Investigation of MHD effect on nanofluid heat transfer in microchannels: an incompressible lattice Boltzmann approach

An incompressible preconditioned lattice Boltzmann method (IPLBM) is proposed to investigate the fluid flow and heat transfer characteristics of nanofluid in microchannel with hydrophilic or superhydrophobic walls and partially under the influence of transverse magnetic field as well as a heat flux. The modified IPLBM is shown to overcome the velocity inaccuracy in developing regime under partial magnetic field with respect to standard LBM. Then, the method is utilized to resolve the velocity and temperature fields at Re = 100 and various volume fractions of nanoparticles (0 ≤ φ ≤ 0.2%), Hartmann numbers (0 ≤ Ha ≤ 30) and slip coefficients (0 ≤ B ≤ 0.1). Superhydrophobic walls are shown to reduce the wall shear stress at B = 0.1 of up to 38.4, 58.5 and 70%, respectively, for Ha = 0, 15 and 30. Ignoring the temperature jump in modeling overestimates the Nusselt number with an error that culminates at B = 0.1 and φ = 0.2% to 19.6, 22.7 and 25%, respectively, for Ha = 0, 15 and 30. It is concluded that with magnetic field presence and realistic temperature jump, the surface material of superhydrophobic walls should be chosen properly to avoid inevitable and uncontrolled reduction in heat transfer, such that the highest hydrophobicity is not always the best choice. Reasonable agreements are achieved by comparing our results with credible analytic and numerical solutions and also with an experimental study.