Effect of thermal instability on fully developed laminar flow with internal heat generation between two horizontal parallel plates

This paper deals with the effect of secondary flow on fully developed laminar flow between horizontal parallel plates with uniform internal heat generation and constant but different heat fluxes at the two wall surfaces. In such a flow, the basic temperature profile prior to the onset of secondary flow is nonlinear and the negative temperature gradient in the direction of buoyant force induces a potential of instability. In the analysis small perturbations are superimposed upon the unperturbed velocity and temperature fields, assuming that the secondary flow forms longitudinal vortex rolls. The instability criterion is obtained by using the linear stability theory in the perturbation equations. Additionally, the amplitude of secondary flow is computed by the power integral method based on the Stuart shape assumption. Numerical values for critical Rayleigh numbers and the amplitude of secondary flow are found for various Prandtl numbers and parameters characterizing the basic temperature profile. In order to ascertain theoretical results, the transverse velocity profile is measured. It is found that theoretical results agree with experimental results