Convection in an internally heated layer

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Abstract
A numerical study has been made of steady laminar convection in an infinite horizontal layer of fluid, bounded above by a rigid plate held at constant temperature, and below by a thermal insulator. The fluid is heated by a uniform distribution of heat sources. Recent methods for the solution of the Navier-Stokes equations by finite differences are discussed, and the results of integrations in two and three space dimensions and time are presented in an attempt to determine the planform and other flow properties as functions of the Rayleigh and Prandtl numbers.These results are compared with a preliminary study by Roberts (1967) using a mean-field equation approach and with experimental observations by Tritton & Zarraga (1967) and Hooper (private communication).