In this chapter I have presented the fully developed profiles of temperature, mass fraction and velocity, and the consequent mass and energy fluxes at the vertical walls, in the space between two parallel walls at different but constant conditions for a perfect Boussinesq mixture of a gas and a vapour with constant properties except for the mixture specific heat. The finite mass transfer effects of interfacial velocity and the interdiffusion of enthalpy were included.
The governing equations were obtained from those for a cuboid by taking the limit as the vertical and spanwise aspect ratios tended to infinity. In this process, the vertical and spanwise gradients of all dependent variables dropped out of the field equations (apart from a uniform vertical pressure gradient). As a consequence, the boundary conditions at the other surfaces had to be abandoned. The solutions presented thus apply equally well to flow in open channels as well as cavities, but only sufficiently far from the ends. The question of how far is sufficiently far must await the solution for the flow in the end regions, which will be treated in chapters 5 and 7.
In the zero mass transfer limit, the temperature and mass fraction vary linearly across the cavity while the horizontal velocity is zero and the vertical velocity is described by a cubic (odd symmetric for a cavity, and tending toward an even symmetric parabola as the imposed pressure gradient becomes large compared to the density perturbation for an open channel). For finite mass transfer, the horizontal velocity is nonzero, but must be constant. This horizontal advection profoundly alters the transport of vapour, energy and momentum across the cavity, so that while their profiles can still be expressed in closed form, this involves exponential functions rather than polynomials. The expression derived for the wall energy flux shows that the overall cavity energy transfer can be very much higher if a vapour condenses at the walls.