Heat and mass transfer analogy for condensation of humid air in a vertical channel

This study examines energy transport associated with liquid film condensation in natural convection flows driven by differences in density due to temperature and concentration gradients. The condensation problem is based on the thin-film assumptions. The most common compositional gradient, which is encountered in humid air at ambient temperature is considered. A steady laminar Boussinesq flow of an ideal gas–vapor mixture is studied for the case of a vertical parallel plate channel. New correlations for the latent and sensible Nusselt numbers are established, and the heat and mass transfer analogy between the sensible Nusselt number and Sherwood number is demonstrated. Received on 15 November 1999     

Local heat transfer from a hot plate to a water jet

Jet impingement boiling is very efficient in cooling of hot surfaces as a part of the impinging liquid evaporates. Because of its importance to many cooling procedures, investigations on basic mechanisms of jet impingement boiling heat transfer are needed. Until now, most of the experimental studies, carried out under steady-state conditions, used a heat flux controlled system and were limited by the critical heat flux (CHF). The present study focuses on steady-state experiments along the entire boiling curve for hot plate temperatures of up to 700°C. A test section has been built up simulating a hot plate. It is divided into 8 independently heated modules of 10 mm length to enable local heat transfer measurements. By means of temperature controlled systems for each module local steady-state experiments in the whole range between single phase heat transfer and film boiling are possible. By solving the two dimensional inverse heat conduction problem, the local heat flux and the corresponding wall temperature on the surface of each module can be computed. The measurements show important differences between boiling curves measured at the stagnation line and those obtained in the parallel flow region. At the stagnation line, the transition boiling regime is characterised by very high heat fluxes, extended to large wall superheats. Inversely, boiling curves in the parallel flow region are very near to classical ones obtained for forced convection boiling. The analysis of temperature fluctuations measured at a depth of 0.8 mm from the boiling surface enables some conclusions on the boiling mechanism in the different boiling regimes.     

Investigation on Heat and Mass Transfer in a Evaporator of a Capillary-Pumped Loop with the Lattice Boltzmann Method: Pore Scale Simulation

A two-dimensional transient numerical model based on the lattice Boltzmann method (LBM) for the global evaporator of a capillary-pumped loop (CPL) is proposed to describe heat and mass transfer with evaporation in the porous wick, heat conduction in the cover plate, and heat transfer in the vapor groove. To indicate the stochastic phase distribution characteristics of most porous wick, the quartet structure generation set (QSGS) is introduced for generating more realistic microstructures of porous media. By using the present lattice Boltzmann algorithm along with the porous structure, the heat and mass transfer of an evaporator on pore scale can be predicted without resorting to any empirical parameters determined case by case. The energy equations for entire evaporator are solved as a conjugate problem, which are solved by means of a spatially varying relaxation time in the lattice Boltzmann model and the liquid flow is driven via the interfacial mass flux. A convective boundary condition considering the latent heat during the evaporation on the interface is introduced into the lattice Boltzmann model based on the nonequilibrium extrapolation rule. Especially, the bounce-back rule and the equilibrium rule of the LBM are, respectively, introduced to deal with the momentum boundary conditions inside the porous wick and on the evaporation interface in order to ensure the stability and the efficiency of the LBM model. Numerical results corresponding to different working conditions and different working fluids are presented, which provide guidance for the evaporator design of a CPL system.     

Effects of boundary reflection on radiative heat transfer in participating media

Radiative heat transfer through a non-isothermal grey participating medium between two parallel surfaces kept at fixed temperature has been investigated. The integro-differential transfer equations for surface reflection were solved in semi-analytical form by projectional methods; conduction and convection were neglected. It was assumed that reflection from the cold wall was diffuse, while that from the hot wall was either diffuse or specular. The heat flux and the temperature distribution in the participating medium were calculated in each physical condition, in order to compare the effects of different reflection modes on heat transfer. The results show that temperature distributions and heat fluxes are only slightly affected by the particular reflection law, the relative difference being less than 1%. This suggests that diffuse reflection only could be considered for practical applications, since it requires a much simpler computational procedure.     

Wärmeübergang bei der Fallfilmverdampfung

At film evaporation in a vertical tube the heat transfer depends on the flow pattern of the falling film and the shear stress at film surface due to a significant flow in the gas phase. For heat transfer without superimposed gas flow equations exist which are checked experimentally. These equations have general validity for film evaporation and film condensation. By describing the influence of gas flow great differences occur between condensation and evaporation. The present work deals with a calculation method which was verified by condensation data. This method is compared and discussed with experimental results of film evaporation. It is shown that the presented method describing the shear stress influence is also applicable.     

Unsteady natural convection Couette flow of heat generating/absorbing fluid between vertical parallel plates filled with porous material

The extended Brinkman Darcy model for momentum equations and an energy equation is used to calculate the unsteady natural convection Couette flow of a viscous incompressible heat generating/absorbing fluid in a vertical channel(formed by two infinite vertical and parallel plates) filled with the fluid-saturated porous medium.The flow is triggered by the asymmetric heating and the accelerated motion of one of the bounding plates.The governing equations are simplified by the reasonable dimensionless parameters and solved analytically by the Laplace transform techniques to obtain the closed form solutions of the velocity and temperature profiles.Then,the skin friction and the rate of heat transfer are consequently derived.It is noticed that,at different sections within the vertical channel,the fluid flow and the temperature profiles increase with time,which are both higher near the moving plate.In particular,increasing the gap between the plates increases the velocity and the temperature of the fluid,however,reduces the skin friction and the rate of heat transfer.     

Laminar heat transfer in parallel plate flow

An exact solution for the fluid temperature due to laminar heat transfer in parallel plate flow is found. The formulas obtained are valid for an arbitrary velocity profile. The basic problem encountered involves finding certain expansion coefficients in a series of nonorthogonal eigenfunctions. This problem is solved by passing to a vector system of equations having orthogonal eigenvectors. The method is applicable to more general problems.     

Effect of flow pulsation on laminar heat transfer between two parallel plates

The problem of heat transfer in viscous laminar pulsatile flow between two parallel plates is solved by means of a finite difference method. Boundary conditions of constant wall temperature and constant wall heat flux are considered separately. The numerical results show that flow pulsations change the instantaneous Nusselt number, but do not have any significant effect on the time-averaged values. A trend in reduction of timeaveraged Nusselt number is observed when the amplitude of flow pulsation increases and the frequency decreases. The validity of the result is limited to the case when no flow reversal exists.     

The effective sky temperature: an enigmatic concept

To properly simulate the condensation process and design a water recovery system from condensation of atmospheric water vapour on a surface maintained below the dew point by radiative heat loss from the surface to night sky, an accurate estimation of the effective sky temperature is required. To estimate the effective night sky temperature, an experimental system consisting of a series of metal plates embedded on a heat transfer panel, a weather station and a control system was used. The results obtained from theoretical analyses and preliminary experiments are presented and discussed. A special emphasis is given to a mathematical solution of the system of equations that need to be solved to obtain the effective sky temperature. It is shown that although the system of equations works well for the direct heat transfer problem, there is a serious difficulty to solve the inverse heat transfer problem to retrieve the desired parameters.     

The optimum shape for converting rectangular fins when condensation occurs

There may be condensation on the fin surfaces of the air conditioning systems due to the temperature of the fin surfaces being below the dew point temperature of the water vapor in the surrounding air. Heat and mass transfer occur from the saturated air layer to the liquid water film and the latent heat of condensation is transferred to the fin. This study presents a quasilinearization solution for vertical rectangular fins when condensation occurs, assuming that the average convective heat and mass transfer coefficients are constant along the height of the fin. Rectangular fins with and without condensation on the surface have been compared and optimum fin dimensions have been given. The optimum fin length, the fin effectiveness and the average fin temperature in the case of condensation were found to be smaller than in the case of no condensation.     

Melting heat transfer in steady laminar flow over a moving surface

The steady laminar boundary layer flow and heat transfer from a warm, laminar liquid flow to a melting surface moving parallel to a constant free stream is studied in this paper. The continuity, momentum and energy equations, which are coupled nonlinear partial differential equations are reduced to a set of two nonlinear ordinary differential equations, before being solved numerically using the Runge–Kutta–Fehlberg method. Results for the skin friction coefficient, local Nusselt number, velocity profiles as well as temperature profiles are presented for different values of the governing parameters. Effects of the melting parameter, moving parameter and Prandtl number on the flow and heat transfer characteristics are thoroughly examined. It is found that the problem admits dual solutions.     

Finite element analysis of flow,heat transfer,and free interfaces in an electron-beam vaporization system for metals

A numerical analysis is made of the liquid flow and energy transport in a system to evaporate metals. The energy from an electron-beam heats an axisymmetric metal disk supported by a water-cooled platform. Metal evaporates from the surface of a hot pool of liquid which is surrounded by a shell of its own solid. Flow in the pool is strongly driven by temperature-induced buoyancy and capillary forces, and is located in the transition region between laminar and turbulent flow. The evaporation rate is strongly influenced by the locations of the free boundaries. A modified finite element method is used to calculate the steady state flow and temperature fields coupled with the interface locations. The mesh is structured with spines that stretch and pivot as the interfaces move. The discretized equations are arranged in an ‘arrow’ matrix and are solved using the Newton–Raphson method. The electron-beam power and platform contact resistance are varied for cases involving the evaporation of aluminum. The results reveal the interaction of liquid flow, heat transfer and free interfaces. © 1998 John Wiley & Sons, Ltd.     

Double tube heat exchanger with novel enhancement: part I—flow development length and adiabatic friction factor

The study is conducted to evaluate the flow characteristics in a double tube heat exchanger using two new and versatile enhancement configurations. The novelty is that they are usable in single phase forced convection, evaporation and condensation. Correlations are proposed for flow development length and friction factor for use in predicting fluid pumping power in thermal equipment as well as in subsequent heat transfer characterization of the surface.     

Effect of viscous dissipation and heat source on flow and heat transfer of dusty fluid over unsteady stretching sheet

This paper investigates the problem of hydrodynamic boundary layer flow and heat transfer of a dusty fluid over an unsteady stretching surface.The study considers the effects of frictional heating(viscous dissipation) and internal heat generation or absorption.The basic equations governing the flow and heat transfer are reduced to a set of non-linear ordinary differential equations by applying suitable similarity transformations.The transformed equations are numerically solved by the Runge-Kutta-Fehlberg-45 order method.An analysis is carried out for two different cases of heating processes,namely,variable wall temperature(VWT) and variable heat flux(VHF).The effects of various physical parameters such as the magnetic parameter,the fluid-particle interaction parameter,the unsteady parameter,the Prandtl number,the Eckert number,the number density of dust particles,and the heat source/sink parameter on velocity and temperature profiles are shown in several plots.The effects of the wall temperature gradient function and the wall temperature function are tabulated and discussed.     

一种全耦合多相流分析的并行计算方法

研究了孔隙介质中热、水和汽流全耦合分析的并行计算方法．模型中采用了考虑毛细压力关系的修正有效应力概念,并考虑了相变和潜热传递．基本变量为位移、毛细压力、汽压和温度．并行程序是在国家高性能计算中心（北京）的曙光１０００Ａ上借助ＰＶＭ（ＰａｒａｌｅｌＶｉｒｔｕａｌＭａｃｈｉｎｅ）软件系统实现的,考题显示出较高的并行加速比和效率     

MHD Flow and heat transfer of non-Newtonian power-law fluid with diffusion and chemical reaction on a moving cylinder

The problem of flow and heat transfer of an electrically conducting non-Newtonian fluid over a continuously moving cylinder in the presence of a uniform magnetic field is analyzed for the case of power-law variation in the temperature and concentration at the cylinder surface. A diffusion equation with a chemical reaction source term is taken into account. The governing non-similar partial differential equation are solved numerically by employing shooting method. The effects of various parameters on the velocity, temperature and concentration profiles as well as the heat and mass transfer rate from the cylinder surface to the surrounding fluid are presented graphically and in tabulated form.     

Heat transfer analysis of Williamson fluid over exponentially stretching surface

This study explores the effects of heat transfer on the Williamson fluid over a porous exponentially stretching surface. The boundary layer equations of the Williamson fluid model for two dimensional flow with heat transfer are presented. Two cases of heat transfer are considered, i.e., the prescribed exponential order surface temperature （PEST） case and the prescribed exponential order heat flux （PEHF） case. The highly nonlinear partial differential equations are simplified with suitable similar and non-similar variables, and finally are solved analytically with the help of the optimal homotopy analysis method （OHAM）. The optimal convergence control parameters are obtained, and the physical fea- tures of the flow parameters are analyzed through graphs and tables. The skin friction and wall temperature gradient are calculated.     

R410A condensation inside a commercial brazed plate heat exchanger

This paper presents the heat transfer coefficients and the pressure drop measured during HFC-410A condensation inside a commercial brazed plate heat exchanger: the effects of saturation temperature, refrigerant mass flux and vapour super-heating are investigated. The heat transfer coefficients show weak sensitivity to saturation temperature and great sensitivity to refrigerant mass flux and vapour super-heating. At low refrigerant mass flux (<20 kg/m² s) the saturated vapour condensation heat transfer coefficients are not dependent on mass flux and are well predicted by Nusselt [W. Nusselt, Die oberflachenkondensation des wasserdampfes, Energy 60 (1916) 541–546, 569–575] analysis for vertical surface: the condensation process is gravity controlled. For higher refrigerant mass flux (>20 kg/m²s) the saturated vapour condensation heat transfer coefficients depend on mass flux and are well predicted by Akers et al. [W.W. Akers, H.A. Deans, O.K. Crosser, Condensing heat transfer within horizontal tubes, Chem. Eng. Prog. Symp. Series 55 (1959) 171–176] equation: forced convection condensation occurs. In the forced convection condensation region the heat transfer coefficients show a 30% increase for a doubling of the refrigerant mass flux. The condensation heat transfer coefficients of super-heated vapour are 8–10% higher than those of saturated vapour and are well predicted by Webb [R.L. Webb, Convective condensation of superheated vapor, ASME J. Heat Transfer 120 (1998) 418–421] model. A simple linear equation based on the kinetic energy per unit volume of the refrigerant flow is proposed for the computation of the frictional pressure drop.     

Stability of the evaporation and condensation surfaces in a porous medium

The stability of a phase transition interface which separates the soil regions saturated with water and humid air, respectively, is investigated. The humid air region contacting with the atmosphere is assumed to be located above the water-saturated region. Water flows through the porous medium in the lower region, while diffuse vapor transfer is implemented in the upper region. Two cases corresponding to water evaporation and vapor condensation are considered. In the first case water flows out from the porous aquifer, evaporates, and comes out into the atmosphere. In the second case, during condensation, the atmospheric moisture saturates soil. The problem is solved in the steady-state case. The investigation of linear stability carried out by means of the normal mode method shows that the evaporation surface can be unstable in both nonwettable and wettable soils in the presence of the capillary pressure gradient. Depending on the parameters, the condensation surface can be unstable also in the neutral medium.     

3-D analysis of temperature distribution in the material during pulsed laser and material interaction

Recently, lasers are being increasingly used in the industry owing to their precision and low cost. Material is heated and evaporated during laser and material interaction due to the absorption of laser beams by the material. In this study, a 3-D Laser heating model including evaporation has been solved using the electron- kinetic theory approach. The basis in examining the problem using the kinetic theory approach is to describe the heat conduction through electron-phonon and molecule-phonon collisions. The problem is solved by using the electron-kinetic theory approach in such a way that heat conduction is taken into account until the material is heated to its melting temperature and non-conduction limited heat transfer is considered after the melting temperature is reached. Non-conduction limited heat transfer through the phase change process is resulted from vacancy-molecule collisions. A numerical scheme is introduced to solve the governing equation, owing to the fact that the energy equation resulted is in the form of integro-differential equation. Four different materials, namely iron, nickel, tantalum and titanium are chosen in this study determine the material response to laser pulse heating. For each material, time dependent temperature distribution through the depth of the material and on the surface of the material is computed and analyzed for four different materials.