On the use of analytic approximations for describing the macroscopic heat flow during solidification

In this paper both conceptual and numerical analyses of the integral profile method as applied to solidification problems are conducted. Two important examples are considered,viz. a case where the nonsteady state exact solution of the thermal field is known and a thermal analysis of continuous casting. It is shown that the method as it was generalized by Hills may lead in the latter case to serious contradictions with basic thermodynamic principles. It is also shown that the method developed by Tien using a different set of boundary conditions is unsuitable for treating general solidification problems. It is thus concluded that approximate solutions of the thermal field during solidification must be evaluated under rather severe boundary conditions.