A Parametric Study of Laminar Natural Convection in Cubical Liquid-Filled Enclosures

................................................................................................................................................ 4 Introduction ........................................................................................................................................... 4 Literature Review ................................................................................................................................. 5 Description of the Studied Problem..................................................................................................... 8 Description of Geometry ...................................................................................................................... 9 Governing Equations .......................................................................................................................... 10 Discretization of Governing Equations ............................................................................................. 14 Evaluation of Gradients and Derivatives .......................................................................................... 20 Flowchart of Computation/Solution Algorithm ................................................................................ 22 Grid Application ................................................................................................................................. 26 Boundary Conditions .......................................................................................................................... 27 Working Fluids and Their Properties ................................................................................................ 29 Discussion—Grid Independence and Flow Patterns ........................................................................ 29 Results Images—Streamlines, Contours and Vector Plots .............................................................. 34 Conclusions ......................................................................................................................................... 45 Acknowledgements ............................................................................................................................ 45 References ........................................................................................................................................... 46 Table of Figures Figure 1--Cube Enclosure Geometry................................................................................................... 9 Figure 2—Simple 3-point grid for 1-D discretization. ..................................................................... 15 Figure 3—Variation of between x= 0 and x= L. .......................................................................... 17 Figure 4—9-point grid for 2-D discretization ................................................................................... 18 Figure 5--Flowchart of the Segregated Pressure Solver................................................................... 25 Figure 6—Screenshot of Meshed Geometry with 117649 cells ...................................................... 26 Figure 7--Diagram of Boundary Conditions ..................................................................................... 28 Figure 8—Grid Independence Graph ................................................................................................ 30 Figure 9--Example of a toroid shape. (Source: Wikipedia.org) ...................................................... 31 Figure 10--Comparison of Streamlines for Condition 2 .................................................................. 32 Figure 11--Velocity Vectors for Condition 2, 100% Glycerol, Case E ......................................... 33 Figure 12---Velocity Vector Plot of Condition 3, 100% Water, Case E ......................................... 34 Figure 13--Diagram of Results Planes .............................................................................................. 35 Figure 14—Color Legend for Table 2 ............................................................................................... 36 Figure 15—Color Legend for Table 3 ............................................................................................... 37 Figure 16—Color Legend for Table 4 ............................................................................................... 38 Figure 17—Color Legend for Table 5 ............................................................................................... 39 Figure 18—Color Legend for Table 6 ............................................................................................... 40 Figure 19—Color Legend for Table 7 ............................................................................................... 41 Figure 20—Color Legend for Table 8 ............................................................................................... 42 Figure 21—Color Legend for Table 9 ............................................................................................... 43