Mixed convection heat and mass transfer over a vertical plate in a power‐law fluid‐saturated porous medium with radiation and chemical reaction effects

Mixed convection heat and mass transfer from a vertical plate embedded in a power‐law fluid‐saturated Darcy porous medium with chemical reaction and radiation effects is studied. The governing partial differential equations are transformed into ordinary differential equations using similarity transformations and then solved numerically using the shooting method. A parametric study of the physical parameters involved in the problem is conducted and a representative set of numerical results is illustrated graphically. © 2013 Wiley Periodicals, Inc. Heat Trans Asian Res; Published online in Wiley Online Library (wileyonlinelibrary.com/journal/htj). DOI 10.1002/htj.21058     

Mixed Convection Over a Vertical Plate in a Doubly Stratified Fluid‐Saturated Non‐Darcy Porous Medium with Cross‐Diffusion Effects

The present article investigates the influence of Dufour and Soret effects on mixed convection heat and mass transfer over a vertical plate in a doubly stratified fluid‐saturated porous medium. The plate is maintained at a uniform and constant wall heat and mass fluxes. The Darcy–Forchheimer model is employed to describe the flow in porous medium. The nonlinear governing equations and their associated boundary conditions are initially transformed into dimensionless forms. The resulting system of nonlinear partial differential equations is then solved numerically by the Keller‐box method. The variation of the dimensionless velocity, temperature, concentration, heat, and mass transfer rates for different values of governing parameters involved in the problem are analyzed and presented graphically. © 2013 Wiley Periodicals, Inc. Heat Trans Asian Res; Published online in Wiley Online Library ( wileyonlinelibrary.com/journal/htj ). DOI 10.1002/htj.21114     

Solutal Dispersion and Viscous Dissipation Effects on Non‐Darcy Free Convection Over a Cone in Power‐Law Fluids

The effects of viscous dissipation and solutal dispersion on free convection about an isothermal vertical cone with a fixed apex half angle, pointing downwards in a power‐law fluid‐saturated non‐Darcy porous medium are analyzed. The governing partial differential equations are transformed into partial differential equations using non‐similarity transformation. The resulting equations are solved numerically using an accurate local non‐similarity method. The accuracy of the numerical results is validated by a quantitative comparison of the heat and mass transfer rates with previously published results for a special case and the results are found to be in good agreement. The effects of viscous dissipation, solutal dispersion, and/or buoyancy ratio on the velocity, temperature, and concentration field as well as on the heat and mass transfer rates are illustrated, by insisting on the comparison between pseudo‐plastic, dilatant, and Newtonian fluids. © 2013 Wiley Periodicals, Inc. Heat Trans Asian Res, 43(5): 476–488, 2014; Published online 11 November 2013 in Wiley Online Library ( wileyonlinelibrary.com/journal/htj ). DOI 10.1002/htj.21095     

Similarity Solution to Hydromagnetic Flow Past a Continuously Moving Semi‐infinite Vertical Porous Plate with Large Suction

The problem of a two‐dimensional free convective mass transfer flow of an incompressible, viscous, and electrically conducting fluid past a continuously moving semi‐infinite vertical porous plate with large suction in the presence of a magnetic field applied normal to the plate is studied. The non‐linear partial differential equations governing the flow have been transformed by a set of similarity transformations into a system of non‐linear ordinary differential equations. The resulting system of the similarity equations are solved analytically adopting the perturbation technique. The expressions for the velocity field, temperature field, concentration field, induced magnetic field, drag coefficient, and the coefficient of the rate of heat and mass transfer at the plate are obtained. The results are discussed in details through graphs and tables to observe the effect of various physical parameters involved in the problem. © 2013 Wiley Periodicals, Inc. Heat Trans Asian Res; Published online in Wiley Online Library ( wileyonlinelibrary.com/journal/htj ). DOI 10.1002/htj.21097     

Influence of heat transfer on the nonorthogonal stagnation point flow of a third‐order fluid towards a stretching surface

The present article looks at the theoretical analysis of a steady stagnation‐point flow with heat transfer of a third‐order fluid towards a stretching surface. The formulation of the problem has been carried out for a third order fluid and constructed partial differential equations are rehabilitated into ordinary differential equations. The consequential ordinary differential equations are solved analytically using the homotopy analysis method (HAM). Graphical illustrations are shown for various parameters involved in the flow equations. Numerical values of skin friction coefficients and heat flux are computed and presented through tables. © 2013 Wiley Periodicals, Inc. Heat Trans Asian Res; Published online in Wiley Online Library (wileyonlinelibrary.com/journal/htj). DOI 10.1002/htj.21042     

Influence of Viscous Dissipation on Mixed Convection in a Non‐Darcy Porous Medium Saturated with a Nanofluid

In this study, the effects of viscous dissipation on mixed convection heat and mass transfer along a vertical plate embedded in a nanofluid‐saturated non‐Darcy porous medium have been investigated. The model used for the nanofluid incorporates the effects of Brownian motion and thermophoresis. The new far‐field thermal boundary condition that has been recently developed is employed to properly account for the effect of viscous dissipation in mixed convective transport in a porous medium. The nonlinear governing equations and the associated boundary conditions are transformed to a set of nonsimilar ordinary differential equations and the resulting system of equations is then solved numerically by an improved implicit finite‐difference method. The effect of the physical parameters on the flow, heat transfer, and nanoparticle concentration characteristics of the model are presented through graphs and the salient features are discussed. As expected, a significant improvement in the heat transfer coefficient is noticed because of the consideration of the nanofluid in the porous medium. With the increase in the value of the viscous dissipation parameter, a reduction in the non‐dimensional heat transfer coefficient is noted while an increase in the nanoparticle mass transfer coefficient is seen. Further, an increase in the mixed convection parameter lowered both the heat and nanoparticle mass transfer rates. Moreover, the increase in the Brownian motion parameter enhanced the nanoparticle mass transfer rate but it reduced the heat transfer rate in the boundary layer. A similar trend is also found with the thermophoresis parameter. © 2013 Wiley Periodicals, Inc. Heat Trans Asian Res, 43(5): 397–411, 2014; Published online 3 October 2013 in Wiley Online Library ( wileyonlinelibrary.com/journal/htj ). DOI 10.1002/htj.21083     

Unsteady Mixed Convection Flow of a Rotating Second‐Grade Fluid on a Rotating Cone

In the present article, we have investigated the unsteady mixed convection flow of a rotating second‐grade fluid in a rotating cone with time‐dependent angular velocities. Two cases of heat transfer are presented which are known as (i) prescribed wall temperature (PWT) and (ii) prescribed heat flux (PHF). The governing coupled nonlinear partial differential equations are simplified with the help of transformations and non‐dimensional similar and non‐similar variables, and solved analytically with the help of the homotopy analysis method (HAM). The effects of pertinent parameters on the velocity, temperature, concentration, skin friction coefficients, Nusselt number, and Sherwood number have been examined through graphs. © 2013 Wiley Periodicals, Inc. Heat Trans Asian Res, 43(3): 204–220, 2014; Published online 30 August 2013 in Wiley Online Library ( wileyonlinelibrary.com/journal/htj ). DOI 10.1002/htj.21072     

MHD boundary‐layer flow over a stretching surface with internal heat generation or absorption

This article is concerned with the steady laminar magnetohydrodynamic boundary‐layer flow past a stretching surface with uniform free stream and internal heat generation or absorption in an electrically conducting fluid. A constant magnetic field is applied in the transverse direction. A uniform free stream of constant velocity and temperature is passed over the sheet. The effects of free convection and internal heat generation or absorption are also considered. The governing boundary layer and temperature equations for this problem are first transformed into a system of ordinary differential equations using similarity variables, and then solved by a new analytical method and numerical method, by using a fourth‐order Runge–Kutta and shooting method. Velocity and temperature profiles are shown graphically. It is shown that the differential transform method solutions are only valid for small values of independent variables but the results obtained by the DTM‐Padé are valid for the entire solution domain with high accuracy. © 2013 Wiley Periodicals, Inc. Heat Trans Asian Res; Published online in Wiley Online Library (wileyonlinelibrary.com/journal/htj). DOI 10.1002/htj.21054     

Non‐Darcian Unsteady Flow of a Micropolar Fluid over a Porous Stretching Sheet with Thermal Radiation and Chemical Reaction

An analysis is presented to investigate the effects of a chemical reaction on an unsteady flow of a micropolar fluid over a stretching sheet embedded in a non‐Darcian porous medium. The governing partial differential equations are transformed into a system of ordinary differential equations by using similarity transformation. The resulting nonlinear coupled differential equations are solved numerically by using a fourth‐order Runge–Kutta scheme together with shooting method. The influence of pertinent parameters on velocity, angular velocity (microrotation), temperature, concentration, skin friction coefficient, Nusselt number, and Sherwood number has been studied and numerical results are presented graphically and in tabular form. Comparisons with previously published work are performed and the results are found to be in excellent agreement. © 2013 Wiley Periodicals, Inc. Heat Trans Asian Res; Published online in Wiley Online Library ( wileyonlinelibrary.com/journal/htj ). DOI 10.1002/htj.21090     

Unsteady MHD Mixed Convective Boundary‐Layer Slip Flow and Heat Transfer with Thermal Radiation and Viscous Dissipation

A numerical analysis has been carried out to investigate the problem of MHD boundary‐layer flow and heat transfer of a viscous incompressible fluid over a moving vertical permeable stretching sheet with velocity and temperature slip boundary condition. A problem formulation is developed in the presence of radiation, viscous dissipation, and buoyancy force. A similarity transformation is used to reduce the governing boundary‐layer equations to coupled higher‐order nonlinear ordinary differential equations. These equations are solved numerically using the fourth‐order Runge–Kutta method along with shooting technique. The effects of the governing parameters such as Prandtl number, buoyancy parameter, slip parameter, magnetic parameter, Eckert Number, suction, and radiation parameter on the velocity and temperature profiles are discussed and shown by plotting graphs. It is found that the temperature is a decreasing function of the slip parameter S_T. The results also indicate that the cooling rate of the sheet can be improved by increasing the buoyancy parameter. In addition the numerical results for the local skin friction coefficient and local Nusselt number are computed and presented in tabular form. The numerical results are compared and found to be in good agreement with previously published results on special cases of the problem. © 2013 Wiley Periodicals, Inc. Heat Trans Asian Res, 43(5): 412–426, 2014; Published online 3 October 2013 in Wiley Online Library ( wileyonlinelibrary.com/journal/htj ). DOI 10.1002/htj.21086     

Heat Transfer in a Casson Rheological Fluid from a Semi‐infinite Vertical Plate with Partial Slip

The laminar boundary layer flow and heat transfer of Casson non‐Newtonian fluid from a semi‐infinite vertical plate in the presence of thermal and hydrodynamic slip conditions is analyzed. The plate surface is maintained at a constant temperature. Increasing velocity slip induces acceleration in the flow near the plate surface and the reverse effect further from the surface. Increasing velocity slip consistently enhances temperatures throughout the boundary layer regime. An increase in thermal slip parameter strongly decelerates the flow and also reduces temperatures in the boundary layer regime. An increase in the Casson rheological parameter acts to elevate considerably the skin friction (non‐dimensional wall shear stress) and this effect is pronounced at higher values of tangential coordinate. Temperatures, however, are very slightly decreased with increasing values of Casson rheological parameter. © 2013 Wiley Periodicals, Inc. Heat Trans Asian Res; Published online in Wiley Online Library ( wileyonlinelibrary.com/journal/htj ). DOI 10.1002/htj.21115     

A study on heat transfer in a second‐grade fluid through a porous medium with the modified differential transform method

This study investigates the boundary‐layer flow and heat transfer characteristics in a second‐grade fluid through a porous medium. The similarity transformation for the governing equations gives a system of nonlinear ordinary differential equations which are analytically solved by the differential transform method (DTM) and the DTM‐Padé. The DTM‐Padé is a combination of the DTM and the Padé approximant. The convergence analysis elucidates that the DTM does not give accurate results for large values of independent variables. Hence the DTM is not applicable for the solution of boundary‐layer flow problems having boundary conditions at infinity. Comparison between the solutions obtained by the DTM and the DTM‐Padé with numerical solution (fourth‐order Runge–Kutta with shooting method) illustrates that the DTM‐Padé is the most effective method for solving the problems that have boundary conditions at infinity. © 2012 Wiley Periodicals, Inc. Heat Trans Asian Res; Published online in Wiley Online Library (wileyonlinelibrary.com/journal/htj). DOI 10.1002/htj.21030     

Numerical Investigation of Nanofluid Mixed‐Convection Flow in the Entrance Region of a Vertical Channel Partially Filled with Porous Medium

In this article, transient two‐dimensional mixed convection of nanofluids in the entrance region of a vertical channel has been studied carefully. The geometry under consideration consisted of a parallel‐plate channel partly filled with a porous medium with a constant wall temperature. In the free flow region, the two‐dimensional flow field has been governed by the Navier–Stokes equations. The general formulation of the momentum equations accounting for the inertial and the viscous effects in the presence of a porous medium has been used. Viscous dissipation effects have also been incorporated in the thermal energy equation. Effects of Brownian diffusion and thermophoresis have also been included for nanoparticles in the nanofluid. The governing equations have been given in terms of the stream function‐vorticity formulation and have been non‐dimensionalized and then solved numerically subject to appropriate boundary conditions. The characteristics of the flow and temperature fields have been presented in the terms of mixed‐convection parameter (GR), Brinkman number (Br), Darcy number (Da), Lewis number (Le), and other important parameters. © 2013 Wiley Periodicals, Inc. Heat Trans Asian Res, 43(7): 607–627, 2014; Published online 21 November 2013 in Wiley Online Library ( wileyonlinelibrary.com/journal/htj ). DOI 10.1002/htj.21099     

Solving of boundary‐layer equations with transpiration effects,governance on a vertical permeable cylinder using modified differential transform method

The suction and injection effects on the free convection boundary‐layer flow over a vertical cylinder are studied. The main stream velocity and wall temperature are proportional to the axial distance along the surface of the cylinder. Both analytic and numerical solutions of the arising mathematical problem are obtained. An analytic solution is derived by a new analytical method (DTM‐Padé) and numerical solutions have been performed by using a fourth‐order Runge–Kutta and shooting methods. Velocity and temperature profiles are shown graphically. It is shown that the differential transform method (DTM) solutions are only valid for small values of the independent variable but the obtained results by DTM‐Padé are valid for the whole solution domain with high accuracy. These methods can be easily extended to other linear and nonlinear equations and so can be found widely applicable in engineering and sciences. © 2011 Wiley Periodicals, Inc. Heat Trans Asian Res; Published online in Wiley Online Library ( wileyonlinelibrary.com/journal/htj ). DOI 10.1002/htj.20366     

Modeling of double diffusive buoyant flow in a solar collector with water‐CuO nanofluid

The behavior of a prism‐shaped solar collector with a right triangular cross sectional area is investigated numerically. The water‐CuO nanofluid is taken as the functioning liquid through the solar collector. The leading differential equations with boundary conditions are solved by the penalty finite element method using Galerkin's weighted residual scheme. The performance of parameters in terms of temperature, mass, velocity distributions, radiative, convective heat and mass transfer, mean temperature and concentration of nanofluid, mid height horizontal‐vertical velocities, and sub‐domain average velocity field are investigated systematically. These parameters include the Rayleigh number Ra and the solid volume fraction φ. The outcome explains that the performance of the solar collector can be enhanced with the largest Ra and φ. The code validation shows excellent concurrence with the hypothetical outcome obtainable in the literature. © 2013 Wiley Periodicals, Inc. Heat Trans Asian Res; Published online in Wiley Online Library (wileyonlinelibrary.com/journal/htj). DOI 10.1002/htj.21039     

Effects of Thermal‐Diffusion,Diffusion‐Thermo,and Space Porosity on MHD Mixed Convective Flow of Micropolar Fluid in a Vertical Channel with Viscous Dissipation

This paper examines thermal‐diffusion and diffusion‐thermo effects on the fully developed MHD flow of a micropolar fluid through a porous space in a vertical channel with asymmetric wall temperatures and concentrations. The homotopy analysis method (HAM) is adopted to obtain the approximate analytical solution for the velocity, micro‐rotation, temperature, and concentration field. The convergence and the accuracy of the solutions are discussed. The role of pertinent parameters on the heat and mass transfer characteristics of the flow are presented graphically. © 2013 Wiley Periodicals, Inc. Heat Trans Asian Res, 43(6): 561–576, 2014; Published online 11 November 2013 in Wiley Online Library ( wileyonlinelibrary.com/journal/htj ). DOI 10.1002/htj.21100     

Magnetogravitational Instability of a Walters B’ Viscoelastic Rotating Anisotropic Heat‐Conducting Fluid in Brinkman Porous Medium

Instability of a Walters B′ viscoelastic rotating anisotropic heat‐conducting plasma with modified Chew–Goldberger–Low equations is discussed under a gravitational force and uniform magnetic field in a Brinkman porous medium. The general dispersion relation is obtained using normal mode analysis, and it is reduced for propagation parallel and perpendicular to the direction of the magnetic field. These conditions are discussed for the axis of rotation along and perpendicular to the magnetic field. The stability of the system in the two directions is discussed both analytically and numerically. The numerical analysis is performed to show the effects of various parameters, namely, rotation, pressure anisotropy, medium permeability, porosity of porous medium, kinematic viscosity, kinematic viscoelasticity, and heat flux on the stability of the considered system. The Jeans condition of gravitational instability is obtained for both cases of propagation. © 2013 Wiley Periodicals, Inc. Heat Trans Asian Res 43(2): 93‐112, 2014; Published online 31 July 2013 in Wiley Online Library ( wileyonlinelibrary.com/journal/htj ). DOI 10.1002/htj.21064     

Mixed convection stagnation point flow and heat transfer of Cu‐water nanofluids towards a shrinking sheet

This work is focused on numerical simulations of mixed convection stagnation point flow and heat transfer of Cu‐water nanofluids impinging normally towards a shrinking sheet. Similarity transformation technique is adopted to obtain the self‐ similar ordinary differential equations and then solved numerically using symbolic software MATHEMATICA. The features of the flow and heat transfer characteristics for different values of the governing parameters are analyzed and discussed through graphs and tables. Both cases of assisting and opposing flows are considered. The physical aspects of the problem are highlighted and discussed. © 2013 Wiley Periodicals, Inc. Heat Trans Asian Res; Published online in Wiley Online Library (wileyonlinelibrary.com/journal/htj). DOI 10.1002/htj.21037 2000 Mathematics Subject Classification : 76M20, 76W05     

MHD Flow of a Couple‐Stress Fluid and a Viscous Fluid in a Vertical Wavy Porous Space with Traveling Thermal Waves and Temperature‐Dependent Heat Source

In this article, the heat transfer analysis is investigated for magnetohydrodynamic (MHD) flow in a vertical wavy porous space with one region filled with couple‐stress fluid and the other region with a viscous fluid in the presence of a temperature‐dependent heat source. The flow is generated by the periodic thermal waves prescribed at the wavy walls of the channel and the transport properties of both fluids are assumed constant. The resulting dimensionless coupled nonlinear equations are assumed into a mean (zeroth‐order) part and a perturbed part, using amplitude as a small parameter. The perturbed quantities are obtained by using the regular perturbation method. The results are graphically presented and the role of pertinent parameters on the heat transfer characteristics of the fluid flow is discussed. © 2013 Wiley Periodicals, Inc. Heat Trans Asian Res 43(2): 134‐147, 2014; Published online 3 September 2013 in Wiley Online Library ( wileyonlinelibrary.com/journal/htj ). DOI 10.1002/htj.21068     

Analytical solution for slip flow and heat transfer due to a stretching sheet

An analysis has been carried out to investigate the analytical solution to the flow and heat transfer characteristics of a viscous flow over a stretching sheet in the presence of second‐order slip in flow. The governing partial differential equations of flow and heat transfer are converted into non‐linear ordinary differential equations by using suitable similarity transformations. The exact solution of momentum equation is assumed in exponential form and analytical solutions of heat transfer for both PST and PHF cases are obtained by the power series method in terms of Kummer's hypergeometric function. The temperature profiles are drawn for different governing parameters. The numerical values of wall temperature gradient and wall temperature are compared with earlier numerical results which have a good agreement. © 2013 Wiley Periodicals, Inc. Heat Trans Asian Res; Published online in Wiley Online Library (wileyonlinelibrary.com/journal/htj). DOI 10.1002/htj.21044