A study of natural convection from a vertical cylinder with variable surface temperature - Shastri Kunal Krishnaraj (2015)
Convective heat and mass transfer is one of the most important topics of study in physics and engineering. Specifically, natural or free convection mode of heat transfer, driven by fluid density variation in the presence of an external force field such as gravitational or magnetic, dominates numerous natural and industrial heat transfer phenomena. This report serves to present the results of a research undertaken to theoretically study the natural convection flow around of a heated vertical cylinder. Recognising the various technological applications, the surface temperature of the cylinder in this study was defined to be proportional to a power function of the distance from the base of the cylinder ($x^n$). The governing equations for the problem were derived from the Navier-Stokes and energy balance equation and simplified using the Boussinesq and boundary layer approximations. These partial differential equations were then numerically solved by implementing a finite difference scheme based on the Keller box discretisation. The program code was written in Mathematica, and results were calculated for various values of $Pr$ (Prandtl number) and $n$ (surface temperature power). The results were analysed and some recommendations made based on the experience.