An asymptotic analysis of free convection boundary layer on a horizontal flat plate due to small fluctuations in surface temperature

Unsteady free convective boundary layer flow, over a semi-infinite horizontal plate is analyzed when the plate temperature oscillates with a non-zero mean, the free stream being at rest. The method of matched asymptotic expansions is employed to solve the singular perturbation problem revealing the existence of four distinct oscillating layers at large distances from the leading edge of the plane surface. It is found that the asymptotic values far downstream are approached through damped oscillations.