The solution of heat transfer problems by the Wiener-Hopf technique. I. Leading edge of a hot film

Abstract

An incompressible fluid of constant thermal diffusivity flows with velocity Sy in the x -direction over the infinite plane wall y = 0. The half-plane y = 0, x > 0 is maintained at a uniform temperature T 1 greater than the temperature T 0 of the oncoming fluid. The adiabatic boundary condition T y = 0 is imposed on the half-plane y = 0, x < 0. An exact solution for the dimensionless heat transfer from the heated half-plane x > 0, incorporating longitudinal diffusion, is obtained by the Wiener-Hopf technique, and is reduced to a single convergent real integral which is evaluated numerically. An asymptotic expansion is made in inverse powers of x , whose leading term is Lévêque’s (1928) boundary-layer solution. Subsequent terms in the expansion lead to a determination of the coefficients of the eigenfunctions of the boundary-layer equations which would remain arbitrary in a direct asymptotic expansion of the governing equation.