Search results

This paper aims to analyze heat and mass transfer of magnetohydrodynamic (MHD) non-Newtonian fluids flow past an inclined thermally stratified porous plate using a numerical approach.

The flow equations are set up with the non-linear free convective term, thermal radiation, nanofluids and Soret–Dufour effects. Thus, the non-linear partial differential equations of the flow analysis were simplified by using similarity transformation to obtain non-linear coupled equations. The set of simplified equations are solved by using the spectral homotopy analysis method (SHAM) and the spectral relaxation method (SRM). SHAM uses the approach of Chebyshev pseudospectral alongside the homotopy analysis. The SRM uses the concept of Gauss-Seidel techniques to the linear system of equations.

Findings revealed that a large value of the non-linear convective parameters for both temperature and concentration increases the velocity profile. A large value of the Williamson term is detected to elevate the velocity plot, whereas the Casson parameter degenerates the velocity profile. The thermal radiation was found to elevate both velocity and temperature as its value increases. The imposed magnetic field was found to slow down the fluid velocity by originating the Lorentz force.

The novelty of this paper is to explore the heat and mass transfer effects on MHD non-Newtonian fluids flow through an inclined thermally-stratified porous medium. The model is formulated in an inclined plate and embedded in a thermally-stratified porous medium which to the best of the knowledge has not been explored before in literature. Two elegance spectral numerical techniques have been used in solving the modeled equations. Both SRM and SHAM were found to be accurate.

The purpose of this paper is to study the influence of thermally stratified medium on a free convection flow from a sphere, which is rotating about the vertical axis, immersed in a stably thermally stratified medium.

An implicit finite‐difference scheme in combination with the quasi‐linearization technique is applied to obtain the steady state non‐similar solutions of the governing boundary layer equations for flow and temperature fields.

The numerical results indicate that the heat transfer rate at the wall decreases significantly with an increasing thermal stratification parameter, but its effect on the skin friction coefficients is rather minimum. In fact, the presence of thermal stratification of the medium influences the heat transfer at wall to be in opposite direction, that is, from fluids to the wall above a certain height. The heat transfer rate increases but the skin frictions decrease with the increase of Prandtl number. In particular, the effect of buoyancy force is much more sensitive for low Prandtl number fluids (Pr = 0.7, air) than that of high Prandtl number fluids (Pr = 7, water). Also the skin friction in rotating direction is less sensitive to the buoyancy force as the buoyancy force acts in the streamwise direction for the present study of thermally stratified medium.

The ambient temperature T_∞∞ is assumed to increase linearly with height $h$. The viscous dissipation term, which is usually small for natural convection flows, has been neglected in the energy equation. The flow is assumed to be axi‐symmetric. The Boussinesq approximation is invoked for the fluid properties to relate density changes to temperature changes, and to couple in this way the temperature field to the flow field.

Free convection in a thermally stratified medium occurs in many environmental processes with temperature stratification, and in industrial applications within a closed chamber with heated walls. Also, free convections associated with heat rejection systems for long‐duration deep ocean powder modules where ocean environment is stratified are examples of such type.

The research presented in this paper investigates the free convection flow on a sphere, which is rotating with a constant angular velocity along its vertical axis in a stably thermally stratified fluid.

This paper aims to address the problem of double-diffusive magnetohydrodynamics (MHD) non-Darcy convective flow of heat and mass transfer over a stretching sheet embedded in a thermally-stratified porous medium. The controlling parameters such as chemical reaction parameter, permeability parameter, etc., are extensively discussed and illustrated in this paper.

With the help of appropriate similarity variables, the governing partial differential equations are converted into ordinary differential equations. The transformed equations are solved using the spectral homotopy analysis method (SHAM). SHAM is a numerical method, which uses Chebyshev pseudospectral and homotopy analysis method in solving science and engineering problems.

The effects of all controlling parameters are presented using graphical representations. The results revealed that the applied magnetic field in the transverse direction to the flow gives rise to a resistive force called Lorentz. This force tends to reduce the flow of an electrically conducting fluid in the problem of heat and mass transfer. As a result, the fluid velocity reduces in the boundary layer. Also, the suction increases the velocity, temperature, and concentration of the fluid, respectively. The present results can be used in complex problems dealing with double-diffusive MHD non-Darcy convective flow of heat and mass transfer.

The uniqueness of this paper is the examination of double-diffusive MHD non-Darcy convective flow of heat and mass transfer. It is considered over a stretching sheet embedded in a thermally-stratified porous medium. To the best of the knowledge, a problem of this type has not been considered in the past. A novel method called SHAM is used to solve this modelled problem. The novelty of this method is its accuracy and fastness in computation.

The problem of laminar natural convection from a vertical circular cone maintained at either a uniform surface temperature or a uniform surface heat flux, and placed in a thermally stratified medium is considered. The governing non‐similarity boundary layer equation for uniform surface temperature are analyzed by using two distinct solution methodologies; namely, (i) a finite difference method and (ii) a local non‐similarity method. For uniform surface heat flux case, the solutions of the governing non‐similarity boundary layer equations are obtained by using three distinct solution methodologies, namely, (i) a finite difference method, (ii) a series solution method and (iii) an asymptotic solution method. The solutions are presented in terms of local skin‐friction and local Nusselt number for different values of Prandtl number and are displayed graphically. Effects of variations in the Prandtl number and stratification parameter on the velocity and temperature profiles are also shown graphically. Solutions obtained by finite difference method are compared with the other methods and found to be in excellent agreement.

The purpose of this paper is to focus on the stratified phenomenon through vertical stretching cylinder in the region of stagnation point with slip effects.

Homotopy analysis method is used to find the series solutions of the governing equations.

Velocity profile decreases with an increase in stratified parameters due to temperature and concentration. Velocity and thermal slips cause a reduction in the velocity profile. Thermally stratified and thermal slip parameters reduce the temperature field.

The present analysis has not been existed in the literature yet.

The purpose of this work is to study the mixed convection boundary layer flow past a vertical cylinder in a porous medium saturated with a nanofluid. Numerical results for friction factor, surface heat transfer rate and mass transfer rate have been presented for parametric variations of the buoyancy ratio parameter Nr, Brownian motion parameter Nb, thermophoresis parameter Nt and Lewis number Le. The dependency of the surface heat transfer rate (Nusselt number) and mass transfer rate on these parameters has been discussed.

Solutions of the set of non-similarity equations are obtained by employing the implicit finite difference method together with Keller box elimination method.

It was found that the heat transfer rate decreases and mass transfer rates increase as Lewis number increases. The heat and mass transfer rates increase as the buoyancy ration parameter increases. As the thermophoresis parameter Nt increases, the heat transfer rate decreases where as the mass transfer rate increases. As the Brownian parameter Nb increases, the heat transfer rate decreases. Brownian motion decelerates the flow in the nanofluid boundary layer. Brownian diffusion promotes heat conduction. The heat and mass transfer rates increase as the buoyancy ratio number Nr increases. The Brownian motion and thermophoresis of nanoparticles increases the effective thermal conductivity of the nanofluid. Both Brownian diffusion and thermophoresis give rise to cross diffusion terms that are similar to the familiar Soret and Dufour cross-diffusion terms that arise with a binary fluid.

The analysis is valid for steady, mixed convection two-dimensional boundary layer flow in a nanofluid-saturated Darcy porous medium. An extension to non-Darcy porous medium is left as a part of future study.

The research is applicable for enhancing heat exchanger effectiveness by employing nanofluids.

The study is useful to engineers interested in designing heat exchangers, water and atmospheric pollution.

The purpose of this study is to present the significance of Joule heating, viscous dissipation, magnetic field and slip condition on the boundary layer flow of an electrically conducting Boussinesq couple-stress fluid induced by an exponentially stretching sheet embedded in a porous medium under the effect of the magnetic field of the variable kind. The heat transfer phenomenon is accounted for under thermal radiation, Joule and viscous dissipation effects.

The governing nonlinear partial differential equations are transformed to the nonlinear ordinary differential equations (ODEs) by using some appropriate dimensionless variables and then the consequential nonlinear ODEs are solved numerically by making the use of the well-known shooting iteration technique along with the standard fourth-order Runge–Kutta integration scheme. The impact of emerging flow parameters on velocity and temperature profiles, streamlines, local skin friction coefficient and Nusselt number are described comprehensively through graphs and tables.

Results reveal that the velocity profile is observed to diminish considerably within the boundary layer in the presence of a magnetic field and slip condition. The enhanced radiation parameter is to decline the temperature field. The slip effect is favorable for fluid flow.

Till now, slip effect on Boussinesq couple-stress fluid over an exponentially stretching sheet embedded in a porous medium has not been explored. The present results are validated with the previously published study and found to be highly satisfactory.

The purpose of this paper is to consider the problem of thermal destratification facing engineers and scientists during the motion of fluids which consist of rigid and randomly oriented particles suspended in a viscous medium under the influence of Lorentz force. This paper provides an insight into the non-linear transfer of thermal radiation within the boundary layer.

Similarity transformation and parameterization of the non-linear partial differential equation are carried out. The approximate analytical solution of the governing equation which models the free convective flow of strong and weak concentration of micro-elements in a micropolar fluid over a vertical surface is presented.

It is observed that the velocity and temperature distribution are decreasing properties of thermal stratification parameter S_t. Maximum local skin friction coefficients are ascertained at an epilimnion level (S_t=0) when the magnitude of thermal radiation is small. Thermal stratification parameter has no significant effect on the temperature distribution in the flow near a free stream.

The relationship between stratification of temperature and the transfer of thermal energy during the problem of thermal destratification facing engineers and scientist during the motion of fluids which consist of rigid and randomly oriented particles suspended in a viscous medium under the influence of Lorentz force is unravelled in this paper.

Natural convection from a semi‐infinite vertical plate embedded in a fluid saturated porous medium is studied both analytically and numerically. The plate is assumed to be heated isothermally or by a constant heat flux. The porous medium, modeled according to Darcy’s law, is anisotropic in permeability with its principal axes oriented in a direction that is oblique to the gravity vector. In the large Rayleigh number limit, the governing boundary‐layer equations are solved in closed form, using a similarity transformation. Comparisons between the numerical solution of the full equations and analytical solutions are presented for a wide range of the governing parameters. The effects of the anisotropic permeability ratio K^*, of the orientation angle of the principal axes θ, and of the Rayleigh number R_H on the flow and heat transfer are investigated. Results indicate that the anisotropic properties of the porous medium considerably modify the heat transfer, velocity and temperature profiles from that expected under isotropic conditions.

The problem of coupled heat and mass transfer by mixed convection in a linearly stratified stagnation flow (Hiemenz flow) in the presence of an externally applied magnetic field and internal heat generation or absorption effects is formulated. The plate surface is embedded in a uniform Darcian porous medium and is permeable in order to allow for possible fluid wall suction or blowing and has a power‐law variation of both the wall temperature and concentration. The resulting governing equations are transformed into similarity equations for the case of linearly varying wall temperature and concentration with the vertical distance using an appropriate similarity transformation. These ordinary differential equations are then solved numerically by an implicit, iterative, finite‐difference scheme. Comparisons with previously published work are performed and excellent agreement between the results is obtained. A parametric study of all involved parameters is conducted and a representative set of numerical results for the velocity and temperature profiles as well as the skin‐friction parameter, local Nusselt number, and the local Sherwood number is illustrated graphically to elucidate interesting features of the solutions.