Abstract
The current analysis is carried out for the Al2O3 nanoparticles transportation through a permeable cubic geometry under the influence of the magnetic force through a hot cubic object. The physical phenomenon described in the basic equations together with the Maxwell's equations. Then D3Q19 model is sketched for the discretization of the velocity vectors for using the <inline-formula> <tex-math notation="LaTeX">3D </tex-math></inline-formula> Lattice Boltzmann Method (LBM). The impact of Brownian motion in the Al2O3-H2O nanofluids is considered by taking the Koo-Kleinstreuer model into consideration. The nanoparticles transportation under the impacts of the buoyancy and Lorentz forces, and permeability is studied with LBM. Numerical simulations are performed for different values of magnetic parameter, Darcy's and Rayleigh numbers. The validation of the applied technique is presented in <xref rid="fig3" ref-type="fig">Fig. 3 in the form of isotherms by comparing the obtained results with Calcagni et al. . For the enhancement of the heat transfer analysis a quantitative comparison of the current study is presented in <xref rid="fig4" ref-type="fig">Fig. 4 . All the results for various parameters are presented in the form of isotherms. The obtained results show the efficient conduction for higher values of <inline-formula> <tex-math notation="LaTeX">Ha </tex-math></inline-formula>. The larger values of <inline-formula> <tex-math notation="LaTeX">Da </tex-math></inline-formula> show reduction in the boundary layer thickness. The average Nusselt number <inline-formula> <tex-math notation="LaTeX">Nu_{ave} </tex-math></inline-formula> enhances with higher values of the permeability parameter. The efficiency of the implemented technique is demonstrated in <xref ref-type="table" rid="table4">Table 4 , where the Nusselt number is tabulated for distinct numbers of <inline-formula> <tex-math notation="LaTeX">Gr </tex-math></inline-formula> and <inline-formula> <tex-math notation="LaTeX">Ha </tex-math></inline-formula>, and are compared with the available literature.