Effect of Gr/Re on Mixed Convection and Combined Mixed Convection-Radiation Heat Transfer Within a Vertical Channel with Variable Wall Temperature

The present paper investigates, numerically, the effect of the Grashof number to a Reynolds number ratio (Gr/Re), on fluid flow and heat transfer within a vertical channel for two cases: Mixed (natural-forced) convection and combined mixed convection-radiation. The flow in the channel is assumed to be two-dimensional, laminar and steady. The wall temperature is defined as a linear function of the channel height. When dealing with the combined mixed convection-radiation case, radiational properties have been taken into account, both for the walls and the fluid. The fluid has a Prandtl number of 0.71 and it is radiationally assumed as a participating medium. A comparison between the two cases at a constant Gr/Re is reported, so as to investigate the influence of radiation, as one of the heat transfer modes, more clearly. To solve the governing equations (i.e., mass continuity, momentum and energy) the Finite Volume method is employed and the SIMPLE algorithm is adopted to couple the velocity and pressure fields. The radiative transfer equation is solved using the Discrete Ordinates Method, by adopting its S_4 order quadrature scheme. The results for both cases are presented as the profiles of axial velocity across the channel width, axial centerline velocity, bulk temperature and pressure versus channel height.