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In the present study, a nonorthogonal multi-relaxation time (MRT) lattice Boltzmann method (LBM) was realized to numerically study the natural convective heat transfer characteristics of Al 2 O 3 -water nanofluid inside a porous corrugated triangular cavity in the presence of a magnetic field. The comparison of the nonorthogonal MRT-LB model with the orthogonal MRT-LB in simulating the natural convective heat transfer considering the magnetic field effect and the filling of porous media was presented. The effects of  Ra  (Rayleigh number),  Da  (Darcy number),  Ha  (Hartmann number),  φ  (nanoparticle volume fraction), and the  d  (structural parameter of the corrugated wall) on the natural convective heat transfer characteristics inside the corrugated triangular cavity were investigated in detail. The results showed that the nonorthogonal MRT-LB model can accurately simulate such problems and it has higher computational accuracy than the orthogonal MRT-LB in simulating the natural convective heat transfer in porous cavities under the magnetic field effect. The magnetic field has no effect on the conduction but suppresses the convection process. The increase of  Ha  number significantly weakens the heat transfer performance when the convection dominates. When  Ra  = 10 4 , the heat transfer performance weakens with increasing  d . When  Ra  = 10 5 , the heat transfer performance fluctuates with increasing  d , among the structural parameters  d  in the current study, the optimal is reached at  d  = 24 while the worst is at  d  = 72. The average Nusselt number increases with increasing the  φ  for different  Ha  numbers at  Ra  = 10 4  and  Ra  = 10 5 .

Numerical study of natural convective heat transfer of nanofluids within a porous corrugated triangular cavity in the presence of a magnetic field