The effects of a directionally emitting and reflecting dielectric surface on the wall heat flux and medium temperature distribution are studied. The system is an infinite square duct enclosing an absorbing and emitting medium. The emissivity and reflectivity of opaque and gray wall vary with direction. Combined effect of conductive and radiative heat transfer is analyzed using finite difference and the direct discrete-ordinates method. The parameters under study are conduction to radiation parameter, optical depth, refractive index ratio. The results with directional and diffuse properties deviate each other when the conduction to radiation parameter is less than around 0.01. The wall heat flux differs fur optical thickness less than around 0.1. However, the medium temperature profiles differ for optical thickness greater than around 1. Deviations from diffuse property calculations are larger for hot wall with directional property than cold wall with directional property. As n increases from 1.5, the trend changes are observed fur refractive index ratio about n=6.10