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.     

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.     

Similarity solution for natural convection flow over an isothermal vertical wall immersed in thermally stratified medium

A similarity solution has been obtained for a natural convection flow on a heated isothermal wall suspended in a quiescent, thermally stratified atmosphere. A new similarity variable is defined which reduces to that for the classical case of an isothermal plate in a uniform temperature, quiescent medium. It also properly represents the case for an isothermal plate in a linear stably stratified atmosphere. This is a unique feature which has not been discussed before. Predicted values of the local temperature defect and flow reversal are in qualitative agreement with results obtained by earlier investigators.     

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.     

Natural convection heat transfer from a horizontal cylinder embedded in a porous medium

This paper presents the results of an experimental investigation of heat transfer by natural convection from a horizontal cylinder embedded in porous media consisting of randomly packed glass spheres saturated by either water or silicone oil. It is shown that the overall range of the Rayleigh number, Ra, can be divided into two subregions, called ‘low’ and ‘high’, in each of which the Nusselt number, Nu, behaves differently. It is demonstrated that the low Ra region corresponds to Darey flow and the high to Forchheimer flow. Correlation equations for Nu for the Darcy regime are presented that account for viscous dissipation, and others for the Forchheimer regime that involve the first and second Forchheimer coefficients. The variation of properties with temperature and the wall effect on porosity (and consequently on heat transfer) are considered. The paper includes information concerning the resistance to flow in porous media that was obtained in conjunction with the heat transfer study.     

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 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 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 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 transfer from a vertical plate to high permeability porous media: an experiment and an approximate solution

The heat transfer rate from an isothermal vertical plate placed next to saturated high permeability porous media is studied experimentally and analytically. The media used are polyurethane foams saturated with air. An integral method is applied in predicting the heat transfer rate by including the non-Darcy effects, which are expected to be significant for high permeabilities and high Rayleigh numbers. Good agreement is found between the experimental and predicted results except when the permeability is relatively low and the Péclet number becomes very small. Although some of the permeabilities encountered are large, for the experimental conditions considered in this study the Rayleigh numbers are not very high; therefore, the non-Darcy effects are not significant.     

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 from a discrete protruding surface

Steady heat transfer from a two dimensional discrete protruding copper block mounted on a vertical wall has been experimentally studied here. The buoyant flow around theblock has been visualized using an interferometer. The average Nusselt number for the heater is found to be considerably larger than values reported in the literature. Local Nusselt numbers derived from the interferograms, however justify the magnitude of the average Nusselt number.     

Effects of heat and mass transfer on MHD nonlinear free convection non-Newtonian fluids flow embedded in a thermally stratified porous medium

This communication examines heat alongside mass transport in a nonlinear free convection magnetohydrodynamics (MHD) non-Newtonian fluid flow with thermal radiation and heat generation deep-rooted in a thermally stratified penetrable medium. The Casson and Williamson fluid considered in this communication flos simultaneously across the boundary layer and are mixed together. The model of heat alongside mass transport is set up with chemical reaction and thermal radiation alongside heat generation to form a system of partial differential equations (PDEs). Appropriate similarity variables are used to simplify the PDEs to obtain systems of coupled ordinary differential equations. An efficiently developed numerical approach called the spectral homotopy analysis method was used in providing solutions to the transformed equations. A large value of Casson term is observed to degenerate the velocity plot while the Williamson parameter enhances the velocity profile. The parameter of thermal stratification is found to enhance the rate of heat transport within the boundary layer. An incremental value of the magnetic parameter declines the velocity of the fluid and the entire boundary layer thickness. The present result was compared with previous studies and was seen to be in good agreement.     

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.