Effects of Time Scale on Solutions of Inverse Heat Conduction Problems

Abstract

A wide variety of inverse heat conduction problems have been studied in the last two decades for the estimation of boundary or initial conditions, thermophysical properties, geometrical parameters, or heat source intensities. In most transient heat conduction problems, the mathematical models were cast in dimensionless forms, by using a diffusion time scale. As the thermal diffusivities are usually small, the physical time scales turn to be rather long. In this way, most works show that the inverse analysis yields satisfactory results, without addressing the implications of the physical time scale. The physical time scale, in fact, influences significantly the quality of the inverse solution. We present here a unified treatment for one-dimensional, linear inverse heat conduction problems using the conjugate gradient method with an adjoint equation, and also show that there are physical limitations by the time scale on the inverse solutions.