Numerical Investigation of Prandtl Number Effects on The Natural Convection Heat Transfer From Circular Cylinder in An Enclosed Enclosure

Abstract

In the present work, the natural convection heat transfer from horizontal circular cylinder situated in a square enclosure is investigated numerically. The work investigates the effect of Prandtl numbers on the flow and heat transfer characteristics. The study uses different Prandtl numbers (0.03, 0.7, 7, and 50), different Raylieh numbers (104, 105, and 106) and different enclosure width to cylinder diameter ratios W/D (1.667, 2.5 and 5). The work included the solution of the governing equations in the vorticity-stream function formulation which were transformed into body fitted coordinate system. The transformations are based initially on algebraic grid generation and elliptic grid generation to map the physical domain between the heated horizontal cylinder and the enclosure into a computational domain. The disecritization equation system are solved by using finite difference method. The code build using Fortran 90 to execute the numerical algorithm.The results were compared with previous numerical results, which showed good agreement. The effect of Prandtl number variation on the average Nusselt numbers, flow patterns and isotherms with different Raylieh numbers and enclosure width ratios were investigated. The flow patterns and temperature distributions are presented by means of streamlines and isotherms, respectively. The results show that the streamlines and isotherms for Pr=0.03 are unique and differ from those of other higher Prandtl numbers for all enclosure widths and Ra≥105. The streamlines and isotherms for Pr≥0.7 are nearly similar and independent of Prandtl number. The same behaviors as streamlines and isotherms occur with Nusselt number for lower and higher values of Prandtl numbers with all ratios of enclosure width to cylinder diameter.