Three-dimensional mixed convective boundary layers along horizontal and inclined cylinders

A numerical study is conducted to investigate the momentum and heat transfer characteristics of three-dimensional, laminar mixed convection boundary layers that arise along isothermal, horizontal and inclined semi-infinite cylinders aligned longitudinally in the direction of a uniform, steady flow. All three buoyancy force components are accounted for in the analysis. The governing dimensionless system of differential equations is solved by an approximate power series expansion and appropriate transformations. Local heat transfer rates are presented for gases with a Prandtl number of 0.7. For a horizontal cylinder, the local Nusselt numbers are found to increase with increasing buoyancy force at the bottom half of the cylinder, and to decrease with increasing buoyancy force at the upper half of the cylinder. As the cylinder is tilted from the horizontal, the decrease of the heat transfer rate at the upper half of the cylinder is reduced, where beyond a certain angle of inclination the local Nusselt numbers start to increase with buoyancy force, for both upper and lower portions of the cylinder. The streamwise and circumferential pressure gradients induced by the radial buoyancy component cause the local Nusselt numbers at small axial locations to increase along the circumference from bottom to top. Further away from the leading edge, the circumferential buoyancy component counteracts the effect of the pressure gradients, thus resulting in the decrease of the heat transfer rate along the circumference.