Rotating flow of Maxwell fluid with variable thermal conductivity: An application to non-Fourier heat flux theory

Abstract

In this work we analytically explore the flow and heat transfer of upper-convected Maxwell (UCM) fluid in rotating frame. Fluid with temperature dependent thermal conductivity is considered. A non-Fourier heat flux term, featuring the thermal relaxation effects, is employed to model heat transfer process. Boundary layer approximations are invoked to simplify the governing system of partial differential equations which are later converted to self-similar forms via similarity transformations. Mathematical model comprises of interesting quantities which include the rotation parameter λ, Deborah number β, Prandtl number Pr, dimensionless thermal relaxation time γ and parameter ε. Uniformly convergent approximate series solutions are obtained by means of homotopy analysis method (HAM). Admissible values of the auxiliary parameter in HAM are determined by plotting the so-called ℏ-curves. We noticed that hydrodynamic boundary layer becomes thinner due to the inclusion of elastic effects. The rotation parameter λ also serves to reduce the boundary layer thickness. A comparative study of Cattaneo–Christov and Fourier models is also presented and analyzed.