Author(s)

Krzysztof Grysa & Artur Maciag

Abstract

On stability of some overdetermined inverse heat conduction problems Krzysztof Grysa & Artur Maci^g 7, Abstract The inverse problem for a flat slab is considered. The problem is discretised with respect to time. A case with many internal temperature responses is investigated. For inaccurate internal responses the constrains for a time step are considered. For the case of three internal responses the question of an optimal placing of the middle thermocouple is discussed. 1 Integral form of an inverse problem solution Consider the heat conduction equation in dimensionless form: 1^*-^)*{*.') = *•(*.<) . MeOx(o,«>) (i) with initial and boundary condition as follows: r(.x,0) = TO(.X) , xeQ (2) T(xb>t)=Tb(xbJ) . % G an , /e(0,oo) (3) Approximation of the derivative with respect to time with a first back difference leads to the following formul

Keywords