相变储热/辐射器式热沉传热特性数值模拟

本文采用焓法建立了具有传导与对流换热耦合边界相变储热装置的三维数学模型,利用整场求解法对控制方程进行了计算。计算过程中考虑了相交材料液相自然对流和空穴的影响,与实验结果进行了对比,验证了模型和程序的可靠性,并对影响相变储热器性能的因素进行了分析.     

Mixed convection heat transfer over a non-linear stretching surface with variable fluid properties

This article presents a numerical solution for the steady two-dimensional mixed convection MHD flow of an electrically conducting viscous fluid over a vertical stretching sheet, in its own plane. The stretching velocity and the transverse magnetic field are assumed to vary as a power function of the distance from the origin. The temperature dependent fluid properties, namely, the fluid viscosity and the thermal conductivity are assumed to vary, respectively, as an inverse function of the temperature and a linear function of the temperature. A generalized similarity transformation is introduced to study the influence of temperature dependent fluid properties. The transformed boundary layer equations are solved numerically, using a finite difference scheme known as Keller Box method, for several sets of values of the physical parameters, namely, the stretching parameter, the temperature dependent viscosity parameter, the magnetic parameter, the mixed convection parameter, the temperature dependent thermal conductivity parameter and the Prandtl number. The numerical results thus obtained for the flow and heat transfer characteristics reveal many interesting behaviors. These behaviors warrant further study of the effects of the physical parameters on the flow and heat transfer characteristics. Here it may be noted that, in the case of the classical Navier-Stokes fluid flowing past a horizontal stretching sheet, McLeod and Rajagopal (1987) [42] showed that there exist an unique solution to the problem. This may not be true in the present case. Hence we would like to explore the non-uniqueness of the solution and present the findings in the subsequent paper.     

Unsteady MHD mixed convection flow over an impulsively stretched permeable vertical surface in a quiescent fluid

The unsteady mixed convection flow of an incompressible laminar electrically conducting fluid over an impulsively stretched permeable vertical surface in an unbounded quiescent fluid in the presence of a transverse magnetic field has been investigated. At the same time, the surface temperature is suddenly increased from the surrounding fluid temperature or a constant heat flux is suddenly imposed on the surface. The problem is formulated in such a way that for small time it is governed by Rayleigh type of equation and for large time by Crane type of equation. The non-linear coupled parabolic partial differential equations governing the unsteady mixed convection flow under boundary layer approximations have been solved analytically by using the homotopy analysis method as well as numerically by an implicit finite difference scheme. The local skin friction coefficient and the local Nusselt number are found to decrease rapidly with time in a small time interval and they tend to steady-state values for t*≥5. They also increase with the buoyancy force and suction, but decrease with injection rate. The local skin friction coefficient increases with the magnetic field, but the local Nusselt number decreases. There is a smooth transition from the unsteady state to the steady state.     

Combined heat and mass transfer by mixed convection MHD flow along a porous plate with chemical reaction in presence of heat source

An exact and a numerical solutions to the problem of a steady mixed convective MHD flow of an incompressible viscous electrically conducting fluid past an infinite vertical porous plate with combined heat and mass transfer are presented.A uniform magnetic field is assumed to be applied transversely to the direction of the flow with the consideration of the induced magnetic field with viscous and magnetic dissipations of energy.The porous plate is subjected to a constant suction velocity as well as a uniform mixed stream velocity.The governing equations are solved by the perturbation technique and a numerical method.The analytical expressions for the velocity field,the temperature field,the induced magnetic field,the skin-friction,and the rate of heat transfer at the plate are obtained.The numerical results are demonstrated graphically for various values of the parameters involved in the problem.The effects of the Hartmann number,the chemical reaction parameter,the magnetic Prandtl number,and the other parameters involved in the velocity field,the temperature field,the concentration field,and the induced magnetic field from the plate to the fluid are discussed.An increase in the heat source/sink or the Eckert number is found to strongly enhance the fluid velocity values.The induced magnetic field along the x-direction increases with the increase in the Hartmann number,the magnetic Prandtl number,the heat source/sink,and the viscous dissipation.It is found that the flow velocity,the fluid temperature,and the induced magnetic field decrease with the increase in the destructive chemical reaction.Applications of the study arise in the thermal plasma reactor modelling,the electromagnetic induction,the magnetohydrodynamic transport phenomena in chromatographic systems,and the magnetic field control of materials processing.     

Combined effect of magnetic field and heat absorption on unsteady free convection and heat transfer flow in a micropolar fluid past a semi-infinite moving plate with viscous dissipation using element free Galerkin method

The fully developed electrically conducting micropolar fluid flow and heat transfer along a semi-infinite vertical porous moving plate is studied including the effect of viscous heating and in the presence of a magnetic field applied transversely to the direction of the flow. The Darcy-Brinkman-Forchheimer model which includes the effects of boundary and inertia forces is employed. The differential equations governing the problem have been transformed by a similarity transformation into a system of non-dimensional differential equations which are solved numerically by element free Galerkin method. Profiles for velocity, microrotation and temperature are presented for a wide range of plate velocity, viscosity ratio, Darcy number, Forchhimer number, magnetic field parameter, heat absorption parameter and the micropolar parameter. The skin friction and Nusselt numbers at the plates are also shown graphically. The present problem has significant applications in chemical engineering, materials processing, solar porous wafer absorber systems and metallurgy.     

Computational treatment of free convection effect on flow of elastico-viscous fluid past an accelerated plate with constant heat flux

Effect of free convection on the visco-elastic fluid (Walter - B’ type) flow past an infinite vertical plate accelerating in its own plane with constant heat flux is examined analytically. It is found that for given values of Grashof number, Prandtl number and Newtonian parameter; flow velocity at any point increases with the increase in time and non-Newtonian parameter, however, it decreases with both, the heating and cooling of the plate.     

Three‐dimensional solidification with two possible crystallization states: Existence of solutions with flow in the melt

In this paper we discuss the existence of solutions of a system of nonlinear and singular partial differential equations constituting a phase field model with convection for non‐isothermal solidification/melting of certain metallic alloys in the case where two different kinds of crystallization are possible. Each one of these crystallization states is described by its own phase field, while the liquid phase is described by another one. The model also allows the occurrence of fluid flow in non‐solid regions, which are a priori unknown, and then we have a free‐boundary value problem. Thus, the model relates the evolutions of these three phase fields, the temperature of the solidification/melting process and the fluid flow in non‐solid regions. Copyright © 2009 John Wiley & Sons, Ltd.     

A Spectral method determination of the first critical Rayleigh number in a cylindrical container

The onset of laminar axisymmetric Rayleigh–Bénard convection is investigated analytically for fluid in a cylindrical container. All surfaces are considered to be solid and no-slip for the flow, whereas for the thermal boundary conditions both a perfectly conducting and an insulated side wall are considered. The governing Boussinesq equations are perturbed and an approximate solenoidal flow field and a temperature field are determined, using the assumption of separation of variables. Subsequently, a Chebysev–Galerkin spectral method is employed to reduce the equations to a system of first-order nonlinear ordinary differential equations. The approximate representation of the flow and temperature fields make it possible to perform the calculations analytically. The first critical Rayleigh number (Ra_cr) is then calculated using local stability analysis. The resulting value of Ra_cr compares favorably with previous numerical and experimental studies. The analytical solution presented here allows for deeper insights into the physics of this extensively studied problem to be identified.     

Dissipative Structure in the Course of Drying Suspensions and Solutions

Summary: Convectional, sedimentation and drying dissipative patterns during the course of dryness of suspensions and solutions are reviewed. The whole processes of convection were analyzed in the seven steps: irregular circulation accompanied with the upward heat transportation, global convectional flow from the central area toward outside edge at the surface layers of liquid, cooperative formation of distorted Benard cells, reversal of global flow of convection, growing of the spoke lines from the outside edge toward central area at the liquid surface layers, cluster and further bundle formation of the spoke lines, and the convectional flow by the pinning effect. The sedimentary colloidal particles were suspended above the substrate by the electric double layers and moved by the balancing of the external force fields including convectional flow and sedimentation. Principal macroscopic drying patterns are broad rings and spoke lines. Microscopic patterns such as star, needle, street road, string and cross-like are formed. The stratified structures form from micro to macro scales. Information on the size, shape, conformation and/or flexibility of particles or polymers is transferred cooperatively, and further accompanied with the amplification and selection processes during the course of dryness.     

Impacts of Forced Convection Generated via High Precision Stirring on Scanning Electrochemical Microscopy Experiments in Feedback Mode

In this study, the effects of forced convection on scanning electrochemical microscopy (SECM) experiments in feedback mode using ferrocenemethanol as redox mediator are presented. Forced convection, which enhances the mass transfer inside the system, was generated via an electrical high precision stirrer integrated into the SECM setup. A thin‐film interdigitated array electrode serving as model substrate was investigated with probe scan curves in z‐direction and SECM imaging in constant height mode utilizing ultramicroelectrodes (UME) with diameters (d_probe) of 25 μm and 12.5 μm. It was found that forced convection increased the overall current during SECM imaging without distorting distinctive features of the imaged structure when working with a 25 μm UME at substrate‐to‐tip distances of 14 μm and 11 μm. Furthermore, the electrochemical contrast was improved under hydrodynamic conditions for a substrate‐to‐tip distance of 11 μm and scan rates of 5 μm s^?1, 10 μm s^?1, 20 μm s^?1 and 40 μm s^?1. When further decreasing the gap between the UME and the substrate to 9 μm almost no effects of the forced convection were observed. Consequently, for a 25 μm UME, forced convection led to higher currents and improved performance during SECM experiments in feedback mode at substrate‐to‐tip distances of 14 μm and 11 μm, whereas no effects were observed for a 12.5 μm UME at a distance of 8 μm.