Calculation procedure for transient heat transfer to a cooled plate in a heated stream whose temperature varies arbitrarily with time

Solutions for the surface temperature and surface heat flux are found for laminar, constant property, slug flow over a plate convectively cooled from below, when the temperature of the fluid over the plate varies arbitrarily with time at the plate leading edge. A simple technique is presented for handling arbitrary fluid temperature variation with time by approximating it by a sequence of ramps or steps for which exact analytical solutions are available.