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

TL;DR

This paper compares two spectral methods, using Fourier series expansions, to analytically solve the eigenvalue problem in convection with a uniform internal heat source, providing theoretical insights and numerical validation.

Contribution

It introduces and compares two spectral methods based on Fourier series for analyzing convection with internal heat sources, including theoretical analysis and numerical validation.

Findings

Good agreement with existing results

Both methods effectively solve the eigenvalue problem

Spectral methods provide accurate analytical solutions

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.