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.

This paper proposes a mathematical model for nanoparticle deposition in the respiratory bronchiole of the human lung airways. The length of the respiratory bronchiole of the human lung is 1.2 mm, and the diameter is 0.5 mm. Therefore, to investigate the impact of inhaled nanoparticles within the lung bronchioles, first, we used the Navier–Stokes equation by including the Darcy term together with Newton’s equation of motion. Then we non-dimensionalized the governing equation, and numerical solutions are obtained using the finite difference technique. Under the assumption of laminar pulsatile flow conditions and axial symmetry, the problem is simplified to a two-dimensional computational domain. The computational framework is implemented using MATLAB R2018 through user-defined code. Velocity propagation, the Reynolds number, and the Darcy number effect are performed to examine the flow conditions inside the respiratory bronchioles.

Emphysema is a chronic lung condition characterized by the destruction of alveolar walls, leading to abnormal air trapping and reduced airflow. This study presents a numerical simulation of airflow dynamics in emphysemic lungs using a porous media approach to model deformed lung structure. The governing equations for air and particle transport were solved using a finite difference scheme under pulsatile flow conditions. We solve these equations using the finite difference method in MATLAB. Key flow parameters such as Reynolds number, porosity, and particle drag were varied to analyze their impact on airflow and dust movement. Simulation results show that both air and dust particle velocities increase with Reynolds number due to reduced viscous resistance and stronger inertial effects, even within a low-Re regime. The porous medium model effectively captures the impaired ventilation and altered flow distribution observed in emphysematous lungs. This work contributes to better understanding of airflow mechanics in diseased lung tissue and can aid future research in drug delivery or particle deposition in respiratory disorders.

Hybrid nanofluids possess exceptional thermal conductivity, but one of the major concerns with nanoparticles is agglomeration. While the usage of surfactants or dispersants can be used to mitigate this issue, numerical investigation and sensitivity analyses can be more affordable when attempting to optimize and design a thermal device. The consideration of thermal radiation with conductive and convective heat transfer and appropriate nanoparticles may provide a greater solution without compromising the efficacy of hybrid nanofluids. In the present work, the concept of magnetohydrodynamics (MHD) is used to examine the impact of thermal radiation on a stable, two-dimensional, incompressible hybrid fluid consisting of nanoparticles (MWNCT)${\mathrm{-Fe}}_3{\mathrm{O}}_4$ and water flowing over a vertical surface. The flow is governed by established equations of fluid dynamics, which use the Rosseland diffusion model to incorporate radiation effects. The implicit finite difference (IFD) was used to solve the mathematical equations. Sensitivity analyses were conducted as functions of volume fraction, radiation and magnetic variables. This study also examines the streamlines and isotherm lines with respect to the volume fraction, radiation parameter and magnetic parameter of the heat source. The results indicate that for a fixed radiation parameter, increasing the nanoparticle volume fraction by up to $20\%$ leads to a reduction of approximately $37\%$ in the skin friction coefficient, while the corresponding Nusselt number increases by nearly $50\%$. Furthermore, the introduction of a magnetic field parameter significantly suppresses wall shear stress and modifies the thermal boundary layer thickness, demonstrating the competing interaction between Lorentz-force-induced momentum damping and radiation-enhanced thermal diffusion. These quantified trends highlight the sensitivity of coupled momentum and heat transport to combined magnetic and radiative effects in hybrid nanofluid systems.