Numerical investigations of nonlinear Maxwell fluid flow in the presence of non-Fourier heat flux theory: Keller box-based simulations

Abstract

We investigate the thermal flow of Maxwell fluid in a rotating frame using a numerical approach. The fluid has been considered a temperature-dependent thermal conductivity. A non-Fourier heat flux term that accurately reflects the effects of thermal relaxation is incorporated into the model that is used to simulate the heat transfer process. In order to simplify the governing system of partial differential equations, boundary layer approximations are used. These approximations are then transformed into forms that are self-similar with the help of similarity transformations. The mathematical model includes notable quantities such as the rotation parameter $ \lambda $, Deborah number $ \beta $, Prandtl number Pr, parameter $ ϵ $ and the dimensionless thermal relaxation times $ \gamma $. These are approximately uniformly convergent. The Keller box method is used to find approximate solutions to ODEs. We observed due to the addition of elastic factors, the hydrodynamic boundary layer gets thinner. The thickness of the boundary layer can be reduced with the use of the k rotation parameter as well. When Pr increases, the wall slope of the temperature increases as well and approaches zero, which is an indication that Pr is decreasing. In addition, a comparison of the Cattaneo-Christov (CC) and Fourier models are provided and discussed.

Keywords

• maxwell fluid
• cc model
• rotating surface
• heat flux
• keller box method