ANALYSIS OF TRANSIENT TEMPERATURE DISTRIBUTIONS IN A PERFUSED MEDIUM DUE TO A SPHERICAL HEAT SOURCE WITH APPLICATION TO HEAT TRANSFER IN TUMORS: HOMOGENEOUS AND INFINITE MEDIUM

The role of conduction and convection in transferring heat through a perfused medium is quantified by analyzing the transient temperature field within and around a spherical heat source embedded in the medium, using the bio-heat transfer equation. Analytical expressions for transient temperature distributions are obtained in terms of the following dimensionless variables: ξ, the relative position; τ, the Fourier number; β²;, the Peclet number, and ratios of thermal conductivities and difFusivities. The perfused medium is assumed to be infinite, isotropic and homogeneous. Frequency response of the probe to sinusoidal power input is also analyzed. The analytical expressions obtained are used to estimate heat transfer characteristics of tumors from in vivo data describing blood flow and temperature distributions around a spherical probe.     

HEAT TRANSFER DUE TO MHD SLIP FLOW OF A SECOND-GRADE LIQUID OVER A STRETCHING SHEET THROUGH A POROUS MEDIUM WITH NONUNIFORM HEAT SOURCE/SINK

An analysis is carried out to study the heat transfer characteristics of a second-grade non-Newtonian liquid due to a stretching sheet through a porous medium under the influence of external magnetic field. The stretching sheet is assumed to be impermeable. Partial slip condition is used to study the flow behavior of the liquid. The effects of viscous dissipation, nonuniform heat source/sink on the heat transfer are addressed. The nonlinear partial differential equations governing momentum and heat transfer in the boundary layer are converted into nonlinear ordinary differential equations using similarity transformation. Analytical solutions are obtained for the resulting boundary value problems in the case of two types of boundary heating, namely, constant surface temperature (CST) and prescribed surface temperature (PST). The effects of slip parameter, second-grade liquid parameter, combined (magnetic and porous) parameter, Prandtl number, Eckert number, and nonuniform heat source/sink parameters on the heat transfer are shown in several plots. Analytical expressions for the wall frictional drag coefficient and wall temperature gradient are obtained.     

ANALYSIS OF HEAT TRANSFER IN A NON-ISOTHERMAL SOLID-GAS REACTING MEDIUM

This article concerns the thermal phenomena occurring in a reacting solid-gas porous medium. The practical application envisaged is the use of these media in chemical heat pumps (CHPs).

The procedure chosen allowed us to almost totally separate the determination of the kinetic characteristics of the medium, presented in the previous article, from the study of the thermal phenomena presented here.

The thermal parameters were estimated or identified, depending on their influence, quite satisfactorily.

Moreover, we show that it is possible to exploit more limited experimental data, by modifying the procedure, to obtain a sufficiently good understanding of the reacting medium. This technique was applied in the study of the effect of mixing a conducting binder with the medium on its thermal parameters.

This model is also used to test configurations having different thicknesses of the reacting bed.     

TEMPERATURE,DISTRIBUTIONS AND HEAT TRANSFER DURING THE DRYING OF LUMBER

ABSTRACT

This paper describes techniques that have been developed for accurately measuring the surface temperature of drying lumber using a radiation thermometer, and interior temperatures at various depths using 30 gauge thermocouples. Methods for calculating heat transfer coefficients during the drying of lumber are also described. Experimental results, showing surface and interior temperatures, and moisture content, as functions of drying time are presented.     

SLIP FLOW AND HEAT TRANSFER OF A SECOND-GRADE FLUID IN A POROUS MEDIUM OVER A STRETCHING SHEET WITH POWER-LAW SURFACE TEMPERATURE OR HEAT FLUX

This article deals with the study of boundary layer flow of a second-grade fluid in a porous medium past a stretching sheet and heat transfer characteristics with power-law surface temperature or heat flux. The flow in the boundary layer is considered to be generated solely by the linear stretching of the boundary sheet adjacent to a porous medium, and boundary wall slip condition is assumed. In the energy equation effects of viscous dissipation, work done due to deformation and internal heat generation/absorption is taken into account. Closed form solutions are obtained for this problem.     

TRANSIENT MASS AND HEAT TRANSFER FROM A CLOUD OF VAPORIZING DROPLETS OF VARIOUS SIZE DISTRIBUTIONS: A SECTIONAL APPROACH

A population of vaporizing liquid droplets of a wide range of sizes suspended in a stagnant heated atmosphere is considered. Interaction between neighboring droplets is taken into account through the 'cooling effect' due to latent heat absorption. To avoid the dimensionality problem associated with the discrete form of droplet population balance equations, “sectional-conservation-equations” are used. Since droplets of various sizes differ in their vaporization rates, “sectional-vaporization-coefficients” are presented. New solutions for the coupled energy and sectional size distribution equations arc presented and the transient changes in droplet size distribution are analyzed. The analysis takes into account the density of the spray, the distribution of interfacial area between the phases, rates of droplet vaporization, and the properties of the surrounding vapor-gas mixture. All the above-mentioned properties of the spray and surrounding gas are combined here to form a new nondimensional group-vaporization number, which expresses the ratio of the characteristic heat of vaporization to the initial enthalpy of the surrounding gas (both, per unit volume). To illustrate the generality of this approach, solutions are presented for various values of the group vaporization number, using three types of initial droplet number distribution: uniform, symmetrical, and nonsymmetrical.     

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.     

NONLINEAR FINITE ELEMENT ANALYSIS OF COUPLED HEAT AND MASS TRANSFER PROBLEMS WITH AN APPLICATION TO TIMBER DRYING*

A finite element formulation and solution of a set of nonlinear coupled heat and mass transfer equations for porous capillary media is presented. The model considers temperature and moisture dependent material properties and can accomodate diffusion of moisture as either a liquid or a vapor. Application was made to drying of timber and predicted results agreed well with the experimental data.     

NONLINEAR FINITE ELEMENT ANALYSIS OF COUPLED HEAT AND MASS TRANSFER PROBLEMS WITH AN APPLICATION TO TIMBER DRYING*

A finite element formulation and solution of a set of nonlinear coupled heat and mass transfer equations for porous capillary media is presented. The model considers temperature and moisture dependent material properties and can accomodate diffusion of moisture as either a liquid or a vapor. Application was made to drying of timber and predicted results agreed well with the experimental data.     

单位熵产分析法在强化传热研究中的应用

引言在余热利用、锅炉、加热炉等设备的设计中需要选择合适的方法强化受热面传热,达到缩小装置体积和优化装置性能的目的。选择强化传热方法的一个重要原则就是分析装置热力性能是否达到优化。目前强化传热热力性能的分析方法有不少,主要包括直接比较法和以热力学第一定律为基础的能量分析法等。用上述方法评价分析传热的综合热力性能,虽然直接方便并可获得确定的结果,但由于分析中没有将传热性能和流动性能有机地结合,没有考虑能量质的变化,因而其结果与实际换热工况会产生一定的差别,有时不能很好地解决能量有效利用的综合评价问题…     

ANALYSIS OF AERODYNAMICS AND HEAT TRANSFER IN VIBRO-FLUIDIZED BEDS

Recent experimental data on aerodynamic and heat transfer characteristics of vibro-fluidized beds of model particles are presented and discussed in the light of the limited prior information. An analysis is presented for the bed dynamics with supporting experimental data. The predicted results for bed flight time, pressure drop and average voidage are shown to agree favorably with experimental data. On the basis of experimental results, a theoretical model and a simple design chart are presented which may be used to determine favorable operating ranges for a vibro-fluid bed apparatus.     

ANALYSIS OF AERODYNAMICS AND HEAT TRANSFER IN VIBRO-FLUIDIZED BEDS

Recent experimental data on aerodynamic and heat transfer characteristics of vibro-fluidized beds of model particles are presented and discussed in the light of the limited prior information. An analysis is presented for the bed dynamics with supporting experimental data. The predicted results for bed flight time, pressure drop and average voidage are shown to agree favorably with experimental data. On the basis of experimental results, a theoretical model and a simple design chart are presented which may be used to determine favorable operating ranges for a vibro-fluid bed apparatus.     

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.     

HYDROMAGNETIC BOUNDARY LAYER FLOW AND HEAT TRANSFER IN VISCOELASTIC FLUID OVER A CONTINUOUSLY MOVING PERMEABLE STRETCHING SURFACE WITH NONUNIFORM HEAT SOURCE/SINK EMBEDDED IN FLUID-SATURATED POROUS MEDIUM

Analytical study for the problem of flow and heat transfer of electrically conducting viscoelastic fluid over a continuously moving permeable stretching surface with nonuniform heat source/sink in a fluid-saturated porous medium has been undertaken. The momentum and thermal boundary layer equations, which are partial differential equations, are converted into ordinary differential equations, by using suitable similarity transformation. The resulting nonlinear ordinary differential equations of momentum are solved analytically assuming exponential solution, and similarly thermal boundary layer equations are solved exactly by using power series method, with the solution obtained in terms of Kummer's function. The results are shown with graphs and tables. The effect of various physical parameters like viscoelastic parameter, porosity parameter, Eckert number, space, and temperature-dependent heat source/sink parameters enhances the temperature profile, whereas increasing the values of the suction parameter and Prandtl number decreases the temperature profile. The results have technological applications in liquid-based system involving stretchable materials.     

气固两相流中颗粒运动强化器壁对流传热的机理

提出了颗粒碰撞壁面过程中颗粒打破边界层和颗粒与壁面导热的强化传热模型,以分析气固两相流中颗粒强化对流传热的机理,通过模型计算研究了风速、颗粒浓度和粒径等因素对颗粒在壁面的停留特性、颗粒在边界层的扰动及对导热和边界层破坏两种强化机制传热比重的影响．以气固两相流横掠圆管的传热过程为例进行计算,计算与实验结果一致,并获得了具有实用价值的关联计算式．     

固定床内传热参数的估计与分析

本文在系统地考察了各种因素对床层径向有效导热系数和壁传热系数影响的实验研究与计算机模拟的基础上,对文献中发表的固定床内传热参数估值离散的原因进行了分析。结果表明,Bi取值在5.0左右时,对床层出口温度比较敏感,是造成h_(?)估值离散的重要原因之一。床层填充的随机性影响床层温度分布,低床层、低Re_p条件下估计参数误差要大。d_(?)取值范围不同,壁冷却和壁加热条件下估计出的参数均会不同。     

SIMULTANEOUSLY DEVELOPING LAMINAR FLOW AND HEAT TRANSFER IN THE ENTRANCE REGION OF A CIRCULAR TUBE WITH CONSTANT WALL TEMPERATURE

The developing flow and heat transfer in the entry region of a heated circular tube is analyzed for the case of constant wall temperature. An integral or boundary-layer solution is presented which has a number of advantages over earlier Karman-Pohlhausen integral analyses. Thus, in the present analysis, the velocity and temperature distributions, the local and mean drag coefficients, and the local and mean Nusselt numbers approach their fully-developed values asymptotically. The new analysis is based on the hydrodynamic inlet-filled region concept originally proposed by Ishizawa (1966) and later adopted by Mohanty and Asthana (1978) to flow through a circular tube. This concept is extended to the combined entry-length problem by introducing a thermal transition region, herein called the thermally-filled region, between the thermal inlet boundary-layer region and the thermally fully-developed region. A thermal shape factor is also introduced which ensures smooth transition of all pertinent thermal quantities from the entrance region to the fully-developed region. Results for the variation of the local and mean Nusselt numbers with axial distance along the tube for Pr = 0.1,0.5,0.7,1,5, and 10 are presented. These results agree well with the numerical solutions of Hombeck (1965), Manohar (1969), and Hwang and Sheu (1974) and also with the correlations of Churchill and Ozoe (1973).     

环形通道内低Pe数高温液钠传热及其初始沸腾壁面过热度研究

对环形通道内低Pe数(20～70)的高温(300～700℃)液钠在由非旺盛湍流转变成旺盛湍流区内(Re=4000～17500)的传热进行了实验研究,并对正压下液钠初始沸腾壁面过热度进行了理论分析与实验研究.结果表明,所提供的计算关系式与实验数据吻合良好.实验采用的环管内径为6mm,外径为10mm,通道外壁绝热,内壁用高热流密度电加热元件加热.     

ANALYSIS OF SIMULTANEOUS RADIATIVE AND CONDUCTIVE HEAT TRANSFER IN FLUIDIZED BEDS

In the bubbling regime of operation for fluidized beds, the major mechanism for heat transfer is transient conduction to periodic packets of densely packed particles at the heat transfer surface. The well known Mickley and Fairbanks model, with various subsequently proposed modifications, adequately describes this transient conduction mechanism. However, no adequate theory exists for heat transfer in high-temperature fluidized beds where radiative contribution becomes significant.

Analysis of the radiative contribution is complicated by the nonlinear interaction of radiation with conduction/convection. This paper describes a differential formulation of the combined radiative/ conductive heat transfer process. The discrete flux method used by Churchill et al. for radiative transport in heterogeneous media is applied here to the problem of transient heat transfer to packets in fluidized beds. Packets are modeled as radiatively participating media with absorption, scattering, and emission of radiation. Simultaneous solution of the governing differential equations for temperature and forward and backward radiation fluxes permits calculation of instantaneous heat flux at the heat-transfer surface. Radiative transfer during bubble contact is added as a time-weighted contribution.

Using experimental data on radiative cross sections (from packed media experiments) and experimental data on packet residence times (from fluidized bed experiments), the combined conductive/radiative heat transfer to packets was obtained for examples of fluidized beds at different fluidizing velocities and wall temperatures. The analytical results indicate that the relative importance of radiation is affected by particle size, average packet residence time, and the radiative attenuation cross sections. For operating conditions representative of fluidized bed combustion, the model estimates a 10 to 20 percent contribution by radiation to the total heat transfer. Comparison to limited experimental data from the literature shows reasonable agreement.