Determination of One Unknown Thermal Coefficient through a Mushy Zone Model with a Convective Overspecified Boundary Condition

Table 1

Formulae for problem (1)–(7). Explicit formulae for the unknown thermal coefficient , , , , , or and coefficient (or the equation that it must satisfy) and the corresponding restrictions on data that guarantee their validity.

Case	Thermal coefficient	Coefficient that characterizes the free boundary	Restrictions on data
1			,
2			, ,
3			, , ,
4		Unique positive solution of; , with defined by (23)
5		Unique positive solution of; , with defined by (23)
6		Unique positive solution of; , with defined by (28)	,