Axisymmetric stagnation-point flow and heat transfer of a viscous, compressible fluid on a cylinder with constant heat flux

Existing solutions of the problem of axisymmetric stagnation-point flow and heat transfer on either a cylinder or flat plate are for incompressible fluid. Here, fluid with temperature dependent density is considered in the problem of axisymmetric stagnation-point flow and heat transfer on a cylinder with constant heat flux. The impinging free stream is steady and with a constant strain rate, k̄. An exact solution of the Navier–Stokes equations and energy equation is derived in this problem. A reduction of these equations is obtained by use of appropriate transformations introduced for the first time. The general self-similar solution is obtained when the wall heat flux of the cylinder is constant. All the solutions above are presented for Reynolds numbers, Re=k̄a2/2υ, ranging from 0.01 to 1000, selected values of compressibility factors, and different values of Prandtl number, where aa is cylinder radius and νν is the kinematic viscosity of the fluid. For all Reynolds numbers and surface heat flux, as the compressibility factor increases, both components of the velocity field, the heat transfer coefficient and the shear-stresses increase, and the pressure function decreases.