Mixed convective flow of water-based nanofluid and melting heat transfer in a partially porous annulus

In this article, we aim to study the effects of applied heat flux, magnetoconvection and nanoparticle concentration on the magnetite-water (${\mathrm{Fe}}_3{O}_4-H_{2}O$) ferrofluid flow and melting heat transfer through a partially-porous annulus. This annular region is bounded by a heated inner cylinder and melting outer cylindrical ice wall. The flow is influenced by an alternating magnetic field generated by a current carrying wire within the inner cylinder, and the Brinkman–Forchheimer model is used to describe the ferrofluid flow through the porous region. Using the finite element method (FEM) on the coupled non-linear system of governing equations, we generate graphical results via MATLAB. The numerical algorithm developed for solving this problem is validated against published work in the literature with a maximum relative error of 5%. Results show that reductions in magnetoconvection, initial thickness of ice, nanoparticle volume fraction, or an increase in heat generated by inner cylinder increases the rate of melting of ice, with computed percentage increases of 12.7%, 72.1%, 4.7%, and 22.1% respectively. The axial velocity of the ferrofluid is decreased with an increase in magnetoconvection or increased rate of melting; however, this increases the amplitude of the radial velocity component. The cooling performance of the ferrofluid increases with increased magnetoconvection (5.2%), nanoparticle volume fraction (5.9%), and initial thickness of ice (52.1%). Based on these results the ferrofluid is more efficient at cooling the heated cylindrical wall than melting the ice.