Alexandria Engineering Journal (Jun 2016)

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

  • Rasool Alizadeh,
  • Asghar B. Rahimi,
  • Reza Arjmandzadeh,
  • Mohammad Najafi,
  • Ahmad Alizadeh

DOI
https://doi.org/10.1016/j.aej.2016.04.017
Journal volume & issue
Vol. 55, no. 2
pp. 1271 – 1283

Abstract

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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.

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