Nanofluids have the proven capacity to significantly improve the thermal efficiency of a heat exchanging system due to the presence of conductive nanoparticles. The aim of this study is to simulate the forced convection on a non-Newtonian hybrid with a nanofluid (Al₂O₃-TiO₂-H₂O) in a hexagonal enclosure by the Galerkin finite element method (GFEM). The physical model is a hexagonal enclosure in two dimensions, containing a heated cylinder embedded at the center. The bottom, middle left, and right walls of the enclosure are all considered cold ($T_c$), while the top wall is considered to be moving, and the remaining middle, upper left, and right walls have the adiabatic condition. The Prandtl number ($Pr$ = $6.2$), Reynolds number ($Re$ = 50, 100, 300 and 500), power law index (n = $0.6$, $0.8$, $1.0$, $1.2$ and $1.4$), volume fractions of nanoparticles ($\varphi$ = $0.00$, $0.01$, $0.02$, $0.03$ and $0.04$), and Hartmann numbers ($Ha$ = 0, 10, 20 and 30) are considered in the model. The findings are explained in terms of sensitivity tests and statistical analysis for various $Re$ numbers, n, and $Ha$ numbers employing streamlines, isotherms, velocity profiles, and average Nusselt numbers. It is observed that the inclusion of $\varphi$ improves the convective heat transfer at the surging values of $Re$. However, if the augmenting heat transfer requires any control mechanism, integrating a non-zero $Ha$ number is found to stabilize the system for the purpose of thermal efficacy.

The present paper aims to study of non-Newtonian fluid flow behaviors in a two-dimensional bifurcated channel using lattice-Boltzmann method (LBM). In this LBM, well known D2Q9 model, and the single-relaxation-time (SRT) called the Lattice-BGK (Bhatnagar-Gross-Krook) approach has been adopted. In a bifurcated channel, the flow patterns are analogous to blood flows in branched arteries. Firstly, the code is validated by comparing the available published results for the Newtonian fluid flows in a channel with T-junction. The numerical results are simulated for the Reynolds number Re = 300, power-law index n = 0.5, 1.0 and 1.5, and the outlet flow rate ratio β. The effects of this relevant parameter on the streamlines, velocity distribution, recirculation zones as well as wall shear stress will be discussed to analyze the hemodynamic of blood flows near arterial bifurcations.

Unsteady natural convection flow in a two dimensional fluid saturated porous enclosure with localized heating from below with heat flux, symmetrical cooling from the sides and the insulated top wall has been investigated numerically. The governing equations are the Darcy’s law for the porous media and the energy equation for the temperature field has been considered. The non-dimensional Darcy’s law in terms of the stream function is solved by finite difference method using the successive over-relaxation (SOR) scheme and the energy equation is solved by Alternative Direction Alternative (ADI) scheme. The uniform heat flux source is located centrally at the bottom wall. The numerical results are presented in terms of the streamlines and isotherms, as well as the local and average rate of heat transfer for the wide range of the Darcy’s Rayleigh number and the length of the heat flux source at the bottom wall.