TRANSIENT CONDUCTION AND RADIATION HEAT TRANSFER WITH VARIABLE THERMAL CONDUCTIVITY

The effect of variable thermal conductivity on transient conduction and radiation heat transfer in a planar medium is investigated. Thermal conductivity of the medium is assumed to vary linearly with temperature, while the other thermophysical properties and the optical properties are assumed constant. The radiative transfer equation is solved using the discrete transfer method, (DTM) and the nonlinear energy equation is solved using an implicit scheme. Transient as well as steady state results are found for an absorbing, emitting, and anisotropically scattering gray medium. Thermal conductivity has been found to have significant effects on both transient as well as steady state temperature and heat flux distributions. Some steady state results are compared with the results reported in the literature.     

同井回灌地下水源热泵地下水渗流理论研究

建立了单一介质承压含水层中定流量同井回灌地下水源热泵抽水和回灌引发的地下水渗流数学模型；利用叠加原理推导了同井回灌地下水源热泵地下水渗流的理论解。通过分析理论解，从中得出稳态降深方程、稳态渗流速度方程、准稳态时间方程和理想井间距方程．定流量同井回灌地下水源热泵引发的地下水渗流能在很短的时间内达到稳态，并且理想井间距仪是含水层厚度和渗透系数比的函数。对于完整型的观测井不论位置如何，其平均降深均为0。     

New approach to the steady state stability analysis of synchronousmachines

A novel method for steady state stability analysis of synchronous machines is presented. The method is based on a novel swing equation, which is a second-order, nonlinear differential equation. Two steady-state stability criteria can be derived by evaluating the eigenvalues of a linearized version of the new equation, one of which is for step-out instability and the other for hunting. Although these two instabilities have mostly been discussed independently so far, this approach makes it possible to handle the two instabilities on a common basis     

Collapse of one-component vapor bubble with translatory motion

Theoretical analysis of one-component vapor bubble collapse with translatory motion in uniformly subcooled liquid has been carried out. The bubble is spherical and flow in the region surrounding the bubble is potential. General solution is obtained in which the function R = R(τ) is defined implicitly by integral equation. General solution is reduced to the quasi steady state and quasi linear problem. Quasi steady state solution is used to obtain a set of simple and explicit expressions by which the bubble radius is determined in function of time. The results of theoretical analysis are compared with those given by other authors and available experimental data. The agreement between compared experimental data and theoretical results is very good.     

Estimation of temperature distribution in biological tissue by using solutions of bioheat transfer equation

A living body has a system for maintaining its temperature. We have investigated the heat transfer characteristics common to each organ and therapy using heat transfer. The one‐dimensional bioheat transfer equation with bioheat generation was converted into a dimensionless form and solved by Laplace transformation on the assumption that biological tissue is homogeneous. A dimensionless steady‐state solution and transient solution were derived analytically. These solutions can represent the characteristics of the temperature distribution common to each organ. Comparison with numerical solutions has confirmed that these solutions can be applied to estimate the temperature distribution of inhomogeneous biological tissue. It is proved that the size of the region where temperature change occurs, the steady‐state thermal penetration depth, is decided by biological properties. Furthermore, the time needed to reach a steady state, or the time it takes for biological tissue to reach a steady state, is calculated by using these solutions. Additionally, a temperature chart was proposed for each organ or tissue. This chart can serve as a guideline for medical doctors in formulating thermal therapy. © 2008 Wiley Periodicals, Inc. Heat Trans Asian Res, 37(6): 374– 386, 2008; Published online in Wiley InterScience ( www.interscience.wiley.com ). DOI 10.1002/htj.20210     

A practical collector efficiency equation for nonconvecting solar ponds

A steady state model for the salt gradient solar pond is developed taking into account the heat losses from the surface and bottom of the pond. The efficiency equation thus obtained is independent of the surface zone temperature and depends only on the geoclimatic parameters. The results obtained are compared with those of Kooi[1]. The results indicate that, depending on the geoclimatic conditions, the thermal efficiency of the pond can deviate considerably from that predicted by Kooi's equation.     

Entropy generation in turbulent natural convection due to internal heat generation

In this study numerical predictions of entropy generation in turbulent natural convection due to internal heat generation in a square cavity are reported for the first time. Results of entropy generation analysis are obtained by solving the entropy generation equation. The values of velocity and temperature, which are the inputs of the entropy generation equation, are obtained by an improved thermal lattice-BGK model proposed in this paper. The analyzed range is wide, varying from the steady laminar symmetric state to the fully turbulent state. Distributions of entropy generation numbers, for various Rayleigh numbers, Prandtl numbers, and Eckert numbers, are given.     

A three-dimensional analytical solution of the microheater temperature before bubble nucleation

A three-dimensional analytical solution of the microheater temperature based on heat diffusion equation is developed and compared with experimental results. Dimensionless parameters are introduced to analyze the temperature rise time and the distribution under steady state. To study the microheater temperatures before bubble nucleation, a set of working fluids and microheaters are considered. It is shown that the dimensionless time ξ₀ required for the temperature rise from room to 95% of the steady state temperature is about 75, not dependent on working fluids and microheaters. Heat transfer to the surrounding liquid is mainly caused by conduction, not by convection and radiation mechanisms. The microheater length affects the surface temperature uniformity, while its width influences the steady temperatures significantly, yielding the transition from heterogeneous to homogeneous nucleation mechanism from square microheaters to narrow line microheaters.     

Interfacial area transport equation: model development and benchmark experiments

The interfacial area transport equation dynamically models two-phase flow regime transitions and predicts continuous changes of the interfacial area concentration along the flow field. It replaces the flow regime-dependent correlations for the interfacial area concentration in thermal-hydraulic system analysis. In the present study, detailed formulation of the interfacial area transport equation is presented along with its evaluation results based on the detailed benchmark experiments. In view of model evaluation, the equation is simplified into one-dimensional steady state one-group interfacial area transport equation. The prediction made by model agrees well with the experimental data obtained in round pipes of various diameters. The framework for the two-group transport equation and the necessary constitutive relations are also presented in view of bubble transport of various sizes and shapes.     

Transient behavior simulation of fin-and-tube heat exchangers for the variation of the inlet temperatures of both fluids

In this article, a transient behavior simulation of fin-and-tube heat exchangers has been studied. Energy equation for fluid flow and tube wall is derived and solved numerically. The variation of the temperatures of both fluids with time and position are obtained for a step-change in the inlet temperatures of the water and air fluids. The results show that in step-change of inlet water-side temperature, outlet water-side temperature will get steady faster than air-side, while in step-change of inlet air-side temperature, outlet air-side temperature will become steady state faster than water-side. Also, the time constant (the time interval that the flow will reach steady state) of the system is not influenced by the step-change amplitude of inlet air and water temperatures. The inlet water temperature expands along the tube and after a time interval, it reaches the outlet section of the tube. But, the inlet air temperature reaches the outlet section without time delay.     

Axisymmetric, laminar, binary shear layer with thermal diffusion and diffusion-thermo effects

Consideration is given to the thermal separation of components across the shear layer between a cold jet mixture (of helium and nitrogen) and a hot ambient gas, both initially at the same concentration levels. An asymptotic steady state solution is obtained assuming the layer to be thin relative to the jet radius. As a consequence of small inhomogeneity the momentum equation may be decoupled from energy considerations and a priori known velocity profiles result with the customary assumption of constant product of density and viscosity. Iterative integration of the concentration and energy relations is completed on the basis of the steady state condition of zero mass transport across the dividing streamline using similarity co-ordinates. Reasonable agreement with available experimental data results from use of the modified hard sphere model for the thermal diffusion ratio.     

Free convection from a vertical plate in a porous media subjected to a sudden change in surface temperature

The unsteady heat transfer process involved in free convection flow along a vertical surface embedded in a porous medium is investigated. An analytical solution has been obtained for the temperature/velocity field for small times in which the transport effects are confined within an inner layer adjacent to the plate. Then, a numerical solution of the full boundary-layer equation is obtained for the whole transient from the initial unsteady state to the final steady state. Detailed results of the effect of the temperature inputs on the transient process are given.     

Reduced order models for induction motors with two rotor circuits

Induction motor behavior is commonly simulated by a fifth order differential equation model which includes two stator state variables, two rotor state variables, and shaft speed. Normally two more variables must be added to account for the effects of a second rotor circuit representing deep bars, a starting cage, or rotor distributed parameters. This paper presents a technique for including the effects of a second rotor circuit without adding more state variables to the fifth order model. Transient, as well as steady state effects are included. The model may be useful in cases where switching introduces transient torques and losses that are invisible to the fifth order model, and it is not desirable to expand the model to include two more state variables. A laboratory test is included     

Entropy generation due to mixed convection in an enclosure with heated corners

Entropy generation due to steady state heat transfer and the motion of the vertical boundaries in a two-dimensional square cavity is numerically studied, using the value of the velocity and temperature obtained by solving the Navier–Stokes equation coupled with the energy equation with the finite element method and an operator splitting scheme. Increasing the Richardson number, the entropy generation by fluid friction is intensified inside the cavity due to the vortex formation at the central part of the cavity. The entropy generation by heat transfer becomes more intense at the vertical walls and the central low part of the cavity due to the stronger temperature gradients at this region.     

Global,nonparametric, noniterative optimization of time-averaged quantities under small,time-varying forcing: An application to a thermal convection field

Abstract

This study demonstrates a global, nonparametric, noniterative optimization of time-mean value of a kind of index vibrated by time-varying forcing. It is based on the fact that the (steady) forced vibration of nonautonomous ordinary differential equation systems is well approximated by an analytical solution when the amplitude of forcing is sufficiently small and its base state without forcing is linearly stable and steady. It is applied to optimize a time-averaged heat-transfer rate on a two-dimensional thermal convection field in a square cavity with horizontal temperature difference, and the globally optimal way of vibrational forcing, i.e. the globally optimal, spatial distribution of vibrational heat and vorticity sources, is first obtained. The maximized vibrational thermal convection corresponds well to the state of internal gravity wave resonance. In contrast, the minimized thermal convection is weak, keeping the boundary layers on both sidewalls thick.     

太阳能集热器热性能动态测试方法研究

对太阳能集热器热性能动态测试方法进行了介绍,并对该方法的数学模型进行了分析;探讨了各项参数在方程中的作用、可以忽略的条件等;分析了稳态测试方法严格规定试验条件的必要性及原因,并对方程的数值求解进行了分析与推导。对同一台太阳能集热器分别进行动态和稳态测试方法的试验数据进行了不确定度分析,对试验结果进行了分析和对比,并分析了太阳能集热器效率曲线截距的差异以及在不同归一化温差处集热器瞬时效率曲线差异的深层次原因。     

Unsteady mixed convection flow over a vertical cone due to impulsive motion

The development of unsteady mixed convection flow of an incompressible laminar viscous fluid over a vertical cone has been investigated when the fluid in the external stream is set into motion impulsively, and at the same time the surface temperature is suddenly changed from its ambient temperature. The problem is formulated in such a way that at t = 0, it reduces to Rayleigh type of equation and as t → ∞, it tends to Falkner–Skan type of equation. The scale of time has been selected such that the traditional infinite region of integration become finite which significantly reduce the computational time. The coupled non-linear partial differential equations governing the unsteady mixed convection flow have been solved numerically by using an implicit finite-difference scheme in combination with the quasi-linearization technique. There is a smooth transition from the initial steady state to the final steady state. The velocity, temperature, and concentration profiles and their gradients at the surface for various values of the governing parameters are reported in the present study.     

Thermodynamic modeling based on a generalized cubic equation of state for kerosene/LOx rocket combustion

Based on a generalized cubic equation of state proposed by Cismondi and Mollerup [Fluid Phase Equilib. 232 (2005) 74–89], this study derived formulations for the thermodynamic properties of mixtures that are needed for combustion simulations of liquid rocket engines. The present model was validated thoroughly against reference data provided by NIST in order to assess its validity over a wide range of critical compressibility factors, pressures, and temperatures. The numerical results clearly indicate that the present model is superior in its handling of fluid mixtures with quite different critical compressibility factors, while maintaining the advantages of the cubic equation of state compared to those of the Soave–Redlich–Kwong and Peng–Robinson equations of state. In addition, steady flamelet analysis has been performed to investigate the effects of detailed chemical kinetics, real fluid behavior, and increased pressure on the local flame structures of the kerosene surrogate and liquid oxygen relevant to liquid rocket engines.     

冷却塔内小型混流式水轮机的设计及数值模拟

为减少冷却塔内小型混流式水轮机生产工艺过程的复杂性和较高的制造成本,以水动风机冷却塔内流量为3 000 t/h的小型混流式水轮机为研究对象进行结构设计。通过CFD对设计后的水轮机模型进行全流道三维定常湍流数值模拟,数值模拟中采用单方程Spalart-Allmars湍流模型,假定水流为不可压缩流体,不考虑能量方程,仅将质量守恒和动量守恒作为控制方程。结果表明,所设计的小型混流式水轮机整体流态较好,水力性能稳定,在设计转速149 r/min时,流量和出力均达到了驱动冷却塔内风机的要求,且水轮机效率较高。     

Mass transfer between a single drop and a continuous phase

The time dependent convective-diffusion equations for mass transfer between a drop and a continuous phase are solved in two cases: (1) the case of small Reynolds numbers and (2) the case of potential flow. The equations are solved by means of a similarity variable η_i = y/δ_i(θ, t) which enable their transformation into an ordinary differential equation for the concentration c_i = c_i(η_i) and a first order equation with partial derivatives for δ_i = δ_i(θ, t). Equations for the mass-transfer coefficient for the unsteady and steady states are obtained. The time in which the steady state is reached is evaluated.