Author(s)

Ronald Ming Cho So¹, Elizabeth Wing Sze Kam^2*

¹Mechanical Engineering Department, the Hong Kong Polytechnic University, Hong Kong, China.
²Department of Mathematical Sciences, Rensselaer Polytechnic Institute, Troy, NY, USA.

Exact solution of the steady Navier-Stokes equations has been obtained for the thermal stagnation-point flow at the leading edge of a turbine blade under the assumptions of constant nose radius and external vorticity, and fluid properties independent of temperature. The solutions reveal that curvature affects local heat transfer and skin friction while external vorticity does not. The effect of external vorticity is to shift the zero skin friction point away from the stagnation point. This solution is valid for all Reynolds number, external vorticity, and nose radius. In the limit of nose radius going to infinity and external vorticity, going to zero, the exact solution for two-dimensional plane stagnation-point flow is recovered identically. In addition, it can be shown that the velocity field around the stagnation point of a rotating curved surface is the same as that around the stagnation point of a stationary curved surface with an external vorticity which equals to twice of the rotational speed. This realization renders the present solution equally valid for thermal stagnation point flow at the leading edge of centrifugal impeller blades.

Navier-Stokes Equations, Exact Solutions, Thermal Stagnation-Point Flow, Displacement Effect

Ming Cho So, R. and Sze Kam, E. (2017) Exact Solution for Thermal Stagnation-Point Flow with Surface Curvature and External Vorticity Effects. Journal of Applied Mathematics and Physics, 5, 966-989. doi: 10.4236/jamp.2017.54085.