UNSTEADY MIXED CONVECTION WITH SORET AND DUFOUR EFFECTS PAST A POROUS PLATE MOVING THROUGH A BINARY MIXTURE OF CHEMICALLY REACTING FLUID

This study investigates the unsteady mixed convection flow past a vertical porous flat plate moving through a binary mixture in the presence of radiative heat transfer and nth-order Arrhenius type of irreversible chemical reaction by taking into account the diffusion-thermal (Dufour) and thermo-diffusion (Soret) effects. Assuming an optically thin radiating fluid and using a local similarity variable, the governing nonlinear partial differential equations have been transformed into a set of coupled nonlinear ordinary differential equations, which are solved numerically by applying shooting iteration technique together with fourth-order Runge-Kutta integration scheme. Graphical results for the dimensionless velocity, temperature, and concentration distributions are shown for various values of the thermophysical parameters controlling the flow regime. Finally, numerical values of physical quantities, such as the local skin-friction coefficient, the local Nusselt number, and the local Sherwood number are presented in tabular form.     

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.     

方腔内耦合传热传质非对称流动数值模拟

对带有质热源的方腔内流体传热传质进行数值研究。针对不同Ra、Nc、Sr和Df，探究对称方腔内流体传热传质的分岔特性。结果表明：存在临界Ra_c使流体流动形态发生转变，当Ra<Ra_c时，流体流线、温度场和浓度场对称分布；当Ra>Ra_c时，流体发生偏斜。增大浮升力，流体更易发生分岔现象。增强Soret和Dufour效应可增强传热对称性并增大流体发生分岔的临界Rayleigh数。     

Numerical simulation of asymmetric flow of coupled heat and mass transfer in a square cavity

The heat and mass transfer of fluid in a square cavity with a solutal and thermal source is numerically investigated. For different Rayleigh numbers, buoyancy ratio, Soret and Dufour numbers, the bifurcation characteristics of heat and mass transfer in a symmetrical square cavity are studied systematically. The results show that there is a critical Ra_c for onset of bifurcation that changes the fluid flow pattern. When Ra < Ra_c, the streamline, temperature and concentration are symmetrically distributed; when Ra > Ra_c, the transition from a symmetrical state to a stable asymmetric state is observed. The fluid is more prone to bifurcation with increasing of buoyancy. An increment to the Soret and Dufour effects enhances heat transfer symmetry and increases the critical Rayleigh number for breaking symmetry.     

A NEW CLASS OF SIMILARITY SOLUTIONS OF AN UNSTEADY ELECTRICALLY CONDUCTING FREE-FORCED CONVECTIVE FLOW IN A VERTICAL POROUS SURFACE WITH DUFOUR AND SORET EFFECTS

The 2-D unsteady magnetohydrodynamic free-forced convective boundary layer flow of a viscous incompressible fluid is studied numerically taking into account heat and mass transfer. The fluid is subjected to uniform heat and mass fluxes embedded in a porous medium by the presence of coupled Dufour and Soret effects. A new class of similarity equations has been obtained by introducing a time-dependent length scale and a corresponding similarity variable. The resulting equations are then integrated numerically using the Nachtsheim-Swigert shooting iteration technique along with the sixth-order Runge-Kutta integration scheme. By developing locally similar solutions of the fluid flow, the behavior of the velocity, temperature, and concentration fields as well as the rate of heat transfer, wall temperature gradient, rate of mass transfer, and skin friction coefficient have been investigated. The effects of Grashof number (Gr), modified Grashof number (Gm), combined effects of the porous and magnetic parameter (S), suction/injection parameter Fw, Brinkman number (Br), Soret number (Sr), and Dufour number (D_f) have been observed on the flow field and discussed.     

多物理场中热扩散效应对传热传质的影响

为了便于消除或控制室内挥发性有机化合物(VOCs),分析了VOCs在室内环境中的扩散规律。基于不可逆过程热力学原理,在考虑交叉耦合扩散效应的基础上,建立了3个物理量的梯度驱动下封闭空间内自然对流传热传质的数学模型。采用数值方法研究了室内环境中同时存在温度梯度、湿度梯度和VOCs浓度梯度时的自然对流传热传质现象,并着重考察了多物理量的梯度耦合作用下热附加扩散效应对传热传质的影响,展示了流场、温度场和浓度场等热附加扩散准则数STC的变化状况,研究结果表明,多物理场中热附加扩散效应对传热传质具有一定的影响,且具有复杂多解性。     

错流降膜液体干燥剂除湿/再生传热传质数学模型及分析

分析了错流降膜液体干燥剂除湿及再生传热传质过程 ,建立了基于实际除湿系统的描述再生和除湿过程的数学模型 ,考虑到除湿过程中产生的热效应 ,以氯化钙溶液为除湿剂时 ,对气侧和液侧的传热传质系数进行了理论和数值求解 .计算结果表明 ,传热传质系数与气流流动状态、除湿剂的热物理性质等因素有关     

SORET AND DUFOUR EFFECTS IN A FREE CONVECTIVE DOUBLY STRATIFIED FLOW OVER A VERTICAL PLATE WITH CHEMICAL REACTION

An investigation was performed to study the influence of thermo-diffusion and diffusion-thermo effects in the transient, free convective flow of a viscous, incompressible, and doubly stratified fluid past an isothermal vertical plate in the presence of first-order chemical reaction. The governing boundary layer equations were solved numerically using an implicit finite difference scheme of the Crank-Nicolson type. The effects of the Soret number, Dufour number, thermal stratification parameter, mass stratification parameter, and chemical reaction parameter are analyzed and presented graphically. Also, the influence of the parameters on local as well the average skin-friction coefficient and the rate of heat and mass transfer are analyzed and discussed. The results are compared with particular solutions available in the literature. The present results are found to be in good agreement with the existing solution.     

Thermal Diffusion and MHD Effects on Combined Free‐Forced Convection and Mass Transfer of a Viscous Fluid Flow Through a Porous Medium with Heat Generation

The problem of thermal diffusion and magnetic field effects on combined free‐forced convection and mass transfer flow past a vertical porous flat plate, in the presence of heat generation is studied numerically. The governing momentum, energy and concentration equations are converted into a system of nonlinear ordinary differential equations by means of similarity transformations. The resulting system of coupled nonlinear ordinary differential equations is solved numerically by using the Shooting method. Numerical results are presented for velocity, temperature and concentration profiles within the boundary layer for different parameters of the problem including suction parameter, heat generation parameter, Soret number, Dufour number, magnetic parameter, etc. In addition, the effects of the pertinent parameters on the skin friction and the rates of heat and mass transfer are discussed numerically and illustrated graphically.     

Cu and Cu-SWCNT Nanoparticles’ Suspension in Pulsatile Casson Fluid Flow via Darcy–Forchheimer Porous Channel with Compliant Walls: A Prospective Model for Blood Flow in Stenosed Arteries

The use of experimental relations to approximate the efficient thermophysical properties of a nanofluid (NF) with Cu nanoparticles (NPs) and hybrid nanofluid (HNF) with Cu-SWCNT NPs and subsequently model the two-dimensional pulsatile Casson fluid flow under the impact of the magnetic field and thermal radiation is a novelty of the current study. Heat and mass transfer analysis of the pulsatile flow of non-Newtonian Casson HNF via a Darcy–Forchheimer porous channel with compliant walls is presented. Such a problem offers a prospective model to study the blood flow via stenosed arteries. A finite-difference flow solver is used to numerically solve the system obtained using the vorticity stream function formulation on the time-dependent governing equations. The behavior of Cu-based NF and Cu-SWCNT-based HNF on the wall shear stress (WSS), velocity, temperature, and concentration profiles are analyzed graphically. The influence of the Casson parameter, radiation parameter, Hartmann number, Darcy number, Soret number, Reynolds number, Strouhal number, and Peclet number on the flow profiles are analyzed. Furthermore, the influence of the flow parameters on the non-dimensional numbers such as the skin friction coefficient, Nusselt number, and Sherwood number is also discussed. These quantities escalate as the Reynolds number is enhanced and reduce by escalating the porosity parameter. The Peclet number shows a high impact on the microorganism’s density in a blood NF. The HNF has been shown to have superior thermal properties to the traditional one. These results could help in devising hydraulic treatments for blood flow in highly stenosed arteries, biomechanical system design, and industrial plants in which flow pulsation is essential.     

The Soret and Dufour Effects in Non-thermal Equilibrium Packed Beds with Forced Convection and Endothermic Reactions

To study the influence of the Soret and Dufour effects on the reactive characteristics of a porous packed bed with endothermic reactions and forced convection, a two-dimensional mathematical model cons...     

HEAT AND MASS TRANSFER IN STAGNATION-POINT FLOW OF A POLAR FLUID TOWARDS A STRETCHING SURFACE IN POROUS MEDIA IN THE PRESENCE OF SORET,DUFOUR AND CHEMICAL REACTION EFFECTS

This work is focused on the numerical solution of steady boundary-layer stagnation-point flow of a polar fluid towards a stretching surface embedded in porous media in the presence of the effects of Soret and Dufour numbers and first-order homogeneous chemical reaction. The governing boundary-layer equations of the problem are formulated and transformed into a self-similar form. The obtained equations are solved numerically by an efficient, iterative, tri-diagonal, implicit finite-difference method. Both assisting and opposing flow conditions are considered. Comparisons of the present numerical results with previously published work under limiting cases are performed and found to be in excellent agreement. Representative results for the fluid velocity, angular velocity, temperature, and solute concentration profiles as well as the local heat and mass transfer rates for various values of the physical parameters are displayed in both graphical and tabular forms.     

Mass transfer from a contaminated fluid sphere

The unsteady mass transfer from a contaminated fluid sphere moving in an unbounded fluid is examined numerically for unsteady‐state transfer. The effect of the interface contamination and the flow regime on the concentration profiles, inside and outside a fluid sphere, is investigated for different ranges of Reynolds number (0 < Re < 200) and Peclet number (0 < Pe < 10⁵), viscosity ratio between the dispersed phase and the continuous phase (0 < κ < 10), and the stagnant‐cap angle (0° < θ_cap < 180°). It was found that the stagnant‐cap angle significantly influences the mass transfer from the sphere to a surrounding medium. For all Peclet and Reynolds numbers and κ, the contamination reduces the mass transfer flux. The average Sherwood number increases with an increase of stagnant‐cap angle and reaches a maximum equal to the average one for a clean fluid sphere at low viscosity ratio and large Peclet numbers. A predictive equation for the Sherwood number is derived from these numerical results. © 2010 American Institute of Chemical Engineers AIChE J, 2011     

THE EFFECT OF THERMAL RADIATION ON THE HEAT AND MASS TRANSFER FLOW OF A VARIABLE VISCOSITY FLUID PAST A VERTICAL POROUS PLATE PERMEATED BY A TRANSVERSE MAGNETIC FIELD

The effect of temperature-dependent viscosity on free convective flow past a vertical porous plate is studied in the presence of a magnetic field, thermal radiation, and a first-order homogeneous chemical reaction. Boundary layer equations are derived and the resulting approximate nonlinear ordinary differential equations are solved numerically by the shooting method. A parametric study of all parameters involved is conducted, and a representative set of numerical results for the velocity and temperature profiles as well as the skin-friction parameter and the Nusselt and Sherwood numbers is illustrated graphically to show typical trends of the solutions. The dynamic viscosity in this study is taken as a function of the temperature although the Prandtl number is considered constant.     

Viscous flow through particle assemblages at intermediate reynolds numbers — a cell model for transport in bubble swarms

The fluid mechanical behaviour of a bubble swarm was simulated using a cell model. The Navier-Stokes equations were solved numerically for the liquid flow in a uniform assemblage of circulating, spherical bubbles. Ranges of parameters studied included, Reynolds numbers, 0–1000 and porosities, 0.4–1. The numerical calculations show the effects of variations in Reynolds numbers and porosity on: surface vorticity and pressure distributions and form and friction drag coefficients. For all Reynolds numbers investigated a standing vortex ring was absent Predicted drag coefficients and Sherwood or Nusselt numbers agree with limiting analytical solutions for low and high Reynolds numbers. The theoretical results show good agreement with experimental data for porosity as a function of superficial gas velocity. Predicted and measured Sherwood and Nusselt Numbers were in substantial disagreement, making detailed comparison unwarranted The calculations should also be valid for dispersions of uniform, circulating, spherical droplets for the special case where the droplet viscosity is much less than the viscosity of the continuous fluid     

Soret Diffusion and Non‐Ideal Dufour Conduction in Macroporous Catalysts with Exothermic Chemical Reaction at Large Intrapellet Damköhler Numbers

The adiabatic temperature rise in catalytic pellets is predicted from a modified version of the Prater equation. Onsager reciprocal relations for coupled heat and mass transfer are violated in an analysis of thermal diffusion in macroporous catalysts with exothermic chemical reaction when Dufour conduction (i.e., the diffusion‐thermo effect) is neglected. In this contribution, Dufour conduction is analyzed for both ideal and non‐ideal pseudo‐binary gas mixtures that simulate the production of methanol from carbon monoxide and hydrogen. In the diffusion‐controlled regime at large intrapellet Damköhler numbers where intermolecular collisions provide the dominant resistance to mass transfer within the catalytic pores, temperatures in the catalytic core could be much greater than predictions based on the original Prater equation when the Prater number exceeds 0.30. The molecular flux of thermal energy includes Fourier's law, the interdiffusional flux, and Dufour conduction. Diffusional mass flux includes Fick's law and the Soret effect. All physicochemical properties of the reactive gas mixture exhibit temperature dependence. There is essentially no difference between maximum intrapellet temperature predictions that include or neglect ideal Dufour conduction when external catalytic surface temperatures range from 300‐400 K and thermal diffusion enhances the flux of “smaller” reactants toward the centre of the catalyst. For “large‐molecule reactants” that participate in exothermic reactions, thermal diffusion opposes Fick's law and Dufour conduction opposes Fourier's law. Under these conditions, it is demonstrated that core temperatures are overestimated by neglecting both off‐diagonal coupling mechanisms (i.e., Soret diffusion and Dufour conduction). Prater numbers greater than unity and unrealistically high gas pressures are required to distinguish between maximum intrapellet temperatures for ideal and real gas simulations, where the latter consider two‐body interactions for Lennard‐Jones molecules in the virial equation of state.     

Kinetic theory based computation of PSRI riser: Part II—Computation of mass transfer coefficient with chemical reaction

The design of circulating fluidized bed systems requires the knowledge of mass transfer coefficients or Sherwood numbers. A literature review shows that these parameters in fluidized beds differ up to seven orders of magnitude.To understand the phenomena, a kinetic theory based computation was used to simulate the PSRI challenge problem I data for flow of FCC particles in a riser, with an addition of an ozone decomposition reaction. The mass transfer coefficients and the Sherwood numbers were computed using the concept of additive resistances. The Sherwood number is of the order of 4 × 10⁻³ and the mass transfer coefficient is of the order of 2 × 10⁻³ m/s, in agreement with the measured data for fluidization of small particles and the estimated values from the particle cluster diameter in part one of this paper. The Sherwood number is high near the inlet section, then decreases to a constant value with the height of the riser. The Sherwood number also varies slightly with the reaction rate constant. The conventionally computed Sherwood number measures the radial distribution of concentration caused by the fluidized bed hydrodynamics, not the diffusional resistance between the bulk and the particle surface concentration. Hence, the extremely low literature Sherwood numbers for fluidization of fine particles do not necessarily imply very poor mass transfer.     

Re-evaluation of the Nusselt number for determining the interfacial heat and mass transfer coefficients in a flow-through monolithic catalytic converter

The two-equation porous medium model has been widely employed for modeling the flow-through monolithic catalytic converter. In this model, the interfacial heat and mass transfer coefficients have been usually obtained using the asymptotic Nusselt and Sherwood numbers with some suitable assumptions. However, previously it seemed that there existed some misunderstanding in adopting these Nusselt and Sherwood numbers. Up to now, the Nusselt number based on the fluid bulk mean temperature has been used for determining the interfacial heat and mass transfer coefficients. However, the mass and energy balance formulations in the two-equation model indicate that the Nusselt number should be evaluated based on the fluid mean temperature instead of the fluid bulk mean temperature. Therefore, in this study, to correctly model the heat and mass transfer coefficients, the Nusselt number based on the fluid mean temperature was newly obtained for the square and circular cross-sections under two different thermal boundary conditions (i.e., constant heat flux and constant temperature at the wall). In order to do that, the present study employed the numerical as well as analytical method.     

Free convective flow over a vertical plate in a doubly stratified medium with electrophoresis, heat source/sink and chemical reaction effects

We analyzed the problem of unsteady, incompressible free convective doubly stratified flow past a semiinfinite vertical plate with the influence of electrophoresis, heat source/sink and chemical reaction. The partial differential equations governing the flow are solved by employing an implicit finite difference scheme of Crank-Nicolson type. The effect of heat generation and absorption in stratified and unstratified flow are examined and hence the influence of stratification on velocity, temperature and concentration are investigated and presented graphically. Further, the impact of the electrophoresis on particle concentration in the presence of generative and destructive reaction is analyzed. As well, the effects of the physical parameters on local and average values of skin friction, Nusselt number and Sherwood number are also investigated and illustrated graphically. The particular solutions of the present results are compared with the existing solution in literature and are found to be in good agreement.     

在有方形障碍物的方腔中对双扩散自然对流的玻尔兹曼晶格模拟(英文)

Double diffusion convection in a cavity with a hot square obstacle inside is simulated using the lattice Boltzmann method. The results are presented for the Rayleigh numbers 104,105 and 106, the Lewis numbers 0.1, 2 and 10 and aspect ratio A (obstacle height/cavity height) of 0.2, 0.4 and 0.6 for a range of buoyancy number N=0 to?4 with the effect of opposing flow. The results indicate that for|N|b 1, the Nusselt and Sherwood numbers decrease as buoyancy ratio increases, while for|N|N 1, they increase with|N|. As the Lewis number increases, higher buoyan-cy ratio is required to overcome the thermal effects and the minimum value of the Nusselt and Sherwood num-bers occur at higher buoyancy ratios. The increase in the Rayleigh or Lewis number results in the formation of the multi-cell flow in the enclosure and the vortices wil vanish as|N|increases.