Conjugate three-dimensional natural convection heat transfer from a horizontal cylinder with long transverse plate fins

Steady three-dimensional conjugate natural convection heat transfer from a horizontal isothermal cylinder with infinitely large transverse nonisothermal fins is studied numerically. The complete Navier-Stokes equations are solved using a vorticity-vector potential approach. Results are obtained for a Rayleigh number of 10³ and a Prandtl number of 5. Effects of the variation of fin spacing and fin conduction are studied. Two limits of this problem at a large fin spacing are an infinitely long isothermal free cylinder and an infinitely large vertical conducting plate fin with a circular isothermal heat source. Results are compared against both limits and the latter limit is used to develop a correlation for the local heat transfer from the fin. It is found that heat is transferred from the fluid to the fin in a sector adjacent to the plume above the heated cylinder. With alt other conditions held fixed, there exists an optimum fin spacing at which the total heat transfer per unit length of cylinder is a maximum.