Forced convection from a microstructure on a flat plate

In this work, a cooling of a flat microelectronic structure with single-phase forced convection is investigated. The axial conduction, usually neglected in boundary layer theory, is considered here since the length of the heated element is in the same order of magnitude as the thickness of the boundary layer. The microstructure represents a package of chips mounted flush with the surface of the plate, and uniformly heated with a constant heat flux. The differential method is used to reduce the governing partial differential equations to ordinary differential ones, which are solved numerically by the use of a computational code developed by the authors. This code is based on Keller–Box method. The temperature profiles and Nusselt numbers are plotted at several locations on the heated element and are given as functions of the Reynolds number at the beginning of heated microstructure and of the ratio of unheated to heated length. Furthermore, the average Nusselt numbers on the heated length are computed for Prandtl numbers in the range 0.7≤Pr≤7,000. The results are compared to the boundary layer solution of unheated starting length problem. The results will be used as a baseline for successively more complex situations of cooling in electronics.     

Effect of heat flux on boundary layer flow under rotating conditions

The boundary layer flow behaviour in a smooth rotating channel with heated walls is measured by particle image velocimetry (PIV). To simulate the real operation environment of an internal coolant channel in a turbine blade, airflow is analysed in a rotating channel, whose four walls are uniformly heated by Indium Tin Oxide (ITO) glass. The flow is measured in the middle plane of the rotating channel with a Reynolds number equal to 10000 and rotation numbers ranging from 0 to 0.52. The results are presented for the boundary layer flow behaviour with and without heated thermal boundary conditions. The buoyancy force generated by the heated walls influences the flow behaviour under rotating conditions. Separated flow occurs, which substantially influences the turbulent flow behaviours. Sometimes, this buoyancy force can determine the flow behaviours. The results also showed that the displacement thickness and the momentum loss thickness present new changes at different radius positions due to the heated thermal boundary conditions. The displacement thicknesses of both the leading and trailing sides with heated walls are both thicker than those of the leading and trailing sides without heated walls. Then, the difference of the boundary layer thickness between these two cases increases with the increase of rotation number. For momentum loss thickness, a sharp drop happens when the rotation number increases to a certain value. At the large radius position, the drop in momentum loss thickness is much greater than that in the small radius position.     

Buckling of thin cylindrical shells heated along an axial strip

The results of buckling tests on circular cylinders heated uniformly along axial strips are presented and discussed. Calculations of critical temperature based upon the small-deflection theory for thin circular cylindrical shells are included and a comparison is made between theoretical and experimental results. Cylinders heated along axial strips of given widths have a theoretically predicted behaivor which corresponds reasonably well to the behavior obtained by experiment. Curves are included showing the variation of critical temperature with respect to heated axial-strip width.     

DNS of heat transfer increase in a cylinder stagnation region due to wake-induced turbulence

Heat transfer in the stagnation point area of a heated cylinder is investigated using Direct Numerical Simulation (DNS). The heated cylinder is subjected to the turbulent wake of a smaller cylinder placed upstream. Two Reynolds numbers based on the diameter of the heated cylinder of 13,200 and 48,000 are chosen. In accordance with correlations in the literature, an increase in heat transfer compared to fully laminar flow is found for all angles along the front circumferential area of the heated cylinder. However, due to the presence of the wake, the maximum increase is shifted away from the centerline. The characteristic turbulence level and Nusselt number in the present study are an order of magnitude higher than those reported in previous simulations. The DNS results obtained, are in good agreement with an existing experimental correlation. Finally, relevant flow structures and instantaneous temperature fields are visualized.     

Magnetothermal force on heated or cooled pipe flow

The effects of the magnetothermal force on the flows of heat and fluid through a pipe are investigated numerically when the pipe wall is either heated or cooled at constant heat flux. The flow is laminar and a paramagnetic fluid is presumed as the working fluid. Because the magnetic susceptibility of a paramagnetic fluid depends on the inverse of its temperature, the magnetothermal force is induced by coupling of the temperature field and magnetic induction. First, the effects are discussed using the case of a magnetic field induced by a single-turn concentrically placed electric coil. It is found that the effects of the magnetothermal force differ according to whether the pipe is cooled or heated. When cooled, the heat and fluid flows are affected behind the coil; the flow is repelled from the wall to the center and the thermal boundary layer thickens. By decomposing the force into the radial and axial directions in the heated and cooled cases, it is clarified that the axial force changes from positive to negative depending on the coil location in the heated case. Therefore, it can be concluded that the effects are not simply oppositional in the heated and cooled cases. In relation to the heat transfer, only when the coil is placed at the threshold of the heating/cooling zone do the effects on the local heat transfer become the opposite of each other. At other coil locations, the suppression of heat transfer is dominant ahead of the coil in the heated case, as indicated in previous work by our group. However, in the cooled case, this effect occurs behind the coil. For a more practical case, a solenoid coil is employed in the simulation. It is then found that the effect on the heat transfer becomes remarkable at the solenoid edges, especially for the heat-transfer suppression in both the heated and cooled cases.     

Thermal imaging study on the surface wave of heated falling liquid films

By using thermal imaging technique and film thickness metering system, the surface wave and film thickness of the heated falling liquid film were experimentally investigated. Temperature variations of the heated film induce surface tension gradient and so-caused Marangoni flow that attempts to avoid the temperature variations. There are three kinds of Marangoni flow appearing in the heated falling liquid film. It is found that the lateral Marangoni flow (MF I) and the streamwise Marangoni flow (MF II) make the heated film thick, while the Marangoni flow in the surface wave (MF III) reinforces the wave and makes the heated film thin. The intensity of Marangoni flow is determined by the flow rate and the heating conditions. MF I and MF II are both enhanced with the increasing liquid flow rate. Moreover, MF III is prominent under moderate flow rates and is gradually weakened at high flow rates. The distance over which MF III starts, increases with a rise in flow rate, but is independent of the heating condition.     

Natural convection in partially cooled tilted cavities

Two-dimensional numerical simulations of laminar natural convection in a partially cooled, differentially heated inclined cavities are performed. One of the cavity walls is entirely heated to a uniformly high temperature (heat source) while the opposite wall is partially cooled to a lower temperature (heat sink). The remaining walls are adiabatic. The tilt angle of the cavity is varied from 0° (heated from left) to −90° (heated from top). The fast false implicit transient scheme (FITS) algorithm, developed earlier by the same authors, is modified to solve the derived variables vorticity-streamfunction formulation. The effects of aspect ratio (AR), sink–source ratio and tilt angle on the average Nusselt number are examined through a parametric study; solutions are obtained for two Grashof numbers, 10⁵ and 10⁷. Flow patterns and isotherms are used to investigate the heat transfer and fluid flow mechanisms inside the cavity. © 1998 John Wiley & Sons, Ltd.     

Effect of Time Periodic Boundary Conditions on Convective Flows in a Porous Square Enclosure with Non-Uniform Internal Heating

The problem of unsteady natural convection in a square region filled with a fluid-saturated porous medium having non-uniform internal heating and heated laterally is considered. The heated wall surface temperature varies sinusoidally with the time about fixed mean temperature. The opposite cold wall is maintained at a constant temperature. The top and bottom horizontal walls are kept adiabatic. The flow field is modelled with the Darcy model and is solved numerically using a finite difference method. The transient solutions obtained are all periodic in time. The effect of Rayleigh number, internal heating parameters, heating amplitude and oscillating frequency on the flow and temperature field as well as the total heat generated within the convective region are presented. It was found that strong internal heating can generate significant maximum fluid temperatures above the heated wall. The location of the maximum fluid temperature moves with time according to the periodically changing heated wall temperature. The augmentation of the space-averaged temperature in the cavity strongly depends on the heating amplitude and rather insensitive to the oscillating frequency.     

金属丝壁面加热湍流标度律的实验研究

通过在固壁表面的平板湍流边界层沿流向平行放置若干通电加热的金属细丝,在平板表面形成沿展向周期性分布的温度场,利用该温度场引起的空气热对流,在湍流边界层近壁区域产生一组沿湍流边界层展向周期分布的流向涡结构。对壁湍流小尺度结构标度律统计特性的研究表明,金属丝加热后形成的规则流向涡结构将壁湍流各种尺度湍涡结构不规则的脉动有序地组织起来,增强了湍流小尺度结构的层次结构相似性,减小了壁湍流中小尺度结构的间歇性和奇异性,抑制了壁湍流中奇异的湍涡结构。     

超音速气流中受热壁板的稳定性分析

采用Galerkin方法建立二维壁板的非线性气动弹性运动方程,用一阶活塞理论模拟壁板 受到的气动力. 基于李雅普诺夫间接法分析了平壁板的稳定性,得到了壁板失稳的边界 曲线;采用牛顿迭代法分析了壁板的屈曲变形,进而分析了后屈曲状态下壁板的稳定性; 在时域中分析了后屈曲状态下壁板的颤振边界. 分析结果表明,为了保证计算精度, 在二维壁板的静态失稳及过屈曲变形分析中,至少要取二阶谐波模态;在平壁板的超音速颤 振(动态失稳)边界分析中至少应取四阶模态. 还对壁板的温升,壁板长厚比、壁板密 度和气流马赫数作了无量纲变参分析,研究了这些参数的变化对壁板稳定性的影响规律. 研 究中发现,当气流速压较低时壁板一般会稳定在低阶谐波模态的屈曲变形位置,但是如果系 统出现多个渐近稳定的不动点,即使作用在壁板上的气流速压很低,壁板也有可能在较低速 压下发生二次失稳型颤振.     

Investigation of the rarefied gas flow around a circular cylinder in stationary and oscillatory regimes

Numerically, on the basis of the Krook kinetic equation, the rarefied gas flow around a circular cylinder is investigated in stationary and oscillatory regimes. The flows around a rotating cylinder and a cylinder with a nonuniformly heated surface are considered. The Knudsen numbers at which the lift force acting on the rotating cylinder changes sign are calculated. It is shown that at low Knudsen numbers a lift force acts on the nonuniformly heated cylinder.     

Soret effect on propagation of thermoconvective waves in a binary mixture

Effects of thermal diffusion (Soret effect) on the propagation of thermoconvective waves (TCW) in a layer of binary mixture are investigated. It is shown that undamped propagation of TCW is possible in a layer heated from below provided the Soret number is large and positive. A novel result of the analysis is that for a layer heated from below, TCW which are strongly damped in the absence of thermal diffusion may propagate almost undamped in the low frequency limit in the presence of thermal diffusion for some negative value of Soret number. It is further shown that for a layer heated from above such that the solute concentration increases vertically upward, weakly damped propagation of TCW in the low frequency limit is inhibited with increase in Soret number. Received on 14 July 1998     

Buoyancy-induced airflow in a side-heated structure consisting of a cubic box and vertical ducts

Buoyancy-induced airflow in a box with one wall heated, an unheated inlet duct connected to its floor, and an exit duct with one side heated connected to its ceiling is experimentally investigated. A flow rate prediction method based on buoyancy and flow resistance balance is proposed and experimentally validated. The flow pattern and thermal stratification in the box; the flow resistance characteristics for low Reynolds numbers; the relationship among buoyancy, flow resistance, and pressure defect; the chimney effect caused by the exit duct; and the heat transfer characteristics of the heated walls are clarified. The flow rate, thermal stratification, and flow enhancement due to the chimney effect are considerably dependent on the size of the gap of the exit duct.     

Optimal discrete distribution of heat flux elements for in-tube laminar forced convection

A new technique is proposed to enhance the heat transfer from a discretely heated pipe to a developing laminar fluid flow. Unlike the common heating situation where the fluid is continuously heated along the pipe wall with uniform heat flux, the proposed technique consists in heating the fluid with stepwise distributed heat flux, namely by placing insulated segments between the heated segments. Applying this technique, the effective length of the thermal entrance region is enlarged and as a result, the average heat transfer is invigorated. In order to maximize the heating performance, an optimal placement of the insulated segments between the heated segments is calculated according to constructal design. This serves to describe the optimal stepwise distribution of the heat flux. Owing that the total heat load is considered fixed, the maximization of the heating performance translates into the minimization of the peak temperature (‘hot spot’) of the pipe wall. The analytical results demonstrate that the optimal location of the insulated segments along with the reduction of the peak temperature strongly depend on the Graetz number. It is also shown that for intermediate values of the Graetz number, the peak temperatures are remarkably reduced in response to the optimal placement of the insulated/heated segments.     

Simulation of void fraction profile evolution in subcooled nucleate boiling flow in a vertical annulus using a bubble-tracking approach

A three-dimensional bubble-tracking model of subcooled nucleate boiling flow in a vertical channel at low-pressure conditions is proposed with specific application to the case of boiling in an annulus with a central heating rod. Vapour is distributed in the liquid in the form of individually tracked bubbles. The overall behaviour of the liquid–vapour system results from motion, interaction, coalescence and boiling mechanisms prescribed mostly at the level of bubbles. Bubbles are nucleated at nucleation sites randomly distributed over the heated surface. After nucleation, bubbles slide on the heated wall, detach and then migrate into the lower-temperature region away from the heated surface, where they condense. The proposed model was applied to experiments on subcooled boiling from Purdue University (USA). Experimental and calculated void fraction radial profiles at different axial locations are compared.     

Critical heat flux of saturated convective boiling on uniformly heated plates in a parallel flow

Employing saturated water and R-113 at atmospheric pressure, experiments are made for critical heat flux (CHF) on a uniformly heated plate of 10, 15 and 20 mm in length submerged parallel to a uniform liquid flow with velocity of 1.5–10 m/s and the data of CHF obtained are successfully correlated by a generalized equation. In addition, it is shown that existing data of CHF for acetone, toluene, monoisopropylbiphenyl and water flowing through internally heated annular channels of very small I/d_he, where I is the axial length and d_he the heated equivalent diameter, agree well with the above-mentioned correlation.     

Transient heating of opaque and semitransparent materials by radiation during processing

Analysis is presented of transient heating of opaque and semitransparent (translucent) materials by external radiation sources. Such problems arise in materials processing and manufacturing applications. Dynamic temperature distributions are calculated in a plate (slab) of material by accounting for spectral nature of the radiation source and the radiative properties of the material. Effects of radiation properties influenced by the choice of material to be heated, chemical and mechanical treatment, radiation source temperature, and convective heat transfer are considered. Differences in temperature response of opaque and semitransparent materials are examined. It is shown that the temperature distribution in a semitransparent material heated by an external radiation source is more uniform than in an opaque material for otherwise the same conditions owing to the “long range” transport of radiation. Treatment of a semitransparent material as opaque results in an unrealistic prediction of temperature distribution when the material is heated by an infrared radiation source. Received on 10 April 2000     

热弹性薄板大挠度弯曲的BEM法

本文首先基于理性力学非线性几何场理论，建立了等效速率形式的热弹性薄板的Ｋａｒｍａｎ方程，通过将热弹性薄板大挠度弯曲问题的看成平板弯曲问题与平面大变形问题的耦合，在固定坐标系及拖带坐标系上推导出两组边界积分方程，从而建立起新的分析热性薄板大挠度弯曲问题的边界元。本文的方法较双往分析此问题的边界法在理论上更准确，合理，算例表明本文的方法理论可靠，精度良好。     

Temperature field of a slightly heated jet in a cross flow

This paper deals with a temperature field of a slightly heated two-dimensional jet injected normal to a cold cross flow. At the blowing rates of 0.2, 1.5 and 3.0 in two kinds of approaching boundary layer, the thermal mixing characteristics of the heated jet with the cross flow are experimentally clarified. The correlation between the temperature field and the complex flow one in the downstream region of the jet is made clear, in relation to the typical jet flow patterns. Comparison of the present results with the existing experimental data are represented.     

Slow flow of gas around a strongly heated or cooled sphere

Problems similar to those considered in [1, 2] are studied, namely, slow flow over a uniformly heated (or cooled) spherical particle and flow past a weakly nonuniformly heated sphere in the absence of external body forces and with allowance for thermal stresses in the gas. The use of an improved method of numerical solution [3] has made it possible to advance into the region of large temperature differences. A new effect is found: allowance for the thermal stresses in the case of flow around a strongly heated sphere leads to the appearance of a suction force instead of a drag. In the case of flow around a nonuniformly heated sphere the influence of thermal stresses is unimportant. The problems are considered for two temperature dependences of the transport coefficients.Translated from Izvestiya Akademii Nauk SSSR, Mekhanika Zhidkosti i Gaza, No. 6, pp. 170–175, October–December, 1981.