In this paper, an inverse analysis of combined radiation and convection heat transfer in a 2-D rectangular duct is presented. The working fluid is a mixture of air including CO2 and H2O as two radiating gases. The purpose is to verify the effects of gas mole fractions on the solution of inverse design problem in which the conjugate gradient method is used to find the temperature distribution over the heater surface to satisfy the prescribed temperature and heat flux distributions over the design surface. The radiating gas is considered to be a gray participating medium with absorption, emission and isotropic scattering. The Planck mean absorption coefficient is calculated and used in radiative calculations. The discrete ordinates method is used to solve the radiative transfer equation. An attempt is made to determine the temperature distributions over the heater surface while the enclosure is filled with different mole fractions of CO2 and H2O. The effects of other parameters such as radiation conduction parameter on the solution of inverse problem is examined.