Exploration of squeezing fibrous duct flow system under a periodically induced magnetic field

Magnetohydrodynamic porous duct flow systems are widely employed in engineering and bioengineering applications, such as thermal exchangers, exhaust ducts, and blood circulation devices. The current study explores the thermal and flow characteristics of a conducting fluid flow within a duct subjected to a spatially varying periodic magnetic field with a soft porous medium. The formulated partial differential equations with boundary conditions are transformed into a dimensionless form through appropriate scaling. These dimensionless equations are numerically resolved by employing the explicit central finite difference scheme in MATLAB R2024a. A graphical visualization and tabular data are provided to evaluate the effects of controlling parameters on velocity, induced magnetic field, volumetric flow rate, temperature, shear stress, and Nusselt number at the walls of the duct. The results highlight that a narrowing duct with a deforming fibrous medium diminishes the velocity magnitude, volumetric flow rate, induced magnetic field, and shear stress at the walls, while improving the rate of heat transfer by 80%. On the other hand, with the widening of the duct, the velocity magnitude, induced magnetic field, volumetric flow rate, and shear stress at the walls increase, whereas the Nusselt number is reduced by 43% in this case. Furthermore, a significant increment in the velocity and temperature maxima is observed with the enhancement of the periodically induced magnetic field within the flow system.