Conjugate free convection from long vertical plate fins in a non-Newtonian fluid-saturated porous medium

The problem of conjugate free convection from long vertical fins in a non-Newtonian fluid-saturated porous medium has been investigated exploiting the boundary layer approximation. The governing equations based on the power-law model appropriate for the Darcy flow are solved exploiting an integral method. The effects of the fin shape exponent and power-law index parameters on the flow and heat transfer characteristics are discussed.     

Study of mixed convection in an annular vertical cylinder filled with saturated porous medium,using thermal non-equilibrium model

The present study deals with numerical investigation of effects of different parameters on enhancement or retardation of the heat transfer rate in an annular vertical cylinder filled with saturated porous medium. The heat transfer is assumed to take place by mixed convection mode. The thermal non-equilibrium approach is considered. The inner surface of the annular cylinder is maintained at constant wall temperature whereas the outer surface remains at ambient temperature. The governing partial differential equations are solved using finite element method. The results are discussed for the effects of Peclet number, interphase heat transfer co-efficient and thermal conductivity ratio.     

Analysis of mixed convection in a vertical porous layer using non-equilibrium model

The problem of two-dimensional steady mixed convection in a vertical porous layer is investigated numerically in the present paper using the thermally non-equilibrium model. The vertical porous layer is assumed to have a finite isothermally heated segment on one vertical wall which is otherwise adiabatic and the other vertical wall is cooled to a constant temperature. Non-dimensionalization of the governing equations results in four parameters for both aiding and opposing flows: (1) Ra, Rayleigh number (2) Pe, Péclet number (3) K_r, thermal conductivity ratio parameter, and (4) H, heat transfer coefficient parameter. The numerical results are presented for 0.01  H  100, 0.01  K_r  100, 0.01  Pe  100 and Ra = 10, 50 and 100. The results show that, the thermal equilibrium model cannot predict the average Nusselt number correctly for small values of H × K_r. In both the aiding and opposing flows, the total average Nusselt number is decreasing with increasing the heat transfer coefficient parameter at low values of Pe, while for high values of Pe, higher H will enhance the total heat transfer rate. Increasing the thermal conductivity ratio leads to increase in the total average Nusselt number. It is found also that the total average Nusselt number depends strongly on the thermal conductivity ratio parameter and depends slightly on the heat transfer coefficient parameter.     

Non-darcy natural convection from a heated vertical plate in saturated porous media with mass transfer

The nonsimilar and self-similar flows for the steady natural convection over a vertical heated surface in a saturated porous medium with mass transfer using non-Darcy model have been studied under boundary layer approximations. The differential equations governing both the nonsimilar and self-similar flows have been solved numerically using an implicit finite-difference scheme developed by Keller. The results indicate that both heat transfer and velocity field are appreciably affected by the modified Grashof number and mass transfer except that the effect of the modified Grashof number on the heat transfer for large suction is very small. It is found that the maximum velocity occurs at the wall and it increases as the modified Grashof number or injection increases.     

Soret and Dufour effects on free convection boundary layer over a vertical cylinder in a saturated porous medium

This paper deals with an analysis of the Soret and Dufour effects on the boundary layer flow due to free convection heat and mass transfer over a vertical cylinder in a porous medium saturated with Newtonian fluids with constant wall temperature and concentration. A suitable coordination transformation is used to derive the similar governing boundary-layer equations, and the cubic spline collocation method is then employed to solve the similar governing boundary-layer equations. The variation of the Nusselt number and the Sherwood number with the Dufour parameter and the Soret parameter for various Lewis numbers and buoyancy ratios have been presented in this work. Results show that an increase in the Soret number leads to a decrease in the local Sherwood number and an increase in the local Nusselt number. The local Nusselt number tends to decrease as the Dufour parameter is increased. Moreover, an increase in the Lewis number enhances the effect of the Dufour parameter on the local Nusselt number.     

Natural convection about a vertical plate embedded in a bidisperse porous medium

The classical Cheng–Minkowycz study of convection past a vertical plate embedded in a porous medium has been extended to the case of a bidisperse porous medium (BDPM). The boundary layer analysis leads to expressions for the velocity and temperature fields in terms of a geometrical parameter, an inter-phase momentum transfer parameter, a thermal diffusivity ratio, a permeability ratio, a thermal conductivity ratio, and an inter-phase heat transfer parameter. For the leading edge region, and for an inner layer, a similarity solution is obtained numerically. This involves the first four parameters, each of which is a characteristic of the BDPM.     

Soret and Dufour effects on free convection along a vertical wavy surface in a fluid saturated Darcy porous medium

In this article, free convection of heat and mass transfer along a vertical wavy surface in a Newtonian fluid saturated Darcy porous medium is studied by considering cross diffusion (namely the Soret and the Dufour effects) in the medium. The vertical wavy wall and the flow governing equations are transformed to a plane geometry case by using a suitable transformation. Then a similarity solution to this problem is presented under the large Darcy–Rayleigh number assumption. The governing partial differential equations are reduced to a set of ordinary differential equations that are integrated using numerical methods to study the nature of the non-dimensional heat and mass transfer coefficients in the medium. The results are presented for a range of the flow governing parameters such as the diffusivity ratio parameter, the buoyancy ratio parameter, the Soret parameter, the Dufour parameter and the amplitude of the wavy surface.     

Linear stability of convection in a vertical channel filled with nanofluid saturated porous medium

The convection in a vertical channel filled with a porous medium saturated by a nanofluid is studied numerically. The effects of Brownian motion and thermophoresis are incorporated in the model used for nanofluid. Also, the flow within the porous region is governed by Brinkman's equation. The generalized eigenvalue problem for the perturbed state is obtained from a normal mode analysis and solved using the Chebyshev spectral collocation method. The Rayleigh number is expressed as an implicit function of the wavenumber with other parameters. The critical wavenumber and the critical Rayleigh number are calculated for different parameters. The preferred modes under critical conditions are detected.     

The effect of uniform lateral mass flux on free convection about a vertical cone embedded in a saturated porous medium

The effect of uniform lateral mass flux on natural convection about a cone embedded in a saturated porous medium is numerically analyzed. The surface is maintained at a uniform wall temperature (UWT) or uniform heat flux (UHF). The transformed governing equations are solved by Keller box method. Numerical data for the dimensionless temperature profiles and the local Nusselt number are presented for a wide range of the mass flux parameter. In general, it has been found that the local surface heat transfer rate increases owing to suction of fluid. This trend reversed for blowing of fluid. The mass flux parameter is found to have a more pronounced effect on the local Nusselt number for the case of UWT than it does for the case of UHF.     

MHD mixed convection from a vertical plate embedded in a porous medium with a convective boundary condition

A numerical approach has been used to study the heat and mass transfer from a vertical plate embedded in a porous medium experiencing a first-order chemical reaction and exposed to a transverse magnetic field. Instead of the commonly used conditions of constant surface temperature or constant heat flux, a convective boundary condition is employed which makes this study unique and the results more realistic and practically useful. The momentum, energy, and concentration equations derived as coupled second-order, ordinary differential equations are solved numerically using a highly accurate and thoroughly tested finite difference algorithm. The effects of Biot number, thermal Grashof number, mass transfer Grashof number, permeability parameter, Hartmann number, Eckert number, Sherwood number and Schmidt number on the velocity, temperature, and concentration profiles are illustrated graphically. A table containing the numerical data for the plate surface temperature, the wall shear stress, and the local Nusselt and Sherwood numbers is also provided. The discussion focuses on the physical interpretation of the results as well their comparison with the results of previous studies.     

Natural convection from a concentrated heat source in a saturated porous medium

A boundary-layer analysis of natural convection resulting from a point heat source in saturated porous medium is re-examined in this paper. The conditions for which the boundary-layer approximation is valid are carefully examined. The boundary-layer equations are shown to have solutions of similarity form for power-law variation of the center-line temperature. Closed-form solutions are presented for both flow and temperature fields.     

Effect of heat generation or absorption on thermophoretic free convection boundary layer from a vertical flat plate embedded in a porous medium

This paper is focused on the study of coupled heat and mass transfer by boundary-layer free convection over a vertical flat plate embedded in a fluid-saturated porous medium in the presence of thermophoretic particle deposition and heat generation or absorption effects. The governing partial differential equations are transformed into ordinary differential equations by using special transformations. The resulting similarity equations are solved numerically by an efficient implicit tri-diagonal finite-difference method. Comparisons with previously published work are performed and the results are found to be in excellent agreement. Many results are obtained and a representative set is displayed graphically to illustrate the influence of the heat generation or absorption coefficient, buoyancy ratio and the Lewis number on the temperature and concentration profiles and the wall thermophoretic deposition velocity.     

Natural convection heat transfer from an isothermal vertical surface to a fluid saturated thermally stratified porous medium

Presented here are the results of a numerical study of natural convection heat transfer in a stably stratified, fluid saturated low porosity medium, in which Darcy flow prevails. In this investigation, the boundary layer approximations are discarded and a wide range of ambient thermal stratification levels is considered. The results indicate that the ambient thermal stratification has a significant effect on the flow and temperature fields, and that this effect differs considerably at higher levels of stratification. The flow reversal and temperature defects are significantly smaller in the porous media than in a viscous fluid, due to the stabilization of the flow by the solid matrix. To generalize the result, the Nusselt number data are correlated with the thermal stratification parameter to yield a functional relationship.     

Doubly diffusive unsteady mixed convection flow over a vertical plate embedded in a porous medium

The unsteady laminar incompressible boundary layer mixed convection flow over a semi-infinite vertical plate with a magnetic field situated in a porous medium has been studied where the buoyancy forces result both from temperature and concentration gradients. The effects of the presence of an isotropic solid matrix and dissipation have been included in the analysis. The governing coupled nonlinear partial differential equations with three independent variables have been solved numerically using an implicit finite-difference scheme in combination with the quasilinearization technique. The effects of the permeability of the medium, magnetic field and dissipation on the skin friction, heat transfer and mass transfer are found to be more pronounced for large value of the streamwise distance. Also, for assisting flow, the skin friction, heat transfer and mass transfer increase with the buoyancy forces, but the effect is exactly opposite for opposing flow.     

Transient free convection in cold water past an infinite vertical porous plate

A finite-difference solution of the transient free convection flow of water near 4°C past an infinite vertical porous plate has been carried out. The most appropriate relation for the density in terms of the temperature, as derived by Gebhart and Mollendorf, is employed. It has been observed that, when the buoyancy force is in the upward direction, the velocity profiles are positive and opposite to those in the case where the buoyancy force is in the downward direction. Also, the skin friction is more when the buoyancy force is in the upward direction than when the buoyancy force is in the downward direction.     

Mixed convection boundary layer flow from a vertical flat plate embedded in a porous medium filled with nanofluids

The steady mixed convection boundary layer flow past a vertical flat plate embedded in a porous medium filled with nanofluids is studied using different types of nanoparticles as Cu (cuprom), Al₂O₃ (aluminium) and TiO₂ (titanium). The model used for the nanofluid is the one which incorporates only the nanoparticle volume fraction parameter. The basic partial equations are reduced to an ordinary differential equation which is solved numerically for some values of the volume fraction and mixed convection parameters. It is shown that the solution has two branches in a certain range of the parameters. The effects of these parameters on the velocity distribution are presented graphically.