On MHD heat and mass transfer over a moving vertical plate with a convective surface boundary condition

In this paper, the magnetohydrodynamics (MHD) boundary layer flow with heat and mass transfer over a moving vertical plate in the presence of magnetic field and a convective heat exchange at the surface with the surrounding has been studied. The similarity solution is used to transform the system of partial differential equations, describing the problem under consideration, into a boundary value problem of coupled ordinary differential equations, and an efficient numerical technique is implemented to solve the reduced system. The results are presented graphically and the conclusion is drawn that the flow field and other quantities of physical interest are significantly influenced by these parameters.     

Stagnation point flow towards a stretching/shrinking sheet in a micropolar fluid with a convective surface boundary condition

The problem of a steady laminar two‐dimensional stagnation point flow towards a stretching/shrinking sheet in a micropolar fluid with a convective surface boundary condition is studied. The governing partial differential equations are transformed into ordinary differential equations using a similarity transformation, before being solved numerically using the Runge–Kutta–Fehlberg method with shooting technique. The effects of the material parameter and the convective parameter on the fluid flow and heat transfer characteristics are disscussed. It is found that the skin friction coefficient and the heat transfer rate at the surface decrease with increasing values of the material parameter. Moreover, dual solutions are found to exist for the shrinking case, while for the stretching case, the solution is unique. © 2011 Canadian Society for Chemical Engineering     

Combined effects of internal heat generation and higher order chemical reaction on the non‐darcian forced convective flow of a viscous incompressible fluid with variable viscosity and thermal conductivity over a stretching surface embedded in a porous medium

In this paper, we study the combined effects of internal heat generation and higher order chemical reaction on a steady two‐dimensional non‐Darcian forced convective flow of a viscous incompressible fluid with variable dynamic viscosity and thermal conductivity in a fluid saturated porous medium passing over a linear stretching sheet. Using similarity transformations, the governing nonlinear‐coupled partial differential equations are made dimensionless and solved numerically for similarity solutions using very robust computer algebra software Maple 8. The non‐dimensional velocity, temperature and concentration distributions are presented graphically for various pertinent parameters such as relative temperature difference parameter, Darcy number, porosity parameter, reaction rate parameter and the order of the chemical reaction. The variations of Prandtl number and Schmidt number within the boundary layer are also displayed graphically when the fluid dynamic viscosity and thermal conductivity are temperature dependent. From the present numerical computations it is found that Prandtl number as well as Schmidt number must be taken as variables within the flow domain when the fluid's dynamic viscosity and thermal conductivity are variable. In the presence of internal heat generation, dynamic viscosity and thermal conductivity of the fluid are found to be higher than when it is absent. Increasing Darcy number reduces dynamic viscosity as well as thermal conductivity whereas increasing pore size reduces the Schmidt number and increases the Prandtl number within the boundary layer. For higher order reaction the rate of increase in mass transfer function is less compared to the rate of increase for the lower order reaction. © 2011 Canadian Society for Chemical Engineering     

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.     

考虑局部非热平衡的流体层流横掠多孔介质中恒热流平板的传热分析

对流体层流横掠多孔介质中恒热流加热的平板,应用Brinkman-Forchheime-extended Darcy流动模型和流体与多孔介质之间局部非热平衡理论建立守恒方程组,应用数量级分析和积分法,得出了速度边界层厚度、热边界层厚度、壁面黏性摩擦系数和对流传热系数、流体与多孔介质之间局部温差的计算公式。结果表明,速度边界层与光板时明显不同,其在平板前端迅速增长,之后越来越平坦,趋于一个恒定值;而热边界层则沿着流动方向不断增长,类似于光板时的情况;局部的表面对流传热系数在平板前端达最大值,之后逐渐减小,也类似于光板时的情况;多孔介质与流体间的局部温差在平板前端达最大值,之后呈现沿着流动方向逐渐减小的变化趋势。     

Effects of radiation and heat source/sink on unsteady MHD boundary layer flow and heat transfer over a shrinking sheet with suction/injection

In this paper, an investigation is made to study the effects of radiation and heat source/sink on the unsteady boundary layer flow and heat transfer past a shrinking sheet with suction/injection. The flow is permeated by an externally applied magnetic field normal to the plane of flow. The self-similar equations corresponding to the velocity and temperature fields are obtained, and then solved numerically by finite difference method using quasilinearization technique. The study reveals that the momentum boundary layer thickness increases with increasing unsteadiness and decreases with magnetic field. The thermal boundary layer thickness decreases with Prandtl number, radiation parameter and heat sink parameter, but it increases with heat source parameter. Moreover, increasing unsteadiness, magnetic field strength, radiation and heat sink strength boost the heat transfer.     

倾角及冷却工况对多通路并联回路板式脉动热管传热性能的影响

针对多通路并联回路板式脉动热管建立实验台,采用铜质模块加热和水浴冷却方式作为热工条件,着重考察脉动热管在不同倾角（90°,75°,60°）及冷却工况（4.5 g·s^-1和9.0 g·s^-1）下的传热性能,通过壁面温度的振荡和传热热阻来评价其传热效果。实验结果表明,重力对多通路并联回路板式脉动热管传热性能的影响较大,随着倾角的减少,工质的回流变弱,传热热阻变大,传热极限变低;脉动热管的加热功率与冷却能力是相互匹配的,匹配度越高,脉动热管越不易干烧,传热极限越高,在有倾角的工况下提高传热极限表现得更为明显;脉动热管运行时存在一个最佳水流量,在最佳冷却工况下,脉动热管的运行热阻最低。     

The significance of the buffer zone of boundary layer on convective heat transfer to a vertical turbulent flow of a supercritical fluid

A two-dimensional model is developed to simultaneously solve the momentum and energy equations in order to predict convective heat transfer to an upward turbulent flow of supercritical carbon dioxide in a round tube. It is very important to choose a proper turbulence model. An appropriate turbulence model, based on the previous studies, has been selected. The main focus of the present study is on significance of the buffer zone in the boundary layer. The results of this study indicate that in enhanced regime of heat transfer, the peak of heat transfer coefficient occurs when the pseudo-critical temperature, or the situation of maximum heat capacity, lies within the buffer layer. In deteriorated regime of heat transfer, the extent of the laminar sub-layer appears to be changed so that the buffer zone is experienced at a farther distance from the wall. This causes a delay in the turbulent diffusion near the wall and leading to a jump in the wall temperatures.     

Free convective flow over a vertical plate in a doubly stratified medium with electrophoresis, heat source/sink and chemical reaction effects

We analyzed the problem of unsteady, incompressible free convective doubly stratified flow past a semiinfinite vertical plate with the influence of electrophoresis, heat source/sink and chemical reaction. The partial differential equations governing the flow are solved by employing an implicit finite difference scheme of Crank-Nicolson type. The effect of heat generation and absorption in stratified and unstratified flow are examined and hence the influence of stratification on velocity, temperature and concentration are investigated and presented graphically. Further, the impact of the electrophoresis on particle concentration in the presence of generative and destructive reaction is analyzed. As well, the effects of the physical parameters on local and average values of skin friction, Nusselt number and Sherwood number are also investigated and illustrated graphically. The particular solutions of the present results are compared with the existing solution in literature and are found to be in good agreement.     

管内强化传热性能的熵产分析与性能评价

通过热力学第一、第二定律,对管内对流换热综合性能进行熵产分析和评价.建立了一种基于流动与传热过程熵增原理的统一分析方法,在等壁温边界条件下进行熵产分析.并以文献中内翅片管的强化传热作为应用,分别对相同流量、泵功、压降在等热负荷限制下进行强化传热性能评价.结果表明：对于给定的管道,量纲1熵产数只与流动Reynolds数和进口与壁面的温度差有关.利用该分析方法不仅可通过参数分析获得几种强化方式的能量综合利用效果,还可确定合理的流动工况参数、结构参数和合理的强化形式.     

Homotopy analysis of heat and mass transfer boundary layer flow through a non‐porous channel with chemical reaction and heat generation

This paper describes the two‐dimensional flow of an incompressible viscous fluid through a non‐porous channel with heat generation and a chemical reaction. Employing similarity transformations the governing non‐linear partial differential equations are solved both analytically and numerically. Analytically, we used the homotopy analysis method and numerically, we used the Matlab in‐built boundary value solver bvp4c. The effects of the Reynolds number Re, the Eckert number Ec, heat generation parameter δ, chemical reaction parameter γ, and the local Grashof number Gc on the velocity, temperature, and concentration fields are shown through tables and graphs and discussed.     

Transient heat conduction and hotspot development prediction in a flaking roll with revolving heat flux and convection boundary conditions

In the oilseed crushing industry, flaking rolls sometimes develop hotspots that cause high thermal stresses. Soybean flakes on contact with hotspots crumble to powder, which is unsuitable for oil extraction. Transient heat conduction equations with revolving boundary conditions were solved using the finite element method. Simulations demonstrated that hotspots arise due to heat flow in three dimensions from the source toward the roll ends and the curved surface. An estimated heat flux value of 56 kW/m² yielded surface temperature values near observed values. Perturbations performed to the base values showed that a 10% increase in thermal conductivity caused a 6–8% reduction in peak thermal gradient, whereas a 20% increase in heat-transfer coefficient caused less than 2% reduction in peak thermal gradient. Therefore, thermal conductivity is a more sensitive parameter affecting thermal gradients than the heat-transfer coefficient. A small change in heat-transfer coefficient caused by aspirating air through the flake outlet of the roll stands would not cause a significant reduction in temperature and thermal gradients in rolls. The higher thermal gradients observed near the outer surface of rolls suggest that casting rolls with subsurface layers of higher thermal conductivity would make rolls less prone to forming hotspots.     

错排孔板封头对板翅式换热器流动与换热的影响

在对板翅式换热器内部物流分配研究的基础上,研究了错排孔板型结构封头对板翅式换热器出口流动与换热的影响。通过实验与工业用基本型封头对比,结果表明错排孔板型封头能够明显地改善换热器出口截面流量和温度分布的不均匀性。在Re=2 000时换热器的出口流量分布不均匀度大幅度地下降;而在Re数较大情况下,能更加显著地改善温度分布的不均匀性。     

MHD flow of a micropolar fluid towards a vertical permeable plate with prescribed surface heat flux

The problem of a steady mixed convection stagnation point flow towards a permeable vertical plate with prescribed surface heat flux immersed in an incompressible micropolar fluid is studied numerically. The governing partial differential equations are first transformed into a system of ordinary differential equations using a similarity transformation, before being solved numerically by a finite-difference scheme known as the Keller-box method and the Runge–Kutta–Fehlberg method with shooting technique. The effects of the material parameter, buoyancy parameter, suction/injection parameter and the Prandtl number on the fluid flow and heat transfer characteristics are discussed. It is found that dual solutions exist for both assisting and opposing flows. The skin friction coefficient and the local Nusselt number increase in the presence of suction and magnetic field. Moreover, suction as well as fluids with larger Prandtl number widens the range of the buoyancy parameter for which the solution exists.     

边界条件和结构尺寸对提升管内气固流动特性的影响

引言提升管是非均匀结构显著的气固两相流动体系,其流动特性主要表现为轴向空隙率的S形分布、径向的"环-核"结构以及团聚物的生成和破碎等。近年来,有关数值计算方法的研究增多,其中双流体模型的应用最为广泛,颗粒动理学则是目前封闭控制方程的最合理有效的方法。     

MHD flow and heat transfer over stretching/shrinking sheets with external magnetic field,viscous dissipation and Joule effects

The present article considers the steady magnetohydrodynamic (MHD) laminar boundary layer flow of a viscous and incompressible electrically conducting fluid near the stagnation point on a horizontal stretching or shrinking surface, with variable surface temperature and a constant magnetic field applied normal to the surface of the sheet. The governing system of partial differential equations is first transformed into a system of ordinary differential equations by introducing an appropriate similarity transformation, which is then solved numerically using a finite‐difference scheme known as the Keller‐box method. The effects of the governing parameters on the skin friction coefficient, the local Nusselt number as well as the velocity and temperature profiles are determined and discussed. Results indicate that for the stretching sheet, solution exists and is unique for all values of the stretching/shrinking parameter $\lambda $ , while for the shrinking sheet, solutions only exist up to some critical values $\lambda = \lambda _{{\rm c}} $ , and these solutions may be unique, dual and sometimes triple. © 2011 Canadian Society for Chemical Engineering     

连续螺旋折流板换热器流动与传热性能及熵产分析

采用数值模拟的方法,研究了螺旋角对连续螺旋折流板换热器流动与传热性能的影响,并以熵产数为指标对换热器性能进行了基于热力学第二定律的分析评价。结果表明,相同质量流量时壳程传热系数和压降均随螺旋角的增大而降低,且后者降低的幅度大于前者。连续螺旋折流板换热器壳程横截面上切向速度分布较弓形折流板换热器更加均匀。在靠近中心假管的内层区域,同一径向位置的轴向速度随螺旋角的增大而降低,而在靠近壳体壁面的外层区域则相反。螺旋角越大,不同径向位置的换热管间的换热量分布均匀性越好。壳程质量流量相等时,换热器中传热引起的熵产占总熵产的比重随着螺旋角的增大而增加,熵产数随着螺旋角的增大而降低。     

Characteristics of the boundary layer with hydrogen combustion with variations of thermal conditions on a permeable wall

The paper describes a numerical study of the influence of thermal and boundary conditions on the structure of laminar and turbulent diffusion flames in the cases with hydrogen injection through a porous surface and with hydrogen combustion in an air flow. Two types of boundary conditions are compared: with a given constant temperature T _w = const over the length of the porous surface for arbitrary intensities of fuel injection and with a constant temperature T′ = const of the fuel injected through the porous wall. The first case occurs during combustion of a liquid fuel whose burning surface temperature remains unchanged. Injection of gaseous fuel usually leads to the second case with T′ = const. Despite significant differences in velocity and temperature profiles, the skin friction coefficients in the laminar flow are close to each other in these two regimes. In the turbulent regime, the effect of the thermal boundary conditions on friction and heat transfer is more pronounced. Moreover, the heat flux to the wall as a function of fuel-injection intensity is characterized by a clearly expressed maximum. A principal difference of the effect of combustion on friction and heat transfer in the laminar and turbulent flow regimes is demonstrated. __________ Translated from Fizika Goreniya i Vzryva, Vol. 45, No. 3, pp. 3–11, May–June, 2009.     

Effect of heat transfer on the distributions of OH and CH radicals in the boundary layer with ethanol combustion

The reasons for formation of superequilibrium concentrations of radicals are studied by means of joint consideration of experimental data on the distributions of CH and OH molecules formed during diffusion combustion of ethanol and data on heat transfer in the chemical reaction region. The air flow velocity near the stagnation point in experiments with combustion is 0.7 m/sec, and the flow velocity along a flat plate is 10 m/sec (the turbulence levels are 1 and 18%). Mutual locations of specific features in the distributions of the heat-release rate and temperature are analyzed and compared with the distributions of OH and CH radicals. For all turbulence levels and flow velocities considered, the maximum concentration of radicals is reached on the boundaries of the heat-release region, whose locations are determined by molecular transport mechanisms. It is demonstrated that this conclusion is applicable to experimental data on diffusion combustion of a submerged hydrogen jet in air. __________ Translated from Fizika Goreniya i Vzryva, Vol. 44, No. 6, pp. 3–11, November–December, 2008.