Mixed convection flow along a vertical plate subjected to time-periodic surface temperature oscillations

The effect of the periodic oscillations of the surface temperature with time on the mixed convection from a vertical plate is investigated. The problem has been simplified by employing the laminar boundary layer and Boussinesq approximations. The fully implicit finite-difference scheme is used to solve the dimensionless governing equations. The results for the laminar flow of air having Pr=0.72 and water having Pr=7.00 are presented for an isothermal flat plate and for the periodic oscillation of the temperature on the plate. The results show the steady periodic variation of the Nusselt number and friction coefficient for both aiding and opposing flows with different amplitudes and frequencies of the oscillating surface temperature. For both aiding and opposing flow, both the Nusselt number and the friction coefficient oscillate with the oscillation of the plate temperature and for some cases (at high amplitudes and frequencies) the Nusselt number becomes negative. For constant Prandtl number and Richardson number, the cyclic average values of the Nusselt number are decreasing with increasing either the amplitude or the frequency of the surface temperature oscillations. The cyclic average values of the friction coefficient, for all the cases considered, are found to be constant and approximately equal to the values for non-oscillating surface temperature.