on existing literature, there is a lack of comparative studies which would specifically examine the effects of curved boundaries on natural convection in closed cavities. Particularly, the application of curved boundaries to an L-shape cavity has not been examined. In this study, curved boundaries are applied to the sharp corners of the bending section in the L-shape and the results of the curved L-shape models are compared to the simple rectangular L-shape model. Hence, a comparative evaluation is performed for the effect of curved boundaries on fluid flow in the L-shape enclosure. [ABSTRACT FROM AUTHOR]

Purpose The purpose of this paper is to first deduce a new form of the exact analytic solution of the well-known nonlinear second-order differential equation subject to a set of mixed nonlinear Robin and Neumann boundary conditions that model the thin film flows of fourth-grade fluids, and second to compare the approximate analytic solutions by the Adomian decomposition method (ADM) with the new exact analytic solution to validate its accuracy for parametric simulations of the thin film fluid flows, even for more complex models of non-Newtonian fluids in industrial applications.Design/methodology/approach The approach to calculating a new form of the exact analytic solution of thin film fluid flows rests upon a sequence of transformations including the modification of the classic technique due to Scipione del Ferro and Niccolò Fontana Tartaglia. Next the authors establish a lemma that justifies the new expression of the exact analytic solution for thin film fluid flows of fourth-grade fluids. Second, the authors apply a modification of the systematic ADM to quickly and easily calculate the sequence of analytic approximate solutions for this strongly nonlinear model of thin film flow of fourth-grade fluids. The ADM has been previously demonstrated to be eminently practical with widespread applicability to frontier problems arising in scientific and engineering applications. Herein, the authors seek to establish the relative merits of the ADM in the context of the thin film flows of fourth-grade fluids.Findings The ADM is shown to closely agree with the new expression of the exact analytic solution. The authors have calculated the error remainder functions and the maximal error remainder parameters in the error analysis to corroborate the solutions. The error analysis demonstrates the rapid rate of convergence and that we can approximate the exact solution as closely as we please; furthermore the rate of convergence is shown to be approximately exponential, and thus only a low-stage approximation will be adequate for engineering simulations as previously documented in the literature.Originality/value This paper presents an accurate work for solving thin film flows of fourth-grade fluids. The authors have compared the approximate analytic solutions by the ADM with the new expression of the exact analytic solution for this strongly nonlinear model. The authors commend this technique for more complex thin film fluid flow models. [ABSTRACT FROM AUTHOR]

Purpose: This paper aims to consider numerical analysis of laminar double-diffusive natural convection inside a non-homogeneous closed medium composed of a saturated porous matrix and a clear binary fluid under spatial sinusoidal heating/cooling on one side wall and uniform salting. Design/methodology/approach: The domain of interest is a partially square porous enclosure with sinusoidal wall heating and cooling. The fluid flow, heat and mass transfer dimensionless governing equations associated with the corresponding boundary conditions are discretized using the finite volume method. The resulting algebraic equations are solved by an in-house FORTRAN code and the SIMPLE algorithm to handle the non-linear character of conservation equations. The validity of the in-house FORTRAN code is checked by comparing the current results with previously published experimental and numerical works. The effect of the porous layer thickness, the spatial frequency of heating and cooling, the Darcy number, the Rayleigh number and the porous to fluid thermal conductivity ratio is analyzed. Findings: The results demonstrate that for high values of the spatial frequency of heating and cooling (f = 7), temperature contours show periodic variations with positive and negative values providing higher temperature gradient near the thermally active wall. In this case, the temperature variation is mainly in the porous layer, while the temperature of the clear fluid region is practically the same as that imposed on the left vertical wall. This aspect can have a beneficial impact on thermal insulation. Besides, the porous to fluid thermal conductivity ratio, Rk , has practically no effect on Shhot wall , contrary to Nuinterface where a strong increase is observed as Rk is increased from 0.1 to 100, and much heat transfer from the hot wall to the clear fluid via the porous media is obtained. Practical implications: The findings are useful for devices working on double-diffusive natural convection inside non-homogenous cavities. Originality/value: The authors believe that the presented results are original and have not been published elsewhere. [ABSTRACT FROM AUTHOR]

Purpose: This paper aims to study the natural convection of a nanofluid inside a cavity which contains obstacles using lattice Boltzmann method (LBM). The results have focused mainly on various parameters such as number and aspect ratio of roughness elements and different nanoparticle volume fraction. The isotherms and streamlines are presented to describe the hydrodynamics and thermal behaviors of the nanofluid flow throughout the enclosure. Design/methodology/approach: The methodology of this paper consists of mathematical model, statement of the problem, nanofluid thermophysical properties, lattice Boltzmann method, LBM for fluid flow, LBM for heat transfer, numerical strategy, boundary conditions, Nusselt (Nu) number calculation, code validation and grid independence. Findings: Natural convection heat transfers of a nanofluid inside cavities with and without rough elements have been studied. Lattice Boltzmann technique has been used as numerical approach. The results showed that at higher Rayleigh number (Ra = 106), there are denser streamlines near the left (source) and right wall (sink) which results in better cooling and enhances convective heat rejection to the heat sink. After a distinctive aspect ratio of rough elements (A = 0.1), change in streamline pattern which arises from increasing of aspect ratio does not have an important effect on isotherms. Results indicate that for lower Rayleigh number (Ra = 103), no variation in average Nu is observed with increasing in number of roughness, while for higher one (Ra = 106) average Nu decreases from N = 0 (smooth cavity) up to N = 4 and then remains constant (N = 6). Originality/value: Currently, no argumentative and comprehensive extraction can be concluded without fully understanding the role of different arrangement of roughness. Some geometrical parameters such as aspect ratio, number and position of rough elements have been considered. Also, the effect of nanoparticle concentration was studied at different Ra number. Briefly, using LBM, this paper aims to investigate the natural convection of a nanofluid flow on the thermal and hydrodynamics parameters in the presence of rough element with various arrangements. [ABSTRACT FROM AUTHOR]

Purpose: The purpose of this paper is to carry out a detailed investigation to study the natural convection of a non-Newtonian nanofluid flow between two vertical parallel plates. In this study, sodium alginate has been taken as a base fluid and nanoparticles that added to it are copper and silver. Maxwell–Garnetts and Brinkman models are used to calculate the effective thermal conductivity and viscosity of nanofluid, respectively. Design/methodology/approach: The authors used two methods in this study, namely, Galerkin's method and homotopy perturbation method. Findings: This paper investigates the velocity and temperature profile of nanofluid and the real fluid flow between two vertical parallel plates. The impacts of physical parameters such as nanofluid volume fraction and dimensionless non-Newtonian viscosity are discussed. Originality/value: Coupled non-linear differential equations are solved for velocity and temperature. A model is proposed in such a way that the authors may get the solution of real fluid from the nanofluid by neglecting the nano term. The authors do not require a further calculation for real fluid problem. [ABSTRACT FROM AUTHOR]

Purpose: The purpose of this paper is concerned with developing two integrable Korteweg de-Vries (KdV) equations of third- and fifth-orders; each possesses time-dependent coefficients. The study shows that multiple soliton solutions exist and multiple complex soliton solutions exist for these two equations. Design/methodology/approach: The integrability of each of the developed models has been confirmed by using the Painlev´e analysis. The author uses the complex forms of the simplified Hirota's method to obtain two fundamentally different sets of solutions, multiple real and multiple complex soliton solutions for each model. Findings: The time-dependent KdV equations feature interesting results in propagation of waves and fluid flow. Research limitations/implications: The paper presents a new efficient algorithm for constructing time-dependent integrable equations. Practical implications: The author develops two time-dependent integrable KdV equations of third- and fifth-order. These models represent more specific data than the constant equations. The author showed that integrable equation gives real and complex soliton solutions. Social implications: The work presents useful findings in the propagation of waves. Originality/value: The paper presents a new efficient algorithm for constructing time-dependent integrable equations. [ABSTRACT FROM AUTHOR]

Purpose The purpose of this paper is the development of a CFD methodology based on LES computations to analyze the rotor–stator interaction in an axial fan stage.Design/methodology/approach A wall-modeled large eddy simulation (WMLES) has been performed for a spanwise 3D extrusion of the central section of the fan stage. Computations were performed for three different operating conditions, from nominal (Q_N) to off-design (85 per cent Q_N and 70 per cent Q_N) working points. Circumferential periodic conditions were introduced to reduce the extent of the computational domain. The post-processing procedure enabled the segregation of unsteady deterministic features and turbulent scales. The simulations were experimentally validated using wake profiles and turbulent scales obtained from hot-wire measurements.Findings The transport of rotor wakes and both wake–vane and wake–wake interactions in the stator flow field have been analyzed. The description of flow separation, particularly at off-design conditions, is fully benefited from the LES performance. Rotor wakes impinging on the stator vanes generate a coherent large-scale vortex shedding at reduced frequencies. Large pressure fluctuations in the stagnation region on the leading edge of the vanes have been found.Research limitations/implications LES simulations have shown to be appropriate for the assessment of the design of an axial fan, especially for specific operating conditions for which a URANS model presents a lower performance for turbulence description.Originality/value This paper describes the development of an LES-based simulation to understand the flow mechanisms related to the rotor–stator interaction in axial fan stages. [ABSTRACT FROM AUTHOR]

Purpose The purpose of this paper is to investigate the optimal geometry parameters in a dimple/protrusion-pin finned channel with high thermal performance.Design/methodology/approach The BSL turbulence model is used to calculate the flow structure and heat transfer in a dimple/protrusion-pin finned channel. The optimization algorithm is set as Non-dominated Sorting Genetic Algorithm II (NSGA-II). The high Nusselt number and low friction factor are chosen as the optimization objectives. The pin fin diameter, dimple/protrusion diameter, dimple/protrusion location and dimple/protrusion depth are applied as the optimization variables. An in-house code is used to generate the geometry model and mesh. The commercial software Isight is used to perform the optimization process.Findings The results show that the Nusselt number and friction factor are sensitive to the geometry parameters. In a pin finned channel with a dimple, the Nusselt number is high at the rear part of the dimple, while it is low at the upstream of the dimple. A high dissipative function is found near the pin fin. In the protrusion channel, the Nusselt number is high at the leading edge of the protrusion. In addition, the protrusion induces a high pressure drop compared to the dimpled channel.Originality/value The originality of this paper is to optimize the geometry parameters in a pin finned channel with dimple/protrusion. This is good application for the heat transfer enhancement at the trailing side for the gas turbine. [ABSTRACT FROM AUTHOR]

Purpose – The purpose of this paper is to present new implementation aspects of unified explicit time integration algorithms, called the explicit GS4-II family of algorithms, of a second-order time accuracy in all the unknowns (e.g. positions, velocities, and accelerations) with particular attention to the moving-particle simulation (MPS) method for solving the incompressible fluids with free surfaces. Design/methodology/approach – In the present paper, the explicit GS4-II family of algorithms is implemented in the MPS method in the following two different approaches: a direct explicit formulation with the use of the weak incompressibility equation involving the (modified) speed of sound; and a predictor-corrector explicit formulation. The first approach basically follows the concept of the explicit MPS method, presented in the literature, and the latter approach employs a similar concept used in, for example, a fractional-step method in computational fluid dynamics. Findings – Illustrative numerical examples demonstrate that any scheme within the proposed algorithmic framework captures the physics with the necessary second-order time accuracy and stability. Originality/value – The new algorithmic framework extended with the GS4-II family encompasses a multitude of pastand new schemes and offers a general purpose and unified implementation. [ABSTRACT FROM AUTHOR]

Purpose – In an earlier paper (Turkyilmazoglu, 2011a), the author introduced a new optimal variational iteration method. The idea was to insert a parameter into the classical variational iteration formula in an aim to prevent divergence or to accelerate the slow convergence property of the classical approach. The purpose of this paper is to approve the superiority of the proposed method over the traditional one on several physical problems treated before by the classical variational iteration method. Design/methodology/approach – A sufficient condition theorem with an upper bound for the error is also presented to further justify the convergence of the new variational iteration method. Findings – The optimal variational iteration method is found to be useful for heat and fluid flow problems. Originality/value – The optimal variational iteration method is shown to be convergent under sufficient conditions. A novel approach to obtain the optimal convergence parameter is introduced. [ABSTRACT FROM AUTHOR]

Purpose: The study of the electro-osmotic forces (EOF) in the flow of the boundary layer has been a topic of interest in biomedical engineering and other engineering fields. The purpose of this paper is to develop an innovative mathematical model for electro-osmotic boundary layer flow. This type of fluid flow requires sophisticated mathematical models and numerical simulations. Design/methodology/approach: The effect of EOF on the boundary layer Williamson fluid model containing a gyrotactic microorganism through a non-Darcian flow (Forchheimer model) is investigated. The problem is formulated mathematically by a system of non-linear partial differential equations (PDEs). By using suitable transformations, the PDEs system is transformed into a system of non-linear ordinary differential equations subjected to the appropriate boundary conditions. Those equations are solved numerically using the finite difference method. Findings: The boundary layer velocity is lower in the case of non-Newtonian fluid when it is compared with that for a Newtonian fluid. The electro-osmotic parameter makes an increase in the velocity of the boundary layer. The boundary layer velocity is lower in the case of non-Darcian fluid when it is compared with Darcian fluid and as the Forchheimer parameter increases the behavior of the velocity becomes more closely. Entropy generation decays speedily far away from the wall and an opposite effect occurs on the Bejan number behavior. Originality/value: The present outcomes are enriched to give valuable information for the research scientists in the field of biomedical engineering and other engineering fields. Also, the proposed outcomes are hopefully beneficial for the experimental investigation of the electroosmotic forces on flows with non-Newtonian models and containing a gyrotactic microorganism. [ABSTRACT FROM AUTHOR]

Purpose As the penalized vortex-in-cell (pVIC) method is based on the vorticity-velocity form of the Navier–Stokes equation, the pressure variable is not incorporated in its solution procedure. This is one of the advantages of vorticity-based methods such as pVIC. However, dynamic pressure is an essential flow property in engineering problems. In pVIC, the pressure field can be explicitly evaluated by a pressure Poisson equation (PPE) from the velocity and vorticity solutions. How to specify far-field boundary conditions is then an important numerical issue. Therefore, this paper aims to robustly and accurately determine the boundary conditions for solving the PPE.Design/methodology/approach This paper introduces a novel non-iterative method for specifying Dirichlet far-field boundary conditions to solve the PPE in a bounded domain. The pressure field is computed using the velocity and vorticity fields obtained from pVIC, and the solid boundary conditions for pressure are also imposed by a penalization term within the framework of pVIC. The basic idea of our approach is that the pressure at any position can be evaluated from its gradient field in a closed contour because the contour integration for conservative vector fields is path-independent. The proposed approach is validated and assessed by a comparative study.Findings This non-iterative method is successfully implemented to the pressure calculation of the benchmark problems in both 2D and 3D. The method is much faster than all the other methods tested without compromising accuracy and enables one to obtain reasonable pressure field even for small computation domains that are used regardless of a source distribution (the right-hand side in the Poisson equation).Originality/value The strategy introduced in this paper provides an effective means of specifying Dirichlet boundary conditions at the exterior domain boundaries for the pressure Poisson problems. It is very efficient and robust compared with the conventional methods. The proposed idea can also be adopted in other fields dealing with infinite-domain Poisson problems. [ABSTRACT FROM AUTHOR]

Purpose: The purpose of this paper is to evaluate the temperature, the Dirichlet conditions have been considered to the parallel horizontal plates. The model of generalized Brinkman-extended Darcy with the Boussinesq approximation is considered and the governing equations are computed by COMSOL multiphysics. Design/methodology/approach: In the current study, the thermodynamic irreversible principle is applied to study the unsteady Poiseuille–Rayleigh–Bénard (PRB) mixed convection in a channel (aspect ratio A = 5), with the effect of a uniform transverse magnetic field. Findings: The effects of various flow parameters on the fluid flow, Hartmann number (Ha), Darcy number (Da), Brinkman number (Br) and porosity (ε), are presented graphically and discussed. Numerical results for temperature and velocity profiles, entropy generation variations and contour maps of streamlines, are presented as functions of the governing parameter mentioned above. Basing on the generalized Brinkman-extended Darcy formulation, which allows the satisfaction of the no-slip boundary condition on a solid wall, it is found that the flow field and then entropy generation is notably influenced by the considering control parameters. The results demonstrate that the flow tends toward the steady-state with four various regimes, which strongly depends on the Hartman and Darcy numbers variations. Local thermodynamic irreversibilities are more confined near the active top and bottom horizontal walls of the channel when increasing the Da and decreasing the Hartmann number. Entropy generation is also found to be considerably affected by Brinkman number variation. Originality/value: In the present work, we are presenting our investigations on the influence of a transverse applied external magnetohydrodynamic on entropy generation at the unsteady laminar PRB flow of an incompressible, Newtonian, viscous electrically conducting binary gas mixture fluid in porous channel of two horizontal heated plates. The numerical solutions for the liquid velocity, the temperature distribution and the rates of heat transport and entropy generation are obtained and are plotted graphically. [ABSTRACT FROM AUTHOR]

Purpose: The purpose of this paper is to investigate thermohydraulic characteristics of turbulent flow of water (4,000 = Re = 10,000) in a rectangular channel equipped with perforated chevron plat-fin (PCPF) with different vortex generators (VGs) shapes. Design/methodology/approach: First, three general shapes of VGs including rectangular, triangular and half circle, are compared to each other. Then, the various shapes of rectangular VGs, (horizontal, vertical and square) and triangular VGs, (forward, backward and symmetric) are evaluated. To comprehensively evaluate the thermohydraulic performance of the PCPF with various VG shapes, the relationship between the Colburn factor and the friction factor (j/f) is presented, then a performance index (η) is applied using these factors. Findings: Results show that the enhanced models of the PCPF, which are equipped with VGs, have higher values of j/f ratio and η as compared with the reference model (R). Further, the half-circle VG with the lowest pressure drop values (about 2.4% and 4.9%, averagely as compared with the S and ST vortex generators), shows the highest thermohydraulic performance among the proposed shapes. The maximum of performance index of 1.14 is found for the HC vortex generator at Re = 4,000. It is also found that the square and forward triangular VGs, have the best thermohydraulic performance among the rectangular and triangular VGs respectively and the highest performance index of 1.13 and 1.11 are reported for these VGs. Originality/value: The thermohydraulic performance of the PCPF with different vortex generators VGs shapes have been investigated. [ABSTRACT FROM AUTHOR]

Purpose The purpose of this paper is to evaluate differences between the results of constant property and variable property approaches in solving the problem of Al2O3-water nanofluid heat transfer in an annular microchannel. Also, the effect of nanoparticle diameter on flow and heat transfer characteristics is investigated.Design/methodology/approach Thermo-physical properties of the nanofluid including density, specific heat, viscosity and thermal conductivity are assumed to be temperature dependent. Governing equations are descritized using the finite volume method and solved by SIMPLE algorithm.Findings The results reveal that the constant property assumption is unable to predict the correct trend of variations along the microchannel for some of the characteristics, especially when the range of temperature change near the wall is considerable. In the fully developed region, constant property solution overestimates the values of shear stress near the walls of the microchannel. In addition, the values of Nusselt numbers are different for the two solutions. Furthermore, a decrease in wall’s shear stress has been observed as a result of increasing nanoparticle size.Originality/value This paper reflects that how the friction factor and heat transfer vary along the microchannel in temperature dependent modeling, which is not reflected in the results of constant property approach. To the best of the authors’ knowledge, there is no similar investigation of the effect of nanofluid variable properties with Pr=5 or in annular geometry. [ABSTRACT FROM AUTHOR]

Purpose: This paper aims to investigate the effect of Powell–Eyring fluid induced by a stretched sheet. Heat and mass transfer under the influence of magnetic dipole over a stretching sheet are taken into account. Design/methodology/approach: Nonlinear coupled governing equations are solved using the optimal homotopy asymptotic technique, and a computer software package BVPh 2.0 is used for numerical computations. Findings: Impact of significant quantities is graphically examined. It is seen that the heat transfer deceases for higher values of viscous dissipation parameter, radiation parameter, Dufour number, whereas it increases for bigger values of Prandtl number. The numerical results have been validated through comparison with existing literature as a special case of proposed model and perceived that the Soret number has reining role to increase the rate of heat transfer. Originality/value: To the best of the authors' knowledge, this study is reported for the first time. [ABSTRACT FROM AUTHOR]

Purpose: The purpose of this paper is to investigate conjugate heat transfer of natural convection and entropy generation of nanofluid in the presence of external magnetic field via numerical approach in an inclined square cavity enclosure. Design/methodology/approach: Control volume finite volume method with collocated arrangement of grids was used for discretization of continuity, momentum, solid and fluid energy equations. Rhie and Chow interpolation technique was applied to avoid checkerboard problem in pressure field and the well-established SIMPLE algorithm was followed to deal with the pressure and velocity coupling. The cavity is filled with water and nanoparticles of the aluminum oxide (Al2O3). This study has been conducted for the certain pertinent parameters of the volume fraction of nanoparticle (φ = 0–0.08), the angle of inclination (ϴ = 0°–330°), the Ra number (Ra = 103–108), the solid to fluid conductivity ratio (ksf = 1–400), the Ha number (Ha = 0–80) and the wall thickness ratio (δ/L = 0–0.3). Findings: The results indicate that averaged Nu number increases by approximately 9% by increasing volume fraction from 0.0 to 0.08. Nu increases with an increasing inclination angle to 40° and decreases abruptly in 90° because of the formation of two weaker vorticity with opposite circulation pattern intensifying the density of isotherm curves in a vertical direction. Nu increases sharply with increasing Ra more than 105. Nu also augments almost 67% by increasing ksf = 1 to ksf = 50 and remains constant by increasing ksf more than 50. Nu number reduction is almost 72% with a variation of wall thickness ratio from d/L = 0 to 0.3. Entropy generation because of fluid flow, magnetic field and heat transfer reduces linearly almost 30%, 19% and 16% by increasing volume fraction, respectively. With increasing ksf, entropy generation because of fluid flow, magnetic field and heat transfer increases asymptotically, but Bejan number decreases. Originality/value: A brief review of conducted research studies in nanofluid flow and heat transfer reveals that the effect of wall thermal inertia was not investigated in MHD natural convection of nanofluids in an inclined enclosure. The aim of the present study is to analyze conjugate heat transfer in an inclined cavity filled with water and Al2O3. [ABSTRACT FROM AUTHOR]

Purpose: This paper aims to examine the hybrid nanofluid flow towards a stagnation point on an exponentially stretching/shrinking vertical sheet with buoyancy effects. Design/methodology/approach: Here, the authors consider copper (Cu) and alumina (Al2O3) as hybrid nanoparticles while water as the base fluid. The governing equations are reduced to the similarity equations using similarity transformations. The resulting equations are programmed in Matlab software through the bvp4c solver to obtain their solutions. Findings: The authors found that the heat transfer rate is greater for Al2O3-Cu/water hybrid nanofluid if compared to Cu/water nanofluid. Besides, the non-uniqueness of the solutions is observed for certain physical parameters. The authors also notice that the bifurcation of the solutions occurs in the downward buoyant force and the shrinking regions. In addition, the first solution of the skin friction and heat transfer coefficients increase with the added hybrid nanoparticles and the mixed convection parameter. The temporal stability analysis shows that one of the solutions is stable as time evolves. Originality/value: The present work is dealing with the problem of a mixed convection flow of a hybrid nanofluid towards a stagnation point on an exponentially stretching/shrinking vertical sheet, with the buoyancy effects is taken into consideration. The authors show that two solutions are obtained for a single value of parameter for both stretching and shrinking cases, as well as for both buoyancy aiding and opposing flows. A temporal stability analysis then shows that only one of the solutions is stable and physically reliable as time evolves. [ABSTRACT FROM AUTHOR]

Purpose The purpose of this paper is to provide a solution for natural convection in a cavity with a partial heater in case of volumetric heating and analysis of the entropy generation.Design/methodology/approach The control volume method based on three-dimensional (3D) vorticity-potential vector was applied to solve governing equations of natural convection in a 3D cavity with a fin for different governing parameters as external Rayleigh numbers (103=RaE=106), internal Rayleigh numbers 103=RaI=106, partition height (0.25=h=0.75) and partition location (0.25=c=0.75). A code was written by using Fortran platform.Findings The edge of the fin becomes important on entropy generation. The ratio of the RaI/RaE plays the important role on natural convection and entropy generation. The variation of external Rayleigh number becomes insignificant for the RaI/RaE>1.Originality/value The originality of this work is to analyze the entropy generation and natural convection in a cubical cavity with volumetrically heating. [ABSTRACT FROM AUTHOR]