Unaxisymmetric stagnation-point flow and heat transfer of a viscous fluid with variable viscosity on a cylinder in constant heat flux

Existing solutions of the problem of axisymmetric stagnation-point flow and heat transfer on either a cylinder or a flat plate are for incompressible fluid. Here, fluid with viscosity proportional to a linear function of temperature is considered in the problem of an unaxisymmetric stagnation-point flow and heat transfer of an infinite stationary cylinder with non-uniform normal transpiration U-0(phi) and constant heat flux. The impinging free-stream is steady and with a constant strain rate (k) over bar. A reduction of Navier-Stokes and energy equations is obtained by use of appropriate similarity transformations. The semi-similar solution of the Navier-Stokes equations and energy equation has been obtained numerically using an implicit finite-difference scheme. All the solutions aforesaid are presented for Reynolds numbers, Re = (k) over bara(2)/2v(infinity), ranging from 0.01 to 100 for different values of Prandtl number and viscosity-variation parameter and for selected values of transpiration rate function, S(phi) - U-0 (phi)/(k) over bara, where a is cylinder radius and v(infinity) is the reference kinematic viscosity of the fluid. Dimensionless shear-stresses corresponding to all the cases increase with the increase in Reynolds number and transpiration rate function while dimensionless shear stresses decrease with the increase in viscosity-variation parameter. The local coefficient of heat transfer (Nusselt number) increases with increasing the transpiration rate function and Prandtl number. (C) 2016 Faculty of Engineering, Alexandria University. Production and hosting by Elsevier B.V.