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     

A STUDY OF NON-NEWTONIAN FLOW AND HEAT TRANSFER OVER A NON-ISOTHERMAL WEDGE USING THE HOMOTOPY ANALYSIS METHOD

The thermoconvective boundary layer flow of a generalized third-grade viscoelastic power-law non-Newtonian fluid over a porous wedge is studied theoretically. The free stream velocity, the surface temperature variations, and the injection velocity at the surface are assumed variables. A similarity transformation is applied to reduce the governing partial differential equations for mass, momentum, and energy conservation to dimensionless, nonlinear, coupled, ordinary differential equations. The homotopy analysis method (HAM) is employed to generate approximate analytical solutions for the transformed nonlinear equations under the prescribed boundary conditions. The HAM solutions, in comparison with numerical solutions (fourth-order Runge-Kutta shooting quadrature), admit excellent accuracy. The residual errors for dimensionless velocity and dimensionless temperature are also computed. The influence of the “power-law” index on flow characteristics is also studied. The mathematical model finds important applications in polymeric processing and biotechnological manufacture. HAM holds significant promise as an analytical tool for chemical engineering fluid dynamics researchers, providing a robust benchmark for conventional numerical methods.     

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.     

SCALE ANALYSIS AND PARAMETRIC STUDY OF TRANSIENT HEAT/MASS TRANSFER IN THE PRESENCE OF NONPOROUS SOLID ADSORPTION

A transient, two-dimensional theoretical analysis of combined heat and mass transfer in the presence of adsorption/desorption is developed to study the fundamentals of heat and mass transfer dynamics. A parallel-plate rectangular channel is used as a model system. Appropriate surface boundary conditions for heat and mass transfer and adsorption/desorption interactions are formulated. A scale analysis of the governing equations is performed in order to identify the dimensionless physical parameters governing the process and to obtain the order-of-magnitude estimates for characteristic time constants of the system dynamics. Predictions of the scale analysis are validated against the results of the parametric study obtained through the numerical solutions of the governing equations. The findings demonstrate that the scale analysis is a very powerful analytical tool which allows one to evaluate the effects of different process parameters on heat and mass transfer dynamics in the presence of adsorption without performing the exhaustive numerical calculations.     

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.     

HEAT AND MASS TRANSFER IN THE ADSORBENT BED OF AN ADSORPTION HEAT PUMP

The heat and mass transfer equations governing an adsorbent bed in an adsorption heat pump and the mass balance equation for the adsorbent particles in the adsorbent bed were solved numerically to simulate the cycle of a basic adsorption heat pump, which includes isobaric adsorption, isosteric heating, isobaric desorption, and isosteric cooling processes. The finite difference method was used to solve the set of governing equations, which are highly nonlinear and coupled. The pressures of the evaporator and condenser were 2 and 20 kPa, respectively, and the regeneration temperature of the bed was 403 K. Changes in the temperature, adsorptive pressure, and adsorbate concentration in the adsorbent bed at different steps of the cycle were determined. The basic simulated cycle is presented in a Clausius-Clapeyron diagram, which illustrates the changes in average pressure and temperature of the adsorbent bed throughout the cycle. The results of the simulation indicated that the most time-consuming processes in the adsorption heat pump cycle were isobaric adsorption and isobaric desorption. The high thermal resistance of the bed slows down heat transfer, prolonging adsorption and desorption processes.     

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.     

自由降膜传热传质数值模拟技术应用进展

自由降膜过程在许多工业领域，特别是在石油化工工业中有着非常广泛的应用。近年来，随着计算机技术的发展，研究人员采用理论分析、数值模拟和实验相结合的技术手段，对降膜传热传质过程进行了深入的研究，为优化降膜传热传质过程和新型设备的开发提供了理论基础。     

DIMENSIONAL ANALYSIS OF HEAT AND MASS TRANSFER CORRELATIONS USING MICRO- AND MACRO-SCALES

A new kind of dimensional analysis, which uses two kinds of scales, provides a powerful tool for analyzing heat and mass transfer correlations as has been demonstrated by Ruckenstein (1986) in the case of forced convection of Newtonian fluids. In this work, the approach based on micro- and macro-scales is extended to free convection of Newtonian fluids, as well as to forced and free convection of power-law fluids.

As the micro-participation and macro-participation dominate in laminar and turbulent flow respectively, bounds on the exponents of the Reynolds number Re and the Grashof number Gr can be established in the case of forced and free convection respectively. An upper bound is obtained for laminar flow and a lower bound for turbulent flow. Thus, for free convection in Newtonian fluids, it is demonstrated that the bounds on the exponent of Gr for laminar and turbulent flow are 0.25 and 0.375 respectively.     

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.     

BOUNDARY LAYER FLOW AND DOUBLE DIFFUSION OVER AN UNSTEADY STRETCHING SURFACE WITH HALL EFFECT

The present investigation is concerned with the effect of Hall currents on boundary layer flow, and heat and mass transfer of an electrically conducting fluid over an unsteady stretching sheet in the presence of a strong magnetic field. The electron-atom collision frequency is assumed to be relatively high, so that the Hall effect is assumed to exist, while the induced magnetic field is neglected. The governing time-dependent boundary layer equations for momentum, thermal energy, and concentration are reduced using a similarity transformation to a set of coupled ordinary differential equations. The similarity ordinary differential equations are then solved numerically by the successive linearization method together with the Chebyshev pseudo-spectral collocation method. Effects of the Prandtl number, Pr, Schmidt number, Sc, magnetic field, M, Hall parameter, m, and the unsteadiness parameter, A, on the velocity, temperature, and concentration profiles as well as the local skin friction coefficient and the heat and mass transfer rates are depicted graphically and/or in tabular form. Favorable comparisons with previously published work on various special cases of the problem are also obtained.     

CONVECTTVE HEAT AND MASS TRANSFER AND EVOLUTION OF THE MOISTURE DISTRIBUTION IN COMBINED CONVECTION AND RADIO FREQUENCY DRYING

ABSTRACT

In a previous study (Dostie and Navarri, 1994), experiments indicated that a non-uniform moisture distribution could develop in radio frequency drying depending on the applied power and initial conditions, making the design and scale-up of such a dryer a more difficult task. Consequently, a thorough study of the combined convection and RF drying process was undertaken. Experimental results have shown that the values of the neat and mass transfer coefficients decrease with an increase in evaporation rate caused by RF energy. This effect is adequately taken into account by the boundary layer theory. Furthermore, the usual analogy between heat and mass transfer has been verified to apply in RF drying. Experiments have also shown that a different mass transfer resistance on both sides of the product should not result in non-uniform drying. However, it appears that non-uniform drying is dependent upon the initial moisture distribution and the relative intensity of heal transfer by convection and RF- It was shown that the maximum drying rate occurs at a higher average water content and that the total drying time increases with non-uniformity of the initial moisture distribution.     

NATURAL CONVECTION HEAT AND MASS TRANSFER FROM A VERTICAL FLAT PLATE WITH VARIABLE WALL TEMPERATURE AND CONCENTRATION TO POWER-LAW FLUIDS WITH YIELD STRESS IN A POROUS MEDIUM

The problem of natural convection coupled heat and mass transfer of non-Newtonian power law fluids with yield stress from a vertical flat plate in a fluid-saturated porous medium is analyzed under boundary layer approximations. Similarity solutions are obtained for the general case of power law variations of the wall temperature and concentration. Velocity, temperature, and concentration profiles as well as local heat and mass transfer rates are presented and discussed for different values of the rheological parameters of a power-law fluid, the Lewis number, and the thermal and concentration buoyancy ratio.     

INTENSIFICATION OF HEAT AND MASS TRANSFER IN CHANNELS OF PLATE CONDENSERS

An analysis is presented for the main factors which control the intensity of vapor condensation in plate condenser channels, such as heat transfer both in single-phase stream of the coolant and in the condensate film, heat and mass transfer in gas-vapor phase, thermal resistance of fouling at heat transfer surface and pressure drop in condensing stream. On the basis of a relationship between the heat transfer and the wall shear stress, an approximate equation is obtained for calculating heat transfer from the pressure drop data. For calculation of heat transfer in condensate film during the condensation of high speed vapor, an analogy between heat and momentum transport has been used. An analysis of fouling deposition on heat transfer surface has been performed and an equation is presented for calculating the reduction of the fouling thermal resistance as compared with shell and lube heat exchangers. Experimental data are in good agreement with theoretical results. These data have shown the improvement of all the mentioned factors, which determine the intensity of the whole condensation process compared to the same factors in shell and tube condensers. Under the equal conditions, the required area of the heat transfer surface is reduced by 1.6 to 3 limes for the plate condenser, as compared with conventional shell and tube units.     

INTENSIFICATION OF HEAT AND MASS TRANSFER IN CHANNELS OF PLATE CONDENSERS

An analysis is presented for the main factors which control the intensity of vapor condensation in plate condenser channels, such as heat transfer both in single-phase stream of the coolant and in the condensate film, heat and mass transfer in gas-vapor phase, thermal resistance of fouling at heat transfer surface and pressure drop in condensing stream. On the basis of a relationship between the heat transfer and the wall shear stress, an approximate equation is obtained for calculating heat transfer from the pressure drop data. For calculation of heat transfer in condensate film during the condensation of high speed vapor, an analogy between heat and momentum transport has been used. An analysis of fouling deposition on heat transfer surface has been performed and an equation is presented for calculating the reduction of the fouling thermal resistance as compared with shell and lube heat exchangers. Experimental data are in good agreement with theoretical results. These data have shown the improvement of all the mentioned factors, which determine the intensity of the whole condensation process compared to the same factors in shell and tube condensers. Under the equal conditions, the required area of the heat transfer surface is reduced by 1.6 to 3 limes for the plate condenser, as compared with conventional shell and tube units.     

传热单元法和传质单元法的类似

提出了传热与传质单元法间存在类似的概念。据此,不仅可由较易取得的、用于套管换热器传热过程的计算式求得用于填料塔气体吸收操作的有关公式,而且也为这二者间的模拟建立了理论基础。     

干燥过程热质传递的简化模型

对多孔介质体积平均理论进行简化,得到简化的热质传递干燥模型,用一个理论式表达模型中有效扩散系数。对香蕉片千燥的研究表明,模型的预测值与实验结果相     

盘式连续干燥器的传质传热模型

建立了盘式连续干燥器内加热盘面物料的传质模型,给出了干燥器内料环高度、盘面积料量及干燥时间的计算方法.应用颗粒传热理论和扩散理论,导出了每道料环的传热计算公式,由该迭代公式可逐步计算出每道料环的出料温度、出料湿含量及干燥速率.扩散理论中的惟一经验参数——搅拌参数N_mix,在本模型中可由不同进料工况下的多组实验数据加以确定.最后给出了应用该模型进行计算的实例,结果表明,理论计算值与实测值吻合较好,误差一般在20%以内.     

DRYING MODEL WITH NON-ISOTROPIC SHRINKAGE DEFORMATION UNDERGOING SIMULTANEOUS HEAT AND MASS TRANSFER

A model of simultaneous heat and moisture transfer in a cylindrical sample was coupled with the virtual work principle applicable to a body undergoing shrinkage deformation in two dimensions. Non-constant physical and thermal properties were also incorporated in the model. Governing equations and boundary conditions were solved numerically using Galerkin's finite element method. To check the mathematical model drying experiments were carried out. A cylindrical potato was used as a drying sample. Experimental conditions were as follows: a drying temperature of 333 K, relative humidity of 5.4%, and air velocity of 1.6 m/s. We obtained the central temperature of the sample, average moisture content, and the shrinkage change in the axial and radial directions during drying. It was observed that the shrinkage coefficients in the axial and the radial directions were significantly different during air-drying. Comparison between predicted and experimental results provides satisfactory agreement.     

HEAT AND MASS TRANSFER WITH POLYCONDENSATION IN RESIN FILM DURING DRYING

ABSTRACT

In a drying process of dielectric resin films coated on electric conductive substances, phenomena such as polymerization of monomers, by-products yield, shrinkage and stress generation lake place simultaneously in addition to heat and mass transfer. For the enhancement of the drying with high efficiency and high quality, it is important to understand the drying mechanism. In this paper, the characteristics of heat and mass transfer in the resin film including polycondensation reaction are presented. The apparent drying rate of polyamideimide varnish films was measured in two different heating modes of radiation and convection. The reaction rate of polycondensation was analyzed both by the thermogravimetry and the differential scanning calorimetry. The apparent drying rate began to drop remarkably when the reaction rate became significant. It implies that the diffusion of the solvent is inhibited by skinning at the surface. Applying the Vrentas/Duda free-volume diffusion model to the prediction of diffusivity, the heat and mass transfer in the resin film were analyzed theoretically with a reasonable accuracy.