Entropy generation analysis of MHD nanofluid in a corrugated vertical walls enclosure with a rectangular baffle using the Brinkmann-Forchheimer model

Copper is abundant and has good conductivity, corrosion resistance, and malleability. These properties affect the behavior of nanofluids by contributing to the interaction between nanoparticles and the magnetic field. This work aims to assess the thermal transfer characteristics of a Cu-water nanofluid filled in an enclosure having vertical wavy walls under the influence of natural convection. The system also experiences the existence of a constant inclined magnetic field and features an inner heated rectangular baffle. In this study, a comprehensive analysis is conducted on several thermo-physical parameters, including the Rayleigh number ( \({10}^{3} \le {\text{Ra}} \le {10}^{5}\) ${10}^3\le \text{Ra}\le {10}^5$ ), Hartmann number \((0 \le {\text{Ha}} \le 150),\) $(0\le \text{Ha}\le 150),$ nanoparticle concentration \((0.00 \le \phi \le 0.09),\) $(0.00\le \varphi \le 0.09),$ and porosity  \((0.2 \le \varepsilon \le 0.8)\) $(0.2\le \epsilon \le 0.8)$ . The Galerkin finite element method (GFEM) is employed in this study to conduct calculations, enabling a comprehensive analysis of streamlines, isotherms, entropy generation, and mean Nusselt numbers. The key findings demonstrate that raising the number of Rayleigh and porosity raises the velocity profile within the enclosure. For the various angles of the inner rectangular baffle \((\theta =0^\circ ,30^\circ ,60^\circ ,\mathrm{ and}\ 90^\circ )\) $(\theta =0^{\circ },{30}^{\circ },{60}^{\circ },\mathrm{and}{90}^{\circ })$ at \({\text{Ra}}={10}^{3}- {10}^{5}\) $\text{Ra}={10}^3-{10}^5$ , the calculated maximum increase in \({{\text{Nu}}}_{{\text{avg}}}\) ${\text{Nu}}_{\text{avg}}$ are  \(77.5\%, 78.3\%\) $77.5\%,78.3\%$ , \(81.9\% ,\) $81.9\%,$ and \(82.2\%,\) $82.2\%,$ respectively. Furthermore, significant rise in the value of ( \({S}_{{\text{Total}}}\) $S_{\text{Total}}$ ) up to  \(96.1\%, 11.1\%\) $96.1\%,11.1\%$ , and \(8.8\%\) $8.8\%$ is experienced when \(\left(Ra\right), \left(\phi \right),\) $\left(R,a\right),\left(\varphi \right),$ and \((\varepsilon )\) $(\epsilon )$ increase, while \(19.5\%\) $19.5\%$ decrement is observed when ( \({\text{Ha}}\) $\text{Ha}$ ) increases. Additionally, the average Bejan number \(({{\text{Be}}}_{{\text{avg}}})\) $({\text{Be}}_{\text{avg}})$ grows as the fraction volume of nanoparticle \((\phi )\) $(\varphi )$ climbs and the Hartmann number \(({\text{Ha}})\) $(\text{Ha})$ declines. The geometry configurations employed in this research have real-world applications across different engineering fields, such as energy storage, chemical processing equipment, biomedical systems, solar collectors, heat exchangers, and cooling systems for electronic devices.