Advanced numerical simulation techniques in MHD fluid flow analysis using distributed fractional order derivatives and Cattaneo heat flux model

This study investigates the flow and heat transfer characteristics of a second-grade fluid over a flat surface with variable heat flux. Utilizing a mathematical model based on distributed order fractional derivatives, we offer a more precise representation of non-Newtonian fluid behavior. The associated highly nonlinear equations are tackled numerically through an innovative amalgamation of the finite difference scheme and the L1${{L}_1}$ technique. Our investigation thoroughly evaluates the influence of several critical parameters on the fluid's motion and thermal characteristics. Notably, the magnetic parameter significantly inhibits the fluid's velocity, illustrating the impact of magnetic forces. Additionally, the power law parameter leads to a decrease in both velocity and temperature profiles, highlighting its influence on fluid dynamics. Furthermore, changes in the Reynold number and the second-grade fluid parameter are observed to cause a substantial increase in skin friction, by approximately 40% to 50%. These simulation results provide valuable insights into the complex interaction between fluid flow and heat transfer characteristics, enhancing our understanding of such systems in industrial applications.