Steady boundary layer flow and heat transfer over a porous moving plate in presence of thermal radiation

An analysis is presented for boundary layer forced convective flow and heat transfer past a moving porous plate parallel to a moving stream. Thermal radiation term is considered in the energy equation. The similarity solutions for the problem are obtained and the reduced nonlinear ordinary differential equations are solved numerically. It is found that dual solutions exist when the plate and the fluid move in the opposite directions. In case of porous plate, fluid velocity increases whereas non-dimensional temperature decreases for increasing values of suction parameter.     

Conjugate free convection above a cooled finite horizontal flat plate embedded in a porous medium

We investigate conjugate free convection in a semi-infinite porous medium above a cold finite plate. Numerical solutions of the coupled governing equations for the fluid and the plate regions are obtained, and an analytical method is developed to predict the average temperature of the conjugate boundary and the Nusselt number.     

Effects of non-Darcian on forced convection heat transfer over a flat plate in a porous medium-with temperature dependent viscosity

The non-Darcian effect on forced convection heat transfer over a flat plate in a porous medium is examined. The fluid viscosity is assumed to vary as an inverse linear function of temperature. The effects of inertia forces and the distance from the leading edge of the plate on the velocity and temperature fields as well as on the skin friction and heat transfer coefficients in the boundary layer over a semi-infinite plate are studied. The nonlinear boundary layer equations, governing the problem under consideration, are solved numerically by applying an efficient numerical technique based on the Keller box method. The velocity profiles, temperature profiles and the skin friction components on the plate are computed and discussed in detail numerically for various values of the variable viscosity parameter, the modified Reynolds number, the stream wise coordinate and the Prandtl number.     

An integral treatment for combined heat and mass transfer by natural convection along a horizontal surface in a porous medium

The heat and mass transfer characteristics of natural convection about a horizontal surface embedded in a saturated porous medium is analyzed. An integral procedure is derived to the heated horizontal surface, where surface temperature and surface concentration are power function of distance from the leading edge of porous plate. Local Nusselt number and local Sherwood number variations in the boundary layer are presented graphically and in the tables for the various values of problem parameters and it is found that the temperature and concentration fields near the plate increases with power law exponent n.     

Effects of thermophoresis particle deposition in free convection boundary layer from a horizontal flat plate embedded in a porous medium

The present contribution deals with the thermophoresis particle deposition effect on the free convection over a horizontal flat plate embedded in a fluid-saturated porous medium. In a certain sense, this study continues that by Chamka and Pop [A. Chamka, I. Pop, Effect of thermophoresis particle deposition in free convection boundary layer from a vertical flat plate embedded in a porous medium, Int. Commun. Heat Mass Transfer 31 (2004) 421–430], where the vertical flat plate configuration was analyzed. The governing equations are transformed into a set of coupled differential equations, which are solved numerically using a finite difference method. For various values of the problem parameters, graphs of the profile concentration in the boundary layer and of thermophoretic deposition velocity are presented.     

Melting of a vertical plate in porous medium controlled by forced convection of a dissimilar fluid

In this paper a boundary layer analysis is presented for the problem of melting of a flat plate embedded in a porous medium. The melting phenomenon is induced by forced convection of the ambient fluid. The ambient fluid and the melt are dissimilar. The density difference between the melt and the ambient fluid is responsible for the boundary layer flow in the melt region. The results of this paper document the dependence of the temperature and flow fields in the system, as well as the dependence of the local heat transfer rate at the solid/ melt interface on the dimensionless groups describing the physics of the problem.     

Natural convection of a Darcian fluid about a cone

The problem of natural convection about a cone embedded in a porous medium at high Rayleigh numbers is analyzed based on the boundary layer approximation and the Darcy's law. Local similarity solutions are obtained for a truncated cone with the prescribed wall temperature or surface heat flux being a power function of distance from the leading edge. It is shown that at a location near the leading edge, the solution behaves like that of an inclined plate. At a location far downstream of the truncated cone, the solution approaches that of a full cone where similarity solutions exist.     

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     

Free convection in a non-Newtonian fluid along a horizontal plate embedded in porous media with internal heat generation

Similarity solutions for the problem of free convection flow over a non-isothermal horizontal plate embedded in porous media are investigated in the presence of internal heat generation. The porous medium is saturated with non-Newtonian power law fluid. Numerical results are obtained for the effect of power law temperature profile and fluid index on the heat transfer characteristics.     

A note to the solution of cheng-minkowycz equation arising in free convection flow in porous media

In this paper we reconsider the problem of boundary layer free convection flow along a vertical flat plate with a power law surface temperature and embedded in a fluid-saturated porous medium. The resulting ordinary differential equation is solved numerically using the method of perturbation series in combination with Shanks transformation. The accuracy of the present solution is discussed and is found to be in excellent agreement with theoretical predictions of Banks[7].     

Effect of chemical reaction and thermal radiation on heat and mass transfer flow of MHD micropolar fluid in a rotating frame of reference

This paper studies the effect of first order chemical reaction and thermal radiation on hydromagnetic free convection heat and mass transfer flow of a micropolar fluid via a porous medium bounded by a semi-infinite porous plate with constant heat source in a rotating frame of reference. The plate is assumed to oscillate in time with constant frequency so that the solutions of the boundary layer are the same oscillatory type. The dimensionless governing equations for this investigation are solved analytically using small perturbation approximation. The effect of the various dimensionless parameters entering into the problem on the velocity, temperature and concentration profiles across the boundary layer are investigated through graphs. Also the results of the skin friction coefficient, couple stress coefficient, the rate of heat and mass transfer at the wall are prepared with various values of the parameters.     

Investigation of combined heat and mass transfer by Lie group analysis with variable diffusivity taking into account hydrodynamic slip and thermal convective boundary conditions

The present paper investigates heat and mass transfer over a moving porous plate with hydrodynamic slip and thermal convective boundary conditions and concentration dependent diffusivity. The similarity representation of the system of partial differential equations of the problem is obtained through Lie group analysis. The resulting equations are solved numerically by Maple with Runge–Kutta–Fehlberg fourth–fifth order method. A representative set of results for the physical problem is displayed to illustrate the influence of parameters (velocity slip parameter, convective heat transfer parameter, concentration diffusivity parameter, Prandtl number and Schmidt number) on the dimensionless axial velocity, temperature and concentration field as well as the wall shear stress, the rate of heat transfer and the rate of mass transfer. The analytical solutions for velocity and temperature are obtained. Very good agreements are found between the analytical and numerical results of the present paper with published results.     

Natural convection heat transfer from an inclined wavy plate in a bidisperse porous medium

This work studies the natural convection heat transfer from an inclined wavy plate in a bidisperse porous medium with uniform wall temperature. The two-velocity two-temperature formulation is used to derive the governing equations of this system. The Prandtl coordinate transformation is used to transform the wavy surface into a regular plane, and the obtained equations are then simplified further by the order-of-magnitude analysis to give the boundary layer equations. The cubic spline collocation method is used to solve the boundary layer governing equations. The effects of dimensionless amplitude, angle of inclination, inter-phase heat transfer parameter, modified thermal conductivity ratio, and permeability ratio on the heat transfer and flow characteristics are studied. Increasing the modified thermal conductivity ratio and the permeability ratio can effectively enhance the natural convection heat transfer of the inclined plate in bidisperse porous media. Moreover, the thermal non-equilibrium effects are significant for low values of the inter-phase heat transfer parameter. As the dimensionless amplitude increases, both the fluctuations of the local Nusselt number for the f-phase and the p-phase with the streamwise coordinate are enhanced.     

Natural convection heat transfer of non-Newtonian fluids in porous media from a vertical cone under mixed thermal boundary conditions

This work studies the problem of the steady natural convection boundary layer flow over a downward-pointing vertical cone in porous media saturated with non-Newtonian power-law fluids under mixed thermal boundary conditions. A similarity analysis is performed, and the obtained similar equations are solved by cubic spline collocation method. The effects of the power-law viscosity index and the similarity exponent on the heat transfer characteristics under mixed thermal boundary conditions have been studied. Under mixed thermal boundary conditions, both the surface heat flux and the surface temperature are found to decrease when the power-law viscosity index of the non-Newtonian power-law fluid in porous media is increased. Moreover, an increase in the similarity exponent tends to increase the boundary layer thickness and thus decreases the surface heat flux under mixed thermal conditions. The generalized governing equations derived in this work can be applied to the cases of prescribed surface temperature and prescribed heat flux.     

Natural convection of a non-Newtonian fluid about a horizontal cylinder and a sphere in a porous medium

The problem of natural convection of a non-Newtonian fluid about a horizontal isothermal cylinder and an isothermal sphere in the porous medium is considered. The present study is based on the boundary layer approximation and only suitable for a high Rayleigh number. Similarity solutions are obtained by using the fourth order Runge-Kutta method. The effects of the wall temperature T_W and the new power-law index n on the characteristics of heat transfer are discussed.     

Comparison of the waves of temperature difference between the solid and fluid phases in a porous slab and in a semi-infinite porous body

In this paper an analytical investigation of the temperature difference between the solid and fluid phases in a porous slab initially at a low temperature whose inlet boundary is suddenly subjected to a flow of a higher temperature incompressible fluid is carried out. A two energy equation model for the porous bed is utilized. It is shown that the temperature difference forms a wave localized in space and propagating from the fluid inlet boundary. Using the perturbation technique, an analytical expression describing the wave of temperature difference is obtained. Results of the present investigation are compared against the results obtained in ref. [1] for a semi-infinite porous body.     

Free convection flow with thermal radiation and mass transfer past a moving vertical porous plate

The combined free convection boundary layer flow with thermal radiation and mass transfer past a permeable vertical plate is studied when the plate moves in its own plane. The plate is maintained at a uniform temperature with uniform species concentration and the fluid is considered to be gray, absorbing–emitting. The coupled unsteady non-linear momentum, energy and concentration equations governing the problem is obtained and made similar by introducing a time-dependent length scale. The similarity equations are solved numerically using superposition method. The resulting velocity, temperature and concentration distributions are shown graphically for different values of parameters entering into the problem. The numerical values of the local wall shear stress, local surface heat and mass flux are shown in tabular form.     

Melting effect on mixed convective heat transfer with aiding and opposing external flows from the vertical plate in a liquid-saturated porous medium

In this paper, melting effect on mixed convective heat transfer from a porous vertical plate with uniform wall temperature in the liquid-saturated porous medium with aiding and opposing external flows is numerically examined at steady state. The resulting boundary value problems (BVPs) are comprehensively solved by Runge–Kutta–Gill method and Newton’s iteration for similarity solutions. As shown in the results, for aiding and opposing external flows, it is all found that the rate of convective heat transfer at the interface of solid and liquid phases is reduced with increasing melting strength. Additionally, the melting phenomenon decreases the thermal boundary layer regions of mixed convection in a porous medium. With melting effect, the heat transfer rate is also shown to be asymptotically approaching the forced or free convection as the value of Gr/Re approaches the limits of zero and infinity for aiding external flow; and the criteria for pure forced and mixed convection from an isothermal vertical flat plate in porous media with aiding and opposing external flows are established in melting process.     

Possible transformations for natural convection on a vertical flat plate embedded in porous media with prescribed wall heat flux

This study derived the transformation of boundary layer equations for two-dimensional steady natural convection on a vertical wall embedded in porous media. Three different kinds of thermal boundary conditions are prescribed for wall heat flux: uniform distribution, power law variation, and exponential variation. The flow pattern contains three subregions based on the distance along the flat plate. When inertia resistance is ignored, similarity solution exists in case wall heat flux is in linear distribution. The known relationships of uniform wall temperature relative to wall heat flux variation and uniform wall heat flux relative to wall temperature variation in both cases of the pure fluid flow and the pure porous flow can all be obtained in the present transformation.