The significance of fluid flow under hydrothermal conditions within a hexagonal enclosure spans across numerous fields, underlining its broad applicability. However, our understanding of the free convection flow in these geometries is still limited despite its potential importance in science and technology. Therefore, this study numerically examines the heat convection and entropy generation within a porous hexagonal cavity containing a heated obstacle while subjected to a static magnetic field of intensity B ₀ . Micropolar hybrid nanofluid, composed of TiO ₂ and graphene oxide nanoparticles, was used to fill the hexagonal cavity with water as the base fluid. The finite difference method is associated with successive over-relaxation, successive relaxation, and Gauss–Seidel techniques, which are used to solve the dimensionless governing partial differential equations. The desired outcomes are computed using in-house developed MATLAB codes. A specific result from prior research findings is used to validate the accuracy of these MATLAB codes. The outcomes demonstrate that an upsurge in Ra from 10 ⁴ to 10 ⁶ and ϕ hnf {\phi }_{{\rm{hnf}}} from 0 to 4% leads to an enhancement in Nu _ABW to 53.05 and 3.14%, respectively. However, Nu _ABW diminishes by approximately 0.797 and 4.135% as Ha increases from 0 to 20 and K ₀ increases from 2 to 7.5, respectively. The average Bejan number (Be _avg ) consistently decreases as Ra increases, but Be _avg improves as Ha, vortex viscosity parameter ( K ₀ ), and ϕ hnf {\phi }_{{\rm{hnf}}} increase. The most important finding of the work is that the position of the heated obstacle significantly influences both the heat convection and entropy generation processes.

In the current research, the influence of a sinusoidal heat flux and a heated rectangular cavity in a partially porous Casson hybrid nanofluid-filled square enclosure being affected by a constant magnetic field imposed in the x -direction having magnitude B ₀ , on natural convection were investigated numerically. A rectangular heated cavity having width H /5 and height H /2 was positioned in the middle of the square enclosure. The sinusoidal heat flux of length H /2 is positioned centrally at the enclosure’s bottom wall, although the top wall is at a lower temperature, say T _c, and the rest of the enclosure was insulated. The finite-difference method, combined with the successive over relaxation, successive under relaxation, and Gauss–Siedel techniques, is employed to address the challenge of solving the nonlinear coupled governing partial differential equations of motion and energy. Numerical calculations were carried out using the values of the relevant parameters in the range 0 ≤ \le Ha ≤ \le 15, 10 ⁴ ≤ \le \hspace{1em} Ra ≤ \le 10 ⁶ , 0.00 ≤ ϕ hnf ≤ 0.04 0.00\le {{\rm{\phi }}}_{{\rm{hnf}}}\le 0.04 , 10 ⁻⁵ ≤ Da \le {\rm{Da}} ≤ \le 10 ⁻³ , 0.1 ≤ \le γ \gamma ≤ \le 1, 4 ≤ \le N ≤ \le 12. The Kirpichev heat number ( K i = 1 {K}_{i}=1 ) and Prandtl number (Pr = 6.26) are fixed throughout the study. Contour plots for isotherms and streamlines were plotted to ascertain the impacts of distinct factors on them. The results of this investigation suggest that the heat transfer rate rises as ϕ hnf {{\rm{\phi }}}_{{\rm{hnf}}} , Ra, and γ \gamma rise and reduce as the Ha and N rises. Finally, it has been observed that decreasing the heated rectangular cavity’s aspect ratio leads to a substantial enhancement in heat transfer from both the heat flux and the heated rectangular cavity.

Numerical investigation of free convection in a micropolar Ag-Al2O3/water hybrid nanofluid filled square cavity with thermal and radiative flux on vertical thic

Marangoni convection is relevant in controlling the heat transfer between surfaces in modern microfluidic and thermal systems. Therefore, this work seeks to elucidate the role of Marangoni-induced convection in the flow and thermal behavior of a micropolar nanofluid within a square enclosure exposed to an oblique static magnetic field. Thermal regulation occurs through partly heated and cooled sections of the vertical walls, whereas the remaining walls are adiabatic. The discretized algebraic equations are obtained through finite-differences and solved iteratively by applying over- and under-relaxation techniques with a tolerance error of 10 ^–7 . The influences of pertinent parameters on flow and thermal regulation are computed and analyzed through graphs. The findings demonstrate that Nu _av upsurges with a rise in Ra and φ but is suppressed with a rise in Ha. Increasing Cu-nanoparticles concentration up to 4%, the Nu _av rises by 11.7037%, 11.8758%, 12.14%, 12.0991%, 12.043%, and 11.9836% for Ma = 0, 200, 400, 600, 800, and 1000, respectively. Also, rising in ‘Ha’ from 0 to 20 reduces Nu _av by 18.43% at Ra = 10 ⁵ but by only 4.46% at Ra = 10 ³ , showing that Lorentz forces become more influential under stronger buoyancy. Furthermore, an upsurge in vortex viscosity from 0.5 to 5 leads to a decline in Nu _av by 36.67%. These findings indicate that heat transfer can be efficiently controlled with changes in the Marangoni number, nanoparticles concentration, and magnetic field direction.