Natural convection heat transfer characteristics of a solid/hollow body with vertical barrel-shaped surface in infinite surroundings: a numerical approach

Buoyancy-driven heat transfer from a vertical barrel-shaped solid/hollow body to air in the infinite surroundings in a turbulent regime, Rayleigh number ( \(Ra\) $\mathit{Ra}$ ) ( \({10}^{10}\le Ra\le {10}^{12}\) ${10}^{10}\le Ra\le {10}^{12}$ ) was numerically investigated. The effect of \(Ra\) $\mathit{Ra}$ , length-to-diameter ratio ( \(L/D\) $L/D$ ) ( \(2\le L/D\le 10)\) $2\le L/D\le 10)$ , and diameter ratio ( \({D}_{\text{max}}/D\) $D_{\text{max}}/D$ ) \((1.2\le {D}_{\text{max}}/D\le 1.9)\) $(1.2\le D_{\text{max}}/D\le 1.9)$ has been performed on the heat transfer to the surroundings. To investigate the impact of turbulence on the thermo-fluid dynamics around the vertical barrel-shaped body, the finite volume method has been implemented. The Reynolds-averaged Navier–Stokes (RANS) equations are employed, coupled with the \(k\) $k$ ~ \(\varepsilon \) $\epsilon$ (Standard) turbulence model. The average Nusselt number ( \(\overline{Nu })\) $\overline{\mathit{Nu}})$ increases with \(Ra\) $\mathit{Ra}$ for a solid/hollow body. The outer surface average Nusselt number \(({\overline{Nu} }_{\text{out}})\) $({\overline{\mathit{Nu}}}_{\text{out}})$ is always larger than the inner surface average Nusselt number ( \({\overline{Nu} }_{\text{in}})\) ${\overline{\mathit{Nu}}}_{\text{in}})$ , irrespective of the \(L/D\) $L/D$ ratios, and \(Ra\) $\mathit{Ra}$ . The \({\overline{Nu} }_{\text{in}}\) ${\overline{\mathit{Nu}}}_{\text{in}}$ hollow body increases up to \(L/D\approx \) $L/D\approx$ 4, thereafter decreases. However, from the outer surface \({\overline{Nu} }_{\text{out}}\) ${\overline{\mathit{Nu}}}_{\text{out}}$ up to \(L/D \approx \) $L/D\approx$ 4 decreases, thereafter remains constant for the entire range of \(L/D\) $L/D$ ratios. The \({\overline{Nu} }_{\text{in}}\) ${\overline{\mathit{Nu}}}_{\text{in}}$ of the hollow barrel-shaped body decreases with \({D}_{\text{max}}/D\) $D_{\text{max}}/D$ , irrespective of \(L/D\) $L/D$ ratios and \(Ra\) $\mathit{Ra}$ . However, the \({\overline{Nu} }_{\text{out}}\) ${\overline{\mathit{Nu}}}_{\text{out}}$ of the hollow barrel-shaped body increases up to \({D}_{\text{max}}/D\approx \) $D_{\text{max}}/D\approx$ 1.6, further increase in \({D}_{\text{max}}/D\) $D_{\text{max}}/D$ , \({\overline{Nu} }_{\text{out}}\) ${\overline{\mathit{Nu}}}_{\text{out}}$ decreases, irrespective of \(L/D\) $L/D$ ratios and \(Ra\) $\mathit{Ra}$ . The thermo-fluid dynamics have been delineated through the thermal plume, velocity vectors, and vortex generation. The present numerical analysis of heat transfer in complex geometries helps enhance the design and efficiency of thermal systems, such as heat exchangers and cooling systems. This leads to more effective and energy-efficient solutions in engineering and industrial applications. Two empirical correlations of the vertical barrel-shaped solid/hollow body have also been developed.