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Purpose: The evaluation of high thermal efficiency has actively highlighted the unique behaviour of hybrid nanofluid. Thus, the purpose of this paper is to emphasize the hybrid nanofluid's stagnation point in three-dimensional flow with magnetic field. Design/methodology/approach: The defined ordinary differential equations systems are addressed using the bvp4c solver. Findings: The results indicate that using dual solutions is possible as long as the physical parameters remain within their specified ranges. Hybrid nanofluid flow has been recognised for its superior heat transfer capabilities in comparison to both viscous flow and nanofluid flow. Furthermore, it has been demonstrated in the current study that augmenting the volume concentration of nanoparticles leads to a corresponding enhancement in the rate of heat transfer. When the velocity gradients ratio is augmented, there is a corresponding reduction in the thermal performance. The separation value grows as the magnetic parameter rises, which signifies the expansion of the boundary layer. Originality/value: The originality of the paper highlights the general mathematical hybrid model of the three-dimensional problem with the magnetohydrodynamics (MHD) effect in the stagnation point flow. The comprehensive examination of the suggested model has not yet been thoroughly addressed in prior research. [ABSTRACT FROM AUTHOR]

Purpose: This paper aims to present the steady dual solutions on three-dimensional flow and heat transfer of nanofluid over a permeable non-linearly shrinking surface with two-order velocity slips conditions. Boundary layer assumption is considered in the mathematical modelling. Authors comprehend from previous studies and papers that the shrinking surfaces are extremely important in current engineering and environmental systems. Design/methodology/approach: Using appropriate similarity variables, the full partial differential equations (PDF) are modified into a specific set of ordinary (similar) differential equations (ODE). The resulting non-linear ordinary differential system is then solved both analytically for some particular cases and numerically for the general case using the function bvp4c from MATLAB for characteristic values of the parameters which govern the equations. The transformed mathematical model is analysed using the bvp4c procedure. Based on the given assumptions, this study is able to produce multiple solutions of the problem. Findings: The ordinary (similarity) differential equations have two branches solutions, upper and lower branch solutions, given some interval of shrinking and velocity slip parameters. The authors consider here a temporal stability analysis, as they want to establish which of the solutions are stable and which are not. In a distinct paragraph, the authors discuss in detail and present in a graphical manner the effects of shrinking and second-order slip flow model on the skin friction coefficient, surface wall heat flux and dimensionless velocity and temperature profiles. The analysis reveals that the second order slip has a big influence on the flow and heat transfer characteristics. Originality/value: The present discoveries are unique and truly new for the research of the three-dimensional stretching/shrinking forced convection flow and heat transfer nanofluids. The nanofluid is a water-based nanofluid (H2O), which contains one type of nanoparticles, namely, copper (Cu). Of course, the analysis can be further extended considering other types of nanoparticles such as alumina (Al2O3). The authors assume that the thermal equilibrium is reached for the base fluid together with the suspended nanoparticles and that the nanoparticles are uniform in dimension and form. [ABSTRACT FROM AUTHOR]

Purpose: The purpose of this paper is to introduce an innovative strategy for the approximate solution of the heat flow problems in two- and three-dimensional spaces. This new strategy is very easy to implement and handles the restrictive variable that may ruin the physical nature of the problem. Design/methodology/approach: This study combines Sawi transform (ST) and the homotopy perturbation method (HPM) to formulate the idea of Sawi homotopy perturbation transform method (SHPTM). First, this study implements ST to handle the recurrence relation and then incorporates HPM to derive the series solutions of this recurrence relation. ST has the advantage in that it does not require any assumptions or hypothesis for the evaluation of series solutions. Findings: This strategy finds the results very accurate and close to the precise solution. The graphical observations and the surface solution demonstrate that SHPTM is a reliable and powerful scheme for finding the approximate solution of heat flow problems. Originality/value: The study presents an original work. This study develops SHPTM for the approximate solution of two- and three-dimensional heat flow problems. The obtained results and graphical representation demonstrate that SHPTM is a very authentic and reliable approach. [ABSTRACT FROM AUTHOR]

Purpose: This paper aims to compare the performance of flow pulsation versus flow stirring in the context of mixing of a passive scalar at moderate Reynolds numbers in confined flows. This comparison has been undertaken in two limits: diffusion can be neglected as compared to convection (very large Peclet) and diffusion and convection effects are comparable. The comparison was performed both in terms of global parameters: pumping power and mixing efficiency and local flow topology. Design/methodology/approach: The study has been addressed by setting up a common conceptual three-dimensional problem that consisted of the mixing of two parallel streams in a square section channel past a square section prism. Stirring and pulsation frequencies and amplitudes were changed and combined at an inlet Reynolds number of 200. The numerical model was solved using a finite volume formulation by adapting a series of open-source OpenFOAM computational fluid dynamic (CFD) libraries. For cases with flow pulsation, the icoFoam solver for laminar incompressible transient flows was used. For cases with stirring, the icoDyMFoam solver, which uses the arbitrary Lagrangian–Eulerian method for the description of the moving dynamical mesh, was used to model the prism motion. At the local flow topology level, a new method was proposed to analyze mixing. Time evolution of folding and wrinkling of sheets made up of virtual particles that travel along streak lines was quantified by generating lower rank projections of the sheets onto the spaces spanned by the main eigenvectors of an appropriate space-temporal data decomposition. Findings: In the limit when convection is dominant, the results showed the superior performance of stirring versus flow pulsation both in terms of mixing and required pumping power. In the cases with finite Peclet, the mixing parameters by stirring and flow pulsation were comparable, but pulsation required larger pumping power than stirring. For some precise synchronization of stirring and pulsation, the mixing parameter reached its maximum, although at the expense of higher pumping power. At the local flow topology level, the new method proposed to quantify mixing has been found to correlate well with the global mixing parameter. Originality/value: A new systematic comparative study of two methods, stirring and pulsation, to achieve mixing of passive scalars in the mini scale for confined flows has been presented. The main value, apart from the conclusions, is that both methods have been tested against the same flow configuration, which allows for a self-consistent comparison. Of particular interest is the fact that it has been found that accurate synchronization of both methods yields mixing parameters higher than those associated to both methods taken separately. This suggests that it is possible to synchronize mixing methods of a different nature to achieve optimum designs. The new theoretical method that has been proposed to understand the mixing performance at the local level has shown promising results, and it is the intention of the authors to test its validity in a broader range of flow parameters. All these findings could be taken as potential guidelines for the design of mixing processes in the mini scale in the process industry. [ABSTRACT FROM AUTHOR]

Purpose: The purpose of this paper is to study the effects of thermal radiation and homogeneous-heterogeneous reactions in the three-dimensional hybrid nanofluid flow past a permeable stretching/shrinking sheet. Design/methodology/approach: The combination of aluminum oxide (Al2O3) and copper (Cu) nanoparticles with total volumetric concentration is numerically analyzed using the existing correlations of hybrid nanofluid. With the consideration that both homogeneous and heterogeneous reactions are isothermal while the diffusion coefficients of both autocatalyst and reactant are same, the governing model is simplified into a set of differential (similarity) equations. Findings: Using the bvp4c solver, dual solutions are presented, and the stability analysis certifies the physical/real solution. The findings show that the suction parameter is requisite to induce the steady solution for shrinking parameter. Besides, the fluid concentration owing to the shrinking sheet is diminished with the addition of surface reaction. Originality/value: The present findings are novel and can be a reference point to other researchers to further analyze the heat transfer performance and stability of the working fluids. [ABSTRACT FROM AUTHOR]

Purpose: This study aims to explore the 3 D separated flow fields and heat transfer characteristics at the end wall of a serpentine channel with various turn clearances using topological analysis and critical points principles of three-dimensional vortex flow. Design/methodology/approach: This aims to explore the 3 D separated flow fields and heat transfer characteristics at the end wall of a serpentine channel with various turn clearances using topological analysis as well as critical points principles of three-dimensional vortex flow. Findings: The endwall heat transfer in the narrow spacing passage is significantly stronger than that in a wide spacing channel. As the gap clearance is kept at 0.87 times of the hydraulic diameter, the endwall heat transfer and thermal performance can be accordingly enhanced with low pressure drops, which is because a relatively strong concentrated impingement flow for the medium gap clearance helps to restrain the downstream fluid flow and enhance the shear effect of the secondary flow. Practical implications: The numerical results can be applied in designing sharp turn of serpentine channel in heat exchangers, heat sinks, piping system, solar receiver and gas turbine blades. Originality/value: The evolution mechanism of the vortices in the turning region under different gap clearance was analyzed, and thermal enhancement characteristics were predicted innovatively using topological analysis method. [ABSTRACT FROM AUTHOR]

Purpose: The purpose of this study is to find the multiple branches of the three-dimensional flow of Cu-Al2 O3/water rotating hybrid nanofluid perfusing a porous medium over the stretching/shrinking surface. The extended model of Darcy due to Forchheimer and Brinkman has been considered to make the hybrid nanofluid model over the pores by considering the porosity and permeability effects. Design/methodology/approach: The Tiwari and Das model with the thermophysical properties of spherical particles for efficient dynamic viscosity of the nanoparticle is used. The linear similarity transformations are applied to convert the partial differential equations into ordinary differential equations (ODEs). The system of governing ODEs is solved by using the three-stage Lobatto IIIa scheme in MATLAB for evolving parameters. Findings: The system of governing ODEs produces dual branches. A unique stable branch is identified with help of stability analysis. The reduced heat transfer rate has been shown to increase with the reduced ϕ2 in both branches. Further, results revealed that the presence of multiple branches depends on the ranges of porosity, suction and stretching/shrinking parameters for the particular value of the rotating parameter. Originality/value: Dual branches of the three-dimensional flow of Cu-Al2 O3/water rotating hybrid nanofluid have been found. Therefore, stability analysis of the branches is also conducted to know which branch is appropriate for the practical applications. To the best of the authors' knowledge, this research is novel and there is no previously published work relevant to the present study. [ABSTRACT FROM AUTHOR]

Purpose: This paper aims to probe the problem of an unsteady mixed convection stagnation point flow and heat transfer past a stationary surface in an incompressible viscous fluid numerically. Design/methodology/approach: The governing nonlinear partial differential equations are transformed into a system of ordinary differential equations by a similarity transformation, which is then solved numerically by a Runge – Kutta – Fehlberg method with shooting technique and a collocation method, namely, the bvp4c function. Findings: The effects of the governing parameters on the fluid flow and heat transfer characteristics are illustrated in tables and figures. It is found that dual (upper and lower branch) solutions exist for both the cases of assisting and opposing flow situations. A stability analysis has also been conducted to determine the physical meaning and stability of the dual solutions. Practical implications: This theoretical study is significantly relevant to the applications of the heat exchangers placed in a low-velocity environment and electronic devices cooled by fans. Originality/value: The case of suction on unsteady mixed convection flow at a three-dimensional stagnation point has not been studied before; hence, all generated numerical results are claimed to be novel. [ABSTRACT FROM AUTHOR]

Purpose: The purpose of this paper is to develop a combined method for three-dimensional incompressible flow and heat transfer by the spectral collocation method (SCM) and the artificial compressibility method (ACM), and further to study the performance of the combined method SCM-ACM for three-dimensional incompressible flow and heat transfer. Design/methodology/approach: The partial differentials in space are discretized by the SCM with Chebyshev polynomial and Chebyshev–Gauss–Lobbatto collocation points. The unsteady artificial compressibility equations are solved to obtain the steady results by the ACM. Three-dimensional exact solutions with trigonometric function form and exponential function form are constructed to test the accuracy of the combined method. Findings: The SCM-ACM is developed successfully for three-dimensional incompressible flow and heat transfer with high accuracy that the minimum value of variance can reach. The accuracy increases exponentially along with time marching steps. The accuracy is also improved exponentially with the increasing of nodes before stable accuracy is achieved, while it keeps stably with the increasing of the time step. The central processing unit time increases exponentially with the increasing of nodes and decreasing of the time step. Research limitations/implications: It is difficult for the implementation of the implicit scheme by the developed SCM-ACM. The SCM-ACM can be used for solving unsteady impressible fluid flow and heat transfer. Practical implications: The SCM-ACM is applied for two classic cases of lid-driven cavity flow and natural convection in cubic cavities. The present results show good agreement with the published results with much fewer nodes. Originality/value: The combined method SCM-ACM is developed, firstly, for solving three-dimensional incompressible fluid flow and heat transfer by the SCM and ACM. The performance of SCM-ACM is investigated. This combined method provides a new choice for solving three-dimensional fluid flow and heat transfer with high accuracy. [ABSTRACT FROM AUTHOR]

Purpose: The purpose of this paper is to study the mechanism and suppression of instabilities induced by cavitating flow around a three-dimensional hydrofoil with a particular focus on cavitation control with a slot. Design/methodology/approach: The transient cavitating flow around a Clark-Y hydrofoil was investigated using a transport-equation-based cavitation model and the stress-blended eddy simulation model was used to capture the flow turbulence. A homogeneous Rayleigh–Plesset cavitation model was used to model the transient cavitation process and the results were validated with test data. A slot was applied to the hydrofoil to suppress cavitation instabilities, and various slot widths and exit locations were applied to the blade and the cavitation behavior, as well as drag/lift forces, were simulated and compared to investigate the effects of slot geometries on cavitation suppression. Findings: The large eddy simulation based turbulence model was able to capture the interactions between the cavitation and turbulence. Moreover, the simulation revealed that the re-entrant jet was responsible for the periodic shedding of cavities. The results indicated that a slot was able to mitigate or even suppress cavitation-induced instabilities. A jet flow was generated at the slot exit and disturbed the re-entrant jet. If the slot geometry was properly designed, the jet could block the re-entrant jet and suppress the unsteady cavitation behavior. Originality/value: This study provides unique insights into the complicated transient cavitation flows around a three-dimensional hydrofoil and introduces an effective passive cavitation control technique useful to researchers and engineers in the areas of fluid dynamics and turbomachinery. [ABSTRACT FROM AUTHOR]

Purpose: The purpose of this study is to investigate the pulsating flow in a three-dimensional channel. Channel flow is laminar and turbulent. After validation, the effect of different channel cross-sectional geometries (circular, hexagonal and triangular) with the pulsating flow are investigated. For this purpose, the alumina nanofluid was considered as a working fluid with different volume percentages (0 per cent [pure water], 3 per cent and 5 per cent). Design/methodology/approach: In this study, the pulsatile flow was investigated in a three-dimensional channel. Channel flow is laminar and turbulent. Findings: The results show that the fluid temperature decreases by increasing the volume percentage of particles of Al2O3; this is because of the fact that the input energy through the wall boundary is a constant value and indicates that with increasing the volume percentage, the fluid can save more energy at a constant temperature. And by adding Al2O3 nanofluid, thermal performance improves in channels, but it should be considered that the use of nanofluid causes a pressure drop in the channel. Originality/value: Alumina/water nanofluid with the pulsating flow was investigated and compared in three different cross-sectional channel geometries (circular, hexagonal and triangular). The effect of different volume percentages (0 per cent [pure water], 3 per cent and 5 per cent) of Al2O3 nanofluid on temperature, velocity and pressure are studied. [ABSTRACT FROM AUTHOR]

Purpose: The purpose of this study is three-dimensional flow and heat transfer investigation of water/Al2O3 nanofluid inside a microchannel with different cross-sections in two-phase mode. Design/methodology/approach: The effect of microchannel walls geometry (trapezoidal, sinusoidal and stepped microchannels) on flow characteristics and also changing circular cross section to trapezoidal cross section in laminar flow at Reynolds numbers of 50, 100, 300 and 600 were investigated. In this study, two-phase water/Al2O3 nanofluid is simulated by the mixture model, and the effect of volume fraction of nanoparticles on performance evaluation criterion (PEC) is studied. The accuracy of obtained results was compared with the experimental and numerical results of other similar papers. Findings: Results show that in flow at lower Reynolds numbers, sinusoidal walls create a pressure drop in pure water flow which improves heat transfer to obtain PEC < 1. However, in sinusoidal and stepped microchannel with higher Reynolds numbers, PEC > 1. Results showed that the stepped microchannel had higher pressure drop, better thermal performance and higher PEC than other microchannels. Originality/value: Review of previous studies showed that existing papers have not compared and investigated nanofluid in a two-phase mode in inhomogeneous circular, stepped and sinusoidal cross and trapezoidal cross-sections by considering the effect of changing channel shape, which is the aim of the present paper. [ABSTRACT FROM AUTHOR]

Purpose: In this paper, a single module of cross-flow membrane humidifier is evaluated as a three-dimensional multiphase model. The purpose of this paper is to analyze the effect of volume flow rate, dry temperature, dew point wet temperature and porosity of gas diffusion layer on the humidifier performance. Design/methodology/approach: In this study, one set of coupled equations are continuity, momentum, species and energy conservation is considered. The numerical code is benchmarked by the comparison of numerical results with experimental data of Hwang et al. Findings: The results reveal that the transfer rate of water vapor and dew point approach temperature (DPAT) increase by increasing the volume flow rate. Also, it is found that the water recovery ratio (WRR) and relative humidity (RH) decrease with increasing volume flow rate. In addition, all mixed results decrease with increasing dry side temperature especially at high volume flow rates and this trend in high volume flow rates is more sensible. Although the transfer rate of water vapor and DPAT increases with increasing the wet inlet temperature, WRR and RH reduce. Increasing dew point temperature effect is more sensible at the wet side is compared with the dry side. The humidification performance will be enhanced with increasing diffusion layer porosity by increasing the wet inlet dew point temperature, but has no meaningful effect on other operating parameters. The pressure drop along humidifier gas channels increases with rising flow rate, consequently, the required power of membrane humidifier will enhance. Originality/value: According to previous studies, the three-dimensional numerical multiphase model of cross-flow membrane humidifier has not been developed. [ABSTRACT FROM AUTHOR]

Purpose: This paper aims to numerically examine the mixed convection of SiO2-water nanofluid flow in a three-dimensional (3D) cubic cavity with a conductive partition considering various shapes of the particles (spherical, cylindrical, blade, brick). The purpose is to analyze the effects of various pertinent parameters such as Richardson number (between 0.1 and 10), Hartmann number (between 0 and 10), solid nanoparticle volume fraction (between 0 and 0.04), particle shape (spherical, cylindrical, blade, brick) and different heights and lengths of the conductive partition on the fluid flow and heat transfer characteristics. Design/methodology/approach: The numerical simulation was performed by using Galerkin-weighted residual finite element method for various values of Richardson number, Hartmann number, solid nanoparticle volume fraction, particle shape (spherical, cylindrical, blade, brick) and different heights and lengths of the conductive partition. Two models for the average Nusselt number were proposed for nanofluids with spherical and cylindrical particle by using multi-layer feed-forward neural networks. Findings: It was observed that the average Nusselt number reduces for higher values of Richardson number and Hartmann number, while enhances for higher values of nanoparticle volume fraction. Among various types of particle shapes, blade ones perform the worst and cylindrical ones perform the best in terms of heat transfer enhancement, but this is not significant which is less than 3 per cent. The average Nusselt number deteriorates by about 6.53per cent for nanofluid at the highest volume fraction of spherical particle shapes, but it is 11.75per cent for the base fluid when Hartmann number is increased from 0 to 10. Conductive partition geometrical parameters (length and height) do not contribute to much to heat transfer process for the 3D cavity, except for the case when height of the partition reaches 0.8 times the height of the cubic cavity, the average Nusselt number value reduces by about 25per cent both for base fluid and for nanofluid when compared to case with cavity height which is 0.2 times the height of the cubic cavity. Originality/value: Based on the literature survey, a 3D configuration for MHD mixed convection of nanofluid flow in a cavity with a conductive partition considering the effects of various particle shapes has never been studied in the literature. This study is a first attempt to use a conductive partition with nanofluid of various particle shapes to affect the fluid flow and heat transfer characteristics in a 3D cubic cavity under the influence of magnetic field. Partial or all findings of this study could be used for the design and optimization of realistic 3D thermal configurations that are encountered in practice and some of the applications were already mentioned above. In this study, thermal performance of the system was obtained in terms of average heat transfer coefficient along the hot surface, and it is modeled with multi-layer feed-forward neural networks. [ABSTRACT FROM AUTHOR]

Purpose: The purpose of this study is to analyze the Entropy generation analysis and heat transport in three-dimensional flow between two stretchable disks. Joule heating and heat generation/absorption are incorporated in the thermal equation. Thermo-diffusion effect is also considered. Flow is conducting for time-dependent applied magnetic field. Induced magnetic field is not taken into consideration. Velocity and thermal slip conditions at both the disks are implemented. The flow problem is modeled by using Navier–Stokes equations with entropy generation rate and Bejan number. Design/methodology/approach: Von Karman transformations are used to reduce the nonlinear governing expressions into an ordinary one and then tackled by homotopy analysis method for convergent series solutions. The nonlinear expressions for total entropy generation rate are obtained with appropriate transformations. The impacts of different flow variables on velocity, temperature, entropy generation rate and Bejan number are described graphically. Velocity, temperature and concentration gradients are discussed in the presence of flow variables. Findings: Axial, radial and tangential velocity profiles show decreasing trend for larger values of velocity slip parameters. For a larger Brinkman number, the entropy generation increases, while a decreasing trend is noticed for Bejan number. Originality/value: To the best of the authors' knowledge, no such analyses have been reported in the literature. [ABSTRACT FROM AUTHOR]

Purpose: The purpose of this work is to revisit the integral transform solution of transient natural convection in differentially heated cavities considering a novel vector eigenfunction expansion for handling the Navier-Stokes equations on the primitive variables formulation. Design/methodology/approach: The proposed expansion base automatically satisfies the continuity equation and, upon integral transformation, eliminates the pressure field and reduces the momentum conservation equations to a single set of ordinary differential equations for the transformed time-variable potentials. The resulting eigenvalue problem for the velocity field expansion is readily solved by the integral transform method itself, while a traditional Sturm–Liouville base is chosen for expanding the temperature field. The coupled transformed initial value problem is numerically solved with a well-established solver based on a backward differentiation scheme. Findings: A thorough convergence analysis is undertaken, in terms of truncation orders of the expansions for the vector eigenfunction and for the velocity and temperature fields. Finally, numerical results for selected quantities are critically compared to available benchmarks in both steady and transient states, and the overall physical behavior of the transient solution is examined for further verification. Originality/value: A novel vector eigenfunction expansion is proposed for the integral transform solution of the Navier–Stokes equations in transient regime. The new physically inspired eigenvalue problem with the associated integmaral transformation fully shares the advantages of the previously obtained integral transform solutions based on the streamfunction-only formulation of the Navier–Stokes equations, while offering a direct and formal extension to three-dimensional flows. [ABSTRACT FROM AUTHOR]

Purpose The contactless inductive flow tomography is a procedure that enables the reconstruction of the global three-dimensional flow structure of an electrically conducting fluid by measuring the flow-induced magnetic flux density outside the melt and by subsequently solving the associated linear inverse problem. The purpose of this study is to improve the accuracy of the computation of the forward problem, since the forward solution primarily determines the accuracy of the inversion.Design/methodology/approach The tomography procedure is described by a system of coupled integral equations where the integrals contain a singularity when a source point coincides with a field point. The integrals need to be evaluated to a high degree of precision to establish an accurate foundation for the inversion. The contribution of a singular point to the value of the surface and volume integrals in the system is determined by analysing the behaviour of the fields and integrals in the close proximity of the singularity.Findings A significant improvement of the accuracy is achieved by applying higher order elements and by attributing special attention to the singularities inherent in the integral equations.Originality/value The contribution of a singular point to the value of the surface integrals in the system is dependent upon the geometry of the boundary at the singular point. The computation of the integrals is described in detail and the improper surface and volume integrals are shown to exist. The treatment of the singularities represents a novelty in the contactless inductive flow tomography and is the focal point of this investigation. [ABSTRACT FROM AUTHOR]

Purpose – The purpose of this paper is to numerically solve the problem of an unsteady squeezing three-dimensional flow and heat transfer of a nanofluid in rotating vertical channel of stretching left plane. The fluid is assumed to be Newtonian, incompressible and electrically conducting embedded with nanoparticles. Effect of internal heat generation/ absorption is also considered in energy equation. Four different types of nanoparticles are considered, namely, copper (Cu), alumina (Al2O3), silver (Ag) and titanium oxide (TiO2) with the base fluid as water. Maxwell-Garnetts and Brinkman models are, respectively, employed to calculate the effective thermal conductivity and viscosity of the nanofluid. Design/methodology/approach – Using suitable similarity transformations, the governing partial differential equations are transformed into set of ordinary differential equations. Resultant equations have been solved numerically using Runge-Kutta-Fehlberg fourth fifth order method for different values of the governing parameters. Effects of pertinent parameters on normal, axial and tangential components of velocity and temperature distributions are presented through graphs and discussed in detail. Further, effects of nanoparticle volume fraction, squeezing parameter, suction/injection parameter and heat source/sink parameter on skin friction and local Nusselt number profiles for different nanoparticles are presented in tables and analyzed. Findings – Squeezing effect enhances the temperature field and consequently reduces the heat transfer rate. Large values of mixed convection parameter showed a significant effect on velocity components. Also, in many heat transfer applications, nanofluids are potentially useful because of their novel properties. They exhibit high-thermal conductivity compared to the base fluids. Further, squeezing and rotation effects are desirable in control the heat transfer. Originality/value – Three-dimensional mixed convection flows over in rotating vertical channel filled with nanofluid are very rare in the literature. Mixed convection squeezing three-dimensional flow in a rotating channel filled with nanofluid is first time investigated. [ABSTRACT FROM AUTHOR]

Purpose – The purpose of this paper is to study the Soret and Dufour effects in three-dimensional flow induced by an exponential stretching surface in a porous medium. Design/methodology/approach – Series solutions are developed. Findings – The authors observed that the temperature profile and thermal boundary layer thickness are enhanced when the authors increase the values of Dufour number. It is also examined that the concentration field and its associated boundary layer thickness are higher for the larger values of Soret number. Originality/value – Such investigation is not available in the literature. [ABSTRACT FROM AUTHOR]

Purpose - The purpose of this paper is to analyze the Eyring Powell fluid over an exponentially stretching surface. Heat and mass transfer effects are taken into account with nanoparticles. Design/methodology/approach - Appropriate transformations are employed to reduce the boundary layer partial differential equations into ordinary differential equations. Series solutions of the problem are obtained and impacts of physical parameters on the velocities, temperature and concentration profiles are discussed. Findings - Numerical values of local Nusselt and Sherwood numbers for all the involved physical parameters are computed and analyzed. A comparative study between the present and previous results is made in a limiting sense. Local Nusselt number -'(0) increases by increasing ε, Pr, λ and N while it decreases for δ, N_{t{, N_{b} and Sc. Originality/value - This analysis has not been discussed in the literature yet. [ABSTRACT FROM AUTHOR]

Purpose - The purpose of this paper is to investigate the three-dimensional mixed convection flow of viscoelastic nanofluid induced by an exponentially stretching surface. Design/methodology/approach - Similarity transformations are utilized to reduce the partial differential equations into the ordinary differential equations. The corresponding non-linear problems are solved by homotopy analysis method. Findings - The authors found that an increase in thermophoresis and Brownian motion parameter enhance the temperature. Here thermal conductivity of fluid is enhanced due to which higher temperature and thicker thermal boundary layer thickness is obtained. Practical implications - Heat and mass transfer effects in mixed convection flow over a stretching surface have numerous applications in the polymer technology and metallurgy. Such flows are encountered in metallurgical processes which involve the cooling of continuous strips or filaments by drawing them through a quiescent fluid and that in the process of drawing, these strips are sometimes stretched. Originality/value - Three-dimensional flows over an exponentially stretching surface are very rare in the literature. Three-dimensional flow of viscoelastic nanofluid due to an exponentially stretching surface is first time investigated. [ABSTRACT FROM AUTHOR]

Purpose -- The purpose of this paper is to address the heat and mass transfer effects in three-dimensional flow of Maxwell fluid over a stretching surface with convective boundary conditions. Mass transfer is considered in the presence of first order chemical reaction. Conservation laws of energy and concentration are based upon the Soret and Dufour effects. Convergent series solutions to the resulting non-linear problems are developed. Effects of Biot and Deborah numbers on the Sherwood number are decreasing. Local Nusselt reduces with an increase in Eckert numbers. It is also interesting to note further that variations of Prandtl and Biot numbers on the Nusselt number are increasing while Sherwood number decreases with an increase in Prandtl number. Design/methodology/approach -- The involved partial differential systems are reduced to the ordinary differential systems using appropriate transformations. Series solutions by homotopy analysis method are constructed and analyzed. Graphical results are presented and examined in detail. Findings -- It is found that roles of Deborah and Biot parameters on the Nusselt number are opposite. However, the Sherwood number is qualitative similar for both Biot and Deborah numbers. It is also interesting to note further that variations of Prandtl and Biot numbers on the Nusselt and Sherwood numbers are similar. Originality/value -- The purpose of present communication is to investigate the three-dimensional flow of Maxwell fluid over a stretching surface with convective condition. Analysis has been carried out in the presence of mass transfer with first order chemical reaction and Soret and Dufour effects. [ABSTRACT FROM AUTHOR]

Purpose -- The purpose of this paper is to analyze the boundary layer flow of an Oldroyd-B fluid with Newtonian heating. Design/methodology/approach -- Series solutions are found by homotopy analysis method. Findings -- Temperature profile increases with an increase in conjugate parameter. Increase in parameter β and Prandtl number Pr decreases the temperature profile. Originality/value -- This work does not currently exist in the literature. [ABSTRACT FROM AUTHOR]

Purpose – The purpose of this paper is to investigate the three-dimensional flow of Maxwell fluid with variable thermal conductivity in presence of heat source/sink. Design/methodology/approach – Similarity transformations are utilized to reduce the nonlinear partial differential equations into ordinary differential equations. The governing nonlinear problems are solved by homotopy analysis method. Findings – The paper found that the velocities decrease while temperature increases for higher Hartman number. It is also seen that the thermal boundary layer thickness and temperature are increased with an increase in variable thermal conductivity parameter and heat source/sink parameter. Practical implications – Heat transfer analysis with heat source/sink has pivotal role in many industrial applications like cooling of an infinite metallic plate in a cooling bath, drawing of plastic films, nuclear plants, gas turbines, various propulsion devices for missiles, space vehicles and processes occurring at high temperatures. Originality/value – This study discusses the magnetohydrodynamic three-dimensional flow of Maxwell fluid with variable thermal conductivity and heat source/sink. No such analysis exists in the literature yet. [ABSTRACT FROM AUTHOR]

Purpose – The purpose of this paper is to present the problem of three-dimensional flow of a fluid of constant density forced through the porous bottom of a circular porous slider moving laterally on a flat plate. Design/methodology/approach – The transformed nonlinear ordinary differential equations are solved via the homotopy perturbation method (HPM) for small as well as moderately large Reynolds numbers. The convergence of the obtained HPM solution is carefully analyzed. Finally, the validity of results is verified by comparing with numerical methods and existing numerical results. Findings – Close agreement of the two sets of results is observed, thus demonstrating the accuracy of the HPM approach for the particular problem considered. Originality/value – Interesting conclusions which can be drawn from this study are that HPM is very effective and simple compared to the existing solution method, able to solve problems without using Padé approximants and can therefore be considered as a clear advantage over the N.M. Bujurke and Phan-Thien techniques. [ABSTRACT FROM AUTHOR]

Three-dimensional flows over backward facing s.tif are analysed by means of a finite element procedure, which shares many features with the SIMPLER method. In fact, given an initial or guessed velocity field, the pseudovelocities, i.e. the velocities that would prevail in the absence of the pressure field, are found first. Then, by enforcing continuity on the pseudovelocity field, the tentative pressure is estimated, and the momentum equations are solved in sequence for velocity components. Afterwards, continuity is enforced again to find corrections that are used to modify the velocity field and the estimated pressure field. Finally, whenever necessary, the energy equation is solved before moving to the next step. [ABSTRACT FROM AUTHOR]