Numerical solutions of free convection from an isothermal inclined plate

The differential equations describing the free convection heat transfer about an inclined plate have been solved by a numerical integration method. The partial differential equations were transformed into a coupled set of ordinary nonlinear differential equations via a similarity transform. These nonlinear differential equations are subject to boundary conditions at the origin and at infinity. A suitable approximation of infinity was made and the solution was obtained via a quasilinearization procedure. The following conclusions are drawn : (1) The thickness of both the hydrodynamic and thermal boundary layers increases with the inclination to the vertical. The maximum velocity within the boundary layer decreases with the increasing inclination. (2) For small and medium inclinations, there is good agreement between the calculated results and experiment results. (3) Boundary layer assumptions, implying that the distance along the plate is much larger than the boundary layer thickness, are valid for the cases of small inclination. (2) A modified empirical Nusselt number (for the vertical plate) was found having excellent correlation with numerical results presented for the cases Prandtl number less than 100. For larger Prandtl number cases, the modified Eckert equation has better correlation.