MHD flow and heat transfer of a micropolar fluid over a nonlinear stretching surface with variable surface heat flux and heat generation

An analysis has been carried out to study magnetohydrodynamic boundary layer flow and heat transfer of an electrically conducting micropolar fluid over a nonlinear stretching surface with variable wall heat flux in the presence of heat generation/absorption and a non‐uniform transverse magnetic field. The governing system of partial differential equations is first transformed into a system of ordinary differential equations using similarity transformation. The transformed equations are solved numerically. Results for the dimensionless velocity, micro‐rotation, and temperature profiles are displayed graphically delineating the effects of various parameters characterising the flow. The results show that the velocity profile decreases as the magnetic parameter and the velocity exponent increase, while it increases as the material parameter increases. The results show also that the temperature profile increases as the magnetic parameter, the velocity exponent, and the heat generation parameter increase. Furthermore, the temperature profile decreases as the material parameter, the heat absorption parameter, and the Prandtl number increase.     

HEAT TRANSFER DUE TO MHD SLIP FLOW OF A SECOND-GRADE LIQUID OVER A STRETCHING SHEET THROUGH A POROUS MEDIUM WITH NONUNIFORM HEAT SOURCE/SINK

An analysis is carried out to study the heat transfer characteristics of a second-grade non-Newtonian liquid due to a stretching sheet through a porous medium under the influence of external magnetic field. The stretching sheet is assumed to be impermeable. Partial slip condition is used to study the flow behavior of the liquid. The effects of viscous dissipation, nonuniform heat source/sink on the heat transfer are addressed. The nonlinear partial differential equations governing momentum and heat transfer in the boundary layer are converted into nonlinear ordinary differential equations using similarity transformation. Analytical solutions are obtained for the resulting boundary value problems in the case of two types of boundary heating, namely, constant surface temperature (CST) and prescribed surface temperature (PST). The effects of slip parameter, second-grade liquid parameter, combined (magnetic and porous) parameter, Prandtl number, Eckert number, and nonuniform heat source/sink parameters on the heat transfer are shown in several plots. Analytical expressions for the wall frictional drag coefficient and wall temperature gradient are obtained.     

HYDROMAGNETIC BOUNDARY LAYER FLOW AND HEAT TRANSFER IN VISCOELASTIC FLUID OVER A CONTINUOUSLY MOVING PERMEABLE STRETCHING SURFACE WITH NONUNIFORM HEAT SOURCE/SINK EMBEDDED IN FLUID-SATURATED POROUS MEDIUM

Analytical study for the problem of flow and heat transfer of electrically conducting viscoelastic fluid over a continuously moving permeable stretching surface with nonuniform heat source/sink in a fluid-saturated porous medium has been undertaken. The momentum and thermal boundary layer equations, which are partial differential equations, are converted into ordinary differential equations, by using suitable similarity transformation. The resulting nonlinear ordinary differential equations of momentum are solved analytically assuming exponential solution, and similarly thermal boundary layer equations are solved exactly by using power series method, with the solution obtained in terms of Kummer's function. The results are shown with graphs and tables. The effect of various physical parameters like viscoelastic parameter, porosity parameter, Eckert number, space, and temperature-dependent heat source/sink parameters enhances the temperature profile, whereas increasing the values of the suction parameter and Prandtl number decreases the temperature profile. The results have technological applications in liquid-based system involving stretchable materials.     

方形微通道热沉的耗散优化分析

基于CFD软件建立了两种不同结构的方形微通道热沉,并对其进行数值计算,模拟得到热沉的温度场和压力场。在此基础上,研究了不同微通道分布方式、不同质量流率和不同热通量对热沉的温度、压降的影响,同时基于耗散理论对比分析来获得方形微通道热沉换热效果较好的优化方案,在固定边界热流条件下,耗散越小,换热效果越好。计算结果表明：随着质量流率的增大,热沉温度逐渐降低,进出口压差逐渐增大,PEC逐渐增大,耗散逐渐减小;随着热通量的增大,热沉温度逐渐升高,进出口压差逐渐降低,PEC逐渐增大,耗散逐渐减小。微通道分布方式为上层内切圆半径-下层外接圆半径分布时热沉的温度更低,PEC更大,耗散更小,传热效率更高。     

Entransy dissipation theory optimization analysis of square microchannel heat sink

Two kinds of square microchannel heat sinks with different structures were established based on CFD software, and numerical calculations were carried out to simulate the temperature field and pressure field of the heat sink. On this basis, the effects of different microchannel distribution patterns, different mass flow rates and different heat fluxes on the temperature and pressure drop of the heat sink are studied. At the same time, based on the comparison analysis of the entransy dissipation theory, a better optimization scheme of heat sink in square microchannel is obtained. A better optimization scheme, under the fixed boundary heat flow condition, the smaller the entransy dissipation, the better the heat exchange effect. The calculation results show that with the increase of mass flow rate, the heat sink temperature gradually decreases, the pressure drop increases gradually, the PEC gradually increases, and the entransy dissipation decreases; as the heat flux density increases, the heat sink temperature gradually increases, the pressure drop gradually decreases, the PEC gradually increases, and the entransy dissipation gradually decreases. The microchannel distribution pattern is the upper inscribed circle radius-lower layer circumcircle radius distribution, the temperature of the heat sink is lower, the PEC is larger, the entransy dissipation is smaller, and the heat transfer efficiency is higher.     

RADIATION EFFECTS ON MHD AXISYMMETRIC STAGNATION POINT FLOW TOWARDS A HEATED SHRINKING SHEET

In this article, a comprehensive numerical study of MHD axisymmetric stagnation point flow with radiation effects towards a heated shrinking sheet immersed in an electrically conducting incompressible viscous fluid in the presence of a transverse magnetic field is analyzed. The governing continuity, momentum, and heat equations together with the associated boundary conditions are first transformed to a set of self-similar nonlinear ordinary differential equations and are then solved by a method based on finite difference discretization. Some significant features of the flow and heat transfer in terms of normal and horizontal velocities and temperature field for various values of the governing parameters are analyzed, discussed, and presented through tables and graphs. The present investigations predict that the shear stresses increase and the thermal boundary layer becomes thinner by applying a strong magnetic field. The heat loss per unit area from the sheet decreases with an increase in the shrinking parameter. The thermal boundary layer thickness decreases with increasing values of the radiation parameter. The present results may be beneficial in flow and thermal control of polymeric processing.     

MAGNETIC FIELD EFFECTS ON LAMINAR FILM CONDENSATION ON A FINITE-SIZE HORIZONTAL WAVY DISK

This work aims to study the laminar film condensation heat transfer with magnetic field effects on a finite-size horizontal wavy disk. Mathematical analysis is used to obtain the dimensionless governing equations and boundary conditions, and the cubic spline collocation method is then used to calculate the flow and heat transfer characteristics along the wavy disk. The effects of the important parameters, such as Hartmann number, condensation parameter, wave number, amplitude-wavelength ratio, and Pr/Ja on the heat transfer characteristics have been successfully examined. The magnetic field effect increases the critical condensate thickness and thus decreases the condensation heat transfer. Odd wave number effects decrease the critical condensate thickness and thus enhance the condensation heat transfer.     

MAGNETIC FIELD EFFECTS ON LAMINAR FILM CONDENSATION ON A FINITE-SIZE HORIZONTAL WAVY DISK

This work aims to study the laminar film condensation heat transfer with magnetic field effects on a finite-size horizontal wavy disk. Mathematical analysis is used to obtain the dimensionless governing equations and boundary conditions, and the cubic spline collocation method is then used to calculate the flow and heat transfer characteristics along the wavy disk. The effects of the important parameters, such as Hartmann number, condensation parameter, wave number, amplitude-wavelength ratio, and Pr/Ja on the heat transfer characteristics have been successfully examined. The magnetic field effect increases the critical condensate thickness and thus decreases the condensation heat transfer. Odd wave number effects decrease the critical condensate thickness and thus enhance the condensation heat transfer.     

Unsteady flow and heat transfer on an accelerating surface with blowing or suction in the absence and presence of a heat source or sink

The problem of unsteady flow and heat transfer in the laminar boundary layer on a linearly accelerating surface with suction or blowing in the absence and presence of a heat source or sink is considered. The governing partial differential equations for this investigation are transformed into the non-dimensional equations by using pseudo-similarity time and pseudo-similarity coordinate. The resulting two points boundary-value problem is solved numerically by the central finite difference method associated with Newton's iteration from the initial stage (ξ=0) to a steady state (ξ=1) completely. A parametric study is performed to illustrate the effects of Prandtl number, power-law surface temperature (PLST) or power-law heat flux (PLHF), heat sink or heat source, and suction or blowing parameter on the dynamic velocity and temperature fields as well as the transient development of the skin-friction coefficients and the Nusselt number. These results are depicted graphically to display special aspects of unsteady flow and heat transfer characteristics in all time.     

Magnetohydrodynamic slip flow and diffusion of a reactive solute past a permeable flat plate with suction/injection

The magnetohydrodynamic (MHD) boundary layer slip flow and solute transfer over a porous plate in the presence of a chemical reaction are investigated. The governing equations were transformed into self-similar ordinary differential equations by adopting the similarity transformation technique. Then the numerical solutions are obtained by a shooting technique using the fourth order Runge-Kutta method. The study reveals that due to the increase in the boundary slip, the concentration decreases and the velocity increases. On the other hand, with an increase in the magnetic field and mass suction, both boundary layer thicknesses decreased. As the Schmidt number and the reaction rate parameter increases, the concentration decreases and the mass transfer increases.     

缠绕管式换热器壳程强化传热性能影响因素分析

由于内部流场信息缺乏,结构参数对流体流动的影响规律不明确,致使缠绕管式换热器壳程强化传热机理不明晰,阻碍其设计准则的进一步规范化和通用。针对上述问题,对缠绕管式换热器壳程流体流动进行几何建模及数值模拟,并通过文献中实验数据进行验证,进而基于该模型对壳程流体流场特性进行详细分析,分析关键结构参数对其壳程传热与阻力性能的影响,并探讨其强化传热机理。结果表明：Realizable k-ε湍流模型可较为准确地描述壳程流体流动;在双对数坐标系内,壳程Nusselt数随Reynolds数的增大而增大,阻力系数f则呈线性降低的趋势;壳程Nusselt数随缠绕管直径d与平均缠绕直径D的增大而增大,随螺距S的增大而减小,阻力系数f则相反;缠绕管直径d对壳程流体传热与阻力性能的影响最大,平均缠绕直径D的影响最小;增大缠绕管直径d与平均缠绕直径D有利于破坏流体速度边界层,增强流体扰动,加快温升速度,强化壳程传热,而增大螺距S则使速度边界层变厚,减小流动阻力的同时降低温升速度,不利于壳程强化传热。     

UNSTEADY MHD BOUNDARY LAYER FLOW WITH DIFFUSION AND FIRST-ORDER CHEMICAL REACTION OVER A PERMEABLE STRETCHING SHEET WITH SUCTION OR BLOWING

In this study, unsteady MHD boundary layer flow with diffusion of chemically reactive species undergoing first-order chemical reaction over a permeable stretching sheet with suction or blowing and also with power-law variation in wall concentration is investigated. Using similarity transformation, the governing partial differential equations are converted into nonlinear self-similar ordinary differential equations. The transformed equations are then solved by the finite difference method using the quasi-linearization technique. Due to the increase in the unsteadiness parameter, the velocity initially decreases, but after a certain point it increases. A similar effect is also observed in case of concentration distribution. The increase in magnetic parameter causes a decrease in velocity and an increase in concentration. For increasing strength of applied suction both momentum and concentration boundary layer thicknesses decrease. On the other hand, applied blowing has reverse effects. Moreover, the mass transfer from the sheet is enhanced with increasing values of Schmidt number, reaction rate parameter, and also power-law exponent (related to wall concentration distribution). For high negative values of the power-law exponent, mass absorption at the sheet occurs. Moreover, due to increase of unsteadiness, this mass absorption is prevented.     

一种新型裂解炉炉管强化传热数值模拟

利用计算流体动力学(computational fluid dynamic,CFD)方法对含新型内插件强化传热辐射炉管(fortified induced turbulence,FIT)进行了流体流动与传热特性的研究,采用RNG双方程模型求解了动量方程和能量方程,给出了FIT炉管内的流体流动和传热特性,包括速度场、湍动强度和温度场的分布;计算了FIT炉管的强化传热因子和压降。研究结果表明,FIT炉管内插件迫使流体流动由活塞流转变为旋转流,增强了流动湍流程度,符合流动-能量场协同理论,同时流体边界层由于FIT炉管的特殊结构而减薄。FIT炉管具有增强辐射传热、减薄边界层、增加比表面积和旋流增强等强化传热特性。相比于普通当量圆炉管,FIT强化传热炉管的整体传热能力提高了20%左右,证明该新型炉管强化传热效果显著,可以在工程实际中应用。     

0.5 mm毛细管内气-液Taylor流动换热数值研究

采用移动计算域方法研究0.5 mm毛细管内充分发展的气液Taylor流动换热特性,分析了Taylor气泡的形状、压降与换热特性。结果表明,随着入口Reynolds数Re的增大,气泡尾部的不稳定区域增大,液膜厚度逐渐增大,气泡长度变长;随着气泡体积分数ξ_g的增大,气泡形状基本不变而长度逐渐增大。阻力因子f随Re、ξ_g增大而降低,两相阻力系数高于单相的情况。平均Nusselt数Nu_tp随Re增大而增大,增大趋势逐渐降低;随ξ_g增大而线性降低。Taylor流的Nu_tp为单相的1.2～3倍,强化换热效果。     

微/小圆柱针肋热沉传热特性

圆柱形微/小针肋热沉热阻由底板及微/小肋热传导热阻、冷却液与肋间对流换热热阻以及冷却液吸热焓变热阻等组成。以去离子水为冷却液,恒定热流下,进行了叉排排布的不同尺寸的微/小圆柱形针肋热沉的单相强制对流传热实验,实验Re为100～1000,加热功率为50～300 W。实验表明：微/小圆柱形针肋热沉的Nu随Re和加热功率的增大而增大,当Re=600时对     

微细铜丝在水中自然对流换热

采用实验与数值模拟相结合的方法分别研究了封闭空间内水平放置的直径为39.9、65.8、119.1 μm的微细铜丝（微丝）在水中的对流换热,分析了微丝表面自然对流换热特性及机理。实验通过焦耳加热的方法测量了不同直径微丝在水中自然对流的传热系数及Nusselt数。同时建立三维不可压数学模型对微丝在水中的自然对流进行数值模拟,并将计算结果与实验值进行了对比。研究表明,数值模拟结果与实验值基本吻合,微丝在水中自然对流的传热系数随直径减小而显著增大,Nu则明显减小,且Nu随热通量增加的变化率也随直径减小而明显降低;微丝表面边界层厚度随直径减小而变薄,但边界层厚度与微丝直径的比值则逐渐增大;另外,对比微丝与常规尺度圆管表面自然对流的流场、温度场以及边界层分布,发现相同温差下微丝表面自然对流换热的边界层与常规尺度下沿壁面由底部向上发展的形状不同,而是沿微细丝表面呈椭圆形包裹于其上,因此削弱了表面对流换热强度,导致温度场呈现出较明显的导热特征。     

非牛顿流体在波节套管换热器中流动与换热的实验研究

针对非牛顿流体在波节套管换热器管程的流动与换热进行了实验研究。重点研究了0.2%黄原胶溶液(XG)在不同波节套管换热器管程流动时的传热与阻力特性,并分析了强化传热机理。结果表明在相同工况下,随着管程黄原胶溶液Reynolds数Re_XG的增大,套管换热器总传热系数k和管程进出口压降Δp逐渐增大;波高H和波距S影响黄原胶溶液在套管换热器管程的流动与换热。随波高H增大,黄原胶溶液受波节处的涡旋效应的影响更明显,流体层间剪切力变大导致黄原胶溶液黏度变小,湍流程度更大,管程传热性能提高,压降也增大,但综合传热性能不断优化;随波距S增大,单位长度波节数量减少,对黄原胶溶液扰动影响降低,湍流程度降低,管程传热系数先增大后减小,流动阻力不断降低,综合传热性能先提高后减弱。当H=3.5 mm、S=30 mm时管程波节管的综合换热因子η_tube达到最大,η_tube是相同条件下圆管的5.11~6.69倍。     

非牛顿流体在波节套管换热器中流动与换热的实验研究

针对非牛顿流体在波节套管换热器管程的流动与换热进行了实验研究。重点研究了0.2%黄原胶溶液(XG)在不同波节套管换热器管程流动时的传热与阻力特性,并分析了强化传热机理。结果表明在相同工况下,随着管程黄原胶溶液Reynolds数Re_XG的增大,套管换热器总传热系数k和管程进出口压降Δp逐渐增大;波高H和波距S影响黄原胶溶液在套管换热器管程的流动与换热。随波高H增大,黄原胶溶液受波节处的涡旋效应的影响更明显,流体层间剪切力变大导致黄原胶溶液黏度变小,湍流程度更大,管程传热性能提高,压降也增大,但综合传热性能不断优化;随波距S增大,单位长度波节数量减少,对黄原胶溶液扰动影响降低,湍流程度降低,管程传热系数先增大后减小,流动阻力不断降低,综合传热性能先提高后减弱。当H=3.5 mm、S=30 mm时管程波节管的综合换热因子η_tube达到最大,η_tube是相同条件下圆管的5.11~6.69倍。     

三叶孔板换热器壳程流动及传热数值模拟

三叶孔板换热器是一种新型纵流换热器,广泛应用于核电装备领域。针对目前使用较多的壳程“单元流道”模型的局限性,建立了三叶孔板换热器壳程整体模型,包括进出口接管。采用商用软件FLUENT14.0及RNG k-ε湍流模型对壳程流体流动与传热进行了数值研究,分析了三叶孔板换热器壳程流动与传热特性。结果表明：流经第一块支撑板后,流体已充分发展,并且随着壳程结构周期性变化,传热与压降也呈现周期性变化。在支撑板附近,流体流速变大,形成射流,并且由于支撑板阻挡,在支撑板前面和尾部产生二次流,能有效冲刷管壁,减薄流动边界层,起到强化传热作用。     

Thermal stress and heat transfer characteristics of a Cu/diamond/Cu heat spreading device

A Cu/diamond/Cu heat spreading device has recently been proposed. This work analyzes its thermal stress and the heat transfer of the diamond device using finite element simulation, to understand the dependence of the thermal stress and the heat transfer. The diamond device operates with a heat source at temperatures from 400 K to 600 K. With a 2 μm Cu top layer, the heat spreader consists of a diamond layer of thickness 40–300 μm and a bottom Cu layer of thickness 5–300 μm. The thermal stress in the diamond layer at the edge is maximal close to the substrate Cu layer, where a peeling point may be present. The thermal stress reaches saturation as the bottom Cu layer becomes thicker up to 60 μm and then does not increase further. The maximum thermal stress increases with the diamond thickness. Effective thermal conductivity increases with the thickness of the diamond layer. The heat transfer increases markedly with the increased thickness of the diamond layer up to 100 μm, heat transfer only slightly improves beyond the range of thickness. The diamond layer with thickness of approximately 100 μm provides greater efficiency of heat transfer than thicker diamond layer. Combining the increase of heat transfer and the contrasting increase of maximum thermal stress we suggest an optimal diamond layer thickness for the construction of a diamond device being of less than 100 μm.