Abstract
A finite-difference scheme is developed for solving the boundary layer equations governing the unsteady laminar free convection flow in open ended vertical concentric annuli. The initial condition considered for the creation of the thermal transient corresponds to a step change in temperature at the inner annulus boundary while the outer wall is maintained adiabatic. Numerical results for a fluid of Pr = 0.7 in an annulus of radius ratio 0.5 are presented. The results show the developing velocity and pressure fields with respect to space and time. Also, the important relationship between the annulus height and the induced flow rate is presented for various values of the time parameter starting from quiescence to the final steady state.