Explicit analytical solutions of axisymmetric laminar natural convection along vertical tubes

Abstract

There are many natural convection processes in various fields, and it is still valuable to investigate the fluid dynamics and heat transfer of natural convection. The analytical solutions are meanindul in both theoretical investigation and practical applications. Specially, they can be used as the benchmark solutions to check the numerical solutions and to develop numerical differencing schemes, grid generation methods and so on. Two explicit analytical solutions of axisymmetric steady laminar natural convection along a vertical tube with porous wall and between two vertical concentric tubes are derived for better understanding of the flow and heat transfer as well as promoting the computational fluid dynamics and computational heat transfer. Supported by National Natural Science Foundation of China (Grant No. 50246003) and Major State Basic Research Development Program of China (Grant No. G20000263)