Thermally Developing Forced Convection in a Porous Medium Occupied by a Rarefied Gas: Parallel Plate Channel or Circular Tube with Walls at Constant Heat Flux

An adaptation of the classical Graetz methodology is applied to investigate the thermal development of forced convection in a parallel plate channel or a circular tube filled by a porous medium saturated by a rarefied gas, with walls held at constant heat flux. The Brinkman model is employed. The analysis leads to expressions for the local Nusselt number Nu as functions of the dimensionless longitudinal coordinate and the Darcy number. It is found that an increase in the velocity slip coefficient generally increases Nu by a small or moderate amount (but the circular tube at large Darcy number is an exception) while an increase in the temperature slip coefficient reduces Nu by a more substantial amount. These trends are uniform as the longitudinal coordinate varies.