Heat transfer with upstream thermal penetration in flow through porous plate passages

The objective of this study is to develop a series solution for determination of the temperature field in parallel-plate ducts with prescribed wall heat flux. Consideration is also given to ducts filled with fluid saturated porous materials. A simple transformation is used to improve the convergence of this series solution. Temperature variations and heat transfer coefficients are determined for infinitely long parallel-plate ducts when the walls undergo a step change in the applied wall heat flux. Axial thermal penetration near the applied wall heat flux location is studied. The solutions with the contribution of axial conduction in these fluid passages are acquired using a modified Graetz-type solution. Finally, this technique is augmented by the contribution of frictional heating.     

Experimental investigation of coupled conduction and laminar convection in a circular tube

Wall heat conduction effects on laminar flow heat transfer are experimentally investigated. The steady flow of water through a uniformly heated copper pipe is considered in the experiment, which covers a range of Reynolds numbers from 500 to 1900. The thermal behaviour of the test section is simulated numerically and the influence of conduction along the pipe wall is therefore accounted for in the reduction of the data. Fully developed flow results satisfactorily compare with predictions by a theoretical method previously developed by the authors [Heat Technol. 2,72 (1984)]. Results are also reported for the case where the velocity profile is partially developed at the inlet of the heat transfer section. The combined effects on heat transfer of flow development and of wall axial heat conduction are discussed.     

A NUMERICAL STUDY OF THE HEAT TRANSFER TO FLUID FLOW THROUGH CIRCULAR POROUS PASSAGES

A detailed numerical study of heat transfer to a fluid passing through a saturated porous medium is the subject of this study. The Green's function solution method is selected in order to accomplish this task. The interesting features of this methodology are the focus of this article. As a test case, primary consideration is given to the computation of heat transfer to a fluid flowing through a circular passage with impermeable walls filled with porous materials. The analysis includes the heating/cooling effects due to a temperature change at the wall of the passage. In addition, the contributions of frictional heating are examined.     

Temperature field in a moving semi-infinite region with a prescribed wall heat flux

Steady state conduction of heat from a stationary wall to a medium moving at a uniform velocity is the subject herein. This medium can be a solid or a fluid moving at a constant velocity. The surface of this medium is insulated until a change in the surface heat flux occurs. The determination of temperature field is the main objective herein. The results show that the surface temperature begins to increase before its arrival to the heater’s location where there is an abrupt change in the surface heat flux. The application of this phenomenon to a moving wall with frictional heating at its surface and to classical heat transfer in ducts can lead to new information.     

The extended Graetz problem with piecewise constant wall temperature for pipe and channel flows

Axial heat conduction effects within the fluid can be important for duct flows if the Prandtl number is relatively low (liquid metals). In addition, axial heat conduction effects within the flow might also be important, if the heating zone is relatively short in length. The present paper shows an entirely analytical solution to the extended Graetz problem with piecewise constant wall temperature boundary conditions. The solution is based on a selfadjoint formalism resulting from a decomposition of the convective diffusion equation into a pair of first order partial differential equations. The obtained analytical solution is as simple to compute as the one without axial heat conduction. The analytical results are compared to available numerical calculations and good agreement is found.     

Improvement in device performance on laminar counterflow concentric circular heat exchangers with uniform wall fluxes

The effects of recycle at the ends on the heat transfer through a concentric circular tube with uniform wall fluxes are studied analytically by an orthogonal expansion technique with eigenfunction power series expansion. The heat transfer problem is solved for fully developed laminar velocity profiles in a double-pass circular heat exchanger with ignoring axial conduction and fluid properties of temperature independence. Analytical results show the external recycle can enhance the heat transfer efficiency compared with that in an open tube (without an impermeable circular tube inserted and without recycle). The compensation between the forced-convection increment and heat-transfer driving force decrement are used to study the heat transfer behavior. The effects of the impermeable-tube location on heat transfer efficiency enhancement as well as the power consumption increment have been also discussed.     

An evaluation of secondary effects on microchannel frictional and convective heat transfer characteristics

The frictional and convective heat transfer characteristics of rarified flows in rectangular microchannels, with either isoflux or isothermal boundary conditions, are evaluated subject to second-order slip boundary conditions, creep flow, viscous dissipation, and axial conduction effects. Numerical results are obtained using a continuum based, three-dimensional, compressible, unsteady computational fluid dynamics algorithm with first- and second-order slip velocity and temperature jump boundary conditions applied to the momentum and energy equations, respectively. The results, reported in the form of Poiseuille and Nusselt numbers, are found to be significant functions of aspect ratio, Knudsen number, slip model parameters, Brinkman number, and Peclet number.     

Microtube liquid single-phase heat transfer in laminar flow

One of the main applications of microscale flow is miniature, high-efficiency heat transfer. The most simple and immediate solution to the problem of concentrated heat exchange is the use of small diameter channels with single-phase water flow, but there is a lack of publicised knowledge about the heat transfer performance in these conditions. In this article, an experimental investigation is reported to accurately characterize the diabatic behaviour of single-phase laminar flow in circular microducts, ranging in diameter from 528 down to 120 μm. The experiments on a capillary of 50 μm ID proved upon analysis to be unaccountable due to the intrinsic error contained in the set-up, which is tied to the large inertia of the pipe wall, etc. in proportion to the small passage of flow at this diameter. The vacuum environment in which experiments were carried out ensured a test section free of convective losses, so that measurements are provided as precise as possible within the geometry of the microchannel. The possible occurrence of scaling effects such as axial conduction in the walls, viscous heating of the fluid and thermal entrance length effects was studied and criteria were established which have been validated by the measurements. Results show a decrease of Nusselt number with decreasing diameter, an axial dependence that is linked to thermal entrance effects and a dependence of the Nusselt number also on Reynolds number, whence the large conductive losses from the test section can be deduced, not necessarily restricted to axial redistribution of the heat flux in the wall only.     

一种新型可变导热管传热与控制温度机理分析与实验

首次提出了一种新型可变导热管换热装置,用于增压沸腾流化床发电系统中出灰管的冷却与温度控制。分析与实验表明：在出灰管内灰渣流动不稳定,即外界加热负荷或者冷却条件显著变化时,热管的工作温度几乎不变,能够控制在要求的范围内;热管工作温度随充气量增大而增高,但控制温度特性没有明显改变;与常规热管不同,可变导热管内蒸汽温度沿冷凝段轴向显著变化,蒸汽凝结受到了抑制,热管传热量有所减少。     

Heat transfer in the thermal entrance region for flow through rectangular porous passages

The study of heat transfer in rectangular passages with prescribed wall heat flux is of practical interest. These passages could be open or filled with saturated porous materials. A solution that uses the Green’s function can accommodate the inclusion of heat flux over the entire surface area or over isolated sections of the boundary. Also, this solution permits the inclusion of frictional heating. Two different boundary conditions are considered: constant wall temperature and constant wall heat flux. The computed heat transfer coefficients show that the thermally fully developed condition may not be attainable in practical applications for very narrow passages with prescribed wall heat flux.     

Asymptotic behaviors of heat transfer in porous passages with axial conduction

As reported in the literature, a sufficiently small Peclet number requires the inclusion of axial conduction within a fluid flowing in a duct. In fluid saturated porous ducts, this phenomenon greatly increases the heat transfer rate within the thermal entrance region. Axial conduction effects near the thermal entrance regions in parallel-plate ducts and in circular ducts are emphasized in this study. Having metallic foams as porous materials can cause the effective thermal conductivity to increase and this decreases the Peclet number. Here, a simple solution is being used for determination wall heat flux near the thermal entrance location and the result leads to a relatively simple correlation for determination of the bulk temperature.     

An experimental study of axial conduction through a thermosyphon pipe wall

The effect of the axial conduction through the pipe wall on the performance of a thermosyphon was experimentally investigated in this study. Two 2-phase closed thermosyphons were tested; each had the same dimensions, materials and partially filled with R134a. The only difference between them was that one had a thermal break within the adiabatic section that resisted axial conduction between the evaporator and the condenser sections. The thermosyphons were heated by a constant-temperature hot bath and cooled by water via a concentric heat exchanger. The experiments were performed for different bath temperatures and different fill ratios. It was found that the axial conduction through the pipe wall caused an increase in the overall heat transfer coefficient, evaporation heat transfer coefficient and condensation heat transfer coefficient of the thermosyphon. However, the fraction of heat transfer associated with axial conduction decreased as the heat flux increased. For small heat flux (T_b = 30 °C), the increment of the evaporation and condensation heat transfer coefficient contributed by axial conduction reached 100% and 25%, respectively. For high heat flux (T_b = 60 °C), the increment was negligible (less than 1%).     

Conjugated heat transfer in circular ducts with a power-law laminar convection fluid flow

This work deals with the study of the steady-state analysis of conjugated heat transfer process for the thermal entrance region of a developed laminar-forced convection flow of a power-law fluid in a circular tube. A known uniform heat flux is applied at the external surface of the tube. The energy equation in the fluid is solved analytically using the integral boundary layer approximation by neglecting the heat generation by viscous dissipation and the axial heat conduction in the fluid. This solution is coupled to the Laplace equation for the solid, where the axial heat conduction effects are taken into account. The governing equations are reduced to an integro-differential equation which is solved by analytical and numerical methods. The results are shown for different parameters such as conduction parameter, α, the aspect ratio of the tube, ε and the index of power-law fluid, n.     

Temperature and entropy generation behavior in rectangular ducts with 3-D heat transfer coupling (conduction and convection)

Temperature and entropy generation fields are evaluated for 3-D heat transfer coupling (conduction and convection) using a mathematical and computational model. Results are obtained from numerical simulation and analyzed for conditions of fully developed laminar flow inside rectangular ducts. Thermal boundary conditions, at the walls cross section and axial direction, are non-uniform and not imposed. A numerical method of modified TDMA algorithm combined with an iterative solution for the system of algebraic equations obtained was developed. Equations were discretised by finite differences. Convergence is guaranteed by applying the first law of thermodynamics. Considering the thinness of the walls, conduction effectiveness is well represented as 1-D. The methodology applied considers air, water and oil as working fluids at 300 K and carbon-steel as wall material. Results for these cases are presented with the intention of finding, the best fluid heating conditions as a first approach to the design of heat exchangers systems.     

Transient heat fluxes measurement analysis from platinum based thin film gauges in open and closed cavities

Platinum thin film gauges (PTFGs) measure heat fluxes in the applications involving very short duration of the heating environment. Heat transfer measurement is the frequently used technique for measuring the surface heat flux using thin film gauges. The present investigation has been focused on the design and manufacturing methods for heat transfer gauge, their stability, and dynamic calibrations in certain situations where the heat load suddenly build up. PTFGs measure heat fluxes in heating environments applications during the very duration. The measurement for heat transfer is a technique used often with thin film gauges to measure the surface heat flux. The convection devices are regarded as the best measuring units in short-term transient temperature measurement applications and are usually used when the heat transfer mode is dominant means gas turbine engines, high speed aircraft, etc. In addition to that, there are many difficulties incurred for convection based measurement practically and few interdisciplinary research fields. A convective heat load is provided with a hot air gun to get the temperature signal. By using thin film gauge through present investigations, it is very ambitious to explore the possibility of short term conduction based transient measurements with pure conduction heat transfer mode. A simple experimental set up is used to supply the thin film gauges with heat flux, which is manually manufactured with platinum as a sensing material and quartz as a substrate material. The body's nose tip to high speed flow is expected to be the maximum heat transfer at the stagnation point. The stagnation point probes are fabricated for PTFGs, and baking material is quartz. The recorded temperature histories are compared with the experimentally recorded temperature signals from the gauges through the finite element method. The heat flux forecast was configured by using the one dimension thermal conduction equation convolution integral and by comparison with the heat input loads. This study reveals the ability of PTFGs to be used for a short period.     

Semi-analytical solution of the extended Graetz problem for combined electroosmotically and pressure-driven microchannel flows with step-change in wall temperature

Analytical solutions are obtained for the temperature and Nusselt number distribution in the thermal entrance region of a parallel plate microchannel under the combined action of pressure-driven and electroosmotic transport mechanisms, by taking into account the effects of viscous dissipation, Joule heating and axial conduction simultaneously, in the framework of an extended Graetz problem. Step changes in wall temperature are considered to represent physically conceivable thermal entrance conditions. The solution of the temperature distributions at the various channel sections essentially involves the determination of a set of eigenvalues and eigenfunctions corresponding to a Sturm Liouiville problem with non self-adjoint operators. The resultant eigenfunctions are non orthogonal in nature, and are obtained in the forms of hypergeometric functions. Parametric variations on the effects of the relative strengths of the pressure gradients and the electric field, ratio of the rate of heat generation to the rate of wall heat transfer, and the Peclet number are analyzed in details, in terms of their influences on the temperature field as well as the Nusselt number distribution.     

湍流_传递方程及其应用

导出了湍流火用传递方程组 ,依此研究了壁面常热流对流换热管的火用传递 ,计算了由于粘性耗散、径向和轴向导热引起的火用损率分布。通过对单位体积总火用损率的计算表明 ,单位体积总火用损率是换热管几何参数和边界条件的多元函数 ,对于给定的几何参数 ,存在使单位体积总火用损率最小的边界条件 ,反之亦然。该结论对优化设计换热器及对给定边界条件的换热器优化选取具有一定的指导意义。     

Unsteady internal boundary layer analysis applied to gun barrel wall heat transfer

Convective heating to gun barrel walls is of considerable importance when attempting to evaluate the degradation of performance in a ballistic device. The purpose of this study was to isolate and examine convective heating in order to calculate gun tube wall temperature as occurs during the firing of a projectile. Internal flow structure was decoupled by specifying in viscid core properties through measured and assumed axial and temporal variations. A fluid mechanics model was then used to solve the unsteady, compressible, and turbulent momentum and energy boundary layer development at discrete piston locations. Shear layer solutions were coupled through the energy equation. A consideration of radial heat conduction into the bore surface of the ballistic device was used to predict the interior wall temperature history at all locations behind a moving projectile. The results, when compared to those predictions which utilize integral methods and assumed known heat transfer coefficients, indicate that conventional integral methods do not adequately represent the convective heat transfer process. The influence of transverse curvature on the surface heating of small bore guns was examined. Recommendations are given for improving the present model.     

Viscous Joule heating MHD–conjugate heat transfer for a vertical flat plate in the presence of heat generation

The problem of steady conjugate heat transfer through an electrically-conducting fluid for a vertical flat plate in the presence of transverse uniform magnetic field taking into account the effects of viscous dissipation, Joule heating, and heat generation is formulated. The general governing equations which include such effects are made dimensionless by means of an apposite transformation. The ultimate resulting equations obtained by introducing the stream function with the similarity variable are solved numerically using the implicit finite difference method for the boundary conditions based on conjugate heat transfer process. A representative set of numerical results for the velocity and temperature profiles, the skin friction coefficients as well as the rate of heat transfer coefficient and the surface temperature distribution are presented graphically and discussed. A comprehensive parametric study is carried out to show the effects of the magnetic parameter, viscous dissipation parameter, Joule heating parameter, conjugate conduction parameter, heat generation parameter and the Prandtl number on the obtained solutions.     

3D FE model of frictional heating and wear with a mutual influence of the sliding velocity and temperature in a disc brake

Numerical simulation of frictional heating in a disc brake of a typical passenger vehicle based on the equation of motion and the boundary-value problem of heat conduction was carried out. An influence of temperature-dependent coefficient of friction on the sliding velocity, braking time, braking distance and the thermomechanical wear was studied. Two materials of the pad combined with the cast-iron brake disc were examined. The dependencies of the coefficient of friction and wear rate on the temperature and contact pressure were derived from experimental measurements and implemented to the computational model of the brake. Comparisons of temperature for validation purposes calculated using the contact model developed in this study were made with the model introducing an approach based on the heat partition adopted from other studies.