Mathematical modeling of convective-conductive heat transfer in a rectangular domain in a conjugate statement

The results of mathematical modeling of convection of a viscous incompressible liquid in a rectangular domain with sources of mass input and output are presented. A conjugate statement within the framework of the Boussinesq approximation is used. The regimes of forced and mixed convection in a domain have been investigated. The domain has two vertical walls and one horizontal wall of finite thickness, two zones of liquid input and output, and a free surface. A plane nonstationary problem within the framework of the Navier-Stokes model for the liquid phase and the heat conduction equation for the solid phase are considered. The distributions of the hydrodynamic parameters and temperatures characterizing the main regularities of the processes under investigation have been obtained. Circulation flows have been identified. The vortex formation mechanism and the temperature distribution in the solution domain under the regimes of forced and mixed convection and different locations of mass input and output zones have been analyzed. It has been found that natural convection should be taken into account when modeling convective heat transfer with Gr number values from 10⁵ and higher.     

含对流与蒸发表面的有限厚度材料的双曲型热传导分析

本文对于含有对流与蒸发表面的有限厚度材料,在遭受一脉冲表面热流作用时的双曲型热传导进行了分析,采用热势函数描述的双曲型热传导方程来描述该问题,并用有限差分法进行数值求解．同时,本文还就表面对流与蒸发对材料表面与内部瞬态温度变化的影响以及材料双曲型热传导对表面蒸发的影响进行了分析．     

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.     

Nested Cartesian grid method in incompressible viscous fluid flow

In this work, the local grid refinement procedure is focused by using a nested Cartesian grid formulation. The method is developed for simulating unsteady viscous incompressible flows with complex immersed boundaries. A finite-volume formulation based on globally second-order accurate central-difference schemes is adopted here in conjunction with a two-step fractional-step procedure. The key aspects that needed to be considered in developing such a nested grid solver are proper imposition of interface conditions on the nested-block boundaries, and accurate discretization of the governing equations in cells that are with block-interface as a control-surface. The interpolation procedure adopted in the study allows systematic development of a discretization scheme that preserves global second-order spatial accuracy of the underlying solver, and as a result high efficiency/accuracy nested grid discretization method is developed. Herein the proposed nested grid method has been widely tested through effective simulation of four different classes of unsteady incompressible viscous flows, thereby demonstrating its performance in the solution of various complex flow–structure interactions. The numerical examples include a lid-driven cavity flow and Pearson vortex problems, flow past a circular cylinder symmetrically installed in a channel, flow past an elliptic cylinder at an angle of attack, and flow past two tandem circular cylinders of unequal diameters. For the numerical simulations of flows past bluff bodies an immersed boundary (IB) method has been implemented in which the solid object is represented by a distributed body force in the Navier–Stokes equations. The main advantages of the implemented immersed boundary method are that the simulations could be performed on a regular Cartesian grid and applied to multiple nested-block (Cartesian) structured grids without any difficulty. Through the numerical experiments the strength of the solver in effectively/accurately simulating various complex flows past different forms of immersed boundaries is extensively demonstrated, in which the nested Cartesian grid method was suitably combined together with the fractional-step algorithm to speed up the solution procedure.     

Measurement of heat transfer coefficients by nuclear magnetic resonance

We demonstrate an experimental method for the measurement of heat transfer coefficient for a fluid system by magnetic resonance imaging. In this method, the temporal variation of thermally induced nuclear shielding is monitored and the average heat transfer coefficient is measured as a function of fluid velocity. We examine the cases of natural convection and forced convection at fluid velocity up to 0.8 m s(-1). These cases correspond to low dimensionless Biot (Bi) number where the heat transfer is limited by thermal convection. We demonstrate the NMR method for two simple geometries, a cylinder and a sphere, to experimentally determine the heat transfer coefficient (h) in two NMR imaging and spectroscopy systems through measuring three NMR parameters, the chemical shift, magnetization and spin self diffusion coefficient.     

具有纵向外肋片的水平复合管外表面自然对流换热的数值计算

为了方便而有效地模拟具有纵向外肋片的水平复合管外表面大空间自然对流换热的数值计算时计算区域外边界条件,本文提出一种新的边界条件处理方式。数值实验表明,用该条件计算的具有恒壁温的水平圆柱外表面自然对流换热数值解与文献中的基准解相比,平均Nu数的误差在0.5％以下。本文在极坐标系下,采用固体区与流体区耦合计算原始变量法,模拟计算了具有纵向外肋片的水平复合管外表面在不同肋片高度和肋片数下的自然对流换热量。数值计算表明,管外布置6个对称的肋片时,在肋片相对高度h/r04.0时,对换热最为有利,对应的肋片管平均肋效率为87.92％;而在相同肋片高度下,布置8个对称的肋片时,换热量最大。     

Convective specific-heat transfer in liquids in the presence of non-uniform electric field

Summary The electroconvective specific-heat transfer coefficient has been measured in various liquids (methanol, kerosene, silicon oil and ethanol) from a single platinum wire (diameter=0.025 mm) mounted along the axis of a copper cylinder (diameter=53 mm). The heat transfer coefficient has been evaluated under the influence of a.c. and d.c. fields. An a.c. field always causes an enhancement in the heat transfer coefficient. A d.c. field causes an inhibition in heat transfer in methanol. A similar trend is noticed in kerosene, but the heat transfer coefficient increases again as the field is increased. An enhancement in the heat transfer coefficient is observed in silicon oil, and a similar trend is noticed in ethanol, but the heat transfer coefficient decreases again as the field is increased. The effect of cylinder orientation on convection is studied. The efficiency of convection has been calculated for various liquids using an empirical relation. The efficiency obtained in a d.c. field is found to be higher than in the a.c. field. A similar trend is also noticed for the electric Nusselt number.     

流体低速绕流振动圆柱对流换热数值研究

运用Fluent的动态网格技术,对空气低速绕流振动圆柱的对流换热进行了研究,分析了流动和振动参数对换热的影响。数值计算表明,在本文计算范围内,壁面振动可使换热强化,最大可强化9倍,换热的强化随振幅和频率的增大而增大。场协同分析表明,圆柱振动强化换热的原因在于速度场和温度梯度场之间的协同程度得到了改善。     

Effects of Thermal Radiation and Slip Mechanism on Mixed Convection Flow of Williamson Nanofluid Over an Inclined Stretching Cylinder

The current investigation highlights the mixed convection slip flow and radiative heat transport of uniformly electrically conducting Williamson nanofluid yield by an inclined circular cylinder in the presence of Brownian motion and thermophoresis parameter.A Lorentzian magnetic body force model is employed and magnetic induction effects are neglected.The governing equations are reduced to a system of nonlinear ordinary differential equations with associated boundary conditions by applying scaling group transformations.The reduced nonlinear ordinary differential equations are then solved numerically by Runge-Kutta-Fehlberg fifth-order method with shooting technique.The effects of magnetic field,Prandtl number,mixed convection parameter,buoyancy ratio parameter,Brownian motion parameter,thermophoresis parameter,heat generation/absorption parameter,mass transfer parameter,radiation parameter and Schmidt number on the skin friction coefficient and local Nusselt are analyzed and discussed.It is found that the velocity of the fluid decreases with decrease in curvature parameter,whereas it increases with mixed convection parameter.Further,the local Nusselt number decreases with an increase in the radiation parameter.The numerical comparison is also presented with the existing published results and found that the present results are in excellent agreement which also confirms the validity of the present methodology.     

Natural and forced convective heat transfer on slender cylinders

This paper presents an experimental study of free and forced convective heat transfer along vertical slender cylinders. The local heat transfer coefficient is determined from the measurement of the surface temperature distribution performed by quantitative infrared thermography. It is found that the convective heat transfer is strongly dependent on the cylinder curvature and misalignment with the flow. The effect of proximity of two cylinders is emphasized in the case of forced convection. Correlations are proposed for the two types of convection. It is worth noting that circumstances exist where the turbulent heat transfer in free convection can be of the same order of magnitude as for laminar forced convection. The outcome of the study demonstrates the suitability of quantitative infrared thermography to solve complex problems and to provide a deeper understanding of the heat transfer on slender cylinders.     

Fully HOC Scheme for Mixed Convection Flow in a Lid-Driven Cavity Filled with a Nanofluid

A fully higher-order compact (HOC) finite difference scheme on the 9-point two-dimensional (2D) stencil is formulated for solving the steady-state laminar mixed convection flow in a lid-driven inclined square enclosure filled with water-$Al_2O_3$ nanofluid. Two cases are considered depending on the direction of temperature gradient imposed (Case I, top and bottom; Case II, left and right). The developed equations are given in terms of the stream function-vorticity formulation and are non-dimensionalized and then solved numerically by a fourth-order accurate compact finite difference method. Unlike other compact solution procedure in literature for this physical configuration, the present method is fully compact and fully higher-order accurate. The fluid flow, heat transfer and heat transport characteristics were illustrated by streamlines, isotherms and averaged Nusselt number. Comparisons with previously published work are performed and found to be in excellent agreement. A parametric study is conducted and a set of graphical results is presented and discussed to elucidate that significant heat transfer enhancement can be obtained due to the presence of nanoparticles and that this is accentuated by inclination of the enclosure at moderate and large Richardson numbers.     

液滴撞击液膜的流热耦合界面追踪方法数值模拟

采用界面追踪方法研究蒸馏过程中液滴撞击高温薄液膜的流动和传热特性,将数值结果与解析解和实验进行比较验证模型的正确性,研究气液界面和热流分布的演变过程.同时,分析液滴We数和无量纲液膜厚度对传热的影响.液滴撞击后的热流密度分布显示：液膜可分为撞击区、过渡区和静态区.由于液滴的撞击作用,强制对流是撞击区内主要的传热机制.增大液滴的韦伯数或减小无量纲液膜厚度会加强热量传递.随着液滴韦伯数的增加,冲击引起的扰动增强,在动量和能量共同作用下,平均热流密度明显增大,撞击区冠状水花越明显.无量纲液膜厚度越小,平均热流密度越大,且有更长的时间保持高热流密度换热.     

方腔内Cu/Al2O3水混合纳米流体自然对流的格子Boltzmann模拟

纳米流体作为一种较高的导热介质, 广泛应用于各个传热领域. 鉴于纳米颗粒导热系数和成本之间的矛盾, 本文提出了一种混合纳米流体. 为了研究混合纳米流体颗粒间相互作用机理和自然对流换热特性, 在考虑颗粒间相互作用力的基础上, 利用多尺度技术推导了纳米流体流场和温度场的格子Boltzmann方程, 通过耦合流动和温度场的演化方程, 建立了Cu/Al₂O₃水混合纳米流体的格子Boltzmann模型, 研究了混合纳米流体颗粒间的相互作用机理和纳米颗粒在腔体内的分布. 发现在颗粒间相互作用力中, 布朗力远远大于其他作用力, 温差驱动力和布朗力对纳米颗粒的分布影响最大. 分析了纳米颗粒组分、瑞利数对自然对流换热的影响, 对比了混合纳米流体(Cu/Al₂O₃-水)与单一金属颗粒纳米流体(Al₂O₃-水)的自然对流换热特性, 发现混合纳米流体具有更强的换热特性.     

基于原油最高温度点变化规律分析停输相变传热

采用分区法数学模型,利用等价比热容法处理析蜡潜热问题,追踪停输相变过程中管道内原油最高温度点位置的变化轨迹,确定管道内原油最终凝固位置,提出管道内原油全凝的判断依据。基于最高温度点位置的变化规律将传热过程分为四个阶段,重点讨论了各阶段中自然对流、潜热释放、传热方式转化对最高温度位置点变化的影响,结合Ra数变化分析了自然对流换热影响从强到弱的变化过程。深入探讨了停输相变过程中管道内固相率的变化及不同位置处原油温降曲线的特点。     

The influence of heat radiation on mixed convection boundary layer flow of a viscoelastic fluid over a circular cylinder with constant surface temperature

The influence of mixed convection boundary layer flow of a viscoelastic fluid over an isothermal horizontal circular cylinder has been analyzed. The boundary layer equations governing the problem are reduced to dimensionless nonlinear partial differential equations and then solved numerically using Keller-box method. Skin friction coefficient and Nusselt number are emphasized specifically. These quantities are displayed against curvature parameter. Effects of mixed convection parameter and radiation-conduction parameter on skin friction coefficient and Nusselt number are illustrated through graphs and table. The boundary layer separation points along the surface of cylinder are also calculated with/without radiation, and a comparison is shown. The presence of radiation helps to reduce the skin friction coefficient in opposing flow case and enhances it for assisting flow case. The increase in value of radiation-conduction parameter helps increase the value of skin friction coefficient and Nusselt number for viscoelastic fluids. The boundary layer separation delays due to thermal radiation.     

Numerical simulation of experiments on turbulent natural convection of heat generating liquid in cylindrical pool

Available experimental data on heat transfer of a melt with volumetric heat generation are analyzed in order to use them for validating the computer codes that describe a core catcher. The problem for CFD simulation of the experiments on heat transfer by laminar and turbulent natural convection is described. Information that can be obtained from experiments for verifying the models of convective heat transfer in a melt is analyzed. The effect of variable viscosity on the integral heat flux is discussed. Calculation results are represented and compared with experimental data on temperature distribution and integral heat transfer. The calculations are in good agreement with the experiment. The results are numerically extrapolated to the range of Rayleigh numbers up to 7 · 10¹⁶. It is concluded that the CFD calculations with the κ-ɛ turbulence model can be used in problems concerned with analysis of melt convection in a core catcher.     

高Rayleigh数条件下竖圆环夹层内自然对流换热的实验研究

对内壁维持恒热流和外壁向环境冷却的大高宽比竖圆环夹层内自然对流换热进行了实验研究。实验装置高宽比分别为２３５和６６６７，半径比分别为２．０３和３．９２。实验数据整理考虑了热辐射影响以获得对流规律。由于已有工作均未考虑高Ｒａ数区域，首次得到Ｒａ数高达１０￣９的区域内平均Ｎｕ数的换热准则式。在低Ｒａ数区域，亦取得了与前人工作一致的结论。本文结果改进了高Ｒａ数区域换热规律的预测能力。     

An immersed boundary-thermal lattice Boltzmann method using an equilibrium internal energy density approach for the simulation of flows with heat transfer

In present paper, a novel immersed boundary-thermal lattice Boltzmann method by the name of “an equilibrium internal energy density approach” is proposed to simulate the flows around bluff bodies with the heat transfer. The main idea is to combine the immersed boundary method (IBM) with the thermal lattice Boltzmann method (TLBM) based on the double population approach. The equilibrium internal energy density approach based on the equilibrium velocity approach [X. Shan, H. Chen, Lattice Boltzmann model for simulating flows with multiple phases and components, Phys. Rev. E 47 (1993) 1815] is used to combine IBM with TLBM. The idea of the equilibrium internal energy density approach is that the satisfaction of the energy balance between heat source on the immersed boundary point and the amount of change of the internal energy density according to time ensures the temperature boundary condition on the immersed boundary. The advantages of this approach are the simple concept, easy implementation and the utilization of original governing equation without modification. The simulation of natural convection in a square cavity with various body shapes for different Rayleigh numbers has been conducted to validate the capability and the accuracy of present method on solving heat transfer problems. Consequently, the present results are found to be in good agreement with those of previous studies.     

Statistical second-order two-scale analysis and computation for heat conduction problem with radiation boundary condition in porous materials

This paper discusses a statistical second-order two-scale(SSOTS) analysis and computation for a heat conduction problem with a radiation boundary condition in random porous materials.Firstly,the microscopic configuration for the structure with random distribution is briefly characterized.Secondly,the SSOTS formulae for computing the heat transfer problem are derived successively by means of the construction way for each cell.Then,the statistical prediction algorithm based on the proposed two-scale model is described in detail.Finally,some numerical experiments are proposed,which show that the SSOTS method developed in this paper is effective for predicting the heat transfer performance of porous materials and demonstrating its significant applications in actual engineering computation.     

ADDENDUM

Abstract

Experiments have been performed to provide basic heat transfer data for thermal convection in a horizontal concentric annulus partially filled with water. A real-time holographic interferometry was employed to map the temperature distribution and a laser shadowgraph system was used to measure local heat transfer coefficients along the heated inner cylinder. Experimental results demonstrate that a minimum average Nusselt number for the water-wetted portion of the inner cylinder occurs at the air-water interface situated flush with the top of the inner cylinder. Corresponding numerical simulations were conducted for the cases of either fully or half-filled with water and the predictions agree well with the experimental results.