Inverse boundary design solution in a combined radiating-free convecting furnace filled with participating medium containing specularly reflecting walls

In this paper, an inverse boundary design problem of combined natural convection-radiation considering specular reflectivity and participating media is solved. The aim of this paper is to find the strength of heaters in a step-like enclosure to produce the desired temperature and heat flux distribution on the design surface. The finite volume method for transition flow (which causes a faster convergence) is used as the direct solver of the energy and momentum equations. The SIMPLE algorithm is utilized to satisfy pressure–velocity coupling in order to solve the free convection heat transfer. Also, the backward Monte Carlo method is employed in order to be able to compute the distribution factors and carry out the radiant exchange calculations. Finally, the goal function which is defined on the basis of square root error is minimized by means of a conjugate gradients method. The effects of variation of specularity ratio for specular surfaces are investigated to compare the results for diffuse and specular surfaces in the enclosure considering radiation and free convection. The effects of variation of range of parameters such as the Rayleigh number, temperature ratio, radiation conduction parameter and the specularity ratio on the relative root mean square and heat flux are investigated and results are compared. The results demonstrate the efficiency and the accuracy of the proposed method.