Search

In this work, the effect of using baffles and vortex generators on the cooling performance of a gas turbine combustion chamber is numerically investigated. The RNG k-ɛ model is utilized in order to simulate the flow turbulence. The effects of baffles and vortex generator pitch, hydraulic diameter and bypass ratio on the Nusselt number and friction coefficient at different Reynolds number are studied. The cooling performance of applying baffles and vortex generators are also evaluated and compared based on the Performance Evaluation Criterion (PEC). The numerical results are verified with available experimental data. The results show that the pitch increment results in the decrement of the Nusselt number and the wall friction coefficient due to the lower vortices generation and the turbulence kinetic energy dissipation. Also, the Nusselt number is increased by increasing both the bypass ratio and the hydraulic diameter. It is also found that vortex generators and baffles improve the cooling performance of the gas turbine combustion chamber by 18.8% and 26% respectively through decreasing the external wall temperature.

The principal goal of the present investigation is to inspect the flow characteristics of an electrically conducting hybrid nanofluid containing copper and graphene nanoparticles past a linearly stretched sheet with velocity slip condition at the interface. Since, the non-Newtonian fluid models result in a better understanding of the flow and heat transfer attributes of the nanofluids, therefore, non-Newtonian Maxwell nanofluid has been chosen as the base fluid in our study with an unsteady magnetic field applied at a certain angle to the direction of the flow. Consideration of thermal radiation along with heat absorption under the mutual influence of viscous and Joule dissipations is one of the key features of this research investigation. With the help of similarity transformations, the governing flow equations have been converted into a system of coupled non-dimensional differential equations. After that, Shooting method along with Runge–Kutta–Fehlberg numerical technique is employed to find the solutions for velocity and temperature of the hybrid nanofluid. The obtained numerical results are well demonstrated with a number of graphs and tables. Apart from this numerical technique, a statistical method is implemented of multiple quadratic regression estimation analysis on the various graphs of skin friction coefficient and wall temperature gradient to establish the connection among physical entities and heat transfer rate. The applications of this investigation in solar energy, ventilation, heating as well as refrigeration , medical science, defence sector etc. Some noteworthy findings include that Maxwell parameter, velocity slip and porosity have a tendency to reduce the hybrid nanofluid velocity whereas graphene Maxwell hybrid nanofluid’s temperature is getting enhanced for rising the values of magnetic field’s inclination angle, radiation, unsteadiness parameters, Biot number and viscous dissipation whereas a reverse trend is visible for heat absorption parameter. Furthermore, the permeability of the porous medium has a more significant impact on changing the nanofluid velocity than that of magnetic parameter whereas the rate of heat transfer is high sensitive for thermal radiation than that of viscous dissipation. As per authors’ knowledge there is no such attempt where the mutual effects of hybrid Maxwell nanofluid (graphene and copper), porous media and viscous dissipation have been considered.

The theoretical analysis of the steady fully developed electrically conducting flow of water based nanofluid in a vertical double passage channel is studied. The governing equations are respectively solved analytically and semi-analytically for each flow using perturbation method and the differential transformation method (DTM). The effects of flow governing parameters on the flow and velocity fields are numerically evaluated and presented in the graphical form. The outcome obtained by semi analytical method is confirmed by comparing with the aid of perturbation method and good agreement is found.

The primary goal of this research is to study the Cattaneo-Christov heat flux model on the impacts of mass and energy transit of MHD Casson-Carreu nanofluid through a permeable vertical accelerating plate with Soret and Dufour mechanism. The non-Newtonian fluids flowed over the porous vertical plate to reach the boundary layer in this investigation. In order to understand the physical model, partial differential equations (PDEs) are used. To get a linked nonlinear set of ordinary differential equations (ODEs), we reduced this set of PDEs by using similarity variables. SHAM, a spectrum basis technique, was utilized to solve these modified equations to understand the physical significance. A good method is to utilize SHAM to decouple the coupled nonlinear ODE systems and divide them into linear and nonlinear equation sets since this helps to separate the systems. As a result, the two non-Newtonian fluids (Carreu and Cassin) flow together through the vertical wall and into the boundary layer, where different parameters’ impacts are scrutinized. The current results showed that an upturn in the Casson parameter (β) degenerates the boundary layer velocity and the total thickness. Upturn in the Weissenberg number (We) on the other hand, raises the velocities and temperatures in both directions. Additionally, increasing the Soret and Dufour parameters sped up the velocity graph.

In this investigation, a comprehensive and accurate numerical analysis of the local thermal non-equilibrium effects on the natural convection characteristics in a horizontal elliptical porous annulus saturated with nanofluid has been carried out using finite volume technique. The internal surface is isothermally heated while the external one is fixed at uniform lower temperature. The nanofluid phase and the solid phase of the porous structure are hors local thermal equilibrium situation. The heat and the hydrodynamics equations in their dimensionless form under Darcy-Brinkman Forchheimer model were solved computationally by the finite volume technique using the standard SIMPLER algorithm. The results have been examined for various porous medium properties under the LTNE condition. The standard 0.05 significance level was used to identify the local thermal equilibrium within the system. According to the obtained results, the higher the Darcy number and the smaller the non-dimensional heat transfer coefficient for the solid/nanofluid interface, the modified thermal conductivity ratio and the media’s porosity, the higher are the LTNE effects. In addition, the spatial distribution contours of the LTNE sources within the porous annulus were schematized.

This research study aims to illustrate the dynamics of water conveying hybrid nanofluid flow over an exponentially stretchable sheet in the presence of Navier's partial slip and thermal jump conditions. The nanoparticles of Cu, TiO2 and Al2O3 are suspended into water (H2O) to prepare three forms of hybrid nanofluids. Also, the influences of Joule dissipation and thermal radiation are considered in the study. The mathematical model embodies the system of highly coupled nonlinear partial differential equations. The set of similarity equations are derived from these partial differential equations by utilizing appropriate similarity variables. Further, these similarity equations together with allied conditions are numerically solved by making use of a finite difference scheme based Lobatto IIIa-bvp4c solver in MATLAB. The significance of emerging dimensionless flow parameters on the water conveying Cu-Al2O3 hybrid nanofluid temperature and velocity are quantified by depicting various graphs. Besides, temperature and velocity profiles are compared for three different water-driven hybrid nanofluids comprising a colloidal mixture of Cu-Al2O3, TiO2-Al2O3 and Cu-TiO2 nanoparticles respectively. The local Nusselt numbers and wall velocity gradients are obtained in numerical form for various emerging physical parameters. Also, to comprehend the linking between heat transfer rate and emergent flow parameters, a statistical method is executed for the investigation of regression (quadratic) approximation on the skin friction coefficients and Nusselt numbers. Finally, the computed numerical results are compared with earlier reported paper and excellent conformity is noticed. The findings infer that the heat transport rate can be improved by the inspirations of suction and thermal radiation while viscous dissipation, magnetic field, injection and thermal slip factor are significant to reduce the heat transport rate of hybrid nanofluid

Here, continuous two-dimensional boundary layer flow of a Fe2O3 CuO/water hybrid nanofluid over a porous stretching/shrinking wedge with radiation and MHD effects has been investigated semi–analytically. The dual solutions of the problem and also its stability analysis are taken into account. Moreover, the mass-based procedure for hybrid nanofluid modeling has been used. According to this procedure, the volume fraction of first and second nanoparticles is written in terms of both nanoparticles as well as base fluid masses. The Tiwari-Das model joined with mass-based hybrid nanofluid procedure is applied to find the governing partial differential equations which are then transferred to a set of dimensionless ordinary differential equations with help of the similarity transform method. The numerical method of solution has been chosen based on a famous finite difference scheme (bvp4c) from MATLAB software. The results demonstrate that dual solutions exist for a certain domain of the wedge stretching/shrinking parameter. Also it is observed that always the first solutions have thinner boundary layer thickness than the second ones. Moreover, the critical value in which the solution is in existence increase with the enhancement of magnetic parameter and suction parameter. The magnetic parameter and the mass suction at the wedge's surface also leads to the increase in the local Nusselt number. Further, it is inferred that the second nanoparticle's mass enhancement results in the amplification of the skin friction coefficient and the local Nusselt number for the first solutions. In addition, the rise in radiation parameter tends to enhance the thermal boundary layer thickness.

This paper is basically devoted to carry out an investigation regarding the unsteady flow of dissipative and heat absorbing hydromagnetic graphene Maxwell nanofluid over a linearly stretched sheet taking momentum and thermal slip conditions into account. Ethylene glycol is selected as a base fluid while graphene particles are considered as nanoparticles. The highly nonlinear mathematical model of the problem is converted into a set of nonlinear coupled differential equations by means of fitting similarity variables. Further, Runge-Kutta Fehlberg algorithms along with the shooting scheme are instigated to analyse the numerical solution. The variations in graphene Maxwell nanofluid velocity and temperature owing to different physical parameters have been demonstrated via numerous graphs whereas Nusselt number and skin friction coefficients are illustrated in numeric data form and are reported in different tables. In addition, a statistical method is implemented for multiple quadratic regression estimation analysis on the numerical figures of wall velocity gradient and local Nusselt number to establish the connection among heat transfer rate and physical parameters. Our numerical findings reveal that the magnetic field, unsteadiness, inclination angle of magnetic field and porosity parameters boost the graphene Maxwell nanofluid velocity while Maxwell parameter has a reversal impact on it. The regression analysis confers that Nusselt number is more prone to heat absorption parameter as compared to Eckert number. Finally, the numerical findings are compared with those of earlier published articles under restricted conditions to validate the numerical solution. The comparison of numerical findings shows an excellent conformity among the results.

Background The exploration of natural convection which is one the substantial types of convective heat transmission in various applications for instance heat exchangers and geothermal systems along with nanofluids (Nanofluids have greater thermal conductivity in comparison to the conventional fluids) engrossed all researchers’ attention. Methods This study is dedicated to the inspection of the free convection of nanofluid as well as entropy generation inside a porous cavity loaded with nano-encapsulated phase change materials (NEPCMs). The wavy bottom section of the enclosure may be subject to a constant heat flux due to the transmitted sunlight comes from a parabolic trough solar collector. The volumetric heat source/sink is comprised in the governing equation. The robust finite element method (FEM) is deployed to handle the transformed governing equations. Findings The numerical simulation of the streamlines and isotherms associated with velocity distribution for diverse factors are displayed. Further, the significant behavior of the contributing parameters on the Nusselt and Bejan numbers are represented. The results demonstrate that the various profiles of wavy bottom section could affect the heat transmission features as well as fluid flow remarkably. Furthermore, it is noteworthy that all the profiles of entropy enhance with increasing the amplitude with respect to the increasing undulation number for the existence of various Rayleigh number.

The MHD flow of hybrid nanofluid between the coaxial, stretching, and rotating discs in the presence of porous medium along with the convective boundary conditions and thermal relaxation time is numerically investigated in this article. We have considered GO–water (gallic oxide nanoparticles with water) and TiO2–water (titanium dioxide nanoparticles with water) hybrid nanofluids. The nonlinear coupled differential equations are solved using a suitable code and ND-solver in Mathematica software, which is based on the finite difference method (FDM). The various interesting results are unfolded from this study. The tangential velocity of both nanofluids is decreased on increasing the values of porosity parameter ( $$\beta $$ ), magnetic parameter (M) and Reynolds number (Re), while it is increased on increasing the value of rotation parameters ( $$\Omega $$ ). The temperature of both nanofluids is reduced on enhancing the values of Prandtl number (Pr), Eckert number (Ec), Re, $$\beta $$ , and M, while it enhances on increasing the values of $$\gamma _1$$ and $$\gamma _2$$ . Further, the temperature of TiO2–water nanofluid reduces on enhancing the values of the thermal relaxation parameter ( $$\gamma $$ ), while the temperature of GO–water nanofluid is enhanced. Since the thermal relaxation time reflects how quickly fluid loses heat energy, parameter $$\gamma $$ has dual nature on temperature profiles for both TiO2–water and GO–water nanofluids.

The article deals with 2D unsteady nanofluid flow past a vertical wedge along with nonlinear mixed convection. Brownian diffusion and thermophoresis effects are considered to model nanofluid flow. ...

This paper examines the capability of hybrid lattice Boltzmann method to simulate developed turbulent buoyancy-driven flows in closed rectangular cavities. The two-relaxation time mesoscopic lattice Boltzmann method is used as a fluid dynamics solver, whereas the thermal behavior is described in terms of the macroscopic energy equation. Numerical simulation is performed for air-filled square and tall cavities in a range of the Rayleigh number $$10^{9} \le Ra \le 10^{11}$$ . An in-house numerical code is developed in this study and successfully validated against up-to-date numerical and experimental data of other researches. It is found that the proposed hybrid approach accurately predicts the location of thermal plumes at the isothermal walls despite an insignificant error in the heat transfer rate with the $$Ra \ge 3 \cdot 10^{10}$$ .

This problem considers the instabilities, which can occur when a horizontal sparsely filled nanofluid porous layer is saturated with a binary mixture with fast chemical reaction. The upper and lower plates are heated isothermally. The model used for the nanofluid incorporates the effects of Brownian motion and thermophoresis. The modified Darcy equation that includes the time derivative term is used to model the momentum equation. The energy equation includes cross and regular diffusion conditions. In conjunction with the Brownian motion, the nanoparticle fraction becomes stratified; hence the viscosity and the conductivity are stratified. The nanofluid is assumed to be diluted and this enables the porous medium to be treated as a weakly heterogeneous medium with variation, in the vertical direction, of conductivity and viscosity. The oscillatory and stationary convection are evaluated analytically. The reaction rate is supposed to be greater than the diffusion rate. We find that both a stationary instability and an oscillatory instability can occur as the first bifurcation, depending on the sign and the value of the heat of reaction. The execution of the porous parameter, Prandtl number, Soret parameter, Dufour parameter, Lewis number, solutal Rayleigh number, chemical reaction and the modified diffusivity ratio parameters is implemented pictorially. It is found that the presence of nanoparticles the critical Rayleigh number is increased and helps to stabilize the system. The presence of chemical reaction parameter destabilizes the system. The results of previously-published work are also obtained as special cases of the general solution.

The problem of transient Magnetohydrodynamic (MHD) combined convection within a wavy-heated rectangular cavity having two inner cylinders is investigated using the non-homogeneous nanofluid scheme. The lower wavy surface of the cavity is kept at a constant hot temperature ( T h ) while the upper flat surface is kept at a constant cold temperature ( T c ). The remaining surfaces (vertical surfaces) are maintained adiabatic. An Al 2 O 3 /water nanofluid is filled inside the cavity and a non-homogeneous approach is adopted to solve governing equations by using the Galerkin method. The effect of some parameters such as the angular rotational speed, the volume fraction of nanoparticles, Hartmann number on the flow and heat transfer characteristics are examined. The results indicate that the waving of the hot base of the cavity enhances the Nusselt number. The maximal Nusselt numbers are obtained when the number of undulations N is 2, where the Nusselt number augments by 18% when N is boosted from 0 to 2 and by 16% from 0 to and 5. Also, the outcomes reveal that the enhancement of the Nusselt number as a result of raising the rotational speed of the two cylinders from 0 to ± 500 is about 315%.

The principal aim of this study is to explore the impact of relaxation-retardation viscous dissipation, nonlinear convection, variable chemical reaction, and nonlinear thermal radiation on the three-dimensional rotating flow of an Oldroyd-B nanofluid over an exponentially extended surface. The Buongiorno model that takes into account the Brownian movement and thermophoresis responsible for nanoparticle motion. Exponentially varying temperature and concentration associated with convective heat transfer coefficients are assumed in the boundary conditions. The system of dimensionless ODEs is solved by the spectral quasi-linearization method. The results of the analysis show, among other results that the relaxation time parameter opposes the momentum transport while assisting heat transportation. The retardation time parameter acts to support momentum growth while reducing and resists heat transport. The present study focused on the investigation the effect of relaxation and retardation viscous dissipation on rotating flow of a non-Newtonian fluid (Oldroyd B fluid) past an exponential stretching sheet.

An exploration of the unsteady MHD boundary layer flow over a moving vertical porous surface with nanofluids under the influence of a uniform transverse magnetic field and heat radiation absorption effects has been brought out. Two different kinds of water-based nanofluids comprising of Al2O3 and TiO2 are adopted into deliberation. The governing equations for the flow are solved by making use of the Laplace transform method, and the solutions are displayed in closed form. The velocity, temperature, concentration, the shear stress, the rate of heat and mass transportations near the surface has been described graphically for numerous values of the relevant parameters. The velocity and temperature enhances with increasing radiation absorption parameter. It is also observed that an increase of volume fraction of nanoparticles leads to the enhancement of the temperature on central line of the flow. Nusselt number might be tracked down to be elevated for alumina than titanium dioxide nanofluid. The present investigation originated applications in aerospace engineering as well as industrial many mechanisms.

The present study analyzes the forced convective boundary layer flow of viscous incompressible time-established fluid. The base fluid containing water-based nanoparticles and gyrotactic microbes. The flat surface is considered with leading-edge accretion (or) ablation. Characteristics of flow are explored by the impacts of thermal radiation and constructive/destructive chemical reaction. The present flow problem is formed with the partial differential equations, and transformed nonlinear boundary value problems are solved mathematically by the finite difference with the collocation method. There is a good correlation between present work and previous work. Results of selected parameters on velocity, temperature, nanoparticles volume fraction, and microbe density function are discovered. Skin friction, heat transport, mass transfer, and microbes transfer rates are tabular. Efforts of the current work rise in progressive microflow devices to bio-modified nanomaterial dispensation.

The current study explores the consequences of thermo-diffusion, chemical reaction, Hall and ion-slip impacts on unsteady heat and mass transport of free convective hydro-magnetic micro-polar liqui...

Drag and lift forces are very important in engineering applications and, therefore, many research projects have been conducted to control these forces. In this paper, the effects of an upstream porous plate on the hydrodynamic forces over a square cylinder are investigated using lattice Boltzmann method. The main idea is to separate the obstacle from the upstream flow by adding such a porous plate, since the magnitudes of the drag and lift forces have a direct relationship with the phenomena of vortices shedding from the obstacle. In order to have a better insight into the problem, streamlines, vorticity contours and lift and drag coefficients are presented for different case studies. Results proved that the porous plate can reduce the drag and lift coefficients. Furthermore, increasing the height and the gap spacing (i.e., the surface-to-surface distance between the porous plate and the obstacle) could significantly affect the flow field characteristics and the forces acting on the obstacle.

The oily water from various sources in combined cycle power plants is collected in oil/water separator in which the oil separates from water due to the density difference. The idea of the presented geometry is taken from conventional oil/water separators. This paper studies the natural convection of the CuO-water nanoliquid in a rectangular cavity with fins attached to the insulated wall and porous media. Discretion of Navier-Stokes equations is done by Finite Element Method and assumptions are laminar, steady and incompressible flow. Heat transfer performance and entropy generation are investigated for distinct Rayleigh numbers (103–105), Darcy numbers (10−2–10−4), and Hartmann numbers (0, 10, 20). Different sizes of the fins are also studied to show consequences of fin size on heat transfer in cavity. This is the first time that these parameters and their impacts on Nusselt number and entropy generation are studied for a conventional oil/water separator cavity. Corollaries demonstrate that increasing Rayleigh number and Darcy number improves heat transfer performance and average Nusselt number. Nevertheless, Hartmann number has a reverse effect with average Nusselt number. Finally, a new equation for average Nusselt number is developed with regard to Rayleigh number, Hartmann number, and Darcy number.

In this numerical contribution, hybrid nanofluid flow behavior, thermal characteristics, and entropy generation analysis through a porous enclosure containing three circular cylinders with magnetic field effects were investigated using finite element approach. The cylinders are arranged in horizontal arrangement in the middle of cavity height, and the active hot central cylinder can move along the vertical central axis while other cold cylinders are considered fixed. The cylinders are enclosed by an adiabatic wavy cavity loaded with Cu-Al2O3-water. The results are discussed for the scrutinized parameters e.g., Rayleigh number (Ra), Darcy number (Da), Hartmann number (Ha), relative position of the hot cylinder (δ), and concentration in volume of nanoparticles (ϕ). It was inferred that the thermal-natural convective flow and overall heat transmission were reinforced by boosting Ra and Da, and lowering Ha. Changing the relative position of the hot cylinder has a remarkable effect on nanoliquid flow patterns, convective heat transfer and entropy generation characteristics.

The present study encountered the impact of non-dimensional fusion temperature on the free convection of conducting nanofluid within a porous enclosure filled with nano-encapsulated phase change materials (NEPCMs). The enclosure is equipped with two parallel fins that have ability to move in both directions such as vertically as well as horizontally. In particular the particles are structured as core-shell with phase change materials. The phase change of the materials is obtained from the solid to liquid and absorbs the surrounding temperature in the hot region and releases in the cold region. The governing transformed equations are tackled by using the Finite Element Method (FEM). The numerical simulation of the isotherms, streamlines and heat transfer coefficient ratio along with velocity distribution for various parameters are presented. These are affecting a key role on the average and local Nusselt number as well as on the local Bejan number. However, the measure outcomes are; both the longitudinal and transverse velocity profiles boost up with an augmented Rayleigh number; however, the weaker flow field is generated for the increasing Hartmann number.

The current study is concerned with the investigation of the combined effects of thermophoretic motion and thermal radiation on steady, viscous, incompressible and two-dimensional mixed convection flow of optically dense grey fluid. The governing equations are made dimensionless by using suitable dimensionless variables and further are transformed into a convenient form for a numerical algorithm. The transformed flow model is integrated by using an efficient finite difference methd. Effects of the assorted parameters involved in the flow model such as Prandtl number, mixed convection parameter, modified mixed convection parameter, Schmidt number, radiation parameter, thermophoresis parameter and thermophoretic coefficient on velocity field, temperature distribution, and mass concentration are demonstrated graphically. The numerical results of skin friction, the heat transfer rate and the mass transfer rate under the effect of pertinent parameters are displayed in tabular form.

The effect of source/sink heat location and size on Magneto-hydrodynamic mixed convection in hybrid nanofluid of Al2O3-Cu/Water within the L-shaped cavity is studied in this paper. Two uniform heat sources are put at the corners of the bottom walls of enclosure and the beginning and the end of L-shape enclosure set to be at the cold temperature. The other parts of enclosure’s walls are supposed to be insulated. The finite difference method and Boussinesq approximation is utilized to discrete the governing equations. The fundamental flow physics and thermal behavior are explored in terms of pertinent parameters such as the effects of sink/source heat generation, magnetic field and angle, Hartmann number, cavity length ratio, and hybrid volume fraction on average and surface Nusselt number, streamlines, isotherms, and entropy generation are studied. The results demonstrate that maximum amount of the sink power causes the best heat transfer performance.

In the current investigative paper, the impact of Hall current on an unsteady magnetohydrodynamic liberated convection revolving flow of a nanofluid restricted with a uniform absorbent medium over an oscillatory moving vertical smooth plate with convective as well as diffusive frontier conditions has been reviewed. The non-dimensionalized governing differential equations by the appropriate frontier conditions are resolved by the perturbations technique. The impacts of the physical constants on the flow as well as the heat transfer features are displayed graphically and analyzed for Cu as well as Al2O3nanoparticles. For the engineering industry, the skin friction coefficient, local Nusselt number, along with the Sherwood’s number are examined numerically in detail.

The impact of wall movements in different directions on mixed convection flow and thermal performance in a wavy chamber is reported. The wavy wall of the chamber is heated non-uniformly, and the upper wall is kept at a constant cold temperature, while the vertical walls of the chamber are adiabatic. Four different cases, namely Case-1, Case-2, Case-3 and Case-4, are considered on the basis of multi-directional movements of the walls of the chamber. Mathematical model of the flow physics consists of the Navier–Stokes (N-S) equations in streamfunction ( $$\psi$$ ) —vorticity ( $$\zeta$$ ) formulation including the energy transport equations which are solved by higher-order compact (HOC) scheme on curvilinear grids Pandit SK, Chattopadhyay A.(Comput Math Appl 74(6):1414–34 2017) [45]. It is found that the fluid flow and thermal performance are both influenced by the direction of moving lids and the undulations of the wavy bottom surface of the chamber. Optimum thermal performance is noticed when the wavy bottom surface of the chamber is employed with one undulation at low Richardson number (Ri). Moreover, for $$Ri=0.01$$ , Case-2, in which the upper lid is moving in left direction and the left lid is moving in upward direction, gives better heat transfer rate with maximum value of average Nusselt number for one undulation. Furthermore, it is noticed that among all the cases, the cases (Case-2 and Case-4) in which upper lid is moving in left direction produce minimum entropy generation for every undulations of the wavy surface with each of the Ri values. So, on the basis of better heat transfer rate and the minimum entropy generation, Case-2 and Case-4 may be recommended as optimum configurations.

The passive feature of natural convection encourages continuous investigation on this field. This research work studies the natural convection inside a cavity of wavy vertical surfaces, including a...

This paper theoretically clarifies the impact of pertinent parameters, including viscous dissipation on the flow of Carreau fluid through a permeable arched elongating sheet. Flow describing equations are metamorphosed as ODEs and executed using the combination of shooting and Runge-Kutta strategies. Consequences are elucidated using tables and graphs. We discovered that (a) an appreciable decline in the concentration against temperature difference and reaction rate parameters (b) curvature parameter and porosity parameters registered opposite behaviour to each other on velocity profile (c) there is a reduction in the heat transfer rate with larger Eckert number and curvature parameters (d) Biot number ameliorates the temperature and local Nusselt number (e) Schmidt number and activation energy parameters are showing different behaviours on local Sherwood number. And also, magnetic field and porosity parameters minimize the velocity and surface drag force and Biot number ameliorates the temperature. Further, present results are validated with the earlier outcomes and perceived an acceptable agreement.

To analyze the influence of the tapered form of the two upper vertices of a rectangular cube placed in a channel and the impact of the insertion of hollow in the center of the obstacle, a three-dimensional study was executed using K-ω SST turbulence model. Different models of the form of the cube were presented to examine the features of the flow with a Reynolds number Re=4×104. The turbulence kinetic energy, 2D and 3D time-averaged streamlines, trace-lines, streamwise velocity profiles, pressure profiles were obtained using the ANSYS CFX calculation code and the finite volume method were employed for resolving the governing equations. The streamlines showed in the model of the tapered cube with hollow a formation of another vortex downstream of the cube at the outlet of the hollow. For the streamwise velocity, there are two recirculation zones: one logarithmic zone due to the main flow, the other is a lower parabolic return zone due to the recirculation vortex.

We have explored theoretically the Hall and ion slip impacts on an unsteady laminar MHD convective rotating flow of heat generating or absorbing second grade fluid over a semi-infinite vertical moving permeable surface. The non-dimensional equations for the governing flow are solved to the most excellent possible investigative solution using perturbation methodology. The effects of parameters on velocity, temperature and concentration are demonstrated graphically and described in detail. For engineering curiosity, the shear stresses, Nusselt number and Sherwood number are obtained analytically, represented computationally in a tabular format as well as explained with respect to foremost parameters. It is concluded that, the resultant velocity is increased with an increasing in Hall and ion slip parameters throughout fluid region. The thermal and solutal buoyancy forces contribute to the resultant velocity ever-increasing to high. The temperature distribution is trim downs through an increasing in heat source parameter. The concentration is reduced with an increase in the chemical reaction parameter in the entire fluid region. Rotation parameter is to diminish the skin friction, whereas it is augmented through an increase of the Hall and ion slip effects. The rate of mass transfer is increased with increasing chemical reaction parameter.

This article explains the effect of magnetite nanofluid taking into account water as the base fluid, over a rotating disk in the presence of external magnetic field. The governing boundary layer equations of laminar and incompressible flow over rotating disk have been formulated under the simultaneous influence of thermophoresis and Brownian motion. Additionally, influence of chemical reaction between species, prompted by Arrhenius activation energy is considered into the model. The Von Karman’s transformations of the Navier-Stokes equations are used to obtain the non-dimensional forms of the governing equations, and then fourth order finite difference scheme is used to find the numerical solutions using Noumerov’s discretization. This technique has strong impact on the accuracy of finite difference scheme. The physical descriptions of fluid velocity, temperature, concentration profiles and quantities of practical interest such as skin friction coefficient, Nusselt number and Sherwood number are presented with the help of graphs. One of the significant findings of this analysis include that an intensification in the thermophoresis parameter causes a downfall in the rate of heat transfer at the surface of the disk whereas another significant outcomes of the present investigation is that there is a downfall in the behaviours of the species concentration with the strengthening of Arrhenius activation energy. The fluid flow due to rotating disks has application in mechanisms of thermal transformations for nuclear propulsion devices.

Mixed convection has been one of the most interesting subjects of study in the area of heat transfer for many years. The entropy generation due to MHD mixed convection heat transfer in L-shaped enclosure being filled with Cu-water nanofluid and having an internal heating generation is explored in this investigation by the finite volume technique. Lid-motion is presented by both right and top parts of walls to induce forced convection and the cavity is under an inclined uniform magnetic field along the positive horizontal direction. The statistics concentrated specifically on the impacts of several key parameters like as the aspect ratio of the enclosure, Hartmann number, nanoparticle volume fraction, and heat source length/location on the heat transfer inside the L-shaped enclosure. Outcomes have been manifested in terms of isotherm lines, streamlines, local and average Nusselt numbers. The obtained results show that addition of nanoparticles into pure fluid leads to increase of heat transfer. The maximum value of local Nusselt pertaining to the heat source occurs when L = 0.1. Impacts of heat source size and location, internal heat generation absorption, angle of magnetic field on heat transfer and entropy generation are completely analyzed and discussed. The best configuration and values of important parameters are also presented using thermal performance criteria.

In the present work, natural convection heat transfer in a differentially heated cavity is considered, in which, source–sink pairs are located on vertical walls with a constant temperature while other wall parts of the enclosure are insulated. The effects of different arrangements, sizes, and number of heat source–sink pairs on the flow and thermal fields are investigated by using the Lattice Boltzmann Method to solve the flow and thermal field equations. In this paper, streamlines, isotherms, the average Nusselt number, and the entropy generation are presented to get a better insight into the nature of the problem. Results of this study showed that the arrangement of the heat source–sink pairs could strongly affect the flow and thermal fields in the cavity due to the formation of the vortices. It was also found that the highest amount of heat transfer with the lowest entropy generation was achieved by splitting the discrete heat source–sink pairs into the smaller segments and putting them alternately on one sidewall.

Heat and flow pattern of a vertical free jet impinging on a hot disk were numerically investigated. A cylinder with various thicknesses and materials exposed simultaneously to uniform heat flux on one side and a free impinging jet on the other side is simulated by ANSYS Fluent 19.3. For simulations, the thermal boundary condition on the hot surface might differ due to the nature of the heat flow. The Volume of Fluid (VOF) approach is used to model the free jet heat transfer and fluid dynamics with the presence of air, while only the energy equation is solved in the cylinder. Heatline equation is solved to reveal the heat flow direction and effects of different geometry conditions. The maximum heat flux of 2.5 MW/m2 was obtained at the edge of stagnation region for hot target made of copper, while the value was 1.5 MW/m2 when the material was combined with stainless steel. However, the general thermal and hydrodynamic features of the jet flow were not influenced. It means that hot object condition may only affect the balance between heat flux and temperature, and the ideal uniform heat flux on the impinging wall may not be achieved in any experimental conditions.

This paper presents the analysis of thermal optimization in magnetic materials based on the entropy generation in a mixed convective MHD flow of an electrically conductive nano liquid having motile microorganisms together with a vertical cylinder. By using the convection boundary condition, the process of heat transport is examined in detail. With coupled linear boundary conditions the related equations (continuity, momentuum and energy) are reduced to five ODE’s. The RKF-4,5 method by shooting algorithm was employed to examine variation of physical parameters under study. The resuts of vital physical parameters on the wall friction, Nusselt number, mass flux, wall of motile microorganism flux, along with velocity profiles, temperature, concentration of nanopar-ticles, and density of motile microbes, were studied in detail. It is detected that heat transport rate is 0.81% greater for cylindrical surface compared to flat plate surface.

This study aims to unfold the significance of numerous physical parameters such as magnetic field, heat absorption, thermal radiation, viscous and Joule dissipations, etc. on the flow of graphene Maxwell nanofluid over a linearly stretched sheet with considerations of momentum and thermal slip conditions. The prevailing mathematical equations are reformed into extremely nonlinear coupled ordinary differential equations (ODE) utilizing similarity variables and then the equations are solved numerically by the scheme of Runge-Kutta Fehlberg method along with the shooting technique. The variations in graphene Maxwell nanofluid velocity and temperature owing to different physical parameters are shown via numerous graphs whereas numerical values of skin friction coefficients and Nusselt numbers are illustrated and reported in different tables. In addition, statistical approach is followed for the multiple regression estimation analysis on the numerical findings of wall velocity gradient and local Nusselt number and are reported in tabular form to demonstrate the relationship among the heat transfer rate and physical parameters. Our results reveal that the graphene Maxwell nanofluid velocity gets reduced owing to enhancement in magnetic field, angle of inclination of magnetic field, porosity and unsteadiness parameters whereas behavior of nanofluid velocity is reversed due to Maxwell parameter. Further, it is noticed that the heat transfer rate of nanofluid is augmented owing to heat absorption, radiation and thermal slip parameters while it is reduced due to increase in viscous dissipation and unsteadiness parameters. The numerical results of the paper are validated by making comparisons with the earlier published paper under the restricted conditions and we found an excellent agreement with those results. A careful review of research papers reported in literature reveals that none of the authors has attempted this problem earlier although the thoughts and methodology explained in this paper can be anticipated to lead to enormously prolific connections across disciplines.

Nanotechnology has infiltrated into duct design in parallel with many other fields of mechanical, medical and energy engineering. Motivated by the excellent potential of nanofluids, a subset of materials engineered at the nanoscale, in the present work, a new mathematical model is developed for natural convection in a vertical duct containing nanofluid. Numerical scrutiny for the double-diffusive free and forced convection within a duct encumbered with nanofluid is performed. Buongiorno’s model is deployed to define the nanofluid. Robin boundary conditions are used to define the surface boundary conditions. Thermal and concentration equations envisage the viscous, Brownian motion, thermosphores of the nanofluid, Soret and Dufour effects. Using the Boussi-nesq approximation the solutal buoyancy effect as a result of gradients in concentration are incorporated. The conservation equations which are nonlinear are numerically estimated using fourth order Runge-Kutta methodology and analytically ratifying regular perturbation scheme. The mass, heat, nanoparticle concentration and species concentration fields on eight dimensionless physical parameters such as thermal and mass Grashof numbers, Brownian motion parameter, thermal parameter, Prandtl number, Eckert number, Schmidt parameter, and Soret parameter are calculated. The impact of these parameters are outlined pictorially. The velocity and temperature fields are boosted with the thermal Grashof number. The Soret and the Schemidt parameters reduces the nanoparticle volume fraction but it heightens the momentum, temperature and concentration. At the cold wall thermal and concentration Grashof numbers reduces the Nusselt values but they increase the Nusselt values at the hot wall. The reversal consequence was attained at the hot plate. The perturbation and Runge-Kutta solutions are equal in the nonappearance of Prandtl number. The (E. Zanchini, Int. J. Heat Mass Transfer 41, 3949 (1998)). results are restored for the regular fluid. The heat transfer rate is high for nanofluid when matched with regular fluid.

Numerical simulation of a non-linear mathematical model governing an arbitrarily oblique slip flow of a nanofluid, with suspended carbon nanotubes in water, agitated by magnetic field, mixed convection currents and thermal radiation is carried out. The cases for both single-wall carbon nanotubes (SWCNTs) and multi-wall carbon nanotubes (MWCNTs) are taken under consideration to gain a wider perspective. Globally, heat transfer rate for SWCNTs is found to be more effective in comparison to the MWCNTs, as the former offers less resistance in terms of the overall drag or shear. In addition, it is found that the magnetic field increases the skin friction by increasing the obliqueness of the flow. Numerical validation with available studies in the literature shows excellent conformity. The results will have bearing in thermal management of the heat exchange processes occurring within the devices used in polymer industries and polymer technology.

The inclusion of complex obstacles within solar channels is the aim of this article. Two obstacles of the form ꞌ+ꞌ interlaced within a two-dimensional and rectangular channel are the subject of our study. The fluid is Newtonian, turbulent, incompressible and has constant properties. The Reynolds number varies from 12,000 to 32,000 with a constant temperature along the upper surface of the channel. The thermal and dynamic analysis of the channel's internal structure has been carefully processed. Different fields of speed and heat, with various profiles of frictions and heat exchange coefficients, have been included in this research. Future work will involve more complex geometries and using nanofluids to assess the optimum conditions for heat transfer enhancements.

The entropy generation due to magnetohydrodynamic mixed convection flow and heat transfer in a Gamma-shaped porous cavity is explored in this research by the finite volume technique. There exists a...

This study investigates thermal natural convective heat transfer in a nanofluid filled-non-Darcian porous and wavy-walled domain under the local thermal non-equilibrium condition. The considered cavity has corrugated and cold vertical walls and insulated horizontal walls except the heated part positioned at the bottom wall. The transport equations in their non-dimensional model are numerically solved based on the Galerkin finite-element discretization technique. The dimensionless governing parameters of the present work are the nanoparticle in volume concentration, the Darcy number, number of undulations, modified heat conductivity ratio, dimensionless heated part length, and location. Comparisons with other published theoretical and experimental results show good agreement with the present outcomes. The findings indicate that the heater length, its position, and the waves number on the side vertical walls as well as the nanoparticles concentration can be the control parameters for free convective motion and heat transport within the wavy cavity.

International audience; Kinematical and geometrical parameters of helical vortices winding in the same (right-handed) or opposite direction (left-handed) to the base Taylor-Couette-Poiseuile flow were studied at low Ta = R-1 d/v < 319 and Re = U-M d/v < 10.5 numbers. The inner cylinder (R-1 = 24.85 mm) rotated and the outer one (R-2 = 30.95 mm) was stationary. The parameters of helical vortices were obtained from flow visualizations and the wall shear rates were deduced from the electrodiffusion currents of three mass transfer probes flush mounted on the wall of the outer cylinder Kristiawan et al. [11] . The vector field of wall shear rate on the outer cylinder was reconstructed using a three-segment mass transfer probe. It is found that the axial component of the wall shear rate of the left-handed helices is greater than that of the right-handed helices. The motion of the flow structures near the outer wall was described by the velocity V resulting from the axial drifting velocity (U-D) and the azimuthal velocity W . It was shown that the axial velocity perceived by an observer or sensor fixed in the laboratory system U-OBS is composed of the drifting velocity U-D and the velocity due to the helix rotation U-Omega, known as Barber pole effect. New insight on the helical structures are revealed from studying the variations of different parameters such as the helix pitch p, the rotation rate and the observed angular velocity of the helices. (c) 2021 Elsevier Ltd. All rights reserved.

The united consequences of diffusion thermo as well as radiation absorption on magnetohydrodynamic (MHD) complimentary convection revolving flows of nanofluids over a semi unlimited porous stirring plate by the invariable temperature resource are investigated. Utilizing the perturbations methodology, the velocity distributions,temperatures as well as the concentrations distributions are obtained and examined through their graphical representation. Besides that, the skin friction coefficient, Nusselt number as well as the Sherwood number are obtained analytically and are also arithmetically discussed with reference to the leading parameters. It is observed that the diffusion thermo parameter or the radiation absorption parameter augments the velocity in addition to the fluid temperatures throughout the fluid region. This enhancement is most significant for silver nanoparticles. This is owing to the higher conductance of the solid particles of Ag than that of TiO2. It is also observed that the concentration frontier layer thickness reduces by an increase in the chemically-reacting parameter. This is because the chemically molecular diffusivity decreases for higher quantities ofKr. Also,the Nusselt number reduces while the Sherwood number enhances by increasing the value of the suction parameter.

The present research explores the features of thermal and solutal transport of a 3D micropolar liquid stream on an elongated convectively heated inclined sheet taking Soret effect. Mathematical modelling is designed with the aid of suitable scaling analysis on the governing PDEs conceiving the small magnetic Reynolds number. The resultant set of coupled nonlinear ODEs are derived with MATLAB to obtain computational solutions. Impression of the emerged flow parameters on the three boundary layers is graphically traced and deliberated. The parameters of magnetic field and stretching ratio and power law index diminished frictional drag. Hike in rate of thermal diffusion is prevailed with stronger surface heat convective and Prandtl numbers. Outcomes are collated with the data available in the literature and found to agree very closely as a limiting case.

Modeling and computations are performed to study the ND-Co3O4/EG hybrid nanoliquid mixed convective flow past a vertical porous cylinder. The flow analysis and formulation are given accounting for slip effects and homogeneous-heterogeneous reaction impacts. The governing complex equations formed with prescribed boundary conditions are simplified into self-similar equations through the use of suitable transformations. The numerical solutions of the drag coefficient, Nusselt number, liquid velocity, liquid temperature, and the liquid concentration are explored through graphs with the setting of pertaining parameter values. From the results, it is noticed that an ND-Co3O4/EG nanofluid plays a more impressive role in the process of energy transfer than a Co3O4/EG nanofluid. Further, it is found that the heterogeneous reaction parameter decreases the concentration whereas multiple slips enhance the temperature.

The intent of this study is to demonstrate an approach for augmenting heat transfer through porous media subjected to nonuniform heating during the magnetohydrodynamic flow of a hybrid nanofluid of Cu–Al2O3/water. The efficacy of such a heating technique is examined utilizing a classical flow geometry consisting of a square cavity. The heating is made at the bottom following a half-sinusoidal function of different frequencies, along with the presence of a uniform magnetic field. The thermal conditions of the cavity, particularly at the bottom wall, drive thermo-hydrodynamics and associated heat transfer. Furthermore, the addition of different types of nanoparticles to the base liquid in order to boost the thermal performance of conventional fluids and mono-nanofluids is a current technique. The coupled nonlinear governing equations are solved numerically in dimensionless forms adapting the finite volume approach, the Brinkman–Forchheimer–Darcy model, local thermal equilibrium and single-phase model. The study is conducted for wide ranges of parametric impacts to analyze global heat transfer performance. The results of this study reveal that the multi-frequency spatial heating during hybrid nanofluid flow can be utilized as a powerful means to improve the thermal performance of a system operating under different ranges of parameters, even with the presence of porous media and magnetic fields. In addition to different heating frequencies, the variations in amplitude (I) and superposed uniform temperature ( $$\theta_{\text{os}}$$ ) to half-sinusoidal heating are also examined thoughtfully in the analysis for different concentrations of Cu–Al2O3 nanoparticles. Compared to the base liquid, the hybrid nanofluid can contribute toward higher heat transfer.

In the case of an electro-magneto-hydrodynamic actuator, little is known about the thermo-magneto-hydrodynamic irreversibilities arising in the dissipative flows of weakly conducting fluids past over a moving Riga plate. In this study, the electro-magneto-hydrodynamic convective flow features of a viscous electrically conducting fluid over a horizontal Riga plate are deliberated comprehensively by considering the wall suction and Joule heating effects. It is assumed that the permanent magnets are of equal width and mounted alternatively on a plane surface. Due to the electromagnetic proprieties of the Riga plate, the exponentially decaying Grinberg term is included in the momentum conservation equation as a resistive drag force in this investigation. The modeled differential equations were non-dimensionalized and simplified mathematically by utilizing suitable dimensionless variables and adopting admissible physical assumptions. Numerical solutions were established herein by utilizing an efficient algorithm based on the generalized differential quadrature method and the Newton–Raphson iterative technique. It is worth concluding that the presence of the wall suction effect enhances noticeably the heat transfer rate and its thermodynamic irreversibility near the Riga plate, while a reverse feature is depicted with the elevating strengths of the magnetization field.

Inspired by various applications (ocean’s renewable power technologies, spinning disc reactor, engineering systems, etc.) of fluid flow between rotating disc, we have investigated magnetohydrodynamic flow of multi-wall and single-wall carbon nanotubes (MWCNTs and SWCNTs)-based fluid between two rotating, coaxial and parallel stretching discs with porous medium and convective thermal condition. The non-vanishing relaxation time in the dissipative process is assumed. The energy equation is developed by using Cattaneo–Christov heat flux model. ND-Solve command of MATHEMATICA software is used for the numerical solution of the governing equations. The physical behaviour of axial, radial and tangential velocity along with temperature of nanofluid is discussed in detail. When porous permeability parameter is small, then tangential velocity of MWCNTs-based fluid is higher than that of the SWCNTs-based fluid. Moreover, when porous permeability parameter is small, the Reynolds number retards the tangential velocity but when porous permeability parameter is large, Reynolds number boots the tangential velocity up.

The free convection flow through a flexible baffle in an L-shaped enclosure has been numerically analyzed. The governing equations are introduced in an Arbitrary Lagrangian–Eulerian moving mesh frame. The full governing equations respect to boundary conditions were solved numerically using FEM. A grid-independent test was performed to ensure the accuracy of the results, and the results of the numerical solver are compared with previous works. The influence of the dimensionless parameters, including Rayleigh number, the elasticity modulus and the length of the flexible baffle investigated on the flow and heat transfer. Results indicate that a stiffer baffle tends to resist the fluid flow and inhibits convective heat transfer. For a higher value of Ra, a larger baffle results in more resistance to the flow and inhibits heat transfer, while, at the same time, increases the stress over the baffle.

The current problem is performed to analyze the heatline visualization of the mixed convection mechanism and heat transfer in a double lid-driven square cavity having a heated wavy bottom surface. The moving vertical surfaces are under adiabatic conditions, and the top surface is at a cold temperature. The finite element method is employed to determine the dimensionless governing equations controlled by specific boundary conditions. The implications of the Reynolds number ( $$10 \le {\mathrm{Re}} \le 500$$ ), the directions of the constant moving wall ( $$\lambda _{\mathrm{l}}= \pm 1, \lambda _{\mathrm{r}}= \pm 1$$ ), Richardson number ( $$0.01 \le {\mathrm{Ri}} \le 100$$ ), Prandtl number ( $$0.015 \le \Pr \le 10$$ ) and the number of oscillations ( $$1 \le {\mathrm{N}} \le 4$$ ) are visualized by the streamlines, isotherms and the heatlines. The same direction of lid-driven cases leads to two primary circulation cells. The Richardson number increases as it imposes the increment of the vertical temperature gradient. At a high Prandtl number, the convection mode of heat transfer is fully established, and heat conduction occurs at a low Prandtl number. Moreover, the number of oscillations has the most significant direct impact on the streamlines and the temperature distributions compared to the flat surface. Higher Reynolds and Prandtl numbers result in an increment in the local and average Nusselt numbers. The result shows that one oscillation of the wavy surface with a low Richardson number yields to have an optimum heat transfer in the cavity.