A note on Leveque's solution to the Cartesian Graetz problem with free convection. (November 2022) - Rosales-Vera, Marco
Abstract: In this paper, an asymptotic analysis of the Cartesian Graetz problem with third kind boundary condition is carried out. The analysis is performed using Leveque's asymptotic method, which is valid for regions near the duct entrance. The solutions for the temperature field are improved by using second order corrections for the solution; this allows to find simple algebraic expressions for the temperature field and Nusselt number, which can be easily applied to thermal engineering problems. The results obtained considering higher order corrections show a notable improvement with respect to the precision obtained considering only first order corrections, with a percentage error with respect to the exact numerical solution that is less than 0.1% for values of the axial coordinate ξ  < 0.1.