Free convection along a vertical cylinder with variable surface temperature

• Main Author: Tan, Guan Han
• Other Authors: Shu Jian Jun
• Format: Final Year Project
• Language: English
• Published: 2014
• Subjects: DRNTU::Engineering
• Online Access: http://hdl.handle.net/10356/60981
• Institution: Nanyang Technological University

This report gives an account of a literature study on free convection boundary layer along a heated vertical cylinder with variable surface temperature. The surface temperature is taken to be proportional to x^n, where x is the axial coordinate along the cylinder and n is a constant. The problem and governing equations was first discussed and modelled by J.J. Shu and I. Pop. Numerous studies had been made for the related problem, where none had discussed and compared the effects on a vertical cylinder with constant surface temperature and on that with variable surface temperature. This report thus serves to investigate the problem from the mentioned aspect. The governing equations were numerically computed by using the mathematical software, MATLAB. In this report, extensive reviews were done on related theories and previous related studies. A detailed analysis of the governing equations and method of solving will also be presented. The stream function, temperature function and their derivatives were then plotted and discussed intensively. Several discussions on the effect of varying parameters such as Prandtl number Pr, stretched stream wise coordinate ξ and constant n will also be made. As part of the solutions to the problem, the velocity and temperature profile were plotted with different varying parameters. In addition, the skin friction coefficient and heat transfer rate were obtained to further investigate the behaviour of heat transfer for the heat convection boundary layer. In between the presentation of solutions, discussions were made on the effect of different curvature patterns and cylinder surface temperatures have on the heat transfer behaviour. Lastly, comparisons with previous related studies were made, followed by a conclusion to discuss the applicability of the governing equations.