Determination of desired geometry by a novel extension of ball spine algorithm inverse method to conjugate heat transfer problems

In the present study, numerical solution of an inverse conjugate heat transfer problem including conduction and forced convection is carried out via the ball spine algorithm (BSA). The BSA inverse method is originally developed for inverse shape design of pure fluid flow problems with a desired pressure distribution along an unknown surface but in this paper it is shown how proposing a novel remedy enables the BSA method of solving inverse heat transfer problems as well. The proposed method has a truly low computational cost accompanied by high convergence rate. The inverse problem is defined as heat source surrounded by a solid medium exposed to free stream in external flow. Heat is generated by a heat source and spreads all over the medium by conduction and then is transferred to free stream by forced convection. The objective is finding a configuration for the solid body to satisfy a prescribed uniform temperature along its surface. Solution of the mentioned inverse problem is dependent on different combinations of the dominant parameters including Reynolds number (Re), thermal conductivity ratio (kf/ks), desired outer surface temperature (θs) and also Prandtl number (Pr).