Solution of inverse problem - regularization via thermodynamical criterion

Abstract

In engineering practice, measuring temperature on both sides of a wall (of, for example, turbine casing or combustion chamber) is not always possible. On the other hand, measurement of both temperature and heat flux on the outer surface of the wall is possible. For transient heat conduction equation, measurements of temperature and heat flux supplemented by the initial condition state the Cauchy problem, which is ill-conditioned In this paper, the stable solution is obtained for the Cauchy problem using the Laplace transformation and the minimisation of continuity in the process of integration of convolution. Test examples confirm proposed algorithm for the inverse problem solution.