Buoyancy effects in plane Couette flow heated uniformly from below with constant heat flux

The onset of buoyancy-driven convection in plane Couette flow heated uniformly from below is analyzed theoretically. For the thermal entrance region with Raq≫816.7, a new set of stability equations involving streamwise variations of disturbances are derived based on the linear theory, the scaling relations and the extended momentary instability concept. It is shown that the critical Rayleigh number that marks the onset of longitudinal vortex rolls increases with a decrease in Prandtl number. Based on the present stability criteria a new mixed convection heat transfer correlation is derived for the whole range of Rayleigh number. The present analysis predicts the available experimental data of water, quite well.