Application of two spectral methods to a problem of convection with uniform internal heat source

Abstract

Two methods based on Fourier series expansions (a Chandrasekhar functions-based method and a shifted Legendre polynomials -based method) are used to study analytically the eigenvalue problem governing the linear convection problem with an uniform internal heat source in a horizontal fluid layer bounded by two rigid walls. For each method some theoretical remarks are made. Numerical results are given and they are compared with some existing ones. Good agrement is found.