Flow and Heat Transfer Characteristics of Forced Convection Past an Isoflux Circular Cylinder in Galinstan for Reynolds Numbers up to 600

A numerical investigation of steady forced convection heat transfer from an isoflux circular cylinder immersed in the liquid metal Galinstan is presented. The governing streamfunction, vorticity, and energy equations are solved using a fourth-order compact finite difference scheme in cylindrical coordinates (FOCS–CC) coupled with a stable pseudo-time iteration (PTI) technique. The influence of the Reynolds number ($1\le Re\le 600$) on the flow and heat transfer characteristics is systematically investigated for Galinstan with a Prandtl number of $Pr=0.025$. The performance and accuracy of the proposed scheme are first established through grid independence studies and validation against previously published numerical results for the average Nusselt number and total drag coefficient over a range of Reynolds numbers. Excellent agreement with the available literature confirms the reliability and robustness of the present formulation. The effects of Reynolds number ($1\le Re\le 600$) on the flow and thermal fields are examined through streamline patterns, isotherm distributions, and local Nusselt number variations. The results reveal that increasing the Reynolds number promotes flow separation, enlarges the wake region, intensifies downstream thermal transport, and significantly enhances convective heat transfer from the cylinder surface. Furthermore, a new empirical correlation for the average Nusselt number is proposed for Galinstan fluid over the Reynolds number range $1\le Re\le 600$, exhibiting excellent agreement with the numerical data with a coefficient of determination of $R^2=0.99939$.