A 3D Shape Optimization Problem in Heat Transfer: Analysis and Approximation via BEM
Thursday 25th March 2004
Abba', A.; Saleri, F.; D'Angelo, C.
In this paper an optimal shape control problem dealing with heat transfer in enclosures is studied. We model and enclosure heated by a flame surface (taking account of radiation, conductor and convection effects), and we try to find an optimal flame shape which minimizes some cost functional defined on the temperature field. This kind of problem arises in industrial furnaces optimization, being temperature uniformity one of the most important aspects in industrial plant analysis and design. Analytical results (smoothness of the control-to-state mapping, existence of an optimal shape in a certain admissible class) as well as numerical optimization results by the boundary element method are obtained we employ the gradient method to optimize the flame shape, exploiting the adjoint equation associated with the state equation and the cost function.