考虑Soret和Dufour效应的方腔内双扩散自然对流格子Boltzmann模拟

采用格子Boltzmann方法,考虑Soret和Dufour效应,对内置高浓度发热圆的方腔内部双扩散自然对流现象进行数值模拟.高浓度发热圆位于方腔中心,四周壁面均为低温低浓度.在该模型中,用三个独立的LBGK方程分别模拟速度场、温度场和浓度场,并通过Boussinesq近似将它们耦合起来.分析Soret数和Dufour数对方腔内部双扩散自然对流的影响,得到流线图、等温线图、等浓度线图、发热圆表面平均Nusselt数和平均Sherwood数.结果表明：Soret和Dufour效应对方腔内双扩散自然对流影响明显,不能忽略.     

Mixed Convection Heat and Mass Transfer in a Micropolar Fluid with Soret and Dufour Effects

A mathematical model for the steady, mixed convection heat and mass transfer along a semi-infinite vertical plate embedded in a micropolar fluid in the presence of Soret and Dufour effects is presented. The non-linear governing equations and their associated boundary conditions are initially cast into dimensionless forms using local similarity transformations. The resulting system of equations is then solved numerically using the Keller-box method. The numerical results are compared and found to be in good agreement with previously published results as special cases of the present investigation. The non-dimensional velocity, microrotation, temperature and concentration profiles are displayed graphically for different values of coupling number, Soret and Dufour numbers. In addition, the skin-friction coefficient, the Nusselt number and Sherwood number are shown in a tabular form.     

Mixed Convective Viscoelastic Nanofluid Flow Past a Porous Media with Soret-Dufour Effects

The present study is carried out to see the thermal-diffusion (Dufour) and diffusion-thermo (Soret) effects on the mixed convection boundary layer flow of viscoelastic nanofluid flow over a vertical stretching surface in a porous medium. Optimal homotopy analysis method (OHAM) is best candidate to handle highly nonlinear system of differ-ential equations obtained from boundary layer partial differential equations via appropriate transformations. Graphical illustrations depicting different physical arising parameters against velocity, temperature and concentration distributions with required discussion have also been added. Numerically calculated values of skin friction coefficient, local Nusselt and Sherwood numbers are given in the form of table and well argued. It is found that nanofluid velocity increases with increase in mixed convective and viscoelastic parameters but it decreases with the increasing values of porosity parameter. Also, it is observed that Dufour number has opposite behavior on temperature and concentration profiles.     

Cross-diffusive effects on the onset of double-diffusive convection in a horizontal saturated porous fluid layer heated and salted from above

Double-diffusive stationary and oscillatory instabilities at the marginal state in a saturated porous horizontal fluid layer heated and salted from above are investigated theoretically under the Darcy's framework for a porous medium. The contributions of Soret and Dufour coefficients are taken into account in the analysis. Linear stability analysis shows that the critical value of the Darcy-Rayleigh number depends on cross-diffusive parameters at marginally stationary convection, while the marginal state characterized by oscillatory convection does not depend on the cross-diffusion terms even if the condition and frequency of oscillatory convection depends on the cross-diffusive parameters. The critical value of the Darcy-Rayleigh number increases with increasing value of the solutal Darcy-Rayleigh number in the absence of cross-diffusive parameters. The critical Darcy-Rayleigh number decreases with increasing Soret number, resulting in destabilization of the system, while its value increases with increasing Dufour number, resulting in stabilization of the system at the marginal state characterized by stationary convection. The analysis reveals that the Dufour and Soret parameters as well as the porosity parameter play an important role in deciding the type of instability at the onset. This analysis also indicates that the stationary convection is followed by the oscillatory convection for certain fluid mixtures. It is interesting to note that the roles of cross-diffusive parameters on the double-diffusive system heated and salted from above are reciprocal to the double-diffusive system heated and salted from below.     

多孔介质传热传质中耦合扩散效应的研究

本文采用加罚函数有限元方法数值模拟在温度梯度和浓度梯度同时存在时双浮升力自然对流及其伴随的传热传质,着重探讨了多孔介质中传热传质的交叉耦合扩散Soret效应和Dufour效应的基本影响规律,展示了流场、温度场和浓度场随热附加扩散准则数和扩散附加热准则数的变化状况。     

Combined effects of viscous dissipation and MHD on free convection flow past a semi-infinite vertical plate with variable surface temperature in the presence of heat source

An unsteady MHD laminar viscous dissipative fluid flow past a semi-infinite vertical plate with variable surface temperature in the presence of heat source is considered in the present analysis. The present approach transforms the governing boundary layer equations into nondimensional form using the appropriate nondimensional quantities, which is valid in the free convection region. The resulting governing equations are solved numerically using the Crank–Nicolson method, an efficient implicit finite-difference scheme. Numerical results are obtained and presented in the form of local as well as average shearing stress, local and average heat transfer rate, velocity and temperature during the transient period. The present results are compared with the available results in the literature and are found to be in an excellent agreement.     

Significance of Stefan blowing effect on flow and heat transfer of Casson nanofluid over a moving thin needle

The current mathematical model explains the influence of non-linear thermal radiation on the Casson liquid flow over a moving thin needle by considering Buongiorno's nanofluid model.The influences of Stefan blowing, Dufour and Soret effects are also considered in the model. The equations which represent the described flow pattern are reduced to ordinary differential equations(ODEs) by using apt similarity transformations and then they are numerically solved with Runge–Kutta-Fehlberg's fourth fifth-order method(RKF-45) with shooting process. The impacts of pertinent parameters on thermal, mass and velocity curves are deliberated graphically.Skin friction, rate of heat and mass transfer are also discussed graphically. Results reveal that, the increase in values of Brownian motion, thermophoresis, Dufour number, heating and radiative parameters improves the heat transfer. The increasing values of the Schmidt number deteriorates the mass transfer but a converse trend is seen for increasing values of the Soret number. Finally,the escalating values of the radiative parameter decays the rate of heat transfer.     

Convective and peristaltic viscous fluid flow with variable viscosity

In the present investigation we have analyzed the peristaltic flow when the viscous fluid with variable viscosity is bounded with convective walls. The combined effects of thermaldiffusion (Soret effects) and diffusion-thermo (Dufour effect) are considered. Convective form of the heat and mass transport phenomenon has been given special attention in addition to the effects of magnetic field. Mathematical formulation for the physical systemis derived and simplified using long wavelength and low Reynolds number approximation. Series solutions for the velocity, temperature andmass concentration fields are computed and elaborated for different physical quantities including magnetic parameter, Soret and Dufour effects, Biot numbers, etc. Streamlines analysis is presented showing the effects of bolus movement.     

Thermal-diffusion and diffusion-thermo effects on combined heat and mass transfer by hydromagnetic three-dimensional free convection over a permeable stretching surface with radiation

The thermal-diffusion and diffusion-thermo effects on the heat and mass transfer characteristics of free convection past a continuously stretching permeable surface in the presence of magnetic field, blowing/suction and radiation are studied. The fluid viscosity is assumed to vary with temperature. The resulting, governing three-dimensional equations are transformed using a similarity transformation and then solved numerically by the shooting method. Comparison with previously published work is performed and full agreement is obtained. A parametric study showing the effects of variable viscosity parameter β, magnetic parameter M, Dufour number Df, Soret number Sr, radiation parameter R and blowing/suction parameter f₀ on the velocity, temperature, and concentration field of a hydrogen-air mixture as a non-chemical reacting fluid pair, as well as the local skin-friction coefficient, the local Nusselt number, and the local Sherwood number is carried out. These are illustrated graphically and in tabular form to depict special features of the solutions.     

Joule heating and viscous dissipation effects on MHD flow past a semi-infinite inclined plate with variable surface temperature

A numerical investigation is performed to study the MHD free convection flow past a semi-infinite inclined plate subjected to a variable surface temperature. The Joule heating and viscous dissipation effects are taken into account in the energy equation. The governing equations of the flow are transformed into a nondimensional form using suitable dimensionless quantities. A fully developed implicit finite-difference scheme of Crank-Nicolson type is engaged to solve the dimensionless governing equations, which is more accurate, fast convergent, and unconditionally stable. The effects of the MHD, inclination angle, power law, Grashof number, Prandtl number, Joule heating, and viscous dissipation effects are studied on the velocity, temperature, shear stress, and heat transfer coefficients during transient periods. It is observed that the MHD has retarding effects on velocity.     

分离比对混合流体Rayleigh-Bénard对流解的影响

混合流体Rayleigh-Bénard对流是研究非平衡对流的非线性动力学特性的典型模型之一.基于流体力学方程组的数值模拟,首先探讨了矩形腔体中具有强Soret效应(分离比Ψ=-0.60)的混合流体行波对流的分叉特性及斑图演化,沿着分叉曲线的上部分支,随着相对瑞利数的增加,此系统依次出现了局部行波对流、具有缺陷的行波对流、行波对流、摆动行波对流及定常对流5种行波对流解.然后,研究了分离比Ψ对对流解的影响,与弱Soret效应(Ψ=-0.11)时的对流解相比较,强Soret效应(Ψ=-0.60)时出现的对流解更丰富.由于有强Soret效应的对流的复杂性,Ψ=-0.60时的对流解与Ψ=-0.20,-0.4时的对流解不同.     

THERMOSOLUTAL CONVECTION WITH COUPLED HEAT AND MASS TRANSFER PROCESS IN A SQUARE ENCLOSURE

Thermosolutal convection flow and its effect on the heat and the mass transfer in a square enclosure is studied experimentally. Both thermal and solute diffusion are induced from the sides, and natural convection is initiated by the combined thermal and solutal buoyancies, which either augment or oppose to each other. The solute diffusion is initiated in an electrochemical system that uses copper sulfate-sulfuric acid solution as an electrolyte. Depending on the magnitude of buoyancy ratio, three different kinds of flow regimes and structures can occur, which lead to different distributions of concentration in the enclosure. The formation and growth of layered flow structure is attributed to the solutal boundary-layer flow that can intrude and accumulate along the horizontal wall. The nearly stagnant layer that occurs can reduce the heat transfer rate. The Nusselt numbers at different flow regimes are measured and correlated in terms of relevant nondimensional parameters. This suggests the correlation of Sherwood number in different ranges of buoyancy ratio. The visualization of flow structures and measurements of both heat and mass transfer allow better understanding of the complicated system.     

饱和含混多孔介质中环绕水平圆柱的自然对流

本文运用达西流模型，对饱和含湿多孔介质中环绕水平等温圆柱发生的自然对流进行了数值模拟和分析。流函数和温度分布采用傅里叶级数的形式，以联立求解二维流动的控制方程组，傅里叶级数项的系数由一维常微分方程的解得到。文中同时给出局部和平均努谢尔数随修正瑞利数的变化关系以及修正瑞利数处在０．１～１０范围内时二维流场和温度场分布。     

旋转环形浅液池内双组分溶液耦合热-溶质毛细对流渐近解

为了了解水平温度梯度作用下旋转环形浅液池内耦合热-溶质毛细对流基本特征, 采用匹配渐近展开法对旋转环形浅液池内耦合热-溶质毛细对流过程进行了求解, 获得了中心区域的速度、温度和浓度分布,分析了旋转、Soret效应、浮力、溶质扩散 系数和液池的几何尺寸对流动结构的影响.将所得到的渐近解和文献中的已有结果进行对比,证明了所求结果的正确性;在浅液池内,耦合热-溶质毛细力对流体流动起主导作用, 旋转和浮力对流动的影响较小,溶质扩散系数和几何尺寸有较明显影响;当各种耦合的 驱动力作用方向相同时,流动增强;否则, 流动减弱. 关键词： 旋转 环形浅液池 耦合热-溶质毛细对流 渐近解     

Modeling the onset of thermosolutal convective instability in a non-Newtonian nanofluid-saturated porous medium layer

The onset of double-diffusive (thermosolutal) convection in horizontal porous layer saturated with an incompressible couple stress nanofluid saturated is studied with thermal conductivity and viscosity dependent on the nanoparticle volume fraction. To represent the momentum equation for porous media, a modified Darcy-Maxwell nanofluid model incorporating the effects of Brownian motion and thermophoresis has been used. The thermal energy equation includes regular diffusion and cross diffusion (Soret thermo-diffusion and Dufour diffuso-thermal) terms. A linear stability analysis depends on the normal mode technique and the onset criterion for stationary and oscillatory convection is derived analytically. The nonlinear theory based on the representation of the Fourier series method is applied to capture the behavior of heat and mass transfer. It is found that the couple stress parameter enhances the stability of the system in both the stationary and oscillatory convection modes. The viscosity ratio and conductivity ratio both enhance heat and mass transfer. Transient Nusselt number is found to be oscillatory when time is small. However, when time becomes very large, all the three transient Nusselt number values approach to their steady state values.     

Soret效应对具有自由表面的圆柱形浅池内双组分溶液热对流影响的实验研究

为了探究Soret效应对具有自由表面的圆柱形浅液池内双组分溶液热对流过程的影响, 通过实验观察了质量分数为50%的正癸烷/正己烷混合溶液在不同深宽比的液池内流动失稳后的自由表面耗散结构及液池内的温度波动. 结果表明, 双组分溶液流动失稳的临界热毛细Reynolds数小于纯工质的值, 且其随液层深宽比的变化规律与纯工质相同. 当深宽比小于0.0848时, 流动失稳后在自由表面观察到热流体波, 监测点处温度波动主频随热毛细Reynolds数增大而增加; 当深宽比大于0.0848时, 随热毛细Reynolds数的增大, 流动失稳后自由表面依次呈现轮辐状、花苞状、分离-合并-分离交替变化的条纹状结构.     

Analytical and numerical exploration of oscillatory convection in porous media

This study is part of the research about the influence of the thermal gradient on the composition and the stability of fluids in geological environments. This paper presents modelling results of oscillatory convection in a porous medium using the METSOR code. The model solves the heat and mass transport equations in a porous medium and takes into account the Soret effect (mass transport under thermal gradient). Oscillatory convection may occur in pure fluids and in binary mixtures (as a consequence of the Soret effect). Experimental data confirm the existence of this phenomenon in porous media. Here, the outputs of the METSOR code are verified against existing analytical solutions. A first modelling attempt of oscillatory convection in mixtures is presented (salt aquifer).     

非牛顿流体沿竖直平板自然对流传热的计算研究

非牛顿幂次流体沿竖直平板层流自然对流为非线性两点边值问题,其速度场与温度场需耦合求解。采用几种数值方法对该问题进行了计算,研究了各种普朗特数(Pr)及不同幂次流体对沿壁面平均努赛尔数(Nu)的影响变化,并与有关文献的结果进行了对比分析。     

Onsager Reciprocity in Premelting Solids

The diffusive motion of foreign particles dispersed in a premelting solid is analyzed within the framework of irreversible thermodynamics. We determine the mass diffusion coefficient, thermal diffusion coefficient and Soret coefficient of the particles in the dilute limit, and find good agreement with experimental data. In contrast to liquid suspensions, the unique nature of premelting solids allows us to derive an expression for the Dufour coefficient and independently verify the Onsager reciprocal relation coupling diffusion to the flow of heat.     

On convection phenomena during high pressure treatment of liquid media

In the current contribution, investigations of the high hydrostatic pressure process up to 400 MPa and temperatures up to 353 K are carried out by means of dimensional analysis. The thermofluiddynamical mechanisms are analysed for three different sizes of a high pressure chamber, two different pressure generation systems and two model-fluids that differ in viscosity. Forced convection during compression/decompression and free convection during constant pressure phase are considered separately. The results contain process parameter study based on dimensionless numbers derived from conservation equations of mass, momentum and energy. Either dimensionless process parameters or the fluid dynamical and thermodynamical time scales are presented as a function of pressure and temperature. Relations according to heat transfer and fluid flow mechanisms during high pressure treatment are discussed.