Numerical assessment for flows of two different viscoelastic fluids and resulting heat transfer over deforming surface

Abstract

Steady boundary layer flows produced by deforming surfaces with heat transfer have significant technical applications. These include studying the cooling process of metallic plates immersed in a cooling bath, analysing the boundary layer during liquid film condensation, , annealing of copper wires, uninterrupted extrusion of polymer sheet from dye and examining the behaviour of boundary layers in polymer industries for glass production. Motivated by such significance, present thesis aims at formulating flows of two different viscoelastic fluids bounded by deforming surfaces with heat transfer. In first problem, Jeffrey fluid with variable physical properties is employed. Mathematical modeling is performed by incorporating exponential variation in viscosity, thermal conductivity, relaxation time and retardation time with temperature. Transport equations are formulated under the aforesaid assumption and are solved for self-similar solutions using a numerical scheme. Illustrative results are included, reflecting the consequences of variable physical properties on the induced viscoelastic fluid motion and accompanying heat transfer. In addition, skin friction factor for Jeffrey fluid with variable properties is evaluated and described. The second problem deals with the examination of partial slip conditions and viscous dissipation effects for analyzing second grade fluid flow over a deforming surface. The theromophoretic force term is factored in the concentration equation, which is vital for the liquids with light molecular weight. The consideration of wall slip condition produces a non-linear Robin-type condition for the velocity field. Akin to the first problem, a self-similar solution is derived for full range of slip coefficients using a numerical scheme. Streamlines and isotherms are generated from the numerical solutions in both the considered problems.