I Investigation of inelastic power-law model under thermal condition by using a developed method

Investigation of inelastic power-law model...

Abstract

This study extends the developed Taylor-Galerkin/Pressure-Correction (DTG/PC) method to simulate the behavior of inelastic, incompressible fluids under thermal conditions, employing a power-law model to describe fluid viscosity. The method is based on the Taylor-Galerkin/Pressure-Correction finite element framework (TG/PC), which is coupled the energy equation with the Navier-Stokes equations to describe fluid motion and temperature. The novelty of this research lies in the development of a highly accurate method to analyze inelastic fluid under thermal conditions. The finite element method utilizing the (TG/PC) framework has been enhanced through the integration of novel stages specifically designed to directly solve the equation of energy. A significant advancement in this refinement process was the implementation of the two-step Lax-Wendroff numerical scheme to the energy equation. This modification introduced two supplementary computational steps dedicated to energy-related calculations within the existing (TG/PC) algorithmic structure. The accuracy and reliability of the numerical method were assessed by examining the effects of the power-law index $ (n) $ and the consistency coefficient $ (m) $ on velocity, pressure, temperature, shear stress, and normal stress. The numerical results showed excellent agreement with established physical principles and previous studies, underscoring the method's validity and effectiveness.