Exploration of an MHD Jeffrey six-constant fluid under the influence of a convective boundary condition

Abstract

This study investigates the magnetohydrodynamic (MHD) flow of a non-Newtonian fluid in an inclined tube, incorporating the effects of cilia-driven transport and convective boundary conditions. The governing equations are formulated considering the influence of magnetic field intensity, ciliary motion, and inclination angle. A numerical simulation is conducted to analyze the velocity and temperature profiles. The results indicate that an increase in the Hartmann number reduces the fluid velocity due to the Lorentz force, while higher values of the Weissenberg number enhance fluid elasticity, impacting flow characteristics. Homotopy perturbation method (HPM) is a semi-analytical technique for solving linear as well as nonlinear ordinary/partial differential equations. The HPM gives the approximated solution in the form of a rapidly convergent series with easily computable components. Unlike the method of separation of variables which requires both initial and boundary conditions, the HPM gives the solution by using the initial conditions only. Since after mathematically modeling our physical phenomenon converted in a highly nonlinear partial differential equation. So, for the best solutions we used this method. The inclination angle significantly affects the flow structure, leading to variations in shear stress and heat transfer rates. Quantitative results demonstrate that for a Hartmann number of five, the velocity decreases by approximately 18%, while increasing the Weissenberg number from 0.2 to 0.5 leads to a 12% rise in elasticity-driven effects. Moreover, the Nusselt number increases by 15% under higher convective boundary conditions, signifying improved heat transfer efficiency. These findings provide insight into optimizing fluid transport in biomedical and industrial applications.