Solid-liquid Interface Location Research Articles

Thermal regime and effect studying on the ablation process of thin films prepared by nanosecond pulsed laser

Thermodynamics effects generated by nanosecond pulsed-laser ablation are very important. In this work, a new ablation model of targets considering vaporization is first built based on superheated theory. Four different heat flux equations for during and after the laser radiation are then presented. Finally, as an example of Si target, a finite difference method is employed to simulate the space-and time-dependence of temperature in the target. The dependence of solid–liquid interface location on time which takes account of the melting relaxation time is derived. The comparison of the present model to our new model shows that vaporization plays an important role during and after the radiation of laser. Superheated liquid layer after the laser radiation will exist for a long period. This work will offer help for the future investigation of thin films prepared by nanosecond pulsed laser.

Inverse finite element technique for identification of thermal resistance of gas-gap between the ingot and mould in continuous casting of metals

Identification of thermal resistance of the gas-gap between the ingot and mould during continuous casting of metals is the subject of the present article. Analysed parameter estimation problem of the steady-state heat conduction belongs to the group of inverse problems. The present work shows the possibility of applying the least square adjustment method with a priori data for identification of thermal resistance as well as the interphase location and the temperature field within the ingot and mould. The most important feature of the approach is that the unknown thermal resistance is identified by solving appropriate inverse problem from the temperature measurements at the number of sensor located in the wall of the mould. The validity of the solution of the inverse problem is checked by comparison with the results of direct problem. In the present work, a front-tracking method with an automatic mesh generation finite element technique (so-called deforming or moving finite-elements) for steady-state equation conduction–advection problems is developed to build the mathematical model of the heat transfer process. Such an approach makes us possible to find solid–liquid interface location, because it is the integral part of the solution of the considered problem. Due to the strong convective nature of the boundary problem (casting velocity, thermal parameters) the special up-wind technique is applied to avoid the oscillation of numerical results.

Approximate analytical model for two-phase solidification problem in a finned phase-change material storage

During the phase change in a phase-change material (PCM) storage system, the solid–liquid interface moves away from the heat transfer surface and the surface heat flux decreases due to the increasing thermal resistance of the molten or solidified medium. Heat-transfer enhancement techniques such as fins and honeycombs have to be used to increase the heat-transfer fraction in the store. The purpose of this paper is to develop a simplified analytical model which predicts the solid–liquid interface location and temperature distribution of the fin in the solidification process with a constant end-wall temperature in the finned two-dimensional PCM store. The storage is initially in a liquid state and its temperature is greater than the solidification temperature of the PCM. The analytical results are compared to the numerical results calculated using the heat-capacity method. The results show that the analytical model gives a satisfactory estimation for the fin temperature and the solid–liquid interface when the length-to-height ratio ( λ) of the storage cell is smaller than 6.0 and the fin length is smaller than 0.06 m. The error made in the fraction of solidified PCM is ±10% when the analytical model is used rather than the two-dimensional numerical model.

Approximate analytical model for solidification in a finite PCM storage with internal fins

In latent heat storage internal heat transfer enhancement techniques such as fins have to be used because of the low heat conductivity of the phase change material. Internal heat transfer enhancement is essential, especially in a solidification process where the main heat transfer mode is conduction. The aim of this paper is to present a simplified analytical model which predicts the solid–liquid interface location and temperature distribution of the fin in the solidification process with a constant end-wall temperature in the finned two-dimensional PCM storage. The analytical results are compared to numerical results and they show that the analytical model is more suited to the prediction of the solid–liquid interface location than the temperature distribution of the fin in the PCM storage. A new factor called the fraction of solidified PCM is also introduced. The fraction of solidified PCM easily gives a good picture of how much of the storage is solidified after a given time.

Analytical model for melting in a semi-infinite PCM storage with an internal fin

The most PCMs with high energy storage density have an unacceptably low heat conductivity and hence internal heat transfer enhancement techniques such as fins or other metal structures are required in latent heat thermal storage (LHTS) applications. Previous work has concentrated on numerical and experimental examination in determining the influence of the fins in melting phase change material. This paper presents a simplified analytical model based on a quasi-linear, transient, thin-fin equation which predicts the solid–liquid interface location and temperature distribution of the fin in the melting process with a constant imposed end-wall temperature. The analytical results are compared to the numerical results and they show good agreement. Due to the assumptions made in the model, the speed of the solid–liquid interface during the melting process is slightly too slow.

Solidification of circular Couette flow with viscous dissipation

A semi-analytic solution is presented for the solidification of laminar circular Couette flow within a one-dimensional annular region with a rotating outer cylinder and stationary inner cylinder. Viscous dissipation in the liquid is taken into account. Closed-form expressions for the dimensionless temperature distribution in the solid and liquid regions, Nusselt number at the solid–liquid interface, dimensionless power and torque per unit length, dimensionless steady-state freeze front location, and dimensionless pressure distribution in the liquid are derived as a function of liquid-to-solid thermal conductivity ratio, Brinkman number, annulus radius ratio, and Stefan number, which is assumed to be small (<0.1) but non-vanishing. The instantaneous dimensionless solid–liquid interface location is determined using numerical integration. The results show that the power and torque requirements can increase by a factor of greater than seven for a thin-gap annulus (radius ratio >0.9). It is also shown that the size of the liquid region within the annular gap has a more controlling influence on the solidification rate at latter times (when the Brinkman number is small) while a Brinkman number of order unity has a dominant influence at earlier times.

The viscous stagnation-flow solidification problem

The viscous stagnation-flow solidification problem for a pure substance is investigated by means of quasi-steady, instantaneous-similarity, as well as finite-difference methods. The liquid velocity field, the solid and liquid temperature distributions, the solid-liquid interface location, as well as its growth rate, are obtained using all three methods and comparisons of the solutions are made. The instantaneous-similarity solution at a sufficiently small time is used as the initial field to start the finite-difference calculation. All three methods show the existence of an asymptotic limit of the solidification-front position. The effect on this limit of several important dimensionless parameters, including the Prandtl number, is presented.

The inviscid stagnation-flow solidification problem

The stagnation-flow Stefan solidification problem is defined and investigated. By applying the method of instantaneous similarity, the temperature field, the solid-liquid interface location and its growth rate, valid for the initial stages of solidification, are obtained. Furthermore, with the use of the quasi-steady approximation, a solution of the problem valid for the final stages of solidification is obtained. The analysis reveals a fundamental difference between the stagnation-flow solidification behavior and that in the classical Stefan solidification problem. Both methods of solution are used to show that the solidification front grows asymptotically to a finite maximum value as time goes to infinity. For large values of time, both methods yield the same temperature distribution and the same value of the solid phase thickness, which are independent of the Stefan number.

NUMERICAL SOLUTION OF THE INVISCID STAGNATION-FLOW SOLIDIFICATION PROBLEM

The inviscid stagnation-flow solidification problem is investigated by applying the finite difference method after a coordinate transformation to a fixed domain. Numerical solutions of the temperature distribution and the solid-liquid interface location as well as its growth rate are obtained, and comparisons with the instantaneous-similarity solution and the quasi-steady solution are made. Since the transformed system of equations for this solidification problem has a singularity at t = 0, the finite difference solution is started at a small time using the instantaneous-similarity solution as the initial field. The numerical solution confirms the existence of an asymptotic limit of the solidification front as previously demonstrated by means of both a quasi-steady and an instantaneous-similarity solution.

Analytical solution of melting in a subcooled semi-infinite solid with boundary conditions of the second kind

The melting problem in a semi-infinite region with constant heat flux boundary condition is solved by a semi-exact method and an integral approximate method. Effect of subcooling on the transient solid-liquid interface location and surface temperature are also discussed in this paper.

Two-dimensional heat transfer study on the keyhole plasma arc welding process

This paper presents a two-dimensional, quasi-stationary finite element numerical model to study the fluid flow and the heat transfer phenomena which occur during constant travel speed, keyhole plasma arc welding of metal plates. A Newton-Raphson iteration procedure was developed in this model to accurately identify the solid-liquid interface location during welding. The finite element method was applied to the study of typical keyhole welding process of an AISI 304 stainless plate. The results show that the method can be used to predict the shape of the welding pool as a function of welding parameters and that the widths of both the fusion zone and the heat effected zone decrease as the welding speed increases while the power required for welding increases with an increase in welding speed.

FINITE-DIFFERENCE ANALYSIS OF GROWTH AND DECAY OF A FREEZE COAT ON A CONTINUOUS MOVING CYLINDER

The process of freeze coating of a polymeric melt on an axially moving continuous cylinder is studied numerically by a finite-difference method, taking into account heat convection from the melt to the freeze coat and spatial variation of the cylinder temperature. The solid-liquid interface location is immobilized in the finite-difference analysis of the problem by transforming the system of equations governing the behavior of the freeze coat and the cylinder temperature into a dimensionless space. Various controlling parameters of the system are identified and their effects on the growth-and-decay behavior of the freeze coat are determined. Also determined are the maximum freeze-coat thickness and the corresponding axial location, based on which criteria for selection of the optimum freeze-coating operation conditions are established. The accuracy of the computational scheme is demonstrated by comparing the numerical results with the similarity solutions that are valid at small dimensionless axial locations.

Non-Fourier Melting of a Semi-Infinite Solid

The melting of a semi-infinite solid subjected to a step change in temperature is solved according to a non-Fourier heat conduction law postulated by Cattaneo and Vernotte. Unlike the classical Fourier theory which predicts an infinite speed of heat propagation, the non-Fourier theory implies that the speed of a thermal disturbance is finite. The effect of this finite thermal wave speed on the melting phenomenon is determined. The problem is solved by following a similar method as used by Carslaw and Jaeger for the corresponding Fourier problem. Non-Fourier results differ from Fourier theory only for small values of time. Comparing the temperature profiles and the solid-liquid interface location for aluminum, differences between the two theories were significant only for times on the order of 10−9–10−11 s and in a region within approximately 10−4–10−5 cm from the boundary surface. However, these results are based on an approximate value of the thermal relaxation time.

On the application of integral-methods to the solution of problems involving the solidification of liquids initially at fusion temperature

Approximate integral-methods, similar to those used in the solution of the boundary layer equations in fluid dynamics, are developed for determining the location and time history of the unidimensional solid-liquid interface during the solidification of liquids initially at the fusion temperature. For isothermal wall condition the configurations treated are the inward solidification of the semiinfinite region, the circular cylinder and the sphere. Series solutions of the thermal equation giving the location of the solid-liquid interface, for small time, are derived for the latter two shapes and are used to estimate the accuracy of the approximate integral-methods. The approximate results for the circular cylinder are also compared with an existing numerical solution obtained by the relaxation method.