Inverse Boundary Design in Heat Transfer Combining Turbulent Convection and Thermal Radiation

Abstract

This work investigates the solutions of an inverse boundary design problem that has multimode (radiation and convection) heat transfer mechanisms. The problem consists of finding the heat flux distribution required on heaters located on the top and side walls of a two-dimensional enclosure that satisfies both the temperature and heat flux distributions prescribed on the design surface of the enclosure. A turbulent air flow is generated by a fan located inside the chamber. The walls are gray, diffuse emitters and absorbers. The combined heat transfer problem is described by a system of non-linear equations, which is expected to be ill-conditioned as an inverse analysis is involved. The system of equations is solved by an iterative procedure: the basic set of equations relates the radiation transferred between the heater and the design surface, while all the other terms involved in the energy exchange are found from the conditions of the previous iteration. This way, the ill-posed part of the problem (which arises from the design surfaces containing two conditions, and the heater elements being unconstrained) is isolated for a more effective treatment. The solution is obtained by regularizing the ill-conditioned system of equations by means of the truncated singular value decomposition (TSVD) method.