Inverse boundary design conduction-radiation problem in irregular two-dimensional domains

An optimization technique is applied to design of heat transfer systems in which both conduction and radiation are important. The inverse methodology is used to find a set of heater inputs over the heater surface to produce the desired temperature and heat flux distributions over the design surface. A combination of the finite-element method with the discrete transfer method is used to solve the conductive-radiative heat transfer equation. The conjugate gradient method is used for minimization of an objective function, which is expressed by the sum of square residuals between estimated and desired heat fluxes over the design surface. The performance and accuracy of the present method for solving inverse conduction-radiation heat transfer problems is evaluated by comparing the results with a benchmark problem and a numerical experiment for an irregular two-dimensional case.