Conjugate mixed convection heat and mass transfer in brick drying

 In this study, a numerical methodology for the solution of conjugate heat and mass transfer problem is presented. Fluid flow, heat and mass transfer over a rectangular brick due to transient laminar mixed convection has been numerically simulated. The coupled non-linear partial differential equations, for both gas phase and solid are solved using finite element procedure. Flow is assumed to be incompressible, two-dimensional, laminar. Analysis has been carried out at a Reynolds number of 200 with Pr = 0.71. The effect of buoyancy on the brick drying has been investigated. Velocity vectors, streamlines in the flow field and temperature and moisture contours and temperature distribution along the solid surface are presented. It is observed that there is considerable effect of buoyancy during drying. The results indicate a non-uniform drying of the brick with the leading edge drying faster than the rest of the brick. Received on 9 December 1998     

Hydromagnetic simultaneous heat and mass transfer by mixed convection from a vertical plate embedded in a stratified porous medium with thermal dispersion effects

The problem of steady, laminar, hydromagnetic simultaneous heat and mass transfer by mixed convection flow over a vertical plate embedded in a uniform porous medium with a stratified free stream and taking into account the presence of thermal dispersion is investigated for the case of power-law variations of both the wall temperature and concentration. Certain transformations are employed to transform the governing differential equations to a local similarity form. The transformed equations are solved numerically by an efficient implicit, iterative, finite-difference scheme. The obtained results are checked against previously published work on special cases of the problem and are found to be in excellent agreement. A parametric study illustrating the influence of the magnetic field, porous medium inertia effects, heat generation or absorption, lateral wall mass flux, concentration to thermal buoyancy ratio, and the Lewis number on the fluid velocity, temperature and concentration as well as the Nusselt and the Sherwood numbers is conducted. The results of this parametric study is shown graphically and the physical aspects of the problem are discussed. Received on 17 November 1998     

Enhanced heat transfer performances of molten salt mixed convection in a vertical annular duct

The mixed convection heat transfer of upward molten salt flow in a vertical annular duct is experimentally and numerically studied. The heat transfer performances of mixed convection are measured under Reynolds number 2,500–12,000 and inlet temperature 300–400 °C, and Nusselt number of molten salt flow with cooled inner wall monotonically increases with buoyancy number. The mixed convection is further simulated by low-Reynolds number k-ε model and variable properties, and the heat transfer tendency from numerical results agrees with that from experiments. At low Reynolds number, the natural convection plays more important role in the mixed convection. As the buoyancy number rises, the thickness of flow boundary layer near the inner wall increases, while the effective thermal conductivity remarkably rises, so the enhanced heat transfer of mixed convection is mainly affected by the effective thermal conductivity due to turbulent diffusion.     

Simultaneous heat and mass transfer under unsteady mixed convection along a vertical slender cylinder embedded in a porous medium

Unsteady laminar mixed convection flow (combined free and forced convection flow) along a vertical slender cylinder embedded in a porous medium under the combined buoyancy effect of thermal and species diffusion has been studied. The effect of the permeability of the medium as well as the magnetic field has been included in the analysis. The partial differential equations with three independent variables governing the flow have been solved numerically using a implicit finite difference scheme in combination with the quasilinearization technique. Computations have been carried out for accelerating, decelerating and oscillatory free stream velocity distributions. The effects of the permeability of the medium, buoyancy forces, transverse curvature and magnetic field on skin friction, heat transfer and mass transfer have been studied. It is found that the effect of free stream velocity distribution is more pronounced on the skin friction than on the heat and mass transfer. The permeability and magnetic parameters increase the skin friction, but reduce the heat and mass transfer. The skin friction, heat transfer and mass transfer are enhanced due to the buoyancy forces and curvature parameter. The heat transfer is strongly dependent on the viscous dissipation parameter and the Prandtl number, and the mass transfer on the Schmidt number.     

MHD mixed convection–radiation interaction along a permeable surface immersed in a porous medium in the presence of Soret and Dufour’s Effects

This work is focused on the numerical modeling of steady, laminar, heat and mass transfer by MHD mixed convection from a semi-infinite, isothermal, vertical and permeable surface immersed in a uniform porous medium in the presence of thermal radiation and Dufour and Soret effects. A mixed convection parameter for the entire range of free-forced-mixed convection is employed and the governing equations are transformed into non-similar equations. These equations are solved numerically by an efficient, implicit, iterative, finite-difference scheme. The obtained results are checked against previously published work on special cases of the problem and are found to be in excellent agreement. A parametric study illustrating the influence of the thermal radiation coefficient, magnetic field, porous medium inertia parameter, concentration to thermal buoyancy ratio, and the Dufour and Soret numbers on the fluid velocity, temperature and concentration as well as the local Nusselt and the Sherwood numbers is conducted. The obtained results are shown graphically and the physical aspects of the problem are discussed.     

Influence of lateral mass flux on mixed convection heat and mass transfer over inclined surfaces in porous media

 The effect of lateral mass flux on mixed convection heat and mass transfer in a saturated porous medium adjacent to an inclined permeable surface is analyzed. A similarity solution is obtained when surface temperature and concentration, free stream velocity and injection/suction velocity of fluid are prescribed as power functions of distance from the leading edge. The cases when the flow and buoyancy forces are in the same and opposite directions are discussed both for aiding and opposing buoyancy effects. The governing parameters are the mixed convection parameter Gr, the Lewis number Le, the buoyancy ratio N, the lateral mass flux parameter f _w, representing the effects of injection or withdrawal of fluid at the wall, and λ which specifies three cases of the inclined plate. The interactive effect of these parameters on heat and mass transfer rates are presented. It is observed that the diffusion ratio (Le) has a more pronounced effect on concentration field than on flow and temperature fields. It is found that the rates of heat and mass transfer increase with suction and decrease with injection of the fluid. Received on 31 August 2000 / Published online: 29 November 2001     

Similarity solutions of mixed convection heat and mass transfer in combined stagnation and rotation-induced flows over a rotating disk

The objective of the present study is to develop a novel similarity model for analysis of mixed convection heat and mas transfer in combined stagnation and rotation-induced flows over a rotating disk. Thermal and concentration (solutal) buoyancy effects stemmed from temperature and concentration gradients in rotational as well as gravitational forces fields are all taken into account. The influences of the forced flow, disk rotation, thermal buoyancy, buoyancy ratio and the fluid properties, i.e. Prandtl and Schmidt numbers, on the flow, temperature and concentration fields and the associated friction factors, heat and mass transfer rates are investigated. The present results reveal the effects of various buoyancy modes with combined forces on the transport phenomena in rotating-disk flows, and the analysis is also useful in understanding the mechanisms of mixed convection in the class of rotating fluids. Received on 30 December 1997     

Coupled heat and mass transfer in mixed convection over a vertical flat plate embedded in saturated porous media: PST/PSC or PHF/PMF

A boundary layer analysis is used to investigate the heat and mass transfer characteristics of mixed convection about a vertical flat plate embedded in a saturated porous medium under the coupled effects of thermal and mass diffusion. The plate is maintained at prescribed surface temperature/concentration (PST/PSC) or prescribed heat/mass flux (PHF/PMF). The nonsimilar governing equations are obtained by using a suitable transformation and solved by Keller box method. Numerical results for the local heat transfer rate and the local mass transfer rate are presented for various parameters. The local heat and mass transfer rates increase with increasing n and m and buoyancy parameter ξ. When buoyancy parameter ξ is very small (large) the value of local Nusselt and the local Sherwood number correspond with the pure forced (free) convection, respectively. Increasing buoyancy ratio N (or N ^*) increases the local heat and mass transfer rates. It is apparent that Lewis number has a pronounced effect on the local mass transfer rate than it does on the local heat transfer rate. Furthermore, increasing Lewis number decreases (increases) the local heat (mass) transfer rate. Received on 8 December 1997     

A numerical study based on a weakly compressible formulation for thermosolutal convection in vertical cavities

Laminar thermosolutal convection in cavities with uniform, constant temperature and mass fraction profiles at the vertical side is studied numerically. The study is conducted in the case where an inert carrier gas (species “1”) present in the cavity is not soluble in species “2”, and do not diffuse into the walls. A mass flux of species “2” into the cavity occurs at the hot vertical wall and a mass flux out of the cavity occurs at the opposite cold wall. The weakly compressible model proposed in this work was used to investigate the flow fields, and heat and mass transfer in cavities filled with binary mixtures of ideal gases. The dimensionless form of the seven governing equations for constant thermophysical properties, except density, show that the problem formulation involves ten dimensionless parameters. The results were validated against numerical results published in the literature for purely thermal convection, and thermodynamic predictions for transient thermosolutal flows. A parametric study has been performed to investigate the effects of the initial conditions, molecular weight ratio, Lewis number, and aspect ratio of the cavity for aiding or opposing buoyancy forces. For the range of parameters considered, the results show that variations in the density field have larger effects on mass transfer than on heat transfer. For opposing buoyancy forces, the numerical simulations predict complex flow structures and possible chaotic behavior for rectangular vertical cavities according to the value of the molecular weight ratio.     

Effect of vapor condensation on forced convection heat transfer of moistened gas

The forced convection heat transfer with water vapor condensation is studied both theoretically and experimentally when wet flue gas passes downwards through a bank of horizontal tubes. Extraordinarily, discussions are concentrated on the effect of water vapor condensation on forced convection heat transfer. In the experiments, the air–steam mixture is used to simulate the flue gas of a natural gas fired boiler, and the vapor mass fraction ranges from 3.2 to 12.8%. By theoretical analysis, a new dimensionless number defined as augmentation factor is derived to account for the effect of condensation of relatively small amount of water vapor on convection heat transfer, and a consequent correlation is proposed based on the experimental data to describe the combined convection–condensation heat transfer. Good agreement can be found between the values of the Nusselt number obtained from the experiments and calculated by the correlation. The maximum deviation is within ±6%. The experimental results also shows that the convection–condensation heat transfer coefficient increases with Reynolds number and bulk vapor mass fraction, and is 1∼3.5 times that of the forced convection without condensation.     

浮力对混合对流流动及换热特性的影响

用热线和冷线相结合的技术测量垂直圆管内逆混合对流流体的平均速度、 温度以及它们的脉动. 较详细地研究了浮力对逆混合对流的流动特性和传热特性的影响. 评 估了实验中采用的冷线测量温度补偿速度探头温度敏感的影响. 逆混合对流的传热结果用无 量纲参数Ω (Ω= Grd / Red2 )来表示，其中，基于管道直 径的雷诺数Red变化范围为900~18000, 浮力参数Ω变化范围为 0.004899~0.5047. 研究结果表明，浮力对逆混合对流的换热有强化作用. 随着葛拉晓夫数Grd的增加，温度脉动，流向雷诺正应力和流向温度通量增 大，并且在靠近壁面的流体区域尤其明显. 热线与冷线相结合的技术适合于研究非绝热的流 动测量，可以用于研究浮力对流动和换热特性的影响.     

Effect of thermo‐solutal stratification on recirculation flow patterns in a backward‐facing step channel flow

This paper presents results on the combined effect of thermo‐solutal buoyancy forces on the recirculatory flow behavior in a horizontal channel with backward‐facing step and the ensuing impact on heat and mass transfer phenomena. The governing equations for double diffusive mixed convection are represented in velocity–vorticity form of momentum equations, velocity Poisson equations, energy and concentration equations. Galerkin's finite‐element method has been employed to solve the governing equations. Recirculatory flow fields with heat and mass transfer are simulated for opposing and aiding thermo‐solutal buoyancy forces by assuming suitable boundary conditions for energy and concentration equations. The effect of Richardson number (0.1?Ri?10) and buoyancy ratio (?10?N?10) on the recirculation bubble and Nusselt and Sherwood numbers are studied in detail. For Richardson number greater than unity, distinct variations in the gradients of Nusselt number and Sherwood number with buoyancy ratio are observed for flow regimes with opposing and aiding buoyancy forces. Copyright © 2009 John Wiley & Sons, Ltd.     

Buoyancy effects on mixed convection heat and mass transfer in a duct with sudden expansions

The present paper deals with the study of heat and mass transfer by mixed convection in an inclined duct preceded with a double step expansion. The control volume based finite element method was used to solve the set of non-dimensional equations for the vorticity, stream function, energy and species conservation. Numerical simulations are carried out for different combinations of the Lewis number, thermal and mass diffusion Grashof numbers for different inclinations. Streamlines, temperature and concentration distributions are presented and discussed. The results show the effect of the secondary flow induced by buoyancy forces and the presence of the double step expansion on the heat and mass transfer mechanism. It is found that the recirculation vortices induced by the expansion can be present along the channel and the flow structure can be wavy. For the vertical orientation, asymmetric fields are observed for the different simulated cases.     

Triple-Diffusive Mixed Convection in a Porous Open Cavity

The triple-diffusive mixed convection heat and mass transfer of a mixture is analyzed in an enclosure filled with a Darcy porous medium. The mass transfer buoyancy effects due to concentration gradients of the dispersed components (pollutant components) are taken into account using the Boussinesq approximation model. The governing equations are transformed into a non-dimensional form, and six groups of non-dimensional parameters, including Darcy–Rayleigh number, Peclet number, two Lewis numbers for pollutant components 1 and 2 and two buoyancy ratio parameters for pollutant components 1 and 2, are introduced. The governing equations are numerically solved for various combinations of non-dimensional parameters using the finite element method. The effect of each group of non-dimensional parameters on the pollutant distribution and the heat transfer in the cavity is discussed. The results indicate that the presence of one pollutant component can significantly affect the pollutant distribution of the other component. When the Lewis number of a pollutant component is small, the increase in the bouncy ratio parameter of the proposed component always increases the Nusselt and Sherwood numbers in the cavity.     

Simultaneous heat and mass transfer by natural convection from a plate embedded in a porous medium with thermal dispersion effects

The problem of steady, laminar, simultaneous heat and mass transfer by natural convection flow over a vertical permeable plate embedded in a uniform porous medium in the presence of inertia and thermal dispersion effects is investigated for the case of linear variations of both the wall temperature and concentration with the distance along the plate. Appropriate transformations are employed to transform the governing differential equations to a non-similar form. The transformed equations are solved numerically by an efficient implicit, iterative, finite-difference scheme. The obtained results are checked against previously published work on special cases of the problem and are found to be in good agreement. A parametric study illustrating the influence of the porous medium effects, heat generation or absorption, wall suction or injection, concentration to thermal buoyancy ratio, thermal dispersion parameter, and the Schmidt number on the fluid velocity, temperature and concentration as well as the skin-friction coefficient and the Nusselt and Sherwood numbers is conducted. The results of this parametric study are shown graphically and the physical aspects of the problem are highlighted and discussed.     

Unsteady natural convection heat and mass transfer in a saturated porous enclosure

A detailed numerical study has been performed to investigate transient natural convection heat and mass transfer in a porous enclosure. Major dimensionless groups governing the present problem areRa,N,Le, φ andAr. Results are particular presented to illustrate the effects of the combined thermal and solutal buoyancy forces on the temporal evolution of local/average Nusselt and Sherwood numbers. The results show that with the increase in the Rayleigh number, the heat and mass transfer is enhanced as a result of greater buoyancy effect. Additionally, the increase in buoyancy ratioN results in an improvement in the heat and mass transfer rates and in the mean time causes a short time duration for the flow to approach the steady-state condition.     

Mixed convection flow over a vertical wedge embedded in a highly porous medium

 The steady mixed convection flow over a vertical wedge with a magnetic field embedded in a porous medium has been investigated. The effects of the permeability of the medium, surface mass transfer and viscous dissipation on the flow and temperature fields have been included in the analysis. The coupled nonlinear partial differential equations governing the flow field have been solved numerically using the Keller box method. The skin friction and heat transfer are found to increase with the parameters characterizing the permeability of the medium, buoyancy force, magnetic field and pressure gradient. However the effect of the permeability and magnetic field on the heat transfer is very small. The heat transfer increases with the Prandtl number, but the skin friction decreases. The buoyancy force which assists the forced convection flow causes an overshoot in the velocity profiles. Both the skin friction and heat transfer increase with suction and the effect of injection is just the reverse. Received on 21 May 1999     

The Effects of Blowing and Suction on Double Diffusion by Mixed Convection over Inclined Permeable Surfaces

A boundary layer analysis is used to investigate the effect of lateral mass flux on mixed convection heat and mass transfer over inclined permeable surfaces in porous media. The conservation equations that govern the problem are reduced to a system of non-linear ordinary differential equations and then the resulting equations is solved by numerical method. The numerical results for heat and mass transfer in terms of Nusselt and Sherwood number are presented in x-y plots for the buoyancy ratio (N) and Lewis number (Le) with mass flux pammeter (Fw). The obtained results are validated against previously published results with on special case of the problem.     

Boundary layer flow and heat transfer over an unsteady stretching vertical surface

The solution to the unsteady mixed convection boundary layer flow and heat transfer problem due to a stretching vertical surface is presented in this paper. The unsteadiness in the flow and temperature fields is caused by the time-dependent of the stretching velocity and the surface temperature. The governing partial differential equations with three independent variables are first transformed into ordinary differential equations, before they are solved numerically by a finite-difference scheme. The effects of the unsteadiness parameter, buoyancy parameter and Prandtl number on the flow and heat transfer characteristics are thoroughly examined. Both assisting and opposing buoyant flows are considered. It is observed that for assisting flow, the solutions exist for all values of buoyancy parameter, whereas for opposing flow, they exist only if the magnitude of the buoyancy parameter is small. Comparison with known results for steady-state flow is excellent.     

Adverse and favorable mixed convection heat transfer in a two-side heated square channel

Experimental heat transfer measurements and analysis for mixed convection in a vertical square channel are presented. Water flow directions are selected such that buoyancy assists or opposes the bulk flow pressure gradient. Unlike most previous experiments with symmetrically heated circular tubes, the present configuration uses an asymmetric heating condition (two sides heated and two sides insulated) and shows significant increase in the Nusselt number for both assisted and opposed flow conditions. Observed heat transfer coefficient distributions are different from the symmetrically heated channels; and this difference in heat transfer coefficient is attributed to the formation of buoyancy driven large-scale flow structures. In general, opposed flow shows higher heat transfer coefficients, and the Nusselt number ratio is observed to increase as Gr/Re or Gr/Re² ratios increase for both assisted and opposed flow conditions. A correlation based on the buoyancy parameter predicts the heat transfer pattern well in both assisted and opposed mixed convection. The range of Reynolds numbers discussed (Re=400–10,000) is of importance for direct numerical simulations and the details provided here can serve as the benchmark data required for complicated buoyancy affected turbulence simulations.