A 'backward' free-convective boundary layer

In this paper the cooling of a low-heat-resistance sheet that moves downwards is considered. The free-convective velocities are assumed to be much larger than the velocity of the sheet. As a result the motion of the fluid is mainly towards the point where the sheet enters the system and a ‘backward’ boundary layer ensues. It is shown that the equations can be reduced by a similarity transformation. For intermediate values of the Prandtl number the equations are solved numerically. Matched asymptotic expansions are used to treat the cases of extremely small and extremely large Prandtl number. The Nusselt number associated with this process is compared with those due to other modes of heat transfer, such as radiation and forced convection. The algebraic behaviour of the boundary-layer functions is discussed.