Natural convective heat transfer from a vertical isothermal surface to a non-Newtonian Sutterby fluid

This paper deals with the laminar natural convection of a non-Newtonian fluid along a vertical isothermal surface. The boundary-layer equations for a Sutterby fluid are solved numerically, and several characteristics of the non-similarity solution are represented graphically. An approximate expression of local Nusselt number Nu_x is proposed as Nu_x = 0·.50(Gr_0xPr₀)^0·.25(1+m), where m= 0−04 Pr₀^0.23 A^{3·7 Pr₀−0.34} Z₀^0·63A0.66Gr_0x and Pr₀ are Grashof number and Prandtl number based on zero viscosity respectively, and A and Z₀ are non-Newtonian parameters.Local heat-transfer coefficients are obtained by experiments with aqueous solutions of polyethyleneoxide (PEO) and carboxymethylcellulose (CMC). The experimental results are in excellent agreement with the theoretical ones.     

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.     

Mixed convection from a wavy surface embedded in a thermally stratified nanofluid saturated porous medium with non-linear Boussinesq approximation

In this article, we have made an attempt to study the convective heat transfer in the influence of non-linear Boussinesq approximation, thermal stratification and convective boundary conditions on non-Darcy nanofluid flow over a vertical wavy surface. The surface of the vertical wavy plate, put up at convective temperature and concentration. A coordinate transformation is used to transform the wavy surface into smooth surface. Using local similarity and non-similarity method the governing nondimensional equations are transformed into coupled nonlinear ordinary differential equations. Effects of thermal convective parameter, thermal stratification parameter, Lewis number, Sherwood number on the wave geometry on the heat and mass transfer characteristics have been studied. Numerical results have been obtained for various physical parameters. A comparison of the present results is made with the earlier published results and is found to be in good agreement.     

Natural convection heat and mass transfer from a vertical truncated cone in a porous medium saturated with a non-Newtonian fluid with variable wall temperature and concentration

This work presents a boundary-layer analysis about the natural convection heat and mass transfer near a vertical truncated cone with variable wall temperature and concentration in a porous medium saturated with non-Newtonian power-law fluids. A coordinate transform is used to obtain the nonsimilar governing equations, and the transformed boundary-layer equations are solved by the cubic spline collocation method. Results for local Nusselt numbers are presented as functions of power-law indexes, surface temperature and concentration exponents, buoyancy ratios, and Lewis numbers. The heat and mass transfer rates of the truncated cones with higher surface temperature and concentration exponents are higher than those with lower exponents. Moreover, an increase in the power-law index of fluids tends to decrease the heat and mass transfer from a vertical truncated cone in a porous medium saturated with non-Newtonian power-law fluids.     

Combined heat and mass transfer in natural convection flow from a vertical wavy surface in a power-law fluid saturated porous medium with thermal and mass stratification

This work studies the coupled heat and mass transfer by natural convection near a vertical wavy surface in a non-Newtonian fluid saturated porous medium with thermal and mass stratification. The surface of the vertical wavy plate is kept at constant wall temperature and concentration. A coordinate transformation is employed to transform the complex wavy surface to a smooth surface, and the obtained boundary layer equations are then solved by the cubic spline collocation method. Effects of thermal and concentration stratification parameters, Lewis number, buoyancy ratio, power-law index, and wavy geometry on the important heat and mass transfer characteristics are studied. Results show that an increase in the thermal and concentration stratification parameter decreases the buoyancy force and retards the flow, thus decreasing the heat and mass transfer rates between the fluid and the vertical wavy surface. It is shown that an increase in the power-law index, the thermal stratification parameter, or the concentration stratification parameter leads to a smaller fluctuation of the local Nusselt and Sherwood numbers with the streamwise coordinate. Moreover, the total heat transfer rate and the total mass transfer rate of vertical wavy surfaces are higher than those of the corresponding smooth surfaces.     

Effect of double stratification on mixed convection heat and mass transfer from a vertical surface in a fluid‐saturated porous medium

This paper presents the mixed convection heat and mass transfer near a vertical surface in a stratified porous medium using an integral method. The conservation equations that govern the problem are reduced to a system of coupled non‐linear ordinary differential equations, which is then reduced into a single algebraic equation using exponential profiles for the temperature and concentration. The results for heat and mass transfer rates in terms of Nusselt and Sherwood number are presented for a wide range of governing parameters like the buoyancy ratio (N), Lewis number (Le), flow driving parameter (Ra/Pe), in addition to both thermal and solutal parameters (S and R). The results indicate that the stratification effects have considerable influence on both the heat and mass transfer rates. © 2010 Wiley Periodicals, Inc. Heat Trans Asian Res; Published online in Wiley Online Library ( wileyonlinelibrary.com ). DOI 10.1002/htj.20300     

Natural convection along a vertical porous surface

This paper describes an experimental study on natural convection along a vertical porous surface consisting of a bank of parallel plates with constant gaps. Compared with a smooth surface, the heat transfer for a porous surface with streamwise gaps is somewhat enhanced owing to enthalpy transport due to flow within the gaps and that with spanwise gaps is enhanced due to the leading- and trailing-edge effects of solid-phase micro surfaces. Observations show that no clear transition to turbulent flow occurs at a critical Rayleigh number for a smooth surface and that the boundary layer oscillates with a dominant frequency at higher Rayleigh numbers. The dominant frequency for a porous surface is nearly the same as that for a smooth surface. This fact obviously indicates that the oscillations of natural convection are almost independent of the porous structure of the heating surface and are mainly dependent on the behavior of the outer boundary layer. © 1998 Scripta Technica. Heat Trans Jpn Res, 26(6): 385–397, 1997     

Natural convection in a heat generating hydrodynamically and thermally anisotropic non-Darcy porous medium

Natural convection in a two-dimensional square cavity containing hydrodynamically and thermally anisotropic porous medium with internal heat generation is analyzed numerically by generalized non-Darcy approach. The properties considered for the study are permeability ratio (K¹), inclination of the principal axes (θ), ratio of Forchheimer constants (F¹) and thermal conductivity ratio (k¹). Results are presented in terms of isotherms, streamlines and maximum temperature in the cavity to understand the flow physics. It is observed that the anisotropic properties have significant influence on the flow behaviour and heat transfer. A correlation for maximum temperature in the cavity for a wide range of parameters (10⁷ ? Ra ? 10⁸, 10^?6 ? Da ? 10^?3, 0° ? θ ? 90°, 1 ? F¹ ? 100, 0.1 ? K¹ ? 10 and 0.1 ? k¹ ? 10) is developed.     

Natural convection heat and mass transfer near a vertical wavy surface with constant wall temperature and concentration in a porous medium

This paper reports a study of the phenomenon of natural convection heat and mass transfer near a vertical wavy surface embedded in a fluid-saturated porous medium. The buoyancy effect is due to the variation of temperature and concentration across the boundary layer. A simple coordinate transformation is employed to transform the complex wavy surface to a flat plate, and the obtained boundary layer equations is then solved by the local nonsimilarity method and the cubic spline collocation method. Effects of the Lewis number, the buoyancy ratio, and the wavy geometry on the local Sherwood number and the local Nusselt number are studied. The harmonic curves for the local Sherwood number and the local Nusselt number have a frequency twice the frequency of the wavy surface. Moreover, increasing the amplitude-wavelength ratio tends to increase the amplitude of the local Sherwood number and the local Nusselt number. Further, the average Sherwood number and the average Nusselt number for a sinusoidal wavy surface are found to be constantly smaller than that of the corresponding flat plate.     

Natural convection heat and mass transfer along a vertical wavy surface

A numerical study of natural convection heat and mass transfer along a vertical wavy surface has been performed. The wavy surface is maintained at uniform wall temperature and constant wall concentration. A simple coordinate transformation is employed to transform the complex wavy surface to a flat plate. A marching finite-difference scheme is used for the analysis. The buoyancy ratio N, amplitude-wavelength ratio α, and Schmidt number Sc are important parameters for this problem. The numerical results, including the developments of skin-friction coefficient, velocity, temperature, concentration, Nusselt number as well as Sherwood number along the wavy surfaces are presented. The effects of the buoyancy ratio N and the dimensionless amplitude of wavy surface on the local Nusselt number and the local Sherwood number have been examined in detail.     

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.     

Transient mass transfer from an isothermal vertical flat plate embedded in a porous medium

Transient mass transfer from an isothermal, vertical flat plate embedded in a fluid—saturated porous medium has been investigated. At t^*=0 the concentration of the fluid at the plate is suddenly changed from the value of the ambient fluid, c_∞, to c_w. The results show that the local Sherwood numbe r decreases with time and monotonically approaches its steady-state value.     

Free convection heat and mass transfer to steady flow in a semi-infinite vertical porous medium

Analytical solutions are derived for flow in a semi-infinite vertical porous medium with heat and mass transfer. When the temperature and mass concentration are uniform a constant pressure is possible and sustains a fully developed flow. Thereafter there is a small perturbation of the wall temperature and concentration, and the subsequent two-dimensional problem is tackled for large Prandtl number and free convection parameters and small Reynolds number. The heat transfer rate at the wall is discussed quantitatively.     

Natural convection heat transfer in horizontal eccentric elliptic annuli containing saturated porous media

The two-dimensional Darcy–Boussinesq equations, governing natural convection heat transfer in a saturated porous medium, are solved in generalised orthogonal coordinates, using high-order compact finites differences on a very fine grid. The mesh is generated numerically using the orthogonal trajectory method. The code is thoroughly validated against results reported in the literature for concentric and eccentric cylinders, obtained using different numerical techniques. The code is applied to horizontal eccentric elliptic annuli containing saturated porous media. The judicious stretching of one of the annular walls in the horizontal direction reduces the heat losses with respect to a concentric cylindrical annulus with the same amount of insulating material. The savings in heat transfer can be further improved if the elliptic annular shape is made eccentric. Previous studies show that, under certain conditions, eccentric cylinders may lead to a more effective insulation than concentric ones. The results presented here provide an alternative approach to optimising the heat transfer rate by a proper choice of the annular shape. The energy savings are of the order of 10%.     

Non-Darcy mixed convection from a line source of heat in saturated porous medium

Local non-similarity solutions are reported for mixed convective heat transfer from a line source of heat in a saturated porous medium. Non-Darcy effects which include the flow inertial and thermal dispersion are considered in this study. The governing parameters are the Ergun number Er, the thermal dispersion coefficient C and mixed convection parameter & (=Ra/Pe). While the inertial effect tends to reduce the mixed convective flow, the thermal dispersion is to increase it. Both effects, however, have considerably thickened the thermal boundary layer.     

Natural convection heat transfer from a horizontal isothermal elliptical cylinder with internal heat generation

This work examines the natural convection heat transfer from a horizontal isothermal cylinder of elliptic cross section in a Newtonian fluid with temperature dependent internal heat generation. The governing boundary layer equations are transformed into a non-dimensional form and the resulting nonlinear systems of partial differential equations are solved numerically applying cubic spline collocation method. Results for the local Nusselt number and the local skin-friction coefficient are presented as functions of eccentric angle for various values of heat generation parameters, Prandtl numbers and aspect ratios. Results show that both the heat transfer rate and skin friction of the elliptical cylinder with slender orientation are higher than the elliptical cylinder with blunt orientation. Moreover, an increase in the heat generation parameter for natural convection flow over an isothermal horizontal elliptic cylinder leads to a decrease in the heat transfer rate from the elliptical cylinder and an increase in the skin friction of the elliptical cylinder.     

Periodic free convection from a vertical plate in a saturated porous medium, non-equilibrium model

The problem of the free convection from a vertical heated plate in a porous medium is investigated numerically in the present paper. The effect of the sinusoidal plate temperature oscillation on the free convection from the plate is studied using the non-equilibrium model, i.e., porous solid matrix and saturated fluid are not necessary to be at same temperature locally. Non-dimensionalization of the two-dimensional transient laminar boundary layer equations results in three parameters: (1) H, heat transfer coefficient parameter, (2) K_r, thermal conductivity ratio parameter, and (3) λ, thermal diffusivity ratio. Two additional parameters arise from the plate temperature oscillation condition which are the non-dimensional amplitude (ε) and frequency (Ω). The fully implicit finite difference method is used to solve the system of equations. The numerical results are presented for 0 ? H ? 10, 0 ? K_r ? 10, 0.001 ? λ ? 10 with the plate temperature oscillation parameters 0 ? Ω ? 10 and 0 ? ε ? 0.5. The results show that the thermal conductivity ratio parameter is the most important parameter. It is found also that increasing the amplitude and the frequency of the oscillating surface temperature will decrease the free convection heat transfer from the plate for any values of the other parameters.     

Combined convection from an isothermal horizontal rod buried in a porous medium

This paper reports the results of a numerical investigation of mixed convection heat transfer from a horizontal rod of circular cross-section that is embedded in a porous medium. The rod temperature is first assumed to be the same as that of the medium and then suddenly increased to a higher constant value. The steady-state problem has been solved by the method of series truncation in combination with a finite-difference scheme for the two flow configurations of parallel and counter-flow regimes. The flow and thermal fields as well as the variations of the average and local heat transfer rates with a wide range of Reynolds number, Grashof number and buoyancy parameter have been examined in detail for a Prandtl number of 0.7. One of the interesting features found is the occurrence of a recirculating flow zone near the upper half surface of the rod in the case of the counter-flow regime. The numerical method and the results presented fill in a gap in the literature on one of the most fundamental problems in the field of mixed convection in porous media.     

Double diffusion, natural convection in an enclosure filled with saturated porous medium subjected to cross gradients; stably stratified fluid

Two- and three-dimensional flows, heat and mass transfer in a horizontal enclosure with aspect ratio of two filled with saturated porous medium were analyzed numerically. The enclosure is heated differentially and stably stratified species concentration is imposed vertically. The Prandtl number is fixed to 10 (aqueous solutions). The Lewis number is varied in the range of 1.0-1000 to cover a wide range of species diffusion material in water. The work is concentrated on stable stratified flow. The results of two- and three-dimensional models were compared. Interesting results are obtained for a wide range of solutal to thermal buoyancy ratios. The difference in the rate of heat and mass transfer between prediction of three- and two-dimensional simulations is not that significant, even though the flow exhibits a three-dimensional structure. This is due to the fact that the spanwise flow is very weak when compared with main flow.