This study addresses the numerical modeling aspects of transport phenomena in steady, two-dimensional, laminar flow accompanied by heat transfer in a differentially heated cavity with moving walls in presence of radiatively absorbing, emitting, and scattering gray medium. The discrete ordinate method has been used in modeling the radiative transport equation and the finite difference method based on a finite volume approach is used as the discretization technique. Two cases of mixed convection arising out of vertical isothermal wall movement and horizontal adiabatic wall movement and their interaction with radiation have been critically examined. Both buoyancy-aided and buoyancy-opposed mixed convection have been investigated, but buoyancy-opposed mixed convection interacting with radiation has been given emphasis in the present work due to some exciting revelations. The effects of Richardson's number (from 0.1 to 10), radiation-conduction parameter, single scattering albedo, and optical thickness on fluid flow and energy transfer have been studied. An exhaustive comparison between influences of radiation on mixed convection arising due to vertical isothermal wall and horizontal adiabatic wall movement has been made.