Conjugate heat transfer in square enclosures

Building elements represented by square vertical enclosures encircled with finite walls or with centered solid body, could maintain the equivalent fluid volumes through the volume ratio scale. Present work aims to investigate the fluid flow and heat transfer in these two building elements. Complete two-dimensional numerical simulation of the conjugate heat conduction and natural convection occurring in both enclosures is carried out. An analytical expression for the minimum size of the inserted body at which the body begins to suppress the natural convection flow is proposed and validated by the numerical results. The fluid flow and heat transfer characteristics are analyzed through the streamlines, heatlines, and total heat transfer rates across both enclosures. Results reveal that heat transfer rates across both enclosures are complex functions of the volume ratio scale, Rayleigh number, and the relative thermal conductivity.     

Interaction of surface radiation with conjugate mixed convection from a vertical channel with multiple discrete heat sources

Important results of a numerical study performed on combined conduction–mixed convection–surface radiation from a vertical channel equipped with three identical flush-mounted discrete heat sources in its left wall are provided here. The channel has walls of identical height with the spacing varied by varying its aspect ratio (AR). The cooling medium is air that is considered to be radiatively transparent. The heat generated in the channel gets conducted along its walls before getting dissipated by mixed convection and radiation. The governing equations for fluid flow and heat transfer are considered without boundary layer approximations and are transformed into vorticity–stream function form and are later normalized. The resulting equations are solved, along with relevant boundary conditions, making use of the finite volume method. The computer code written for the purpose is validated both for fluid flow and heat transfer results with those available in the literature. Detailed parametric studies have been performed and the effects of modified Richardson number, surface emissivity, thermal conductivity and AR on various pertinent results have been looked into. The significance of radiation in various regimes of mixed convection has been elucidated. The relative contributions of mixed convection and radiation in carrying the mandated cooling load have been thoroughly explored.     

MHD natural convection flow and heat transfer in a laterally heated partitioned enclosure

This study looks at MHD natural convection flow and heat transfer in a laterally heated enclosure with an off-centred partition. Governing equations in the form of vorticity–stream function formulation are solved using the polynomial differential quadrature (PDQ) method. Numerical results are obtained for various values of the partition location, Rayleigh, Prandtl and Hartmann numbers. The results indicate that magnetic field significantly suppresses flow, and thus heat transfer, especially for high Rayleigh number values. The results also show that the x-directional magnetic field is more effective in damping convection than the y-directional magnetic field, and the average heat transfer rate decreases with an increase in the distance of the partition from the hot wall. The average heat transfer rate decreases up to 80% if the partition is placed at the midpoint and an x-directional magnetic field is applied. The results also show that flow and heat transfer have little dependence on the Prandtl number.     

Heat transfer by conduction,natural convection and radiation across a rectangular cellular structure

This paper describes results on the effects of wall conduction and radiation heat exchange among surfaces on laminar natural convection heat transfer in a two-dimensional rectangular cavity modelling a cellular structure. Parametric heat transfer calculations have been performed, and numerical results are presented in graphical and tabular form. Local and average Nusselt numbers along the cavity walls are reported for a range of parameters of physical interest. The findings suggest that the local or the average Nusselt number is one of many parameters that control conjugate heat transfer problems. The results indicate that natural convection heat transfer in the cavity is reduced by heat conduction in the walls and radiation exchange among surfaces. The results obtaibed for the total heat transfer rate through the system using the two-dimensional model are compared with those based on a one-dimensional model.     

Review of nucleate pool boiling bubble heat transfer mechanisms

Enhanced convection, transient conduction, microlayer evaporation, and contact line heat transfer have all been proposed as mechanisms by which bubbles transfer energy during boiling. Models based on these mechanisms contain fitting parameters that are used to fit them to the data, resulting a proliferation of “validated” models. A review of the recent experimental, analytical, and numerical work into single bubble heat transfer is presented to determine the contribution of each of the above mechanisms to the overall heat transfer. Transient conduction and microconvection are found to be the dominant heat transfer mechanisms. Heat transfer through the microlayer and at the three-phase contact line do not contribute more than about 25% of the overall heat transfer.     

高超声速飞行器大面积热防护系统的传热数值分析

隔热毡是高超声速飞行器防热系统中重要的组成部分。隔热毡内存在复杂的多种传热形式的耦合,本文详细地分析了隔热结构内导热与辐射的复合换热问题,用光学厚极限法分析了隔热层纤维席内辐射热流。建立了高温绝热毡有效热导率的数值计算模型,分析了温度和压力对传热机制的影响。该模型预测的有效导热系数与试验结果最大误差不超过6%。通过应用数值分析方法得到有效导热系数,建立了防热结构一维瞬态传热模型,该模型结果与瞬态实验结果最大误差为8%。最后还计算出不同厚度隔热毡蒙皮结构的温度响应,并分析讨论了隔热毡厚度对隔热效果的影响。本文研究表明:TPS隔热毡的厚度达到63.3mm后,继续增加尺寸,其隔热效率将明显降低。     

A steady conjugate heat transfer problem with conduction and free convection

Summary A steady conjugate heat transfer problem dealing with conduction in a heat-generating slab and free convection in the surrounding fluid is studied analytically. Free convection is analyzed by a Görtler-type series solution to the boundary-layer equations for non-uniform surface-temperature variations, while conduction is treated by the standard technique of Fourier transforms. Interfacial temperature and heat flux variations from both solutions in series forms are then formally matched to yield algebraic relations for the coefficients in the series. These coefficients can then be simply evaluated in a given problem in terms of three physical parameters. A numerical example is shown.     

MHD mixed convective heat transfer flow about an inclined plate

Mixed convection heat transfer about a semi-infinite inclined plate in the presence of magneto and thermal radiation effects is studied. The fluid is assumed to be incompressible and dense. The nonlinear coupled parabolic partial differential equations governing the flow are transformed into the non-similar boundary layer equations, which are then solved numerically using the Keller box method. The effects of the mixed convection parameter R _i, the angle of inclination α, the magnetic parameter M and the radiation–conduction parameter R _d on the velocity and temperature profiles as well as on the local skin friction and local heat transfer parameters. For some specific values of the governing parameters, the results are compared with those available in the literature and a fairly good agreement is obtained.     

An analytical solution to the heat transfer problem in thick-walled hunt flow

The flow of a liquid metal in a rectangular duct, subject to a strong transverse magnetic field is of interest in a number of applications. An important application of such flows is in the context of coolants in fusion reactors, where heat is transferred to a lead-lithium eutectic. It is vital, therefore, that the heat transfer mechanisms are understood. Forced convection heat transfer is strongly dependent on the flow profile. In the hydrodynamic case, Nusselt numbers and the like, have long been well characterised in duct geometries. In the case of liquid metals in strong magnetic fields (magnetohydrodynamics), the flow profiles are very different and one can expect a concomitant effect on convective heat transfer. For fully developed laminar flows, the magnetohydrodynamic problem can be characterised in terms of two coupled partial differential equations. The problem of heat transfer for perfectly electrically insulating boundaries (Shercliff case) has been studied previously (Bluck et al., 2015). In this paper, we demonstrate corresponding analytical solutions for the case of conducting hartmann walls of arbitrary thickness. The flow is very different from the Shercliff case, exhibiting jets near the side walls and core flow suppression which have profound effects on heat transfer.     

Simulation studies on multi-mode heat transfer from an open cavity with a flush-mounted discrete heat source

Prominent results of a simulation study on conjugate convection with surface radiation from an open cavity with a traversable flush mounted discrete heat source in the left wall are presented in this paper. The open cavity is considered to be of fixed height but with varying spacing between the legs. The position of the heat source is varied along the left leg of the cavity. The governing equations for temperature distribution along the cavity are obtained by making energy balance between heat generated, conducted, convected and radiated. Radiation terms are tackled using radiosity-irradiation formulation, while the view factors, therein, are evaluated using the crossed-string method of Hottel. The resulting non-linear partial differential equations are converted into algebraic form using finite difference formulation and are subsequently solved by Gauss–Seidel iterative technique. An optimum grid system comprising 111 grids along the legs of the cavity, with 30 grids in the heat source and 31 grids across the cavity has been used. The effects of various parameters, such as surface emissivity, convection heat transfer coefficient, aspect ratio and thermal conductivity on the important results, including local temperature distribution along the cavity, peak temperature in the left and right legs of the cavity and relative contributions of convection and radiation to heat dissipation in the cavity, are studied in great detail.     

Transportation of heat through Cattaneo-Christov heat flux model in non-Newtonian fluid subject to internal resistance of particles

Thermal conduction which happens in all phases(liquid,solid,and gas) is the transportation of internal energy through minuscule collisions of particles and movement of electrons within a working body.The colliding particles comprise electrons,molecules,and atoms,and transfer disorganized microscopic potential and kinetic energy,mutually known as the internal energy.In engineering sciences,heat transfer comprises the processes of convection,thermal radiation,and sometimes mass transportation.Typi...     

Entropy analysis in electrical magnetohydrodynamic(MHD) flow of nanofluid with effects of thermal radiation,viscous dissipation,and chemical reaction

The unsteady mixed convection flow of electrical conducting nanofluid and heat transfer due to a permeable linear stretching sheet with the combined effects of an electric field, magnetic field, thermal radiation, viscous dissipation, and chemical reaction have been investigated. A similarity transformation is used to transform the constitutive equations into a system of nonlinear ordinary differential equations.The resultant system of equations is then solved numerically using implicit finite difference method.The velocity, temperature, concentration, entropy generation, and Bejan number are obtained with the dependence of different emerging parameters examined. It is noticed that the velocity is more sensible with high values of electric field and diminished with a magnetic field. The radiative heat transfer and viscous dissipation enhance the heat conduction in the system. Moreover, the impact of mixed convection parameter and Buoyancy ratio parameter on Bejan number profile has reverse effects. A chemical reaction reduced the nanoparticle concentration for higher values.     

Unsteady Free Convection along an Infinite Vertical Flat Plate Embedded in a Stably Stratified Fluid-Saturated Porous Medium

The problem of unsteady free convection heat transfer from a one-dimensional (parallel) flow along an infinite vertical flat plate embedded in a thermally stratified fluid-saturated porous medium is considered. Flows are induced by a sudden change in the arbitrary temporal plate temperature. By a formal reduction of the corresponding boundary value problems to well-known Fourier heat conduction problems, analytical solutions of the Darcy and energy equations are obtained. Several special cases are discussed in detail.     

Influence of magnetic field and thermal radiation by natural convection past vertical cone subjected to variable surface heat flux

A numerical study is performed to examine the heat transfer characteristics of natural convection past a vertical cone under the combined effects of magnetic field and thermal radiation.The surface of the cone is subjected to a variable surface heat flux.The fluid considered is a gray,absorbing-emitting radiation but a non-scattering medium.With approximate transformations,the boundary layer equations governing the flow are reduced to non-dimensional equations valid in the free convection regime.The dimensionless governing equations are solved by an implicit finite difference method of Crank-Nicolson type which is fast convergent,accurate,and unconditionally stable.Numerical results are obtained and presented for velocity,temperature,local and average wall shear stress,and local and average Nusselt number in air and water.The present results are compared with the previous published work and are found to be in excellent agreement.     

Effects of boundary reflection on radiative heat transfer in participating media

Radiative heat transfer through a non-isothermal grey participating medium between two parallel surfaces kept at fixed temperature has been investigated. The integro-differential transfer equations for surface reflection were solved in semi-analytical form by projectional methods; conduction and convection were neglected. It was assumed that reflection from the cold wall was diffuse, while that from the hot wall was either diffuse or specular. The heat flux and the temperature distribution in the participating medium were calculated in each physical condition, in order to compare the effects of different reflection modes on heat transfer. The results show that temperature distributions and heat fluxes are only slightly affected by the particular reflection law, the relative difference being less than 1%. This suggests that diffuse reflection only could be considered for practical applications, since it requires a much simpler computational procedure.     

Conjugate mixed convection with surface radiation from a vertical electronic board with multiple discrete heat sources

The problem of combined conduction-mixed convection-surface radiation from a vertical electronic board provided with three identical flush-mounted discrete heat sources is solved numerically. The cooling medium is air that is considered to be radiatively transparent. The governing equations for fluid flow and heat transfer are converted from primitive variable form to stream function-vorticity formulation. The equations, thus obtained, are normalised and then are converted into algebraic form using a finite volume based finite difference method. The resulting algebraic equations are then solved using Gauss–Seidel iterative method. An optimum grid system comprising 151 grids along the board and 111 grids across the board is chosen. The effects of various parameters, such as modified Richardson number, surface emissivity and thermal conductivity on temperature distribution along the board, maximum board temperature and relative contributions of mixed convection and radiation to heat dissipation are studied in detail. Further, the contributions of free and forced convection components of mixed convection to board temperature distribution and peak board temperature are brought out. The exclusive roles played by surface radiation and buoyancy in the present problem are clearly elucidated.     

Conjugate heat transfer inside a porous channel

Analytical and numerical analyses have been performed for fully developed forced convection in a fluid-saturated porous medium channel bounded by two parallel plates. The channel walls are assumed to be finite in thickness. Conduction heat transfer inside the channel wall is also accounted and the full problem is treated as a conjugate heat transfer problem. The flow in the porous material is described by the Darcy–Brinkman momentum equation. The outer surfaces of the solid walls are treated as isothermal. A temperature dependent volumetric heat generation is considered inside the solid wall only. Analytical expressions for velocity, temperature, and Nusselt number are obtained after simplifying and solving the governing differential equations with reasonable approximations. Subsequent results obtained by numerical calculations show an excellent agreement with the analytical results.     

Analytical simulation in heat storage systems

Packed bed heat exchangers for thermal energy storage systems are investigated by means of two phase heat transfer models. The paper is mainly aimed at deriving analytical solutions to the thermal balance equations relevant to different kinds of packed beds, taking into account the roles played by heat capacity and conduction effects. The results are shortly discussed and some graphs are shown for situations typical of various operational modes.     

Magnetohydrodynamic effects on natural convection flow of a nanofluid in the presence of heat source due to solar energy

The objective of the present work is to investigate theoretically the MHD convective flow and heat transfer of an incompressible viscous nanofluid past a porous vertical stretching sheet in the presence of variable stream condition due to solar radiation (incident radiation). The governing equations are derived using the usual boundary-layer and Boussinesq approximations and accounting for the presence of an applied magnetic field and incident radiation flux. The absorbed radiation acts as a distributed source which initiates buoyancy-driven flow and convection in the absorbed layer. The partial differential equations governing the problem under consideration are transformed by a special form of Lie symmetry group transformations viz. one-parameter group of transformation into a system of ordinary differential equations which are solved numerically using Runge Kutta Gill based shooting method. The conclusion is drawn that the flow field and temperature are significantly influenced by radiation, heat source and magnetic field.     

Natural convection and radiation heat transfer of an externally-finned tube vertically placed in a chamber

A three-dimensional numerical study was made to investigate effects of fin angle, fin surface emissivity, and tube wall temperature on heat transfer enhancement for a longitudinal externally-finned tube placed vertically in a small chamber. The numerical model was first validated through comparison with experimental measurements and the appropriateness of general boundary conditions was examined. The numerical results show that the mean Nusselt number increases with Rayleigh number for all the fin angles investigated. The maximum heat transfer rate per mass occurs when the fin angle is about 60° for fin surface emissivity between 0.7 and 0.8 and 55° when the surface emissivity increases to 0.9. With increasing tube wall temperature, both the natural convection and radiation heat transfer are enhanced, but the fraction of radiation heat transfer decreases in the temperature range studied. Radiation fraction increases with increasing fin surface emissivity. Both convection and radiation heat transfer modes are important.