Free Convection Effects on the Developing Laminar Flow in Vertical Concentric Annuli

Coupled energy and momentum boundary layer equations have been numerically solved for the problem of combined forced-free laminar convection in the entrance region of vertical concentric annuli. Both upflow and downflow of a fluid with Pr = 0.7 are considered under the thermal conditions of one wall being isothermal and the other adiabatic. Results for the development of velocity profiles, axial distance at which the axial velocity gradient normal to the wall vanishes, pressure drop, and heat transfer characteristics are presented at various values of the parameter Gr/Re ranged from −700 to 1500.