NATURAL CONVECTION OF A BINARY MIXTURE IN A VERTICAL CLOSED ANNULUS

This article reports an analytical and numerical study of natural convection of a binary mixture within a vertical closed annulus. Neumann boundary conditions for temperature are applied to the vertical walls of the enclosure, while the short walls are insulated. The solutal buoyancy forces are assumed to be induced either by the imposition of constant fluxes of mass on the vertical walls (double-diffusive convection, a = 0) or by temperature gradients (Soret effect, a = 1). The governing parameters for the problem are the thermal Rayleigh number R_T, Prandtl number Pr, Lewis number Le, buoyancy ratio ϕ, aspect ratio A, constant a, and curvature parameter η. An analytical solution, based on the assumption of parallel flow over a large portion of enclosure, is derived. Numerical confirmation of the analytical results is also presented.     

NATURAL CONVECTION OF A BINARY MIXTURE IN A VERTICAL CLOSED ANNULUS

This article reports an analytical and numerical study of natural convection of a binary mixture within a vertical closed annulus. Neumann boundary conditions for temperature are applied to the vertical walls of the enclosure, while the short walls are insulated. The solutal buoyancy forces are assumed to be induced either by the imposition of constant fluxes of mass on the vertical walls (double-diffusive convection, a = 0) or by temperature gradients (Soret effect, a = 1). The governing parameters for the problem are the thermal Rayleigh number R_T, Prandtl number Pr, Lewis number Le, buoyancy ratio ?, aspect ratio A, constant a, and curvature parameter η. An analytical solution, based on the assumption of parallel flow over a large portion of enclosure, is derived. Numerical confirmation of the analytical results is also presented.     

TRANSIENT MIXED CONVECTION ALONG A VERTICAL PLATE EMBEDDED IN POROUS MEDIA WITH INTERNAL HEAT GENERATION AND OSCILLATING TEMPERATURE

The effects of oscillating plate temperature on transient mixed convection heat transfer from a porous vertical surface embedded in a saturated porous medium with internal heat generation or absorption are studied. The governing equations are transformed into dimenionless form by a set of variables and solved using the Galerkine finite element method. As the energy generation increases, the temperature near the wall will be higher than the wall temperature, thus increasing buoyancy forces inside the boundary layer and consequently increasing the velocity. The increase of energy absorption term for either space or temperature dependence will decrease the velocity inside the boundary layer and increase heat transfer rates. Different temperature and velocity profiles are drawn for different dimensionless groups. Numerical values for Nusselt numbers as well as local skin friction coefficient are also tabulated.     

TRANSIENT MIXED CONVECTION ALONG A VERTICAL PLATE EMBEDDED IN POROUS MEDIA WITH INTERNAL HEAT GENERATION AND OSCILLATING TEMPERATURE

The effects of oscillating plate temperature on transient mixed convection heat transfer from a porous vertical surface embedded in a saturated porous medium with internal heat generation or absorption are studied. The governing equations are transformed into dimenionless form by a set of variables and solved using the Galerkine finite element method. As the energy generation increases, the temperature near the wall will be higher than the wall temperature, thus increasing buoyancy forces inside the boundary layer and consequently increasing the velocity. The increase of energy absorption term for either space or temperature dependence will decrease the velocity inside the boundary layer and increase heat transfer rates. Different temperature and velocity profiles are drawn for different dimensionless groups. Numerical values for Nusselt numbers as well as local skin friction coefficient are also tabulated.     

HYDROMAGNETIC NATURAL CONVECTION OF A BINARY FLUID IN A VERTICAL POROUS ENCLOSURE

An analytical and numerical investigation is conducted to study the effect of an electromagnetic field on natural convection in a vertical rectangular porous cavity saturated with an electrically conducting binary mixture. Uniform heat fluxes are applied to the vertical walls while the horizontal walls are adiabatic. Governing parameters of the problem under study are the thermal Rayleigh R_T, Hartmann number Ha, buoyancy ratio ?, Lewis number Le, and aspect ratio A. An analytical solution, valid for tall enclosures (A > > 1), is derived on the basis of the parallel flow approximation. In the range of the governing parameters considered in this study, a good agreement is found between the analytical predictions and the numerical results obtained by solving the full governing equations.     

NATURAL CONVECTION FLOW OF SECOND-GRADE FLUID ALONG A VERTICAL HEATED SURFACE WITH POWER-LAW TEMPERATURE

In this study we investigated the effects of free convection flow of a viscoelastic second-grade fluid along a vertical flat surface with power-law temperature distribution. The boundary layer equations for the momentum and the energy transport have been reduced to local similarity equations using appropriate transformations. Solutions of the reduced equations are obtained employing the local non-similarity method as well as the implicit finite difference method against ξ (the local Deborah number) in the range [0, 10] for fluids having Prandtl numbers of 10, 50, and 100. The regular perturbation solutions are also been obtained for smaller values of ξ together with the Padé approximation. Results thus obtained are discussed in terms of the local skin friction and local rate of heat transfer for different values of the physical parameters, like n and Pr. Effect of the Deborah number, De, on the velocity and temperature profiles has also been shown graphically. It is observed that both the local skin friction and heat transfer coefficients decrease with increase in the value of De for given values of n and Pr.     

多孔介质对流干燥机理及其模型

在对现有的多孔介质对流干燥传热、传质模型归类分析的基础上,从介质内部热湿迁移机制出发,建立了能较完善、较准确地描述多孔介质在恒速段及降速段热质传递规律的“三耦合-六场量”混合理论模型.同时针对干燥问题数值模拟中的移动边界问题,提出了一种迭代修正的思想,并发展了相应的数值计算方法.对砖的干燥模拟计算结果表明,本文的模型较其他模型具有更好的精确性.     

CFD MODELLING OF NATURAL CONVECTION HEAT AND MASS TRANSFER IN HYGROSCOPIC POROUS MEDIA

Abstract

This paper presents the derivation of a model to predict heat and mass transfer in a system consisting of a turbulently flowing fluid overlying a saturated hygroscopic porous medium. Comparisons with experimental and numerical simulations have been carried out to check the accuracy of components of the model. Finally, a case study using silica gel as a representative hygroscopic porous medium is presented as an application of the model. It is shown that moisture is convected from the warm interior of a bulk of porous medium to the relatively cool periphery. This result has profound practical implications when the hygroscopic medium is stored agricultural produce as the region of high moisture content may become moldy.     

MHD FLOW WITH SLIP EFFECTS AND TEMPERATURE-DEPENDENT HEAT SOURCE IN A VERTICAL WAVY POROUS SPACE

This study examines the problem of MHD flow in a vertical wavy porous space in the presence of a temperature-dependent heat source with slip-flow boundary condition. The equations of momentum, energy, and concentration are subject to a set of appropriate boundary conditions assuming that the solution consists of two parts: a mean part and a perturbed part. The solution of the perturbed part has been obtained by using the long-wave approximation. The mean part (zeroth-order), first-order velocity, and the total solution of the problem have been evaluated numerically for several sets of values of the parameters relating to the problem. The skin friction and the rate of heat and mass transfer coefficients at the walls are obtained and illustrated graphically.     

NATURAL CONVECTION IN A SHALLOW POROUS CAVITY HEATED FROM THE SIDE WITH A UNIFORM HEAT FLUX

Thermally driven flow in a thin rectangular cavity filled with a fluid saturated porous layer is studied analytically and numerically. A constant heat flux heating and cooling is applied on both vertical walls while the horizontal ones are assumed to be insulated. On the basis of the Darcy-Oberbeck-Boussinesq equations, the problem can be solved analytically, in the limit of a thin layer, using asymptotic expansions and an integral form of the energy equation. The flow field and temperature distributions are obtained explicitly in terms of the Rayleigh number in the conduction as well as intermediate regimes. A numerical study of the same phenomenon, obtained by solving the complete system of governing equations, is also presented. A very good agreement is found between the numerical simulations and the analytical predictions. The various physical processes in this type of flow are discussed based on the findings of the analytical and numerical studies.     

THE EFFECT OF FREE STREAM CONCENTRATION ON HEAT AND BINARY MASS TRANSFER WITH THERMODYNAMIC COUPLING IN CONVECTION ON A ROTATING DISC†

Simultaneous heat and mass transfer, which arises from injecting a gas (helium or hydrogen) from or through the solid surface into a flowing external stream, has been studied for a rotating disc geometry. The effects of concentration levels of the injected gas in the external stream on the thermodynamic coupling in the presence of centrifugal force have been investigated over a wide range of T_w/T_e.

Boundary layer equations for heat and mass transfer were solved numerically. Exact and linearized approximate solutions were obtained. The results have shown that the thermal diffusion effect on mass transfer becomes increasingly important as the free stream concentration increases and as T_w/T_e departs from unity. The diffusion thermo effect on heat transfer was found to be the most important when the free stream concentration is zero and as T_w/T_e approaches unity.     

SLIP FLOW AND HEAT TRANSFER OF A SECOND-GRADE FLUID IN A POROUS MEDIUM OVER A STRETCHING SHEET WITH POWER-LAW SURFACE TEMPERATURE OR HEAT FLUX

This article deals with the study of boundary layer flow of a second-grade fluid in a porous medium past a stretching sheet and heat transfer characteristics with power-law surface temperature or heat flux. The flow in the boundary layer is considered to be generated solely by the linear stretching of the boundary sheet adjacent to a porous medium, and boundary wall slip condition is assumed. In the energy equation effects of viscous dissipation, work done due to deformation and internal heat generation/absorption is taken into account. Closed form solutions are obtained for this problem.     

THERMAL-DIFFUSION AND DIFFUSION-THERMO EFFECTS ON NATURAL CONVECTION ALONG AN INCLINED STRETCHING SURFACE IN A POROUS MEDIUM WITH CHEMICAL REACTION

The steady natural convection along an inclined stretching surface in the presence of chemical reaction under thermal-diffusion and diffusion-thermo effects is studied. The governing equations for continuity, momentum, energy, and concentration are transformed by similarity transformation and then solved numerically using the Runge-Kutta integration with shooting scheme. Comparisons between the present data with previously published work are performed and found to be in very good agreement with each other. The obtained results show that the flow, thermal, and diffusion fields are influenced appreciably by the effects of endothermic or exothermic chemical reaction, angle of inclination, thermal radiation, magnetic field, and Soret and Dufour numbers. The physical phenomenon can be realized from the graphical profiles and in tabular form to depict special features of the solutions.     

HOMOTOPY ANALYSIS OF FREE CONVECTION BOUNDARY LAYER FLOW WITH HEAT AND MASS TRANSFER

A steady two-dimensional laminar boundary layer flow of an incompressible viscous fluid over a semi-infinite surface is considered to investigate the accuracy of the homotopy analysis method. The governing coupled nonlinear system of differential equations is solved by means of the HAM approach. Explicit analytical series solutions are obtained and compared with numerical solutions. Good agreement is observed between the numerical results and HAM analytical solutions.     

UNSTEADY MHD HEAT AND MASS TRANSFER BY MIXED CONVECTION FLOW IN THE FORWARD STAGNATION REGION OF A ROTATING SPHERE AT DIFFERENT WALL CONDITIONS

This study is focused on the problem of MHD heat and mass transfer by mixed convection flow in the forward stagnation region of a rotating sphere in the presence of heat generation and chemical reaction effects. The surface of the sphere is maintained at constant fluid temperature and species concentration. The governing equations of the problem are converted into ordinary differential equations by using suitable similarity transformations. Two cases are considered, namely, constant wall temperature and mass (CWTM) and constant heat and mass fluxes (CHMF). The obtained self-similar equations for both cases are solved numerically using an efficient iterative implicit finite-difference method. The numerical results are compared with previously published results on special cases of the problem and found to be in excellent agreement. The obtained results are displayed graphically to illustrate the influence of the different physical parameters on the velocity components in x- and y-directions, temperature, and concentration profiles as well as the local surface shear stresses and local heat and mass transfer coefficients.     

边界层方程求解传热传质复合自然对流的偏差分析

引　言动量、能量及质量的边界层方程是Naveir Stokes完整方程的简化形式 ,自上世纪初提出以来 ,应用极广 .传热传质复合自然对流是自然界和工业过程中常见的现象 ,由于存在热与物质扩散两种浮力相对大小及方向的差异以及Prandtl数和Schmit数的影响 ,使该问题颇为复杂 .Bottema     

UNSTEADY HEAT AND MASS TRANSFER BY MHD MIXED CONVECTION FLOW OVER AN IMPULSIVELY STRETCHED VERTICAL SURFACE WITH CHEMICAL REACTION AND SORET AND DUFOUR EFFECTS

This work considers unsteady, laminar, and coupled heat and mass transfer by MHD mixed convective boundary-layer flow of an electrically conducting fluid over an impulsively stretched vertical surface in an unbounded quiescent fluid with aiding external flow in the presence of a transverse magnetic field, homogeneous chemical reaction, and Soret and Dufour effects. The stretching velocity and surface temperature and concentration are assumed to vary linearly with the distance along the surface. The flow is impulsively set into motion and both the temperature and concentration at the surface are also suddenly changed from those of the ambient fluid. The governing partial differential equations are transformed into a set of nonsimilar equations and solved numerically by an efficient implicit, iterative, finite-difference method. A parametric study illustrating the influence of various physical parameters is performed. Numerical results for the steady-state velocity, temperature, and concentration profiles as well as the time histories of the skin-friction coefficient, local Nusselt number, and local Sherwood number are presented graphically and discussed.     

SIMILARITY SOLUTION FOR UNSTEADY HEAT AND MASS TRANSFER FROM A STRETCHING SURFACE EMBEDDED IN A POROUS MEDIUM WITH SUCTION/INJECTION AND CHEMICAL REACTION EFFECTS

An analysis is presented to investigate the effects of chemical reaction on unsteady free convective heat and mass transfer on a stretching surface in a porous medium. The governing partial differential equations have been transformed by a similarity transformation into a system of ordinary differential equations, which are solved numerically using an efficient tri-diagonal implicit finite-difference method. The results obtained show that the flow field is influenced appreciably by the presence of unsteadiness parameter, chemical reaction parameter, permeability parameter, and suction/injection parameter.     

MHD MIXED-CONVECTION INTERACTION WITH THERMAL RADIATION AND nTH ORDER CHEMICAL REACTION PAST A VERTICAL POROUS PLATE EMBEDDED IN A POROUS MEDIUM

This article investigates the hydromagnetic mixed convection heat and mass transfer flow of an incompressible Boussinesq fluid past a vertical porous plate with constant heat flux in the presence of radiative heat transfer in an optically thin environment, viscous dissipation, and an nth order homogeneous chemical reaction between the fluid and the diffusing species. The dimensionless governing equations for this investigation are solved numerically by the fourth-order Runge-Kutta integration scheme along with shooting technique. Numerical data for the local skin-friction coefficient, the plate surface temperature, and the local Sherwood number have been tabulated for various values of parametric conditions. Graphical results for velocity, temperature, and concentration profiles based on the numerical solutions are presented and discussed.