Nonlinear inverse problem for the estimation of time-and-space-dependent heat-transfer coefficients

The aim of this paper is to describe a method for the direct estimation of the time-and-space-dependent heat-transfer coefficients from transient temperature data measured at appropriate points inside a heat-conducting solid. This inverse estimation problem is called herein the inverse heat-transfer coefficient problem. An application considered in the present is the quenching of a solid in a liquid. The solution method used here is an extension of the sequential temperature future-information method introduced by Beck for solving the inverse heat-conduction problem. The finite-difference method, based on the control-volume approach, was used for the discretization of the direct heat-conduction problem. Numerical results show that the proposed method is accurate and capable of estimating sudden and large changes in time-and-space-dependent heat-transfer coefficient functions.