Mathematical Modeling of Mixed Convective and Heat-Loss Effects on Ferrofluid Flow Through a Partially Porous Cylindrical Annulus in the Presence of an Alternating Magnetic Field

This study considers the flow of magnetite-water ferrofluid, under the effects of an alternating magnetic field, through a partially porous cylindrical annulus bounded by a heated inner cylinder and an outer melting ice boundary of finite thickness. Effects of natural and forced convection are studied, along with the consequences of heat loss to the environment on the fluid after the ice has completely melted. The described system was explored mathematically via the relevant non-linear coupled differential equations derived from the Brinkman-Darcy-Forchheimer model to describe fluid flow, as well as the conservation of energy to describe the thermal relations. The generated system of equations was solved via the finite-element method and results were simulated graphically using MATLAB R2024a. Findings showed that an increase in natural convection significantly increases the axial component of velocity but has negligible effects on the radial velocity component, temperature, and the melting of ice. The increase in forced convection significantly increases the axial velocity, temperature, and the melting rate of the cylindrical ice wall; however, it significantly decreases the radial component of velocity and the heat transfer from the heated cylindrical wall to the ferrofluid. Finally, results showed that an increase in heat loss to the surroundings reduces the axial velocity component as well as the thermal energy of the ferrofluid within the annulus, but increases the heat transfer from the heated cylindrical wall to the ferro-liquid; the effects of heat loss to the surroundings on the radial component of velocity are negligible. This study may be applicable in the field of electrical engineering, namely in cold areas where electrical current delivery may be needed.