Title: Finite element solution of oblique stagnation-point flow of viscoelastic fluid and heat transfer with variable thermal conductivity

Authors: Minakshi Poonia; Rama Bhargava

Addresses: Department of Mathematics, Indian Institute of Technology Roorkee, Roorkee, 247667, India ' Department of Mathematics, Indian Institute of Technology Roorkee, Roorkee, 247667, India

Abstract: The oblique stagnation-point boundary layer flow of an incompressible viscoelastic fluid impinging on an infinite vertical plate and heat transfer characteristics with variable thermal conductivity is studied. The governing partial differential equations are transformed into non-dimensional, nonlinear coupled ordinary differential equations which are solved numerically by robust Galerkin finite element method. The streamline patterns and numerical results for the dimensionless shear rate and temperature profiles are displayed graphically for various physical parameters such as Prandtl number, Weissenberg number, thermal conductivity parameter and two parameters α and β, the later being a free parameter. The local Nusselt number is found to be the decreasing function of Weissenberg number whereas it increases with increasing values of Prandtl number. The present problem finds significant applications in cooling of nuclear reactors and electronic devices by fans, where the angle plays an important role in cooling.

Keywords: viscoelastic fluids; stagnation point; oblique flow; variable thermal conductivity; heat transfer; FEM; finite element method; incompressible fluids; partial differential equations; PDEs; dimensionless shear rate; temperature profiles; cooling.

DOI: 10.1504/IJCSM.2015.073578

International Journal of Computing Science and Mathematics, 2015 Vol.6 No.6, pp.519 - 537

Received: 21 May 2013
Accepted: 19 Jan 2014
Published online: 13 Dec 2015 *

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