The fluid flow and heat transfer in the cavity is assumed to be governed by the Navier-Stokes equations together with the energy equation with the following restrictions: steady state, laminar flow, Newtonian fluid behaviour, negligible viscous dissipation and without radiation effects. Effect of variable physical properties with temperature has been considered. The corresponding differential equations in cartesian coordinates and three dimensions can be represented by the following tensor notation:

д(рТ) д(рТ) _ к d2T

dt + U’ dxj cp dx2

The air layer is bounded by two sides at constant temperature and the remaining sides are assumed to be adiabatic. Thus the air layer is subjected to Dirichlet boundary condition on top and bottom surfaces, both being at a fixed hot and cold Tc temperatures respectively. The remaining faces are subjected to Neumann boundary condition.

A non-dimensionalization of the governing equations and the boundary conditions shows that Nusselt number depends on the Rayleigh number, the aspect ratio in both planes, Prandtl number and the inclination. Thus:

= /( )

where the Rayleigh number is defined as Ra=gf3(Th — Tc)b3/v2 and is evaluated at the mean temperature.