Surface roughness and joule heating effects on peristalsis of fractional second grade nanofluid in a converge and diverge channel with a periodic magnetic field

This study presents a comprehensive analysis of peristaltic transport in a converge and diverge channel filled with a fractional second-grade nanofluid, incorporating the effects of surface roughness, Joule heating, and a periodic magnetic field. The mathematical model is developed under the assumptions of extended wavelength and minimal Reynolds number. The dimensional equations are transformed into a non-dimensional form using appropriate scaling variables. Caputo’s fractional derivative is employed to capture the memory effects inherent in complex fluids, and analytical solutions are obtained for the resulting system. Effects of boundary conditions on flow and thermal characteristics are analyzed and presented graphically. An analytical solution is constructed applying the Homotopy Analysis Method (HAM). Higher magnetic parameter corresponds to a reduction in fluid’s velocity. Heat transfer in the system is primarily driven by Joule heating, while magnetic parameters inversely affect fluid velocity. Increasing the Hartmann number from 10 to 20 reduces axial velocity by 33.12% (converge) and 45.40% (diverge) due to Lorentz force resistance. Conversely, raising the Joule heating parameter from 0.4 to 0.6 enhances fluid temperature by 6.26% and 8.02% in converge and diverge channels, respectively. The analysis reveals that surface roughness enhances flow resistance, whereas Joule heating intensifies temperature profiles. The magnetic field significantly modifies velocity and thermal distributions, providing a comprehensive understanding of the coupled transport mechanisms in fractional second-grade nanofluids.