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Heat transfer analysis in the time-dependent axisymmetric stagnation point flow over a lubricated surface

Mahmood Khalid (International Islamic University, Department of Mathematics and Statistics, Islamabad, Pakistan)
Sajid Muhammad (International Islamic University, Department of Mathematics and Statistics, Islamabad, Pakistan)
Ali Nasir (International Islamic University, Department of Mathematics and Statistics, Islamabad, Pakistan)
Javed Tariq (International Islamic University, Department of Mathematics and Statistics, Islamabad, Pakistan)

In this paper time-dependent, 2-D, axisymmetric flow and heat transfer of a viscous incompressible fluid impinging orthogonally on a disc is examined. The disc is lubricated with a thin layer of power-law fluid of variable thickness. It is assumed that surface temperature of the disc is time-dependent. Continuity of velocity and shear stress at the interface layer between the fluid and the lubricant has been imposed to obtain the solution of the governing partial differential equations. The set of partial differential equations is reduced into ordinary differential equations by suitable transformations and are solved numerically by using Keller-Box method. Solutions are presented in the form of graphs and tables in order to examine the influence of pertinent parameters on the flow and heat transfer characteristics. An increase in lubrication results in the reduction of surface shear stress and consequently viscous boundary layer becomes thin. However, the thermal boundary layer thickness increases by increasing lubrication. It is further observed that surface shear stress and heat transfer rate at the wall enhance due to unsteadiness. The results for the steady case are deduced from the present solutions and are found in good agreement with the existing results in the literature.

Keywords: axisymmetric stagnation point flow, power law fluid, Keller-Box method, heat transfer, lubricated surface