Abstract
Abstract A mathematical model is developed to study laminar, nonlinear, non-isothermal, steady-state free convection boundary layer flow and heat transfer of a micropolar viscoelastic fluid from a vertical isothermal cone. The Eringen model and Jeffery’s viscoelastic model are combined to simulate the non-Newtonian characteristics of polymers, which constitutes a novelty of the present work. The transformed conservation equations for linear momentum, angular momentum and energy are solved numerically under physically viable boundary conditions using a finite difference scheme (Keller Box method). The effects of Deborah number (De), Eringen vortex viscosity parameter (R), ratio of relaxation to retardation times (λ), micro-inertia density parameter (B), Prandtl number (Pr) and dimensionless stream wise coordinate (ξ) on velocity, surface temperature and angular velocity in the boundary layer regime are evaluated. The computations show that with greater ratio of retardation to relaxation times, the linear and angular velocity are enhanced whereas temperature (and also thermal boundary layer thickness) is reduced. Greater values of the Eringen parameter decelerate both the linear velocity and micro-rotation values and enhance temperatures. Increasing Deborah number decelerates the linear flow and Nusselt number whereas it increases temperatures and boosts micro-rotation magnitudes. The study is relevant to non-Newtonian polymeric thermal coating processes.
Highlights
The e ects of Deborah number (De), Eringen vortex viscosity parameter (R), ratio of relaxation to retardation times (λ), micro-inertia density parameter (B), Prandtl number (Pr) and dimensionless stream wise coordinate (ξ ) on velocity, surface temperature and angular velocity in the boundary layer regime are evaluated
Coating hydrodynamics has been an area of considerable interest since the monumental paper by Landau and Levich (1942) in which an elegant formulation was developed for the thickness of the lm of a uid which is deposited on a plate withdrawn vertically from a bath at constant velocity
We examine the in uence of several key parameters, namely Deborah number (De), ratio of relaxation to retardation times (λ), Prandtl number (Pr), micropolar parameter (R) i.e. vortex to dynamic viscosity ratio and micro-inertia density parameter (B)
Summary
Coating hydrodynamics has been an area of considerable interest since the monumental paper by Landau and Levich (1942) in which an elegant formulation was developed for the thickness of the lm of a uid which is deposited on a plate withdrawn vertically from a bath at constant velocity. Zevallos et al (2005) presented a nite element simulation of forward roll coating ows of viscoelastic liquids using both Oldroyd-B and FENE-P models. Campanella et al (1986) investigated dip coating of a circular cylinder in non-Newtonian power-law uids. These studies ignored heat transfer which may be critical in certain coating systems (Mitsoulis, 1986). Choudhury and Keywords: Je rey’s viscoelastic model, Eringen micropolar model, non-Newtonian polymers, Deborah number, Keller-box method, heat transfer, boundary layers, skin friction, Nusselt number, thermal coating systems
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