Natural convection in a porous medium at high Rayleigh numbers - Application of Prandtl's analogy

The problem of natural convection heat transfer from an isothermal vertical cylinder to a saturated porous medium is solved by the integral method making use of one-seventh profiles for velocity and temperature variation in the boundary layer. Prandtl's analogy is used to obtain the wall heat transfer coefficients. The results obtained for Rayleigh numbers greater than 10(9) and Prandtl numbers 4 and 0.12 are compared with experimental data from literature show satisfactory agreement. Also an approximate closed form solution is presented for the case of a flat wall to predict local Nusselt numbers.