Laminar free convection boundary layer flow over cylinders of elliptic cross section with constant surface heat flux

Numerical solutions for the steady laminar free convection boundary layer flow over horizontal cylinders of elliptic cross section when the major axis is both horizontal (blunt elliptic cylinder) and vertical (slender elliptic cylinder) subjected to a constant surface heat flux in an incompressible viscous fluid are presented in this paper. The governing boundary layer equations are first transformed into non-dimensional forms. These equations are then transformed using a nonsimilar transformation, which are solved numerically using an implicit finite-difference scheme known as the Keller box method. The governing boundary layer equations are then reduced to ordinary differential equations near the lower stagnation point of the cylinder, x ≈ 0. The reduced governing equations are also solved using the Keller box method numerically. The solutions are being obtained for large and small values of the Prandtl number with various parameter b/a (the ratio of the major and minor axis of the cylinder) for both blunt and slender orientations. The effects of various values of Prandtl number on the velocity profiles, the temperature profiles, the cylinder temperature and local skin friction coefficient are presented in tables and figures. For this present problem, it is also shown from the numerical results that the velocity profiles, the temperature profiles, the local skin friction coefficient and cylinder temperature decrease as Prandtl number increases