Transient Free Convection From a Vertical Flat Plate

Abstract The method of characteristics is employed to obtain solutions to the time dependent free-convection equations of momentum and energy placed in integral form (Karman-Pohlhausen method). Two boundary conditions are considered for a vertical flat plate of infinite width and semi-infinite length which is initially at ambient temperature in quiescent fluid: (a) The plate is suddenly raised to a uniform higher temperature, and (b) the plate suddenly begins to produce a uniform heat flux at its surface. The results yield the time required for steady flow to be established as a function of position along the plate. Heat-transfer coefficients are obtained for the initial stage of motion during which the convective process is one dimensional. The approximate velocity and temperature profiles obtained from the analysis are compared with more precise solutions of the differential equations for the initial stage of motion and for steady state.