This paper aims to present a second-order accurate algorithm with high computational efficiency for analyzing the hydrodynamic and thermal characteristics of modified Bingham fluid flow under a uniform wall temperature and stick-slip conditions.
The paper presents two unique aspects. The first is a numerical algorithm that uses the Taylor-Galerkin finite element method, based on the extension of artificial compressibility equations. This algorithm is compared with another similar algorithm of equivalent accuracy to showcase its effectiveness. The second aspect examines the dependence of viscosity on temperature and highlights the importance of considering the viscous dissipation term. The authors compare this scenario with cases that neglect temperature effects on one side and viscous dissipation on the other.
The comparison reveals that the proposed algorithm exhibits a faster convergence with nearly half the time steps and provides highly accurate results. All findings showed excellent agreement with the results of others, reinforcing the efficacy of our approach. In addition, our analysis indicated that neglecting thermal effects led to inaccurate estimates of parameter values.
The present investigation has provided a highly efficient algorithm and deserves to be in the limelight. Furthermore, the paper emphasizes the importance of considering viscous dissipation and viscosity variability with temperature.
