Entropy optimization and Joule heating in Darcy-Forchheimer fluid flow past a moving needle with variable thermal conductivity and radiation effects

Abstract

In this study, the boundary layer flow of fluid through a thin needle with thermal radiation is investigated. Magnetohydrodynamic (MHD), entropy generation, variable thermal conductivity, and viscosity are considered. By employing similarity transformation boundary layer equations are converted into non-dimensional systems. HAM is applied for solving nonlinear equations with appropriate boundary conditions. The influence of porosity parameter, variable viscosity parameter, size of the needle, thermal radiation, magnetohydrodynamic, variable thermal conductivity, velocity ratio parameter, Prandtl number, inertial parameter on temperature, Nusselt number, entropy generation, velocity, and skin friction are examined by graphical illustration. It is detected that the velocity profile declines by approximately 15% with a rise in the inertial parameter from 0.2 to 0.5, and by 12% for an upsurge in the porosity parameter from 0.1 to 0.4. Velocity and temperature profiles display a reverse relationship with magnetic parameter; for illustration, the velocity profile reduce by 10% as M rises from 0.9 to 1.5, while the temperature profile rises by 8% under the same variation. The temperature profile decreases by 20% when the Prandtl number increases from 0.7 to 3.0. A reduction in needle size parameter reduces both thermal boundary layer thickness and temperature field by approximately 18%. Intensification in Eckert number and thermal radiation parameter significantly enhances the temperature field; an increase in $Rd$ results in a 12% rise in the temperature profile. Entropy generation is enhanced by 25% when the magnetic parameter increases from 0.9 to 1.5, and by 30% for a rise in the temperature difference parameter. These results offer important new information for maximizing heat transmission and reducing energy losses in real-world applications requiring tiny needle geometries.