Geometrical inverse problems in three-dimensional non-linear steady heat conduction

Abstract

This paper presents results of research involving the inverse thermal design of coolant flow passage shapes in arbitrary, three-dimensional, internally cooled configurations. A computer program has been developed to demonstrate this methodology in which a thermal systems designer can simultaneously enforce the desired temperature and heat flux distribution on the hot outer surface of the object while enforcing either the desired temperature, desired heat flux or desired convective heat transfer boundary conditions on the cooled interior surfaces of the coolant flow passages. The program's objective is to meet the overspecified thermal boundary conditions of the outer surface by iteratively altering the geometries of the coolant passages. This is achieved with an automatic, constrained optimization algorithm that minimizes the difference between the user-specified and the intermittently computed hot outer surface heat flux distribution. A quasi-Newtonian gradient search algorithm was used for the optimization. A simple method for escaping stationary points was employed and involved the switching of the objective function when the optimization process stalled at a local minimum. The analysis of the steady-state, non-linear heat conduction within the solid was done using the boundary element method.