Lattice Boltzmann Model for the Axisymmetric Natural Convection and Heat Transfer of Nanofluids

In this paper, a lattice Boltzmann model for the natural convection and heat transfer of axisymmetric nanofluids is proposed. Three multi-relaxation time lattice Boltzmann models are constructed to solve the Navier-Stokes equations, the energy equation, and the nanoparticle volume fraction equation in the cylindrical coordinate system. Furthermore, the above models are adjusted to make it suitable for numerical simulation under the action of constant gradient magnetic field. In the results and discussion section, the axisymmetric lattice Boltzmann models of temperature field and flow field were first validated. The numerical simulation results in this paper demonstrate excellent agreement with analytical solutions and numerical data from prior references. Then the effects of Rayleigh number, nanoparticle volume fraction, and the magnetic number on isotherm, local Nusselt number, and velocity of nanofluids were analyzed by natural convection of Cu-\(\mathrm{H}_2\mathrm{O}\) nanofluids and \(\mathrm{Fe}_3\mathrm{O}_4\)-\(\mathrm{H}_2\mathrm{O}\) nanofluids. The results show that the proposed model effectively captures the evolution characteristics of temperature field, flow field, and volume fraction field during nanofluids convection.