Irreversibility analysis of magneto-thermogravitational convection of radiative hybrid nanofluid in a U-shaped curvilinear porous container with a T-shaped baffle

In this study, we investigate the intricate dynamics of magneto-thermogravitational convection conjugated with entropy generation analysis within a U-shaped porous enclosure, enriched with the inclusion of a T-shaped cold baffle and a radiative hybrid nanofluid. Our investigation focuses on a configuration where a segment of the lower border is maintained at a warm temperature, while the rest of the border is subjected to adiabatic conditions, with the outer boundaries kept cold. Notably, we introduce a novel element to this setup: a T-shaped cooled baffle positioned at the cavity’s geometric center, introducing complexity to the U-shaped porous structure. The governing Navier–Stokes equations are effectively worked out by employing a higher-order compact technique. Rigorous validation of our in-house program against established experimental and computational benchmarks ensures the reliability of our simulations. Our analysis scrutinizes the impact of key parameters, including the Darcy number ( \(10^{-4} \le Da \le 10^{-2}\) ${10}^{-4}\le Da\le {10}^{-2}$ ), Hartmann number ( \(0 \le Ha \le 50\) $0\le Ha\le 50$ ), inclination of angle ( \(0^{0} \le \gamma \le 90^{0}\) $0^0\le \gamma \le {90}^0$ ), Rayleigh number ( \(10^{4} \le Ra \le 10^{6}\) ${10}^4\le Ra\le {10}^6$ ), volumetric heat source/sink coefficient ( \(-10 \le Q \le 10\) $-10\le Q\le 10$ ), radiation parameter ( \(1 \le Rd \le 10\) $1\le Rd\le 10$ ), length of the heater ( \(0.2 \le b \le 0.8\) $0.2\le b\le 0.8$ ) and solid volume fraction ( \(0.0 \le \phi _{\text{hnp}} \le 0.04\) $0.0\le {\varphi }_{\text{hnp}}\le 0.04$ ) of the hybrid nanofluid. Visualization of our computed results through streamlines, isotherms, \(Nu_{\text{avg}}\) $N{u}_{\text{avg}}$ , \(E_\text{T}\) $E_{\text{T}}$ and Be offers deeper insights into the heat transfer phenomena. Optimal heat transfer conditions are identified at specific parameter combinations, such as \(b=0.2\) $b=0.2$ , \(Ra=10^{6}\) $Ra={10}^6$ , \(Da=10^{-2}\) $Da={10}^{-2}$ , \(Ha=0\) $Ha=0$ , \(\gamma =90^{0}\) $\gamma ={90}^0$ , \(Rd=10\) $Rd=10$ , \(Q=-10\) $Q=-10$ and \(\phi _{\text{hnp}}=0.04\) ${\varphi }_{\text{hnp}}=0.04$ . Conversely, maximum total entropy generation occurs under different conditions, notably at \(b=0.8\) $b=0.8$ , \(Ra=10^{6}\) $Ra={10}^6$ , \(Da=10^{-2}\) $Da={10}^{-2}$ , \(Ha=0\) $Ha=0$ , \(\gamma =90^{0}\) $\gamma ={90}^0$ , \(Rd=10\) $Rd=10$ , \(Q=10\) $Q=10$ and \(\phi _{\text{hnp}}=0.0\) ${\varphi }_{\text{hnp}}=0.0$ . Our outcomes allow a deeper understanding of convective energy transport phenomena in complex porous geometries with implications for various engineering applications.