Unsteady Convection in a Binary Mixture in the Neighborhood of a Plane Vertical Surface

The problem of the development of convection in a binary mixture in the neighborhood of an infinite vertical plate, on which a constant (after initial switch-on) heat flux and zero admixture flow are given, is solved. In particular, the cases of neutral and stable density stratification of the medium are considered. It is found that heat transfer to the medium can lead not to an increase but to a decrease in its temperature. This can be interpreted as the effective negative heat capacity of the stratified binary mixture.     

Wall Heat Flux and Thermal Stratification Investigations during the Compression Stroke of an engine-like Geometry: A comparison between LES and DNS

The near wall regions in internal combustion engines contain a significant amount of the gaseous mass in the cylinder and thus have a high relevance for the amount of unburned hydrocarbons, the wall heat transfer and the thermal stratification in the cylinder. In this context in the following study the predictive capability of Large Eddy Simulation (LES) with respect to wall heat flux and thermal stratification during the compression stroke i.e. under non-reactive conditions in an Internal Combustion Engine (ICE) are investigated based on a comparison with Direct Numerical Simulations (DNS). Two different modeling approaches for the near wall region, the low Reynolds damping approach and the LES adapted model from Plengsaard and Rutland, have been tested. During the first half of the compression stroke the low Reynolds damping approach agreed well with the DNS data, but increasing deviations were observed after 270° CA (piston halfway up). The underprediction of the wall heat flux at later stages was found to stem from the underestimation of the y ₊ values of the first cell centroid, compared to values obtained by evaluating the DNS data at the same location, and originates from the model used to determine the friction velocity. As a consequence of the underpredicted y ₊ value, the cell is not located in the viscous sublayer as expected, and the temperature gradient which is needed for the heat flux calculation is underpredicted. The results of the LES wall heat transfer model from Plengsaard and Rutland on the other hand showed overall reasonable agreement with the DNS data, but the model strongly depended on the modeling constants. With respect to the increasing thermal stratification during the compression both methods were found to significantly under predict the DNS results. These findings are especially relevant for LES of auto ignition phenomena in engines, since ignition timing and location are known to strongly depend on the temperature distribution.     

稳定分层湍流中逆梯度输运的关联分析研究

本文采用关联分析方法研究了稳定温度分层湍流中的结构特性、输运特性,以及热量、动量逆梯度输运现象的尺度效应及其参数演化.首先采用大涡模拟方法对稳定分层湍流中的结构特性和输运特性进行了分析,将逆梯度输运发生的时间尺度作为已知条件,结合关联量分析方法在波数空间中的解析解,对逆梯度输运现象的尺度效应进行了分析研究.结果发现,稳定分层强度较大的流动中发生垂向热量及动量逆梯度输运现象,发生的结构尺度与关联分析所发现垂向热量、动量逆梯度输运的波数形成了呼应.随着分层强度增加,热量、动量的输运强度均受抑制,与逆梯度输运关联的流场结构尺度减小,同样的效应也发生在流场结构向下游演化的过程中.     

A possible explanation of countergradient fluxes in homogeneous turbulence

This study addresses the phenomenon of persistent countergradient (PCG) fluxes of momentum and heat (density) as observed in homogeneous turbulence forced by shear and stratification. Countergradient fluxes may occur at large scales when stratification is strong. However, they always occur at small scales, independently of stratification. A conceptional model is introduced to explain PCG fluxes at small scales as the result of the collision of large-scale fluid parcels. The large parcels collide under the driving force of inclined vortex structures (in a shear-dominated flow) or of buoyancy (in a strongly stratified shear flow). This collision model also explains the PCG heat flux in an unsheared stratified flow with zero average momentum flux. It is found that the energy of the small-scale PCG motions is provided (i) by quick transport of kinetic energy from the scales of production to relatively slowly dissipating scales if the flow is shear-driven and (ii) by conversion of available potential energy to kinetic energy at small scales when the flow is stratified. The collision mechanism is an inherent property of the turbulence dynamics. Therefore, the PCG fluxes at small scales reflect a universal character of homogeneous turbulence, and are found over a large range of Reynolds numbers. The Prandtl (or Schmidt) number influences the rate of dissipation of temperature (or density) variance but not the dissipation rate of the velocity variance. In stratified flows, therefore, the number directly affects the strength of the PCG heat flux at small scales. It is found, however, that the PCG momentum flux is also altered slightly when the Prandtl number is large enough to sustain small buoyantly moving parcels after collision.     

Transient natural convection in a cavity with heat input and a constant temperature wall on opposite sides

The transient natural convection of a fluid with Prandtl number of order 200 in a two-dimensional square cavity has been numerically studied. One of the vertical walls of the cavity is kept at a constant (ambient) temperature and a constant heat flux is applied on the opposite wall. The other walls are adiabatic. Initially, a boundary layer is formed near the heated wall; subsequently, a large vortical structure is generated, together with an upper intrusion layer. As time progresses, the average temperature in the cavity increases, and a descending boundary layer is formed near the constant temperature wall. During the transition to the steady-state regime, a thermal stratification pattern is formed. The results are compared with the scale analysis presented by Patterson and Imberger (1980).     

高超声速高焓条件下的内嵌式温敏漆测量方法

热流密度点测量结果并不能完全反映详细的热流分布特征, 尤其是针对热流梯度较大、热流分布复杂的区域, 需要热流密度场测量技术以获取全场精细的热流分布特征. 应用温敏漆测量热流密度场的方法得到了广泛应用, 但实验条件来流总温较低, 与真实飞行环境存在明显差异, 真实飞行条件下的辐射效应严重限制了温敏漆技术的应用. 针对高超声速高焓条件下缺乏热流密度场测量方法的难题, 提出了内嵌式温敏漆测量方法, 基本思想是利用温敏漆测量内壁面温度的变化历程结合热传导反问题的求解确定热流密度. 本文详细介绍了内嵌式温敏漆测量方法的测量原理、测量系统构成、数据处理方法、设计原则及该测量方法的优势. 针对高超声速风洞实验中常见的阶跃、线性和局部突变等热流密度分布进行了数值验证, 验证了内嵌式温敏漆测量方法的可行性, 并分析了风洞实验温度测量精度及噪声对测量结果的影响. 内嵌式温敏漆测量方法可用于测量高超声速真实飞行环境下细致的气动热特征, 扩展了温敏漆测量方法的应用范围, 解决了高超声速高焓条件下缺乏热流密度场测量方法的难题.      

零重力条件下低温射流抑制大尺寸液氢储罐热分层的数值研究

液氢是一种常用的沸点低、易蒸发的空间低温推进剂.空间微重力环境中浮力对流被极大减弱,当推进剂储罐壁面存在局部漏热时,储罐内部气液两相流体系会出现环绕漏热源的热分层现象,引起局部过热沸腾,导致储罐内部压力急剧增大,危害系统结构安全.利用低温射流抑制储罐热分层现象是一种有效手段.低温流体通过设置在储罐内部的射流喷嘴与储罐内...     

Non-fourier heat conduction in a plane slab with prescribed boundary heat flux

The non-stationary heat conduction in an infinitely wide plane slab with a prescribed boundary heat flux is studied. An arbitrary time dependent boundary heat flux is considered and a non-vanishing thermal relaxation time is assumed. The temperature and the heat flux density distributions are determined analytically by employing Cattaneo-Vernotte's constitutive equation for the heat flux density. It is proved that the temperature and the heat flux density distributions can be incompatible with the hypothesis of local thermodynamic equilibrium. A comparison with the solution which would be obtained by means of Fourier's law is performed by considering the limit of a vanishing thermal relaxation time.     

Transient heat flux measurement of natural convection in an inclined enclosure with time-periodically-varying wall temperature

The transient natural convection in an inclined enclosure filled with water is studied experimentally for the time-periodically-varying wall temperature on one side wall and constant average temperature on the opposing side wall. This system has no temperature difference between the opposing two side walls in time-averaged sense. The temperatures of two opposing walls and the heat flux across the enclosure are measured by a heat flux meter. Based on the experimental results, the effects of time-periodically-varying wall temperature and inclined angles of the enclosure on heat transfer characteristics are studied. The experimental results show that, with the upper wall temperature oscillating, the heat flux across the enclosure is also periodically varied with time, and the net heat flux is from the lower wall to the upper wall. Numerical computations are also conducted and numerical results are qualitatively assured by the experimental measurements.     

Heat transfer in a hydromagnetic flow over a stretching sheet

Exact solutions are obtained for the heat transfer in an electrically conducting fluid past a stretching sheet subjected to the thermal boundary with either a prescribed temperature or a prescribed heat flux in the presence of a transverse magnetic field. The solutions for the heat transfer characteristics are evaluated numerically for different parameters, such as the magnetic parameterN, the Prandtl numberPr, the surface temperature indexs, and the surface heat flux indexd. It is observed that for the prescribed surface temperature case the fluid temperature increases due to the existance of the magnetic field, and decreases as the Prandtl number or the surface temperature index increases; for the prescribed surface heat flux case, the surface temperature decreases as the Prandtl number of the surface heat flux index increases, and the magnetic parameter decreases. In addition, varying the prescribed surface temperature indexs affects the mechanism of heat transfer.     

Laminar forced convection with sinusoidal wall heat flux distribution: axially periodic regime

Stationary and laminar forced convection in a circular tube with a sinusoidal axial distribution of wall heat flux is studied under the hypothesis that both axial heat conduction and viscous dissipation in the fluid are negligible. Two cases are considered: a sinusoidal wall heat flux distribution with a vanishing mean value; a sinusoidal wall heat flux distribution which does not change its sign. In both cases, the temperature field and the local Nusselt number are evaluated analytically in the fully developed region, i.e. where the local Nusselt number depends periodically on the axial coordinate. It is shown that, in the first case, the fully developed region presents an infinite sequence of axial positions where the local Nusselt number is singular. In these positions, the wall heat flux has a non-vanishing value even if the wall temperature equals the bulk temperature.     

Heat conduction and thermal stress induced by an electric current in an infinite thin plate containing an elliptical hole with an edge crack

A uniform electric current at infinity was applied to a thin infinite conductor containing an elliptical hole with an edge crack. The electric current gives rise to two states, i.e., uniform and uneven Joule heat. These two states must be considered to analyze the heat conduction problem. The uneven Joule heat gives rise to uneven temperature and thus to heat flux, and to thermal stress.Using a rational mapping function, problems of the electric current, the Joule heat, the temperature, the heat flux, the thermal stress are analyzed, and each of their solutions is obtained as a closed form. The distributions of the electric current, the Joule heat, the temperature, the heat flux and the stress are shown in figures.The heat conduction problem is solved as a temperature boundary value problem. Solving the thermal stress problem, dislocation and rotation terms appear, which complicates this problem. The solutions of the Joule heat, the temperature, the heat flux and the thermal stress are nonlinear in the direction of the electric current. The crack problems are also analyzed, and the singular intensities at the crack tip of each problem are obtained. Mode II (sliding mode) stress intensity factor (SIF) is produced as well as Mode I (opening mode) SIF, for any direction of the electric current. The relations between the electric current density and the melting temperature and between the electric current density and SIF are investigated for some crack lengths in an aluminum plate.     

Momentum and heat transfer of a special case of the unsteady stagnation-point flow

This paper investigates the unsteady stagnation-point flow and heat transfer over a moving plate with mass transfer, which is also an exact solution to the unsteady Navier-Stokes(NS) equations. The boundary layer energy equation is solved with the closed form solutions for prescribed wall temperature and prescribed wall heat flux conditions. The wall temperature and heat flux have power dependence on both time and spatial distance. The solution domain, the velocity distribution, the flow field, ...     

Retrieving the heat transfer coefficient for jet impingement from transient temperature measurements

Algorithm of retrieving the heat transfer coefficient (HTC) from transient temperature measurements is presented. The unknown distributions of two types of boundary conditions: the temperature and heat flux are parameterized using a small number of user defined functions. The solutions of the direct heat conduction problems with known boundary temperature and flux are expressed as a superposition of auxiliary temperature fields multiplied by unknown parameters. Inverse problem is formulated as a least squares fit of calculated and measured temperatures and is cast in a form of a sum of two objective functions. The first results originates from an inverse problem for retrieving the boundary temperature the second comes from the inverse problem for reproducing the boundary heat flux. The final form of the objective function is obtained by enforcing constant in time value of the heat transfer coefficient. This approach leads to substantial regularization of the results, when compared with the standard technique, where HTC is calculated from separately reconstructed temperature and heat flux on the boundary. The validation of the numerical procedure is carried out by reconstructing a known distribution of the HTC using simulated measurements laden by stochastic error. The proposed approach is also used to reconstruct the distribution of the HTC in a physical experiment of heating a cylindrical sample using an impinging jet.     

Dynamical temperature and generalized heat-conduction equation

By means of a dynamical non-equilibrium temperature we derive a generalized heat-conduction equation which accounts for non-local, non-linear, and relaxation effects. The dynamical temperature is also capable to reproduce several enhanced heat equations recently proposed in literature. The heat flux is supposed to be proportional to the gradient of the dynamical temperature, and the material functions are allowed to depend on temperature. It is also pointed out that the heat flux cannot assume arbitrary values, but it is limited from above by a maximum value which ensures that the thermal conductivity remains positive.     

Exact solution of heat transfer from a stretching surface with variable heat flux

An exact expression of the temperature distribution is constructed for the heat transfer from a stretching surface with prescribed power law heat flux. The stretching velocity is inversely proportional to the one third power of the distance measured along the surface from a thin slit. The final result is expressed in terms of hypergeometric functions. Although the exact solution is accomplished, some physically unrealistic phenomena are encounters for specific conditions. The temperature parameter which prescribe the surface heat flux, strongly affects those situations. Two types of temperature distribution are discussed: dimensionless temperatures with and without scaling to the dimensionless surface temperature. The expression of the temperature distribution without scaling is lucid to understand the heat transfer characteristics. Received on 23 July 1997     

Free convection on a vertical plate with uniform and constant heat flux in a thermally stratified micropolar fluid

This paper analyzes flow and heat transfer characteristics of the free convection on a vertical plate with uniform and constant heat flux in a thermally stratified micropolar fluid. The dimensionless forms of boundary layer equations and their associated boundary conditions have been derived and the numerical results have been obtained using the method of cubic spline collocation with a finite difference scheme. The effects of the micropolar and stratification parameters on the dimensionless wall temperature, skin friction parameter and wall couple stress are discussed.     

Experimental investigation of micro-scale temperature transients in sub-cooled flow boiling on a horizontal heater

Surface temperature fluctuations that occur locally underneath departing bubbles in pool boiling are shown to result in local heat transfer coefficients ranging from 1 to 10 kW/cm². These estimates were reported in the literature involved both numerical and experimental approaches. Significantly higher heat fluxes are associated with flow boiling than pool boiling under similar conditions of wall superheat and liquid subcooling (e.g. at boiling inception and at critical heat flux). These enhancements are primarily caused by the convective transport, acceleration/distortion of the bubble departure process as well as the resultant potential enhancement of the local surface temperature fluctuations.In this study we measure the surface temperature fluctuations using temperature micro/nano-sensors fabricated on a silicon wafer during flow boiling on the silicon wafer which is heated from below. The silicon wafer is clamped on a constant heat flux type calorimeter consisting of a vertical copper cylinder with embedded cartridge heaters and K-type thermocouples. Micro/nano-thermocouples (thin film thermocouples or “TFT”) are fabricated on the surface of the silicon wafer. High speed data acquisition apparatus is used to record temperature data from the TFT at 1 kHz. A fluorinert was used as the test fluid (PF-5060, manufacturer: 3M Co.). The calorimeter and surface temperature measurement apparatus is housed in a test section with glass walls for visual observation. The liquid is pumped from a constant temperature bath to maintain a fixed subcooling during the experiments under steady state conditions. The transient temperature data from the FFT array during flow boiling on the silicon wafer is analyzed using fast Fourier transform (FFT). The FFT data is analyzed as a function of the wall heat flux and wall superheat. The number of temperature peaks in the FFT data is observed to increase with increase in wall heat flux and the peaks are found to cover a wider spectrum with peaks at higher frequencies with enhancement of heat flux. The surface temperature fluctuations, especially at small length and time scales, are perturbed potentially by the coupled hydrodynamic and thermal transport processes, resulting in enhanced local and global heat flux values. Boiling incipience condition and the flow boiling data are compared with correlations reported in the literature.     

On moving heat sources

The two-dimensional thermal problem due to relative motion of a medium and a suddenly activated circular heat source is solved for several boundary conditions. The solutions can be interpreted as for a moving heat source in a stationary medium or a medium moving past a stationary heat source. Uniform and non-uniform temperature, and uniform and non-uniform heat flux boundary conditions are considered. The effect of velocity and radial direction on the temperature distribution is examined. Average, steady-state Nusselt numbers are derived. The transient response of a continuous line source is obtained as a limiting case of the prescribed heat flux solution. Received on 24 September 1996