Effect of magnetic field on natural convection in a nanofluid-filled semi-circular enclosure with heat flux source

• I studied the effect of vertical magnetic field on nanofluid inside semi-circular cavity.
• The convection effect decreases as the magnetic field strength increases.
• The streamline tends to follow the enclosure at low values of Hartmann number.
• The strength of magnetic field affects noticeably on average Nusselt number ratio for high Rayleigh number.

In the present paper, the effect of constant magnetic field on natural convection in a semi-circular enclosure that is filled with nanofluids (copper (nanoparticles) with pure water (base fluid)) with present heat flux is investigated numerically. The heat flux (q″) is supplied partly in the center of the base wall, and the other parts of base wall of the enclosure are assumed adiabatic. The center of the circular arc (−45° ⩽ γ ⩽ +45°) is assumed at constant cold temperature (Tc) and the other parts of the circular arc are adiabatic. The gravity (g) acts normal to the y-direction and the uniform external magnetic field (Bo) is applied parallel to gravity. Finite element method based on the variational formulation is employed to solve momentum and energy balance as well as post-processing streamfunctions and heatfunctions. The results are based on visualization of heat flow via temperature lines and heatfunctions, and fluid flow via streamfunctions. Comparisons with previously published work are performed and the results are found to be in good agreement. This paper examines the influence of pertinent parameters such as Rayleigh number (104 ⩽ Ra ⩽ 107), Hartmann number (0 ⩽ Ha ⩽ 80 step 20), and solid volume fraction of nanoparticles (0 ⩽ ϕ ⩽ 0.15 step 0.05) on the flow, temperature fields and the heat transfer performance of the enclosure.The results show that the heat transfer rate increases with an increase of the Rayleigh number and the nanoparticles volume fraction but it decreases with an increase of the Hartmann number. The effect of the magnetic field on heat transfer increases with the increase of Rayleigh number and it decreases with the increase of the nanoparticles fraction effect.