Optimal design of a minimum weight thermal diffuser with constraint on the output thermal power flux
This paper presents an application of the theory of optimal design to find the optimal shape of a minimum weight thermal diffuser with a priori specifications on the inward thermal power flux (TPP) and a bound on the outward T.P.F. The authors prove the differentiability of the scaled temperature with respect to the shape and from that deduce the Eulerian derivative of the cost function (the volume of the domain) and of the constraint. With these results, by introducing an appropriate adjoint system, a practical method of computation of the gradient of the associated penalized cost function is given. From a numerical point of view, the problem is approximated by a finite element method and the expression of the gradient for the approximate problem is obtained. Finally numerical results are presented.
scientific article; zbMATH DE number 3890222