A transient one-dimensional inverse heat conduction problem with overspecified data at one boundary

Abstract

For one-dimensional transient heat conduction, a procedure is developed to estimate the temperature at one boundary when both the temperature and heat flux are measured at the other boundary. The Laplace transform technique is employed and the inverse Laplace transform is carried out by using a novel technique. Exact and noisy data are used to infer the unknown boundary temperature. It is shown that the present procedure is accurate and also stable to measurement errors.