Abstract

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 U0(φ ) and constant heat flux. The impinging free-stream is steady and with a constant strain rate k¯. 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¯a2/2υ∞, 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(φ)=U0(φ)/k¯a, where a is cylinder radius and υ∞ 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.

Abstract

This study is devoted to investigate the steady fully developed natural convection flow in a vertical annular micro-channel having temperature dependent viscosity in the presence of velocity slip and temperature jump at the annular micro-channel surfaces. The governing equations of the motion are a set of ordinary differential equations and their analytical solutions in dimensionless form have been obtained for the temperature field and velocity field. The effect of various flow parameters entering into the problem is discussed with the aid of line graphs. During the course of numerical investigation, it is found that increase in viscosity variation parameter enhances the fluid velocity and velocity slip. Furthermore, an increase in viscosity variation parameter leads to increase in the volume flow rate and skin friction.