Effects of blowing or suction on the laminar boundary layer flow over a rotating cone

The effects of suction or blowing at the surface of a rotating cone in a quiet fluid on the skin friction and heat transfer are described. The equations which govern the fluid motion and thermal energy transfer are transformed by the boundary layer approximations and the resulting equations are solved under the condition that the suction or blowing velocity varies as xⁿ (x: distance measured from the apex of the cone, n: arbitrary constant). The solutions are obtained as a perturbation from the basic laminar flow of an incompressible viscous fluid over the impermeable rotating cone. Detailed numerical calculations are performed for the case of an isothermal rotating cone with uniform blowing or suction, i.e. n=0, the Prandtl number being 0.72. Results are given for the shear stress, heat transfer and velocity and temperature fields. It is shown from the analysis that suction sharply increases the circumferential shear stress and the heat transfer at the surface.Nomenclature c proportional constant - C_fx dimensionless skin friction factor, _x/(V²) - C_fx0 dimensionless skin friction factor for an impermeable cone - C_fy dimensionless circumferential skin friction factor, _y/(V²) - C_fy0 dimensionless circumferential skin friction factor for an impermeable cone - c_p specific heat at constant pressure - f_k function of - g_k function of - h heat transfer coefficient, q/(T_w–T) - k thermal conductivity of fluid - n arbitrary constant - Nu_x local Nusselt number, hx/k - Nu_x0 local Nusselt number for an impermeable cone - Pr Prandtl number - q heat transfer rate - r radius of a circular cross section of the cone, x sin - R_x Reynolds number, Vx/ - T temperature - T_w surface temperature of the cone - T temperature of the surrounding fluid - u fluid velocity in x-direction - v fluid velocity in y-direction - V circumferential velocity at the cone surface, r - w fluid velocity in z-direction - x coordinate along meridional section - y coordinate along a circular cross section - z coordinate perpendicular to both x and y - perturbation parameter, cxⁿ/(x sin )^1/2 - dimensionless z-coordinate, z( sin /)^1/2 - _k function of - kinematic viscosity - density of fluid - _x skin friction in x-direction - _y circumferential skin friction - stream function - angular speed of the cone