Question

Consider a vertical parallel-plate channel of indefinite length, with walls at different temperatures. The channel width is 2L and the wall temperatures are T1 and T2. It is assumed that T2 > T1. In this system, the heat fluxes in and out of the fluid will come into balance, yielding a thermally fully developed region with no streamwise temperature variations. With the temperature (and buoyancy) force independent of x, it is feasible to have fully developed flow.
(a) Sketch the velocity and temperature profiles in the space between the plates.
(b) Assume laminar and fully developed flow, by incorporating the relevant boundary conditions, evaluate the temperature distribution.
(c) By applying the Boussinesq approximation and no-slip conditions, evaluate the velocity distribution.

Answer 1