Natural Convective Nanofluid Flows Immersed in Oscillating Magnetic Fields Simulated by a Sub-Continuous Lattice Boltzmann Model

Natural convective nanofluid flows immersed in oscillating magnetic fields are simulated with a sub-continuous nondimensional lattice Boltzmann model. The effective electrical conductivity model is built including coupled effects of nanoparticle concentrations and two Knudsen numbers. Effects of directions, frequencies, and strength amplitudes of the magnetic fields are studied in wide ranges of Hartmann numbers (0:1 ≤ Ha_f,L ≤ 600) and Rayleigh numbers (10³ ≤ Ra_f,L ≤ 10⁷). To achieve higher values of cycle averaged Nusselt numbers Nu ^c_f ,L, optimal magnetic directions are along or opposite from the gravity directions. Effects of the magnetic frequency f̃_B are negligible, in the conduction dominating lower Rayleigh number regime of Ra_f,L < 10⁴. In the convection dominating regime, Nu ^c_f ,L increase with Ra_f,L in orders of Ra⁰_f,L^:48 and Ra⁰_f,L^:45 for vertical and horizontal magnetic directions, respectively, and maximum values of Nu ^c_f,L appear at the optimal magnetic frequency of f̃_B ¼ 1=5c^∗_s Ma_LðL=U_LÞ for all magnetic directions. With Ra_f,L as high as 10⁶, the oscillating amplitudes of the transient wall mean Nusselt numbers Nu_f,L increase with increasing Ha_f ,L, but the cycle averaged Nusselt numbers Nu ^c_f,L decrease from 9.35 to 1.42 with increasing Ha_f,L in the transient regime of 5 ≤ Ha_f,L ≤ 500. Meanwhile, heat transfer patterns transit back from convection to conduction dominating patterns with increasing Ha_f ,L, as illustrated by transient streamlines and isotherms.