Effect of thermal radiation on natural convection over cylinders of elliptic cross section

Summary The effect of conduction-radiation on natural convection flow of an optically dense viscous incompressible fluid along an isothermal cylinder of elliptic cross section has been investigated. The boundary layer equations governing the flow are shown to be nonsimilar. Full numerical solutions of the governing equations are obtained using the implicit finite difference method. The solutions are expressed in terms of the Nusselt number Nu against the eccentric angle in the range 0, ]. The working fluid is taken to have unit value of the Prandtl number, Pr, and the effects of varying the Planck number,R _d, the surface temperature parameter, _w, and the parameterA _O representing the ratio of the major and minor axes of the cylinder are investigated. From the present analysis it is found that the rate of heat transfer from the slender body is higher than from the blunt body and that these higher values become even higher due to an increase in the effect of radiation in the flow field.Nomenclature a semi-major axis of the cylinder - a _r Rosseland mean absorption coefficient - b semi-minor axis of the cylinder - C _p specific heat at constant pressure - f dimensionless stream function - g acceleration due to gravity - Gr Grashof number - Nu Nusselt number - Q _w surface heat flux - Pr Prandtl number - R _d Planck number (radiation-conduction parameter) - T temperature of the fluid - T _w temperature of the heated surface - T temperature of the ambient fluid - u velocity in thex-direction - v velocity in they-direction - x coordinate measuring distance round the cylinder - y coordinate measuring distance normal to the cylinder Greek symbols eccentric angle - coefficient of cubial expansion - coefficient of thermal diffusivity - v kinematic viscosity