The analysis on heat transmission and fluid flow characteristics within the cavity is useful to improve the features of several applications including energy storage devices and hybrid fuel cells. With this motivation, the present model investigates the characteristics of magneto-convective heat transmission and fluid flow within a square porous enclosure with hot and cold slits. The heat transfer features of electrically conducting hybrid nanofluids Fe₃O₄-MWCNT-water and Fe₃O₄-MWCNT-kerosene is analyzed inside the enclosure. The non-Fourier thermal flux model is deployed and the internal heat absorption/generation effect is considered. The Marker-And-Cell (MAC) numerical scheme is adopted to solve the transformed dimensionless mathematical model with associated initial-boundary conditions. An exhaustive parametric investigation is implemented to estimate the influence of key parameters on the transport phenomena. The computations show that augmenting the Hartmann number values modify the fluid flow and temperature features substantially for both the hybrid nanofluids. Enhancing the values of nanoparticles volume fraction promotes the heat transfer. When 5% Fe₃O₄-MWCNT nanoparticles are suspended into water and kerosene base fluids, Fe₃O₄-MWCNT-kerosene hybrid nanofluid achieves 6.85% higher mean heat transfer rate compared to Fe₃O₄-MWCNT-water hybrid nanoliquid. In the existence of heat absorption, the mean rate of heat transfer of Fe₃O₄-MWCNT-water hybrid nanofluid is 78.92% lower than Fe₃O₄-MWCNT-kerosene hybrid nanoliquid. Greater energy transmission is noticed in the case of Fe₃O₄-MWCNT-kerosene hybrid nanofluid and the enhanced fluid flow is noticed in the case of Fe₃ O₄-MWCNT-water hybrid nanofluid. Fourier's model (δ_e=0) estimates higher heat transfer rate than that of the Cattaneo-Christov (non-Fourier) heat flux model (δ_e≠0).

Inspired by the applications in electromagnetic nanomaterials processing in enclosures and hybrid fuel cell technologies, a mathematical model is presented to analyze the mixed convective flow of electrically conducting nanofluids ($\gamma$ -$\mathrm{A}{\mathrm{l}}_2{\mathrm{O}}_3-{\mathrm{H}}_2\mathrm{O}$ and $\gamma$ -$\mathrm{A}{\mathrm{l}}_2{\mathrm{O}}_3-{\mathrm{C}}_2{\mathrm{H}}_6{\mathrm{O}}_2$ ) inside a square enclosure saturated with porous medium under an inclined magnetic field. The Tiwari–Das model, along with the viscosity, thermal conductivity, and effective Prandtl number correlations, is considered in this study. The impacts of Joule heating, viscous dissipation, and internal heat absorption/generation are taken into consideration. Strongly nonlinear conservation equations, which govern the heat transfer and momentum inside the cavity with associated initial and boundary conditions, are rendered dimensionless with appropriate transformations. The marker-and-cell technique is deployed to solve the non-dimensional initial-boundary value problem. Validations with a previous study are included. A detailed parametric study is carried out to evaluate the influences of the emerging parameters on the transport phenomena. When $5\% \gamma$ -$\mathrm{A}{\mathrm{l}}_2{\mathrm{O}}_3$ nanoparticles are suspended into ${\mathrm{H}}_2\mathrm{O}$ base-fluid, the average heat transfer rate of $\gamma$ -$\mathrm{A}{\mathrm{l}}_2{\mathrm{O}}_3-{\mathrm{H}}_2\mathrm{O}$ nanoliquid is increased by $25.63\%$ compared with the case where nanoparticles are absent. When $5\% \gamma$ -$\mathrm{A}{\mathrm{l}}_2{\mathrm{O}}_3$ nanoparticles are suspended into ${\mathrm{C}}_2{\mathrm{H}}_6{\mathrm{O}}_2$ base-fluid, the average heat transfer rate of $\gamma$ -$\mathrm{A}{\mathrm{l}}_2{\mathrm{O}}_3-{\mathrm{C}}_2{\mathrm{H}}_6{\mathrm{O}}_2$ nanofluid is increased by $43.20\%$ compared with the case where nanoparticles are absent. Furthermore, when the heat source is present, the average heat transfer rate of $\gamma$ -$\mathrm{A}{\mathrm{l}}_2{\mathrm{O}}_3-{\mathrm{C}}_2{\mathrm{H}}_6{\mathrm{O}}_2$ nanofluid is $194.92\%$ higher than that in the case of $\gamma$ -$\mathrm{A}{\mathrm{l}}_2{\mathrm{O}}_3-{\mathrm{H}}_2\mathrm{O}$ nanofluid.

In this paper, we consider a generalization of Horadam sequence $\left\{w_{n}\right\} $ which is defined by the recurrence $w_{n}=aw_{n-1}+cw_{n-2},$ if $n$ is even, $w_{n}=bw_{n-1}+cw_{n-2},$ if $n$ is odd with arbitrary initial conditions $w_{0},w_{1}$ and nonzero real numbers $a,b,$ and $c.$ We investigate some congruence properties of the generalized Horadam sequence $\{ w_{n}\}$.