Heat transfer analysis on a moving flat sheet emerging into quiescent fluid

Abstract

The conjugated heat conduction process of a continuously moving flat sheet emerging from a slot or orifice in contact with a quiescent fluid is analyzed. Because of the finite thermal conductivity of the sheet, longitudinal and transverse temperature gradients arise within it and, thus, change the mathematical character of the problem from parabolic to elliptic. The momentum and energy balance equations are reduced to a nonlinear system of partial differential equations with three parameters: the Prandtl number Pr, a nondimensional sheet thermal conductance beta, and a suitable Peclet number Pe. The limits beta << 1 and beta Pe(2) << 1 are identified as the most relevant from a practical point of view. In this case, the problem is governed by an universal integral equation to obtain the spatial evolution of the sheet temperature as a function of the nondimensional longitudinal coordinate.