Numerical investigation of heat transfer in a power-law non-Newtonian fluid in a C-shaped cavity with magnetic field effect using finite difference lattice Boltzmann method. (English) Zbl 1410.76013
Summary: The present study aimes to investigate the natural convection heat transfer in a power-law, non-Newtonian fluid under an applied magnetic field inside a C-shaped cavity using the finite difference lattice Boltzmann method (FDLBM). Temperature distribution at the wall on the left side is non-uniform and sinusoidal with the cold wall on the right side. Both top and bottom horizontal walls of the cavity were insulated against heat and mass transfer. The Boussinesq approximation is used due to negligible density variations, making the hydrodynamic field sensitive to the thermal field. Furthermore, the D\(_2\)Q\(_9\) lattice arrangement was used for the density and energy distribution functions. This study investigates the effects of the Rayleigh number, exponential function index, aspect ratio, and the Hartmann number on the flow and temperature fields. The results show that the heat transfer rate increases with increasing Rayleigh number. Moreover, it is found that the Nusselt number decreases with increasing power-law index (\(n\)) at higher Rayleigh numbers and that an increase in the Hartmann number results in a reduced heat transfer rate. The reduction in the heat transfer rate caused by the increased Hartmann number in the shear thinning fluids is more than that in shear thickening fluids. The Nusselt number decreases with increasing cavity aspect ratio for the Newtonian and shear thinning fluids, whereas for shear thickening fluids, the Nusselt number initially increases and then decreases.
MSC:
| 76A05 | Non-Newtonian fluids |
| 76M28 | Particle methods and lattice-gas methods |
| 76M20 | Finite difference methods applied to problems in fluid mechanics |
Keywords:
power-law non-Newtonian fluid; C-shaped cavity; magnetic field; finite difference lattice Boltzmann methodReferences:
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