COMBINED FORCED AND NATURAL-CONVECTION IN LAMINAR-FILM FLOW

A mathematical model for the flow and heat transfer in a gravity-drive n liquid film is presented, in which the strict Boussinesq approximati on is adopted to account for buoyancy. A similarity transformation red uces the governing equations to a coupled set of ordinary differential equations. The resulting two-parameter problem is solved numerically for Prandtl numbers ranging from 1 to 1000. Favourable buoyancy arises when the temperature T(w) of the isothermal surface is lower than the temperature T0 of the incoming fluid, and the principal effects of th e aiding buoyancy are to increase the wall shear and heat transfer rat e. For unfavourable buoyancy (T(w) > T0), the buoyancy force and gravi ty act in opposite directions and the flow in the film boundary layer decelerates, whereas the friction and heat transfer are reduced. The o bserved effects of buoyancy diminish appreciably for higher Prandtl nu mbers.