Numerical Solutions to an Inverse Problem of Heat Conduction for Simple Shapes

Numerical methods are presented for solving an inverse problem of heat conduction: Given an interior temperature versus time, find the surface heat flux versus time. The analysis is developed specifically for spheres; it applies to other simple shapes. The system is treated as linear, permitting use of the superposition principle. The essence of the method is the numerical inversion of a suitable direct problem: Given a surface heat flux versus time, find an interior temperature versus time. Care is required in selecting a time spacing for, if it is chosen too small in relation to the conditions, undesirable oscillation results. Simplifying suggestions are presented, and the use of the methods are illustrated by examples.