Heat transfer measurement using thermochromatic liquid crystal

The present study describes the results of an experimental investigation of heat transfer rate on the wall surface downstream of vortex generators and includes the effect of different angles of attack of the vortex generators on heat transfer. Heat transfer measurements are made with thermochromatic liquid crystal (TLC) to provide the local distributions of heat transfer coefficients. The major conclusions are obtained from this study. The boundary layer is thinned in the regions where the secondary flow is directed to the wall and thickened where it is directed away from the wall. The peak augmentation of the local heat transfer occurs in the downwash region near the point of minimum boundary layer thickness, and the common-flow-down cases show better heat transfer enhancement than the common-flow-up cases.     

Heat transfer for boundary layers with cross flow

An analysis is presented to study the dual nature of solutions for the forced convective boundary layer flow and heat transfer in a cross flow with viscous dissipation terms in the energy equation. The governing equations are transformed into a set of three self-similar ordinary differential equations by similarity transformations. These equations are solved numerically using the very efficient shooting method. This study reveals that the dual solutions of the transformed similarity equations for velocity and temperature distributions exist for certain values of the moving parameter, Prandtl number, and Eckert numbers. The reverse heat flux is observed for larger Eckert numbers; that is, heat absorption at the wall occurs.     

Mixed Convection in Viscoelastic Boundary Layer Flow and Heat Transfer over a Stretching Sheet

An investigation is carried out on mixed convection boundary layer flow of an incompressible and electrically conducting viscoelastic fluid over a linearly stretching surface in which the heat transfer includes the effects of viscous dissipation, elastic deformation, thermal radiation, and non-uniform heat source/sink for two general types of non-isothermal boundary conditions. The governing partial differential equations for the fluid flow and temperature are reduced to a nonlinear system of ordinary differential equations which are solved analytically using the homotopy analysis method (HAM). Graphical and numerical demonstrations of the convergence of the HAM solutions are provided, and the effects of various parameters on the skin friction coefficient and wall heat transfer are tabulated. In addition, it is demonstrated that previously reported solutions of the thermal energy equation given in [1] do not converge at the boundary, and therefore, the boundary derivatives reported are not correct.     

Axisymmetric convection flow of fractional Maxwell fluid past a vertical cylinder with velocity slip and temperature jump

A novel finite volume method is developed to investigate the axisymmetric convection flow and heat transfer of fractional viscoelastic fluid past a vertical cylinder. Fractional cylindrical governing equations are formulated by fractional Maxwell model and generalized Fourier's law. The velocity slip and temperature jump boundary conditions are considered across the fluid-solid interface. Numerical results are validated by exact solutions of special case with source terms. The effects of fractional derivative parameter and boundary condition parameters on flow and heat transfer characteristics are discussed. The viscoelastic fluid performs evident shear thickening property in the fractional Maxwell constitutive relation. Moreover, the boundary condition parameters have remarkable influence on velocity and temperature distributions.     

波纹壁面降膜过程的一种近似模型

对高粘度液体在正弦形波纹壁面上的自由降落和蒸发建立了分析模型。对控制微分方程及边界条件作无量纲处理,引入流函数,采用摄动展开得到了0级近似和一级近似的微分方程组,讨论了液膜的流动和传热特性与壁面之间的关系。     

Analytical study of Cattaneo–Christov heat flux model for a boundary layer flow of Oldroyd-B fluid

We investigate the Cattaneo–Christov heat flux model for a two-dimensional laminar boundary layer flow of an incompressible Oldroyd-B fluid over a linearly stretching sheet. Mathematical formulation of the boundary layer problems is given. The nonlinear partial differential equations are converted into the ordinary differential equations using similarity transformations. The dimensionless velocity and temperature profiles are obtained through optimal homotopy analysis method(OHAM). The influences of the physical parameters on the velocity and the temperature are pointed out. The results show that the temperature and the thermal boundary layer thickness are smaller in the Cattaneo–Christov heat flux model than those in the Fourier's law of heat conduction.     

Effect of boundary heat flux on solidification in a forced liquid metal flow: a phase-field simulation

A phase-field model coupling with velocity field is employed to study the effect of boundary heat flux on the microstructure formation of a Ni-40.8%Cu alloy with liquid flow during the solidification, and an anti-trapping current is introduced to suppress the solute trapping due to the larger interface width used in simulations than a real solidifying material. The effect of the flow field coupling with boundary heat extractions on the microstructure formation as well as distributions of concentration and temperature fields are analyzed and discussed. The forced liquid flow can significantly affect the heat and solute diffusions, thus influencing morphology formation, concentration and temperature distributions during the solidification. The solute segregation and concentration diffusion are changed by boundary heat extractions, and the morphology, concentration and temperature distributions are significantly influenced by increasing the heat extraction, which relatively makes the effect of liquid flow constrained. By increasing the initial velocity of liquid flow, the lopsided rate of the primary dendrite arm is enlarged and the growth manner of dendrite arms gets changed, and the transition of the microstructure from dendrite to cellular moves to the large heat extraction direction. Therefore, there exists the competition between the heat flux, temperature gradient and forced liquid flow that finally determines the microstructure formation during directional solidification.     

Beyond the Fourier heat conduction law and the thermal no-slip boundary condition

The problem of heat slip flow along solid walls is investigated within the framework of modern thermodynamics. The underlying idea is to elevate the heat flux at the boundary to the status of independent variable. General boundary conditions are obtained from the constraint imposed by the second law of thermodynamics expressing that the rate of entropy production is non-negative. In parallel, evolution equations for the heat flux inside the bulk of the system are also formulated.     

高速流绕平板边界层特性研究

本项高超声速流绕平板的边界层特性实验研究在中国航天空气动力技术研究院(CAAA)的炮风洞中完成.为了研究分离流动特性, 选择了一项实验研究, 通过实验分别提供绕模型的附着流动与分离流动实验结果.其中第1个模型为顺流平板, 第2个模型为平板上安装突起物, 它们分别对应附着流与分离流动.文章专题研究平板绕流, 为附着流, 它是分离流动的基础.      

Unsteady MHD Non-Darcian Flow over a Vertical Stretching Plate Embedded in a Porous Medium with Thermal Non-Equilibrium Model

An analysis is performed to study the influence of local thermal non-equilibrium (LTNE) on unsteady MHD laminar boundary layer flow of viscous, incompressible fluid over a vertical stretching plate embedded in a sparsely packed porous medium in the presence of heat generation/absorption. The flow in the porous medium is governed by Brinkman-Forchheimer extended Darcy model. A uniform heat source or sink is presented in the solid phase. By applying similarity analysis, the governing partial differential equations are transformed into a set of time dependent non-linear coupled ordinary differential equations and they are solved numerically by Runge-Kutta Fehlberg method along with shooting technique. The obtained results are displayed graphically to illustrate the influence of different physical parameters on the velocity, temperature profile and heat transfer rate for both fluid and solid phases. Moreover, the numerical results obtained in this study are compared with the existing literature in the case of LTE and found that they are in good agreement.     

单面加热矩形通道热入口段层流对流换热特性的场协同分析

对单面加热矩形通道热入口段的层流对流换热问题进行了数值模拟研究,给出了不同截面比的局部努赛尔数。推导出单面加热时的场协同方程,以此分析了不同截面比下加热边界条件对努赛尔数的影响规律。     

Heat and mass transfer of MHD convective boundary layer flow past a stretching porous wall embedded in a porous medium

The hydromagnetic convective boundary layer flow past a stretching porous wall embedded in a porous medium with heat and mass transfer in the presence of a heat source and under the influence of a uniform magnetic field is studied. Exact solutions of the basic equations of motion, heat and mass transfer are obtained after reducing them to nonlinear ordinary differential equations. The reduced equations of heat and mass transfer are solved using a confluent hypergeometric function. The effects of the flow parameters such as a suction parameter (N), magnetic parameter (M), permeability parameter (K _p ), wall temperature parameter (r), wall concentration parameter (n), and heat source/sink parameter (Q) on the dynamics are discussed. It is observed that the suction parameter appears in the boundary condition ensuring the variable suction at the surface. Transverse component of the velocity increases only when magnetic field strength exceeds certain value, but the thermal boundary layer thickness and concentration distribution increase for all values. Results presented in this paper are in good agreement with the work of the previous author and also in conformity with the established theory.     

氩等离子体射流在空气环境中冲击平板层流流动与传热的数值模拟

本文采用组合扩散系数方法处理不同气体组分之间的扩散，对氩等离子体的流射入空气环境并撞击平板时的层流流动和传热进行了数值模拟．这种新的处理混合气体中质量扩散的方法有助于更准确地描述等离子体条件下的组分扩散与能量输运。文中给出了射流中速度、温度及氩质量分数的分布情况，以及基板处热流密度分布的若干典型的数值模拟结果．     

Velocity,temperature, and Reynolds-stress scaling in the wall region of turbulent boundary layer on a permeable surface

A finite total number of flow parameters in the wall region of a turbulent boundary layer points to universal behavior of turbulent shear stress as a function of mean-velocity gradient and turbulent heat flux as a function of both mean-velocity and mean-temperature gradients. Combined with dimensional arguments, this fact is used to reduce the momentum and heat equations to first-order ordinary differential equations for temperature and velocity profiles amenable to general analysis. Scaling laws for velocity and temperature in boundary layer flows with transpiration are obtained as generalizations of well-known logarithmic laws. Scaling relations are also established for shear stress and rms transverse velocity fluctuation. The proposed method has substantial advantages as compared to the classical approach (which does not rely on fluid-dynamics equations [1–3]). It can be applied to establish scaling laws for a broader class of near-wall turbulence problems without invoking closure hypotheses.     

Advanced Study of Unsteady Heat and Chemical Reaction with Ramped Wall and Slip Effect on a Viscous Fluid

This paper investigate the effect of slip boundary condition, thermal radiation, heat source, Dufour number,chemical reaction and viscous dissipation on heat and mass transfer of unsteady free convective MHD flow of a viscous fluid past through a vertical plate embedded in a porous media. Numerical results are obtained for solving the nonlinear governing momentum, energy and concentration equations with slip boundary condition, ramped wall temperature and ramped wall concentration on the surface of the vertical plate. The influence of emerging parameters on velocity,temperature and concentration fields are shown graphically.     

Casson fluid flow and heat transfer over a nonlinearly stretching surface

A boundary layer analysis is presented for non-Newtonian fluid flow and heat transfer over a nonlinearly stretching surface. The Casson fluid model is used to characterize the non-Newtonian fluid behavior. By using suitable transformations, the governing partial differential equations corresponding to the momentum and energy equations are converted into non-linear ordinary differential equations. Numerical solutions of these equations are obtained with the shooting method. The effect of increasing Casson parameter is to suppress the velocity field. However the temperature is enhanced with the increasing Casson parameter.     

Mixed Convective Viscoelastic Nanofluid Flow Past a Porous Media with Soret-Dufour Effects

The present study is carried out to see the thermal-diffusion (Dufour) and diffusion-thermo (Soret) effects on the mixed convection boundary layer flow of viscoelastic nanofluid flow over a vertical stretching surface in a porous medium. Optimal homotopy analysis method (OHAM) is best candidate to handle highly nonlinear system of differ-ential equations obtained from boundary layer partial differential equations via appropriate transformations. Graphical illustrations depicting different physical arising parameters against velocity, temperature and concentration distributions with required discussion have also been added. Numerically calculated values of skin friction coefficient, local Nusselt and Sherwood numbers are given in the form of table and well argued. It is found that nanofluid velocity increases with increase in mixed convective and viscoelastic parameters but it decreases with the increasing values of porosity parameter. Also, it is observed that Dufour number has opposite behavior on temperature and concentration profiles.     

变系数瞬态热传导问题边界元格式的特征正交分解降阶方法

提出了一种基于边界元法求解变系数瞬态热传导问题的特征正交分解(POD)降阶方法,重组并推导出变系数瞬态热传导问题适合降阶的边界元离散积分方程,建立了变系数瞬态热传导问题边界元格式的POD降阶模型,并用常数边界条件下建立的瞬态热传导问题的POD降阶模态,对光滑时变边界条件瞬态热传导问题进行降阶分析.首先,对一个变系数瞬态热传导问题,建立其边界域积分方程,并将域积分转换成边界积分;其次,离散并重组积分方程,获得可用于降阶分析的矩阵形式的时间微分方程组;最后,用POD模态矩阵对该时间微分方程组进行降阶处理,建立降阶模型并对其求解.数值算例验证了本文方法的正确性和有效性.研究表明:1)常数边界条件下建立的低阶POD模态矩阵,能够用来准确预测复杂光滑时变边界条件下的温度场结果;2)低阶模型的建立,解决了边界元法中采用时间差分推进技术求解大型时间微分方程组时求解速度慢、算法稳定性差的问题.     

Thermo-physical characteristics during the flow and heat transfer analysis of GO-nanoparticles adjacent to a continuously moving thin needle

Nanofluids have shown significant promise in thermal enhancement of many industrial systems and they have been used extensively in energy applications during recent years. Keeping such applications in mind, the present work exhibits a two-dimensional numerical simulation for the boundary layer flow of Graphene oxide (GO)-nanofluids adjacent to a thin needle along with heat transfer. Influence of heat generation/absorption and viscous dissipation have been included to explore the heat transport analysis. The nanofluid flow is generated due to a continuously moving horizontal thin needle. The non-linear expressions governing the flow and heat transfer analysis are changed into dimensionless form by introducing new dimensionless variables. The novelty of current study is to predict the multiple numerical solutions for dimensionless velocity and temperature fields. Numerical computations and graphical delineations were done with the assistance of MATLAB software. This study explores the impacts of several dimensionless key parameters, like, magnetic parameter, Prandtl number, nanoparticles volume fraction and ratio of needle's velocities on the flow and thermal distributions. The computational results have proved that the fluid temperature enhances for higher values of nanoparticles volume fraction while an opposite is true for velocity distributions. In addition, the computed outcomes revealed that for the case of upper branch solution, significant reduction in skin-friction coefficient is seen for higher magnetic parameter.     

MHD flow of nanofluids over an exponentially stretching sheet in a porous medium with convective boundary conditions

This article concentrates on the steady magnetohydrodynamic(MHD) flow of viscous nanofluid. The flow is caused by a permeable exponentially stretching surface. An incompressible fluid fills the porous space. A comparative study is made for the nanoparticles namely Copper(Cu), Silver(Ag), Alumina(Al2O3) and Titanium Oxide(TiO2). Water is treated as a base fluid. Convective type boundary conditions are employed in modeling the heat transfer process. The non-linear partial differential equations governing the flow are reduced to an ordinary differential equation by similarity transformations. The obtained equations are then solved for the development of series solutions. Convergence of the obtained series solutions is explicitly discussed. The effects of different parameters on the velocity and temperature profiles are shown and analyzed through graphs.