Analysis of oscillatory flow and heat transfer of Maxwell fluid through a porous circular microchannel with Hall effects

Abstract

The oscillatory flow and heat transfer of a viscoelastic Maxwell fluid through a porous, rough circular microchannel are investigated in the presence of magnetohydrodynamic and Hall effects, velocity slip, and internal heat generation or absorption. The governing continuity, momentum and energy equations, coupled with the Maxwell constitutive relation, are formulated in cylindrical coordinates and non-dimensionalised. An analytical solution is obtained using the regular perturbation technique by treating wall roughness as a small parameter. Closed-form expressions for velocity and temperature are derived in terms of modified Bessel functions, and the shear stress and Nusselt number are evaluated. The results show that the magnetic parameter suppresses the axial velocity due to the Lorentz force, whereas the Hall parameter and Darcy number enhance the flow by alleviating electromagnetic and porous resistance. Velocity slip increases the near-wall velocity, while wall roughness reduces the overall flow intensity. Thermal analysis indicates that the temperature and Nusselt number increase with the heat source parameter and the Peclet number.