Magnetic field effects upon heat transfer for laminar flow of electrically conducting liquid over a melting slab

A mathematical model is presented to study the role of an applied magnetic field on heat transfer during melting of a semi-infinite slab swept by a laminar flow of an electrically conducting liquid. The integral forms of the governing equations were solved by taking into account the sensitivity of the velocity profile to the magnetic field. Numerical results were obtained for a specified set of characteristic dimensionless numbers, i.e. Reynolds number, Prandtl number, Stefan numbers and magnetic parameter and their influence on heat transfer and melt generation is reported.     

无电晕高温静电除尘技术的最新进展

无电晕静电除尘技术是一种在高温条件下,以阴极的热电子发射使烟气中的粉尘荷电,然后靠电场力的作用将粉尘捕集,适合高温场合下应用的新颖除尘技术。本文介绍了它的最新研究成果。     

ON THE NUMERICAL SOLUTION OF CONTINUUM MIXTURE MODEL EQUATIONS DESCRIBING BINARY SOLID-LIQUID PHASE CHANGE

This paper deals with some numerical aspects of the solution of continuum mixture model equations for analyzing solid-liquid phase change problems involving binary materials. It is found that the procedure used for iteratively updating the solid fraction with temperature has an important bearing on the convergence behavior of the overall method; here, based on our previous work, we present one such stable and rapidly converging solid fraction-temperature updating scheme. The implementation of the procedure is illustrated via a two-dimensional example problem dealing with freezing in a square cavity with buoyancy driven flow in the melt.     

Analysis of close-contact melting heat transfer

The foremost characteristic of close-contact melting is that the source and the solid are continuously separated by a very thin melt film in which the flow is predominantly in one direction (i.e. along the thin film channel). This fact is used to formulate a mathematical model and develop a marching integration solution procedure for the model equations. As an example, the problem of melting under a descending, horizontal, cylindrical source at constant surface heat flux is solved. The results indicate that the heat transfer from the source to the solid is dominated by conduction across the thin melt layer. For this configuration, the effects of Stefan number and the relative density of the source on its velocity are investigated and reported. The predicted heat source velocity and its dependence on its relative density is in good agreement with the experiments.     

A boundary layer analysis of electro-magneto-hydrodynamic forced convective transport over a melting slab

In this work, a boundary layer based integral approach is employed for analyzing the coupled problem of electro-magneto-hydrodynamic convection and melting of an electrically conducting material. The melting process is assumed to occur on a semi-infinite flat horizontal slab. The simultaneous non-linear ordinary differential equations, originated out of the boundary layer analysis, are solved by employing the fourth order Runge–Kutta method, in a novel iterative framework. Simulation studies are executed for representative systems of materials, with a wide range of variation of processing parameters. Effects of melt superheat and the strengths of magnetic and electric fields on the melting process are analyzed in details. Fundamental physical principles are subsequently outlined for controlling the melting process through combined electrical and magnetic fields, on the employment of judicious combinations of the relevant operating parameters.     

Thermal characteristics of packed bed storage system

The thermal behaviour of a packed bed storage system charged with hot air is modelled using two partial differential equations representing the energy conservation in the air and solid phases constituting the bed. These two equations are coupled through the heat exchange process between the two phases. A fully implicit numerical scheme based on forward, upwind and central differencing for the time, first and second space derivatives, respectively, is used to solve the modelling equations. Marching technique is used for the air equation and a tri-diagonal matrix solver is employed to solve the solid equation. The solution yields the thermal structure of the bed, namely the air and solid temperature distribution inside the bed at any particular time, and the variation of total energy stored in the bed with time. The effect of bed length, solid diameter and void fraction on the thermal characteristics of the packed bed is studied. Further, the performance of the bed under variable inlet air temperature and mass flow rate is investigated.     

A Two-Dimensional Generalized Electromagneto-Thermoelastic Problem for a Half-Space

A two-dimensional coupled problem in electromagneto-thermoelasticity for a thermally and electrically conducting half-space solid whose surface is subjected to a time-dependent heat is studied in this paper. The problem is in the context of the Green and Lindsay's generalized thermoelasticity theory with two relaxation times. There acts an initial magnetic field parallel to the plane boundary of the half-space. The medium deforms because of heat, and due to the application of the magnetic field, there results an induced magnetic field and an induced electric field in the medium. The Maxwell's equations are formulated and the electromagneto-thermoelastic coupled governing equations are established. The normal mode analysis is used to obtain the exact expressions for the considered variables. The distributions of the considered variables are represented graphically. From the distributions, it can be found the wave type heat propagation in the medium.     

NUMERICAL MODELING OF ELECTROHYDRODYNAMIC (EHD) EFFECT ON NATURAL CONVECTION IN AN ENCLOSURE

Mathematical and numerical modeling of electrohydrodynamic (EHD) enhancement of natural convection in enclosures is carried out. An electric current in dielectric liquid is modeled as a directed motion of electrically charged particles injected into a neutral fluid; the electric body force and Joule heat are added to the momentum and energy equations, respectively. Based on this, numerical studies are carried out for EHD effects on natural convection in enclosures. It is found that, at the same electric field intensity, the EHD enhancement of heat transfer is different for different electric density injections; applying a nonuniform electric field offers better EHD enhancement of heat transfer than applying a uniform electric field.     

Buoyancy convection in cylindrical conducting melt with low Grashof number under uniform static magnetic field

Damping of convection is key in the precise measurement of a diffusion coefficient in melt, and applying a static magnetic field to the melt is a promising method of realizing damping in electrically conducting melt such as a semiconductor and metal. Convection behavior in a melt with a low Grashoff number under a uniform static magnetic field was calculated on the basis of the finite element method. Using the results, the specimen geometry and the direction of the applied magnetic field in diffusion experiments with a diffusion-couple method were evaluated by the numerical simulation.     

圆环腔内有相变非稳态传热的数值分析

卧式螺旋管锅炉反应器是一种内装固态锂的圆环形容器 ,点火药埋置于固态锂中 ,点火后发出的大量热量使固态锂升温熔化。采用焓法模型 ,考虑变物性、有散热损失的情况 ,建立了此问题的三维有相变非稳态传热的控制方程组 ,用有限差分法离散化方程组 ,确定了锅炉内锂的瞬态温度场分布及熔化波阵面推进情况。     

NUMERICAL SOLUTION OF MELTING PROCESSES FOR FIXED AND UNFIXED PHASE CHANGE MATERIAL IN THE PRESENCE OF MAGNETIC FIELD--SIMULATION OF LOW-GRAVITY ENVIRONMENT

Transport processes associated with melting of an electrically conducting phase change material (PCM), placed inside a rectangular enclosure, under a low-gravity environment, and in the presence of a magnetic field, is simulated numerically. Electromagnetic forces damp the natural convection as well as the flow induced by sedimentation and/or floatation, and thereby simulate the low-gravity environment of outer space. Computational experiments are conducted for both side-wall heating and top-wall heating under a horizontal magnetic field. The governing equations are discretized using a control-volume-based finite difference scheme. Numerical solutions are obtained for a true low-gravity environment as well as for the simulated low-gravity conditions that are a result of the presence of a horizontal magnetic field. The effects of magnetic field on the natural convection, solid phase floatation/sedimentation, liquid/solid interface location, solid melting rate, and the flow patterns are investigated. It is found that the melting under a low-gravity environment reasonably can be simulated on earth via applying a strong horizontal magnetic field. However, the flow patterns obtained for the true low-gravity environment are not similar to the corresponding cases solved for the simulated low gravity.     

Modeling and Simulation of a Phase Change Regenerator System

The modeling, simulation, and setup of an energy storage system encapsulated with phase change materials in which energy is absorbed in the hot period and released in the cold period are discussed. An algorithm to solve the coupled partial differential equations for heat transfer and storage in the phase change regenerator on the bed scale and the phase change material scale is presented. The bed is simulated via the tanks in series approximation. The phase change material scale is solved by Orthogonal Collocation applied to the equations transformed to immobilize the melt/solid interface and eliminate the effect of spherical geometry. Parametric studies show the effects of specific dimensionless group. A phase change material consisting of water in spherical support is used in a lab scale to verify the mathematical model. Experiments with heated or cooled air passing through the system are described. The measured outlet temperature results are compared qualitatively with the model predictions.     

An enhanced thermal conduction model for the prediction of convection dominated solid–liquid phase change

An enhanced thermal conduction model for predicting convection dominated solid–liquid phase change is presented. The main feature of the model is to predict (1) the overall thermal behavior of the system and (2) the phase front position without recurring to the full solution of the Navier–Stokes equations. The model rests entirely on the conduction equation for both the solid and liquid phases. The effect of convection in the melt is mimicked via an enhanced thermal conductivity that depends on the dimensionless numbers and the geometry of the flow. The model is tested and confronted to full CFD solutions for a freezing duct flow problem and for buoyancy driven melting in an enclosure. In both cases, the predictions of the enhanced thermal conduction model show excellent agreement with that of the CFD model. Not only is the enhanced thermal conduction model simpler to implement but its simulations run at least ten times as fast as those of the CFD model. Consequently, the enhanced thermal conduction model is well suited for controlling real-time solid–liquid phase change processes that occur in industrial applications as well as in latent heat thermal energy storage systems.     

Non-Darcy hydromagnetic free convection from a cone and a wedge in porous media

Continuum equations governing non-Darcy hydromagnetic free convection flow of an electrically conducting and heat-generating fluid over a vertical cone and a wedge adjacent to a porous medium are developed. These equations account for such effects as buoyancy, boundary and inertia effects of porous media, Hartmann effects of magnetohydrodynamics, and heat generation or absorption of fluid. Similarity variables were employed for the case of variable surface temperature and the resulting ordinary differential equations are solved numerically by an implicit, iterative, finite-difference method. Flow and heat transfer numerical results are obtained for various combinations of physical parameters. Graphical results illustrating interesting features of the physics of the problem are presented and discussed.     

Electrospray cooling for microelectronics

The challenge of effectively removing high heat flux from microelectronic chips may hinder future advancements in the semiconductor industry. Spray cooling is a promising solution to dissipate high heat flux, but traditional sprays suffer from low cooling efficiency partly because of droplet rebound. Here we show that electrosprays provide highly efficient cooling by completely avoiding the droplet rebound, when the electrically charged droplets are pinned on the heated conducting surface by the electric image force. We demonstrate a cooling system consisting of microfabricated multiplexed electrosprays in the cone-jet mode generating electrically charged microdroplets that remove a heat flux of 96 W/cm² with a cooling efficiency reaching 97%. Scale-up considerations suggest that the electrospray approach is well suited for practical applications by increasing the level of multiplexing and by preserving the system compactness using microfabrication.     

Diffusion flames over a melting polymer disk in von kármán swirling flows

A laminar diffusion flame that is established over a spinning, thermoplastic, polymer fuel disk in a quiescent, oxidizing environment under microgravity is analyzed theoretically. The conservation equations for the polymer melt layer coupled to the gas-phase equations are solved numerically using similarity transformations. The polymer melting rate, the thickness of the melt layer, and the fraction of melted fuel that is burned in the gas-phase are predicted as functions of the ambient conditions and polymer property values. In these calculations the melt viscosity is assumed to vary with temperature in an Arrhenius form. Results are presented for polymethylmethacrylate (PMMA) disks burning in air at atmospheric pressure and compared against earlier experimental results.     

Melting of PCM around a horizontal cylinder with constant surface temperature

A numerical study of melting of phase change material (PCM) around a horizontal circular cylinder of constant wall temperature and in the presence of the natural convection in the melt region is presented. A two dimensional mathematical model is formulated in terms of primitive variables and a coordinate transformation technique is used to fix the moving front. The finite volume approach is used to discretize the system of governing equations to obtain a system of linear algebraic equations. An implicit scheme is used for the momentum and energy equations and an explicit scheme for the energy balance at the interface. The numerical predictions were compared with available results to establish the validity of the model and additional results are obtained to demonstrate the effects of Rayleigh and Stefan numbers as well as the wall temperature on the time for complete fusion and total melt volume.     

Numerical investigation of the interfacial characteristics during Bridgman growth of compound crystals

The effects of the Bridgman process parameters and the double diffusive convection in the melt on the melt/solid interface shape and the solute distribution were numerically investigated for the II–VI semiconductor material HgCdTe. The results show that the melt/solid interface is concave at the center and the solute concentration at the interface is not uniform. A clockwise eddy forms near the interface in the melt when double diffusive convection is considered. With this eddy flow, the solute near the interface is well mixed so the solute distribution at the interface is very different from the case of no flow, but there are no significant changes in the interface shape or the thermal field. However, the growth parameters such as Bi, St, U and A significantly affect the melt/solid interface shape, position and the solute distribution at the interface.     

Numerical Study of an Electro-Osmotically Driven Microchannel Flow with Joule Heating Effect

A convection-diffusion reaction scheme is applied to solve the transient transport equations for the prediction of steady electro-osmotic microchannel flow behavior. The governing equations for the total electric field include the Laplace equation for the effective electrical potential and the Poisson-Boltzmann equation for the electrical potential established in the electric double layer. The transport equations governing the hydrodynamic field variables comprise mass conservation equation for the electrolyte and equations of motion for the incompressible charged fluid flow subject to an electro-osmotic body force. The main aim of the study is to elucidate the effect of Joule heating, which can affect the electrohydrodynamic behavior. Investigation into the region near the negatively charged channel wall is made through the simulated velocity boundary layer, diffuse layer, and electric double layer.