Solid–liquid phase change driven by internal heat generation

2012 ◽  
Vol 340 (7) ◽  
pp. 471-476 ◽  
Author(s):  
John Crepeau ◽  
Ali S. Siahpush
Keyword(s):  
Liquid Phase ◽  
Phase Change ◽  
Heat Generation ◽  
Internal Heat ◽  
Internal Heat Generation ◽  
Solid Liquid

Integral Solutions of Phase Change With Internal Heat Generation

2004 ◽  
Author(s):  
Ali Siahpush ◽  
John Crepeau
Keyword(s):  
Differential Equation ◽  
Phase Change ◽  
Heat Generation ◽  
Numerical Solutions ◽  
Internal Heat ◽  
Melting Rate ◽  
Internal Heat Generation ◽  
Stefan Number ◽  
Temperature Boundary ◽  
Solid Liquid

This paper presents solutions to a one-dimensional solid-liquid phase change problem using the integral method for a semi-infinite material that generates internal heat. The analysis assumed a quadratic temperature profile and a constant temperature boundary condition on the exposed surface. We derived a differential equation for the solidification thickness as a function of the internal heat generation (IHG) and the Stefan number, which includes the temperature of the boundary. Plots of the numerical solutions for various values of the IHG and Stefan number show the time-dependant behavior of both the melting and solidification distances and rates. The IHG of the material opposes solidification and enhances melting. The differential equation shows that in steady-state, the thickness of the solidification band is inversely related to the square root of the IHG. The model also shows that the melting rate initially decreases and reaches a local minimum, then increases to an asymptotic value.

On the Stefan Problem With Internal Heat Generation and Prescribed Heat Flux Conditions at the Boundary

2019 ◽  
Author(s):  
Lyudmyla Barannyk ◽  
Sidney D. V. Williams ◽  
Olufolahan Irene Ogidan ◽  
John C. Crepeau ◽  
Alexey Sakhnov
Keyword(s):  
Heat Flux ◽  
Steady State ◽  
Phase Change ◽  
Heat Generation ◽  
Separation Of Variables ◽  
Outer Boundary ◽  
Internal Heat ◽  
Internal Heat Generation ◽  
The Difference ◽  
Solid Liquid Interface

Abstract We study the evolution of the solid-liquid interface during melting and solidification of a material with constant internal heat generation and prescribed heat flux at the boundary for a plane wall and a cylinder. The equations are solved by splitting them into transient and steady-state components and then using separation of variables. This results in an ordinary differential equation for the interface that involves infinite series. The initial value problem is solved numerically, and solutions are compared to the previously published quasi-static solutions. We show that when the internal heat generation and the heat flux at the boundary are close in value to each other, the motion of the phase change front takes longer to reach steady-state than when the values are farther apart. As the difference between the internal heat generation and the heat flux increases, the transient solutions become more dominant and the numerical solution of the phase change front does not reach steady-state before the outer boundary or centerline is reached. The difference between the internal heat generation and the heat flux at the boundary can be used to control the motion and speed of the interface. The problem has applications for a nuclear fuel rod during meltdown.

Effects of Internal Heat Generation on Solidification

2005 ◽  
Author(s):  
John C. Crepeau ◽  
Ali Siahpush
Keyword(s):  
Heat Generation ◽  
Solid Phase ◽  
Freezing Point ◽  
Internal Heat ◽  
Internal Heat Generation ◽  
Square Root ◽  
Stefan Number ◽  
Temperature Boundary ◽  
Geometry Problem ◽  
Solid Liquid

We present solutions for solid-liquid phase change in materials that generate internal heat. This problem is solved for both cylindrical and semi-infinite geometries. The analysis assumes a temperature profile in the solid phase and constant temperature boundary conditions on the exposed surfaces. We derive differential equations governing the solidification thickness for both geometries as functions of the Stefan number and the internal heat generation (IHG). For the cylindrical geometry, the solidification layer obtains a steady-state value which is related to the inverse of the square root of the IHG. The solutions to the semi-infinite geometry problem show that when the surface is cooled to below the freezing point, a solidification layer forms along the edge and begins to grow until it reaches a maximum, then begins remelt.

Numerical Investigation of Melting With Internal Heat Generation in a Vertical Cylindrical Geometry

2012 ◽  
Author(s):  
Amber Shrivastava ◽  
Brian Williams ◽  
Ali S. Siahpush ◽  
John Crepeau
Keyword(s):  
Experimental Data ◽  
Heat Source ◽  
Phase Change ◽  
Numerical Investigation ◽  
Heat Generation ◽  
Nuclear Power ◽  
Internal Heat ◽  
Internal Heat Generation ◽  
Cylindrical Geometry ◽  
Melting Phenomenon

There have been significant efforts by the heat transfer community to investigate the melting phenomenon of materials. These efforts have included the analytical development of equations to represent melting, the numerical development of computer codes to assist in the modeling, and the collection of experimental data. The understanding of the melting phenomenon has application in several areas of interest, for example, the melting of a phase change material used as a thermal storage medium as well as the melting of the fuel bundle in a nuclear power plant during an accident scenario. The objective of this paper is to present a numerical investigation, using computational fluid dynamics (CFD), of melting with internal heat generation for a vertical cylindrical geometry. As a precursor to the development of this numerical model, two classical configurations were also modeled. The first configuration consists of pure convection (no phase change) of a liquid with an external heat source and the second is melting with an externally applied heat source. For both of these two configurations, the numerical results were compared with experimental data from previous work.

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