MOMENTUM INTEGRAL METHOD FOR FORCED CONVECTION IN THERMAL NONEQUILIBRIUM POWER-LAW FLUID-SATURATED POROUS MEDIA

Forced convection heat transfer for power-law fluid flow in porous media was studied analytically. The analytical solutions were obtained based on the Brinkman-extended Darcy model for fluid flow and the two-equation model for forced convection heat transfer. As a closed-form exact velocity profile is unobtainable for the general power-law index, an approximate velocity profile based on the parabolic model is proposed by subscribing to the momentum boundary layer integral method. Heat transfer analysis is based on the two-equation model by considering local thermal nonequilibrium between fluid and solid phases and constant heat flux boundary conditions. The velocity and temperature distributions obtained based on the parabolic model were verified to be reasonably accurate and improvement is justified compared to the linear model. The expression for the overall Nusselt number was derived based on the proposed parabolic model. The effects of the governing parameters of engineering importance such as Darcy number, power-law index, nondimensional interfacial heat transfer coefficient, and effective thermal conductivity ratio on the convective heat transfer characteristics of non-Newtonian fluids in porous media are analyzed and discussed.     

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     

Computation and measurements of mass transfer and dispersion coefficients in fluidized beds

Conventional design of circulating fluidized beds requires the knowledge of dispersion and mass transfer coefficients, expressed in dimensionless forms as Sherwood numbers. However, these are known to vary by five or more orders of magnitude. Furthermore, the Sherwood numbers for fine particles reported in the literature are several orders of magnitude lower than the Sherwood number of two for diffusion to a single particle. We have shown that by replacing the particle diameter in the conventional Sherwood number with cluster or bubble diameter, the modified Sherwood number is again of the order of two.We have also shown that the kinetic theory based computational fluid dynamics codes correctly compute the dispersion and mass transfer coefficients. Hence, the kinetic theory based computational fluid dynamics codes can be used for fluidized bed reactor design without any such inputs.     

Effect of Thermal Asymmetry on Heat Transfer in a Laminar Annular Flow

The effect of thermal asymmetry on heat transfer in a hydrodynamically developed annular flow has been investigated numerically. The surfaces confining the fluid space are kept at constant but different temperatures. Depending on the fluid inlet temperature, the thermal asymmetry can lead to a discontinuity of the Nusselt number on one surface. With the thermally developed flow the exact expressions for the Nusselt numbers have been obtained.     

液固磁稳定床中的传热与传质特性研究

以电化学方法测定了SRNA-4催化剂为固相的液固磁稳定床中的液固传质系数,采用浸没的微型传热探头测量了液固传热系数。实验结果表明：随磁场强度、液体黏度的增大,液固传质系数及传热系数减小;增加表观液速,传质系数、传热系数均增大。进而建立了由物性参数及操作参数估算液固传质Sherwood数及液固传热Nusselt数的关联式,实验值与预测值吻合良好,可为磁稳定床反应器的放大设计和操作优化提供一定的依据。     

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.     

TRANSIENT NATURAL DRYING-INDUCED BOUNDARY LAYERS

This work presents a methodology far obtaining heat and mass transfer coefficients for problems involving natural convection along a flat plate. In order to simulate drying conditions, a set of data has been obtained for the temperature range between 20 and 98° C and for various absolute humidities, both of the wall and ambient. It is shown that for drying at temperatures above 80° C, Nusselt and Sherwood numbers change very appreciably with respect to values obtained at smaller temperatures. The simulated results show that even for very low temperature differences, the transient period in natural convection along a flal vertical plate is smaller than 3s.     

The Drying of Sludge in a Cyclone Dryer Using Computational Fluid Dynamics

A control volume-based technique implemented in FLUENT (ANSYS Inc., Canonsburg, PA) computational fluid dynamics (CFD) package was applied along with the kinetic theory of granular flow (KTGF) to simulate the flow pattern and heat and mass transfer processes for sludge material in a large-scale cyclone dryer. The drying characteristics of sludge at the dryer inlet were obtained from a previous study on the drying of sludge in a large-scale pneumatic dryer. User-defined subroutines were added to extend FLUENT's capability to account for mixture properties and to simulate the constant and falling rate drying periods. The convective heat and mass transfer coefficients were modeled using published correlations for Nusselt and Sherwood numbers. Sensitivity analysis was conducted to determine the effect of gas-phase velocity and temperature on the final product outcome. Numerical predictions for the multiphase flow hydrodynamics showed a highly diluted region in the dryer core and a higher concentration of particles close to the wall region, an indication of nonuniform distribution of particles at a cross-sectional area. The numerical predictions for the hydrodynamic profiles qualitatively depicted the flow behavior natural to these designs. The work demonstrated the successful application of CFD in the design stage of a combined pneumatic-cyclone dryer model.     

Heat and mass transfer correlations and bifurcation analysis of catalytic monoliths with developing flows

We review and compare the literature correlations for estimating the heat and mass transfer coefficients as well as pressure drop in catalytic monoliths with simultaneously developing velocity, concentration and temperature profiles. We present accurate correlations for estimating the local Nusselt and Sherwood numbers for developing flows with constant flux (slow reaction) and constant wall concentration or temperature (fast reaction) cases for a channel of arbitrary shape. These new correlations need only a single parameter, namely, the asymptotic value, which depends on the channel geometric shape. We establish the accuracy of the proposed correlations by comparing the predicted values with the exact numerical values available for a few cases. We use the new correlations to analyze the effect of flow conditions near the inlet of the channel on the ignition and extinction behavior of catalytic monoliths used in combustion and after-treatment applications as well as laboratory experiments. It is shown that the bifurcation behavior, such as the number and location of the ignition/extinction points, the number of stable steady-states and the hysteresis locus is sensitive to the flow conditions in the entry region, and hence the heat and mass transfer correlations used, especially for large values of the transverse Peclet number (high space velocities or very short monoliths) or adiabatic temperature rise or when the axial catalyst loading is not uniform.     

TRANSIENT NATURAL DRYING-INDUCED BOUNDARY LAYERS

ABSTRACT

This work presents a methodology far obtaining heat and mass transfer coefficients for problems involving natural convection along a flat plate. In order to simulate drying conditions, a set of data has been obtained for the temperature range between 20 and 98° C and for various absolute humidities, both of the wall and ambient. It is shown that for drying at temperatures above 80° C, Nusselt and Sherwood numbers change very appreciably with respect to values obtained at smaller temperatures. The simulated results show that even for very low temperature differences, the transient period in natural convection along a flal vertical plate is smaller than 3s.     

Computation of the mass transfer coefficient of FCC particles in a thin bubbling fluidized bed using two- and three-dimensional CFD simulations

In this study, the standard kinetic theory based model with a modified drag correlation was successfully used to compute the mass transfer coefficients and the Sherwood numbers of FCC particles in a thin bubbling fluidized bed column using the additive diffusional and chemical reaction resistances concept. Also, the effects of the computational domain (two- or three-dimensional) and the reaction rate constant (low and high) are discussed.The computations show that the Sherwood numbers are in agreement with the measurement ranges for small particles in the fluidized bed system. The mass transfer coefficients and the Sherwood numbers are high near the inlet section, and decrease to a constant value with increasing height in the column. The two-dimensional computational domain simulations provide enough information to explain the phenomena inside a symmetrical system, but three-dimensional computational domain simulations are still needed for asymmetrical systems. Finally, the mass transfer coefficients and the Sherwood numbers increased with the larger reaction rate constant.     

The effect of liquid film vaporization on natural convection heat and mass transfer in a vertical tube

A numerical analysis was carried out to investigate the effects of film vaporization on natural convection heat and mass transfer in a vertical tube. Results for interfacial Nusselt and Sherwood numbers are presented for air-ethanol and air-water systems for various conditions. Predicted results show that heat transfer along the gas-liquid interface is dominated by the transport of latent heat in association with the vaporization of the liquid film. Additionally, the predicted results obtained by including transport in the liquid film are contrasted with those where liquid film transport is neglected, showing that the assumption of an extremely thin film made by Chang et al. (1986) and Yan and Lin (1990) is only valid for systems with small liquid mass flow rates. For systems with a high liquid film Reynolds number, Re₁₀, the assumption of an extremely thin film is seriously in error.     

COMPREHENSIVE, THEORETICALLY BASED, CORRELATING EQUATIONS FOR FREE CONVECTION FROM ISOTHERMAL SPHERES

Correlating equations are developed for the local and mean Nusselt number for free convection from an isothermal sphere as a function of the Rayleigh and Prandtl numbers. These expressions are based primarily on theoretical solutions for limiting cases, and hence are presumed to be more reliable than purely empirical correlations. The predictions of the proposed expressions are, however, validated by comparisons with prior experimental data. The expressions for the mean Nusselt number are shown to be applicable for all Ra and Pr. The expressions for the local Nusselt number are limited in applicability to the laminar boundary layer regime. The same equations are applicable to mass transfer and to combined heat and mass transfer in terms of the Sherwood, Schmidt and appropriately modified Rayleigh numbers.     

边界条件对颗粒-流体对流传热的影响

对单个球形颗粒与周围流体的对流传热进行数值模拟,考察了等温边界、等热流量边界和流固耦合边界条件的影响。结果表明,流固耦合边界和等温边界所得时均面积加权努塞尔数与经验公式计算结果基本一致,等热流量边界模拟结果大于其它两种边界条件结果。时间平均局部面积加权努塞尔数的分布表明,当流动稳定且不发生分离时,努塞尔数从前滞点到后滞点逐渐减小;当出现非稳态涡旋时,努塞尔数从前滞点到分离角附近逐渐减小并出现最小值,后逐渐增大直至后滞点。     

COMPREHENSIVE,THEORETICALLY BASED,CORRELATING EQUATIONS FOR FREE CONVECTION FROM ISOTHERMAL SPHERES

Correlating equations are developed for the local and mean Nusselt number for free convection from an isothermal sphere as a function of the Rayleigh and Prandtl numbers. These expressions are based primarily on theoretical solutions for limiting cases, and hence are presumed to be more reliable than purely empirical correlations. The predictions of the proposed expressions are, however, validated by comparisons with prior experimental data. The expressions for the mean Nusselt number are shown to be applicable for all Ra and Pr. The expressions for the local Nusselt number are limited in applicability to the laminar boundary layer regime. The same equations are applicable to mass transfer and to combined heat and mass transfer in terms of the Sherwood, Schmidt and appropriately modified Rayleigh numbers.     

中空纤维膜管束液体除湿再生过程中的热湿耦合传递

研究了中空纤维膜管束液体除湿再生过程中的热湿耦合传递特性。选择了两根膜纤维管及其管内部溶液流和管间空气流作为研究对象,建立了控制流体流动与传热传质过程的偏微分方程,并采用有限容积离散方法和贴体坐标转换方法进行求解,获得了计算单元内的阻力系数、Nusselt数和Sherwood数,分析了耦合边界条件下的Nusselt数和Sherwood数与相应等壁温和等热流密度边界条件下的相应准则数之间的差异。这些研究结果可以为用于液体除湿再生过程的中空纤维膜管束构成的膜接触器的结构设计提供理论基础。     

Effect of Thermal Asymmetry on Laminar Forced Convection Heat Transfer in a Porous Annular Channel

The effect of thermal asymmetry on laminar forced convection heat transfer in an annular porous channel with a Darcy dissipation of fluid kinetic energy was investigated numerically. The cylindrical surfaces making the channel boundaries were kept at constant but different temperatures. The thermal asymmetry thus imposed on the system results in an asymmetric temperature field and different heat fluxes across the channel boundaries. Depending on the Darcy, Péclet and Reynolds numbers, the thermal asymmetry may lead to a reversal of the heat flux along the channel at least at one of the channel walls. The corresponding Nusselt number becomes zero and subsequently experiences a discontinuity, thereby jumping from infinite negative to infinite positive, or vice versa. This feature is observed in the region of thermal development. In the fully developed heat transfer region, the Nusselt numbers can be positive or negative for the same inlet conditions, depending on the heat source strength. In the case of a plug flow, the analytical expressions for the Nusselt numbers have been obtained.     

Natural-convection heat and mass transfer from a vertical cone in porous media filled with nanofluids using the practical ranges of nanofluids thermo-physical properties

The present study aims to analyze the effects of Brownian motion and thermophoresis forces on the natural convection heat transfer of nanofluids around a vertical cone placed in a saturated porous medium. The range of non-dimensional parameters and the definition of two important parameters of heat and mass transfer are discussed. The results show that the range of Lewis number as well as Brownian motion and thermophoresis parameters and also the definition of the reduced Nusselt and Sherwood numbers, used in the previous analyses, should be reconsidered. In the present study, reasonable definitions of reduced Nusselt and Sherwood numbers have been proposed and discussed in details. In contrast with previous researches, the present results show that the heat transfer associated with migration of nanoparticles is negligible compared with heat conduction and convection mechanisms.     

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.     

叉排微柱群内顶部缝隙对传热效率的影响

以去离子水为工质,实验研究了直径为500 μm、高度为500 μm以叉排排列的微柱群内顶部缝隙对传热效率的影响规律。采用电加热棒进行加热,测量微柱群板Reynolds数在8～400之间在不同顶部缝隙时的进出口温度与流量,获得微柱群内流动阻力系数及Nusselt数,进而掌握微柱群内传热效率与Re关系。研究结果表明,在较低Re时,顶部缝隙对微柱群内流动阻力和Nu影响较小;随着Re增加,其对流动阻力与Nu的影响越来越显著。微柱群传热效率一开始随着Re增加而快速增加,随着Re进一步增加,其传热效率开始缓慢增加甚至出现下降。根据实验结果,尽管微柱群顶部缝隙存在降低了其内Nu,但提高了微柱群的传热效率。