A new accurate solution method for steady forced convection in an unbounded flow around a circular cylinder in continuum and slip regimes

A new accurate numerical solution method for steady forced convection in an unbounded bidimensional flow around a circular cylinder is presented, addressing both the no-slip and slip regimes for Reynolds numbers and Knudsen numbers within the range 0.01 ≤ Re ≤ 47 and 0 ≤ Kn ≤ 0.1. The challenge of singular behaviour in infinite domains, which degrades numerical precision, is effectively mitigated by our new approach, unlike previous methods that truncate the flow domain. This method provides complete and correct description of the flow near the cylinder and in the far field perfectly reproducing the asymptotic solutions at large distances. We also present a new effective analytical solution for Oseen flow with slip effects, accurately representing flow at low Reynolds numbers. The validity of our numerical solution is confirmed by extensive comparisons with analytical solutions and numerical and experimental data from the literature. Additionally, we derive a new accurate correlation formula for the Nusselt number in slip flow regimes, involving both scenarios with and without temperature jump. This formula is crucial for engineering applications, especially in constant temperature hot-wire anemometry, as it avoids the requirement to correct heat transfer measurements due to slip and temperature jump effects when using very small diameter wires. • A new accurate solution method is presented for solving steady forced convection in an unbounded flow around a circular cylinder in no-slip and slip regimes. • Our approach effectively reduces the effect of singular behaviour of the solution at infinity, thus obtaining for the first time, accurate results for all flow characteristics in an unbounded domain. • This solution has the potential to describe the flow, not only near the cylinder surface but also in the far field, a region previously unexplored in earlier studies. • The validation is clearly demonstrated by the results obtained for the hydrodynamic and thermal profiles that perfectly reproduce the analytical asymptotic solutions at large distances in the wake of cylinder, and through several comparisons of the flow characteristics with numerical and experimental data from the literature. • We also provide new effective analytical solution for the Oseen flow with slip effects, offering an accurate representation of the flow, particularly for low Reynolds numbers. • We further derive a precise correlation for the Nusselt number as a function of Reynolds and Knudsen numbers, which considers both scenarios with and without temperature jump.