The application of an inverse formulation in the design of boundary conditions for transient radiating enclosures

This study considers the design of thermal systems that are built to radiatively heat objects from a specified initial condition to a specified steady state following a prescribed temperature history. The enclosure housing the object, the object itself and the heaters all have thermal capacity. The necessary power input distributions for the heaters during the heating process are sought to satisfy the design specifications. The problem is thus a transient inverse boundary condition estimation problem, where the geometry and the properties of the surfaces are specified and the boundary condition on. the heater wall is to be found by making use of the information provided at the design surface for each time step. The boundary condition estimation problem requires the solution of a set of Fredholm equations of the first kind. Such a problem is known to be ill-posed. The introduction of the transient nature makes the inverse problem nonlinear and even more interesting, challenging, and realistic. A solution algorithm is proposed and used to produce a solution for a sample problem. In order to model radiative heat transmission, the Monte Carlo method is used, which enables us to handle specularly reflecting surfaces and blockage effects. The inverse problem is solved by the conjugate gradient method, which provides smooth and accurate results after the first few steps.