A generalized laplace transform technique for phase-change problems
- Univ. of Wisconsin, Milwaukee (United States)
Analytical solutions of transient heat transfer problems involving melting or solidification are inherently difficult to obtain because of the nonlinearity associated with the moving boundary condition at the solid-liquid interface. A few exact solutions of phase-change problems are currently available (Ozisik, 1980; Carslaw and Jaeger, 1959). The mathematical approach used to achieve these solutions, however, is quite crude. Instead of solving the problem, a solution is assumed for the temperature profile. The assumed solution satisfies the governing differential equation, one of the boundary conditions and, in some cases, the initial condition as well. The assumed solution depends on the nature of the problem. It could be an error function or a complementary error function with coefficients to be determined by applying the remaining boundary condition. The interface condition is then applied to yield normally a transcendental equation, from which the transient interface location can be determined. The present note proposes a technique to extend the Laplace Transform method to obtain a closed-form solution for nonlinear phase-change problems. Solutions to a few problems are demonstrated to elucidate the essence of the technique.
- OSTI ID:
- 6068326
- Journal Information:
- Journal of Heat Transfer (Transactions of the ASME (American Society of Mechanical Engineers), Series C); (United States), Journal Name: Journal of Heat Transfer (Transactions of the ASME (American Society of Mechanical Engineers), Series C); (United States) Vol. 112:2; ISSN 0022-1481; ISSN JHTRA
- Country of Publication:
- United States
- Language:
- English
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