Inverse boundary design problem of combined radiation convection heat transfer in a duct with diffuse-spectral design surface

Abstract

In the present work, an optimization technique is applied for inverse boundary design problem of radiative convective heat transfer of laminar duct flow by numerical method. The main goal is to verify how the solution of inverse problem is affected by the spectral behavior of the boundary surfaces. The conjugate gradient method is used to find the unknown temperature distribution over the heater surface to satisfy the prescribed temperature and heat flux distributions over the design surface. The bottom boundary surface (including design surface) is diffuse-spectral, while the top wall (heater surface) behaves as gray one. The variation of emissivity with respect to the wavelength is approximated by considering a set of spectral bands with constant emissivity and then the radiative transfer equation is solved by the discrete ordinates method for each band. The performance of the present method is evaluated by comparing the results with those obtained by considering a diffuse-gray design surface. Finally an attempt is made to investigate the spectral behavior of the design surface on the calculated temperature distribution over the heater surface.