Nonlinear Finite Element Thermal Modeling of Casson Flow in Sinusoidal Chamber with Lorentz’s Force

Abstract

The remarkable properties of Casson fluid significantly contribute to its importance in technical and industrial sciences, establishing it as an essential variety among non-Newtonian fluids. Lorentz’s force is a crucial study area with profound implications for science and technology. It enhances our understanding of physical laws, drives technological innovation, and improves industrial processes. This study employs the finite element method to analyze the behavior of Casson fluid flow, applying thermal and velocity constraints in a square domain with a sinusoidal shape, and incorporating the effects of an inclined Lorentz force. The chamber has a sinusoidal pattern on its bottom and upper borders. The vertical and bottom borders are kept at consistently lower and higher temperatures, respectively, while no heat is transferred from the top border. Lorentz’s force is applied at an angle opposite the clockwise direction. The energy transport and velocity distribution mechanism are examined precisely for a wide range of pertinent factors of magnetic field (Ha), buoyancy force (Ra), Prandtl number (Pr), Casson factor (β), magnetic orientation (γ), and wave number (m). The results indicate that increasing the Lorentz force reduces the heat transfer through conduction, which is the dominant mechanism for fluid movement. When the buoyancy force increases, the maximum heat transport rate of about 135.86% occurs at m = 2. At low β, the strength of the stream function is weak due to the conduction mechanism of thermal transfer. For the increase in β, a higher value of approximately 118.50% of the heat transfer amount is observed at wave number 2. The results derive a new linear regression equation with various variables. Comparisons are conducted with existing literature, and the data agree.