Magnetohydrodynamic natural convection flow on a sphere with uniform heat flux in presence of heat generation

Summary Magnetohydrodynamic natural convection boundary layer flow on a sphere with uniform heat flux in presence of heat generation has been investigated in this paper. The governing boundary layer equations are transformed into a non-dimensional form and the resulting nonlinear system of partial differential equations is then solved numerically by two distinct efficient methods, namely (i) implicit finite difference method together with the Keller box scheme and (ii) perturbation or series solution technique. The results of the surface shear stress in terms of local skin friction and the rate of heat transfer in terms of local Nusselt number, velocity distribution as well as temperature distribution are shown graphically for a selection of parameter sets consisting of the heat generation parameter and the magnetic parameter.     

Numerical analysis of choked converging nozzle flows with surface roughness and heat flux conditions

Choked converging nozzle flow and heat transfer characteristics are numerically investigated by means of a recent computational model that integrates the axisymmetric continuity, state, momentum and energy equations. To predict the combined effects of nozzle geometry, friction and heat transfer rates, analyses are conducted with sufficiently wide ranges of covergence half angle, surface roughness and heat flux conditions. Numerical findings show that inlet Mach and Nusselt numbers decrease up to 23.1% and 15.8% with surface heat flux and by 15.13% and 4.8% due to surface roughness. Considering each convergence half angle case individually results in a linear relation between nozzle discharge coefficients and exit Reynolds numbers with similar slopes. Heat flux implementation, by decreasing the shear stress values, lowers the risks due to wear hazards at upstream sections of flow walls; however the final 10% downstream nozzle portion is determined to be quite critical, where shear stress attains the highest magnitudes. Heat transfer rates are seen to increase in the streamwise direction up to 2.7 times; however high convergence half angles, heat flux and surface roughness conditions lower inlet Nusselt numbers by 70%, 15.8% and 4.8% respectively.     

Effects of tube flattening on the fluid dynamic and heat transfer performance of nanofluids

In the present article, numerical simulation of Al₂O₃–water nanofluid flow in different flat tubes are performed to investigate the effects of tube flattening on the fluid dynamic and heat transfer performance of nanofluids. The numerical simulations of nanofluids are performed using two phase mixture model by FORTRAN programming language. The flow regime and the wall boundary conditions are assumed to be laminar and constant heat flux respectively. The simulated results are compared with previously published data and good agreement is observed. The effects of tube flattening on different parameters such as heat transfer coefficient, wall shear stress, nanoparticles distribution, temperature distribution, secondary flow and velocity profiles are presented and discussed. The results show that with increasing the flattening, the heat transfer coefficient and wall shear stress increase. The rate of increasing is soft for all flat tubes except for the tube with the most flattening which has a severe increasing in heat transfer and wall shear stress values.     

均匀热流下导热裂纹Ⅱ型温度应力强度因子的解析解

研究含中心裂纹无限大板受远场均匀热流作用,热流密度方向与裂纹有一夹角的情况。当垂直于裂纹面方向有定量热流穿过裂纹时,采用复变函数理论,得出了温度、应力与位移场解析解。利用位移单值条件,确定出温度应力强度因子的解析表达式。针对铝合金LY12材料进行了数值计算,研究了裂纹导热情况与热流方向对温度场及温度应力强度因子的影响。研究表明:该文给定的温度边界条件下,只产生Ⅱ型温度应力强度因子,不产生Ⅰ型温度应力强度因子。热荷载可等效为一个远场均匀作用的剪应力。Ⅱ型温度应力场取决于热流密度沿垂直裂纹面方向的分量,平行于裂纹方向的热流分量对温度应力场没有影响。     

Coupled heat and mass transfer during nonisothermal absorption by falling droplet with internal circulation

We considered mass and heat transfer during nonisothermal absorption of a gas by a falling droplet with internal circulation. Gas phase is assumed to be free of inert admixtures and mass transfer is liquid phase controlled. Mass flux is directed from a gaseous phase to a droplet, and the interfacial shear stress causes a fluid flow inside the droplet. Droplet deformation under the influence of interface shear stress is neglected. Absorbate accumulation and temperature increase in the bulk of liquid phase are taken into account. The problem is solved in the approximations of a thin concentration and temperature boundary layers in the liquid phase. The thermodynamic parameters of the system are assumed constant. The system of transient partial parabolic differential equations of convective diffusion and energy balance with time-dependent boundary conditions is solved by combining the similarity transformation method with Duhamel's theorem, and the solution is obtained in a form of Volterra integral equation of the second kind which is solved numerically. Theoretical results are compared with available experimental data for water vapor absorption by falling droplets of aqueous solution of LiBr.     

Marangoni effect on wave structure in liquid films

Liquid films are encountered in space systems as well as in numerous industrial processes and everyday life. The present work is a part of the preparation of the SAFIR experiment of the European Space Agency onboard the International Space Station. Wave characteristics of the water film flow over a vertical or an inclined plate with a heater have been studied. The fluorescence method was used to measure local instantaneous film thickness. In addition to measure wave characteristics eight capacitance sensors were located as a line across the flow. The process of rivulet formation in a heated film was registered. Two zones of the heat flux effect on liquid film deformation were distinguished. At low heat fluxes, the film flow is hardly deformed. At high heat fluxes the thermocapillary forces provide formation of rivulets and a thin film between them. The measured values of the distance between rivulets depend slightly on the plate inclination angle. It was found that for a positive temperature gradient along the flow, heating may increase the wave amplitude because thermocapillary forces are directed from the valley to the crest of the wave. This effect was shown in the interrivulet zone, where relative wave amplitude and Marangoni number increase with a rise of the heat flux density.     

An XFEM model for cracked porous media: effects of fluid flow and heat transfer

In this work, a numerical model is developed to investigate the influence of fluid flow and heat transfer on the thermo-mechanical response of a cracked porous media. The fluid flow, governed by the Darcy’s law, is discretized with the nonconforming finite element method. Time splitting is used with the energy conservation equation to solve the fluid and the solid phases separately. A combination of Discontinuous Galerkin (DG) and multi-point flux approximation methods is used to solve the advection-diffusion heat transfer equation in the fluid phase. While the conductive heat transfers equation in the solid phase is solved using the eXtended finite element method (XFEM) to better handle the temperature discontinuities and singularities caused by the cracks. Further, the resulted temperature is used as body force to solve the thermo-mechanical problem using the XFEM. In the post processing stage, the thermal stress intensity factor is computed using the interaction integral technique at each time step and used to validate the obtained results. A good agreement was found when the results were compared with the existing ones in the literature.     

Conjugate heat transfer in solar collector panels with internal longitudinal corrugated fins-Part II: Local results

A computational study is conducted to determine, for laminar flow in a solar collector panel or a parallel-plate channel with an internal, longitudinal, corrugated fin, the effects of varying the fin angle (or the fin pitch), the fin thickness, the wall-to-fluid thermal conductivity ratio, and the thermal boundary condition on the local surface temperature and heat flux distributions. The corrugated fin and the two walls form individual triangular flow passages in the collector panel or parallel-plate channel. The results of the investigation show that the variation of the local surface temperature is large when the fin is thin and when the wall/fluid thermal conductivity ratio is small. The local surface heat flux is low near the corners of both the upper and lower triangular flow passages. Near the point of fin attachment on the heated wall, heat may be transferred from the fluid to the fin. Heat may also be transferred from the fluid to the unheated wall near the point of fin attachment. When the thermal conductivity ratio is small, the temperature field in the flow cross section is predominantly stratified. In the limit as the thermal conductivity ratio approaches infinity, the temperature field is that of the thermally fully developed laminar flow in a triangular duct with a streamwise uniform heat flux and peripheral uniform surface temperature boundary condition.     

周边固支的矩形板的动力耦合热弹性问题分析

本文研究的是周边固支的矩形板上表面受均匀分布热流冲击的动力耦合热弹性问题，在热冲击过程中，板的周边温度场保持稳定，下表面绝热。采用算子法将热传导方程由三维降为二维问题，以和二维的热弹性动力方程相协调，二方程相互耦合，故用带补充项的双重富里叶级数消去对坐标的微分项，再用拉普拉斯变换消去方程中对时间的微分项，然后尝试用加权最佳逼近法作数值拉普拉斯逆变换，给出问题在原象空间的解。为防止误差的扩大，本文利用正交齐异分解法求解方程，并对计算结果中动力项和耦合项的影响作出分析。     

Refrigerant R134a vaporisation heat transfer and pressure drop inside a small brazed plate heat exchanger

This paper presents the experimental heat transfer coefficients and pressure drop measured during refrigerant R134a vaporisation inside a small brazed plate heat exchanger (BPHE): the effects of heat flux, refrigerant mass flux, saturation temperature and outlet conditions are investigated. The BPHE tested consists of 10 plates, 72 mm in width and 310 mm in length, which present a macro-scale herringbone corrugation with an inclination angle of 65° and corrugation amplitude of 2 mm.The experimental results are reported in terms of refrigerant side heat transfer coefficients and frictional pressure drop. The heat transfer coefficients show great sensitivity both to heat flux and outlet conditions and weak sensitivity to saturation temperature. The frictional pressure drop shows a linear dependence on the kinetic energy per unit volume of the refrigerant flow.The experimental heat transfer coefficients are also compared with two well-known correlations for nucleate pool boiling and a correlation for frictional pressure drop is proposed.     

三个关键几何参数对人字形波纹钎焊板式换热器换热性能影响的分析

以水-水热交换器为例,以CFD模拟软件为手段,以κ-ε模型为基础构建人字形波纹板式换热器模型,并系统分析波纹倾角、波纹深度、波纹间距这3个重要几何参数对换热器内部温度场、压力场、流场及平均努塞尔数和流动阻力的影响。研究结果表明,触点是板间换热效果最好的点,触点的扰流作用使流体在触点周围湍流程度最高,传热得到强化,这也是板式换热器内流体在雷诺数较低时发生湍流的主要原因;另一方面,流体经过触点后压力损失较大,是产生阻力损失的主要原因。波纹倾角是最重要的一个影响参数,最优波纹倾角在60°附近,此时换热效果较好而阻力尚未达到最大;波纹深度增加,平均努塞尔数增大,换热效果趋于好转,板间压力降也逐渐降低。但随着波纹深度的增加,结垢的倾向也会增加,因此较为合理的波纹深度应该在4～5mm之间;在给定的边界条件下,通过计算所得的波纹间距与波纹深度之比在3～4范围内时换热器性能较好。     

Free convection flow past a vertical flat plate embedded in a saturated porous medium

A numerical solution for the free convection flow past a vertical semi-infinite flat plate embedded in a highly saturated porous medium by allowing the plate to have a non-uniform temperature or a non-uniform heat flux distributions has been developed. Both local heat transfer rate and excess surface temperature as a function of the distance along the plate are tabulated for a few cases of prescribed wall temperature and heat flux distributions. Such tabulations serve as a reference against which other approximate solutions can be compared in the future.     

Influence of loading path on fatigue crack growth under multiaxial loading condition

In this study, the specimens made of carbon steel S45 with an initial surface straight edge notch were subjected to combined cyclic axial‐torsion loading at room temperature. The fatigue life, surface crack extension direction and crack length were experimentally investigated. The effects of loading path, stress amplitude ratio and phase angle on the crack growth behaviour were also discussed. The results showed that, under the combination of cyclic axial and torsion loading, the tension stress amplitude had more effect on the initial crack growth path than the latter. The shear stress amplitude contributed mainly to the latter crack extension. The crack extension path was mainly determined by the stress amplitudes and the ratio of the normal stress to the shear stress, and almost independent of the mean stresses. The increase of the tension stress amplitude and shear stress amplitude would both accelerate the crack growth rate.     

Study of thermocapillary film rupture using a fiber optical thickness probe

Rupture of a subcooled water film flowing down an inclined plate with a 150×150 mm heater is studied using a fiber optical thickness probe. The main governing parameters of the experiment and their respective values are: Reynolds number (3.2–30.2), plate inclination angle from the horizon (3–90 deg), heat flux (0–1.53 W/cm²). The effect of the heat flux on the film flow leads to the formation of periodically flowing rivulets and thin film between them. As the heat flux grows the film thickness between rivulets gradually decreases, but, upon reaching a certain critical thickness, the film spontaneously ruptures. The critical film thickness is practically independent on the film Reynolds number as well as on the plate inclination angle and lies in the neighborhood of 60 µm (initial film thickness varies from 93 to 368 µm). The heater surface temperature prior to rupture is also independent of Re and Θ, and is about 45°C (initial film temperature is 24°C). The process of rupture involves two stages: 1) abrupt film thinning down to a very thin residual film remaining on the heater; 2) rupture and dryout of the residual film. The threshold heat flux required for film rupture is scarcely affected by the plate inclination angle but grows with the Reynolds number.     

均匀热流作用下含裂纹板I 型温度应力强度因子的解析解

研究一种新的温度边值问题。含中心裂纹无限大板受远场均匀热流作用,热流密度方向与裂纹有一夹角。当裂纹面上维持一恒定温差时,采用复变函数理论,得出了温度场、温度应力场与位移场的解析解。利用位移单值条件,确定出温度应力强度因子的解析表达式。针对铝合金LY12 材料进行了相应数值计算,分析了热流密度大小与方向对温度分布与温度应力强度因子的影响。研究表明:该文给定的温度边界条件下,只产生Ⅰ 型温度应力强度因子,不产生Ⅱ 型温度应力强度因子。温度应力场取决于热流密度沿裂纹方向的分量,垂直于裂纹方向的分量对温度应力场没有影响。     

Performance of extended surface from a cryocooler for subcooling liquid nitrogen by natural convection

Natural convection of subcooled liquid nitrogen under a horizontal flat plate is measured by experiment. This study is motivated mainly by our recent development of cryocooling systems for HTS power devices without any forced circulation of liquid nitrogen. Since the cold surface of a GM cryocooler is very limited, the cooling plate immersed in subcooled liquid nitrogen is thermally anchored to the cryocooler located at the top in order to serve as an extended surface. A vertical plate generating uniform heat flux is placed at a given distance under the cooling plate so that subcooled liquid may generate cellular flow by natural convection. The temperature distributions on the plates and liquid are measured during the cool-down and in steady state, from which the heat transfer coefficients are calculated and compared with the existing correlations for a horizontal surface with uniform temperature. A fair agreement is observed between two data sets, when the heat flux is small or the plate temperatures are relatively uniform in horizontal direction. Some discrepancy at higher heat flux is explained by the cellular flow pattern and the fin efficiency of the extended surface, resulting in the non-uniformity of the horizontal plate.     

Three-dimensional stagnation point flow of a second grade fluid towards a moving plate

The problem dealing with the steady three-dimensional flow of a second grade fluid near the stagnation point of an infinite plate moving parallel to itself with constant velocity has been investigated. By using the appropriate transformations for the velocity components and temperature, the basic equations governing flow and heat transfer have been reduced to a set of ordinary differential equations. These equations have been solved approximately subject to the relevant boundary conditions by employing a numerical technique. The effect of a nondimensional elastic parameter on the velocity components, wall shear stress, temperature and heat transfer has been examined carefully.     

薄板在周期热流作用下的热响应(Ⅰ):温度响应

基于具有热流延迟相的双曲型热传导方程,研究了薄板在周期热流作用下的温度响应。首先采用分离变量法,求解了以热流矢量为基本未知量的热传导方程,得到了板内热流场分布,然后再利用能量守恒方程,获得了板内温度响应的解析表达式。通过计算,分析了板内温度响应随不同热流矢量延迟相以及边界热流频率的变化趋势,并与经典的Fourier热传导方程所得到的结果进行了比较。结果表明,在高频热流加热下,双曲型热传导模型所给出的温度响应与经典的Fourier热传导模型具有显著的差别。     

一种基于反问题算法的管道壁面热流密度测量技术

为了解决目前传统测量方法中无法准确计量热流密度的问题,在已知管道内沿层流的几处不同点的测温数据的基础上,建立了热流密度计量的反问题数学模型,采用共轭梯度法,给出了简明的热流测量步骤。数值实验表明,在存在较大温度测量误差的情况下,这种方法仍具有较高的计量精度。     

Thermal radiation effects on magnetohydrodynamic mixed convection flow of a micropolar fluid past a continuously moving semi-infinite plate for high temperature differences

Summary An analysis is presented to study the effect of radiation on magnetohydrodynamic mixed convective steady laminar boundary layer flow of an optically thick electrically conducting viscous micropolar fluid past a moving semi-infinite vertical plate for high temperature differences. A uniform magnetic field is applied perpendicular to the moving plate. The density of the micropolar fluid is assumed to reduce exponentially with temperature. The usual Boussinesq approximation is neglected because of the high temperature differences between the plate and the ambient fluid. The Rosseland approximation is used to describe the radiative heat flux in the energy equation. The resulting governing equations are transformed using a similarity transformation and then solved numerically by applying an efficient technique. The effects of radiation parameter R, magnetic parameter M, couple parameter Δ and density/temperature parameter n on the velocity, angular velocity and temperature profiles as well as the local skin friction coefficient, wall couple stress and the local Nusselt number are presented graphically and in tabular form.