  Motion in the atmosphere or mantle convection are two among phenomena of
natural convection induced by internal heat sources. They bifurcate from the
conduction state as a result of its loss of stability. In spite of their
importance, due to the occurrence of variable coefficients in the nonlinear
partial differential equations governing the evolution of the perturbations
around the basic equilibrium, so far these phenomena were treated mostly
numerically and experimentally. No rigorous study is known. In this paper we
realize for the first time such a linear study for the eigenvalue problem
associated with those equations for a convection problem with an uniform
internal heat source in a horizontal fluid layer bounded by two rigid walls.
Our method uses Fourier series expansions for the unknown functions. Numerical
results and graphs are given showing a destabilizing effect of the presence of
the heat source.
