The Effect of Longitudinal Oscillations on Free Convection From Vertical Surfaces

The free-convection flow along a vertical plate oscillating in its own plane is given analytical treatment. The basic equations of boundary-layer flow and heat transfer are linearized and the first three approximations are considered. The first approximation, being the case of steady-state free convection, is the classical problem of Schmidt and Beckman extended by Ostrach. The second approximation is the frequency response of the fluid temperature and velocity for which limiting solutions are obtained in two regions; namely, the regions of small and large ω* = ωδ²/ν where ω is the circular frequency, δ the steady-state velocity boundary-layer thickness, and ν the fluid kinematic viscosity. The approximate range of validity of the asymptotic solution is estimated in terms of parameter ω₀* which is a function only of Prandtl number. Part of the third approximation is time independent and gives rise to a net change in the steady values of the wall heat flux and shear stress. It is found that within the domain of laminar flow this net change is a decrease for the rate of heat transfer and an increase for the shear stress both evaluated for large values of ω₀*. Heat-transfer measurements are made for a vertical cylinder in air. It is found that in the laminar regime the average coefficient of heat transfer experiences a slight decrease relative to its measured steady state value. For higher values of oscillatory velocity amplitude the average coefficient of heat transfer undergoes an increase over its measured steady-state value. This reversal in the behavior of average coefficient of heat transfer appears to be due to flow transition which is confirmed by smoke studies along a vertical cylinder.