Applications to nuclear reactors have revived interest in natural convection. A rectangular closed cavity with internal heat generation and wall-cooling roughly simulating a channel of an internally-cooled homogeneous reactor core has been studied theoretically and experimentally. The basic equations of continuity, Navier-Stokes, and a modified energy relation including a volumetric heat source are normalized to show the dependence on the following nondimensional parameters: i) Nusselt number based on width; ii) Prandtl number, and iii) product of Rayleigh number based on width and aspect ratio, a/b, of the cavity. The complexity of these equations allows only numerical solutions, which are obtained following a modified Squire's method consisting in assuming temperature and velocity profiles. These are substituted into the nondimensional equations, and integrated across the cavity, resulting in a still complex system of differential equations in which the dependent variables and unknown functions are the thickness, velocity, and temperature of the rising core of fluid. The coefficients in the equations are functions of the core thickness, more or less complicated according to the velocity and temperature profiles assumed. Two cases are considered: a simplified temperature profile, as used by Lighthill; and a more sophisticated profile with a positive maximum. Both velocity profiles are Lighthill's. Digital computer calculations using a fourth-order Runge-Kutta method yielded solutions that follow the typical one-fourth power law: Nu = C(m, σ)[(a/b)Ra]1/4, where 1/2m is the slope of the wall temperature distribution, assumed linear. To include liquid metals, C was computed for 0.01 ≤ σ ≤ 10. The parallel experimental study confirms the existence of a positive maximum in the temperature profile, previously not reported. Introduction of this innovation in the theoretical treatment leads to excellent agreement with experimental results, and has the general effect of lowering the theoretical curves Nu = f[σ,(a/b)Ra]. Semiquantitative experimental data on the velocity field also indicate the existence of a positive maximum in the velocity profile until now not reported.