Inverse boundary design problem of natural convection-radiation in a square enclosure

The inverse boundary design problem of combined natural convection-radiation has been solved numerically. The aim of this study is to find the strength of heaters in a 2-D enclosure to produce desired temperature and heat flux distribution on the design surface. To obtain the optimal solution, the Levenberg-Marquardt algorithm is chosen to perform the iterative search procedure. Moreover to reduce the computation time, the sensitivity matrix is updated by Broyden combined update method. The direct problem is solved using the finite volume method for both fluid and radiative transfer equations. SIMPLE algorithm is utilized to satisfy pressure-velocity coupling. Cases of surface-to-surface radiation and radiation in a grey, emitting, absorbing and scattering media are investigated. Effects of Rayleigh number, optical thickness, scattering albedo, wall emissivity and number of heating and design elements are studied. The results show that for various cases, estimated heat fluxes on the design surface are very close to the desired values and the maximum root mean square error is less than 1%.