A solution for the complex eigenvalues and eigenfunctions of the periodic Graetz problem

The periodic Graetz problem arising in laminar transient forced convection inside a parallel-plate channel is analyzed. Nayfeh's method is applied to the complex eigenvalue problem yielding a single uniformly Valid closed form asymptotic solution for the complex eigenfunctions. The asymptotic solution presented is accurate for all normalized complex eigenfunctions except for those corresponding to the smaller eigenvalues. Another solution of the complex eigenvalue problem, which is accurate for the smaller eigenvalues, is presented based on the finite Fourier transform technique and is utilized for checking the accuracy of the closed form asymptotic solution. (C) 1998 Elsevier Science Ltd.