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ABSTRACT
In part I of this paper, a new physical-based computational approach for the solution of convection heat transfer problems on co-located non-orthogonal grids in the context of an element-based finite volume method was discussed. The test problems are presented here, in part II of the paper. These problems include five steady two-dimensional convection heat transfer problems. In all test cases, the convergence history, the required under-relaxations for the iterative solution of the linearized equations, and the order of accuracy of the method are discussed and the streamlines as well as isotherms are presented. The computational results show that the proposed method is second order accurate and might occasionally need mild under-relaxation in relatively complex problems. Excellent match between the computational results and the corresponding reliable published results is observed.
Nomenclature
| g | = | gravitational acceleration |
| = | Grashof number | |
| H | = | grid size, heat transfer coefficient |
| K | = | conductivity |
| L | = | length |
| N | = | number of nodes |
| N | = | normal direction |
| Nu | = | Nusselt number |
| P | = | dimensionless pressure |
| P | = | pressure |
| = | Peclet number | |
| = | Prandtl number | |
| Q | = | heat flux |
| r | = | radius |
| = | Rayleigh number | |
| = | Reynolds number | |
| Res | = | residual |
| = | Richardson number | |
| T | = | temperature |
| U, V | = | dimensionless velocity components |
| u, v | = | velocity components |
| X, Y | = | dimensionless Cartesian coordinates |
| x, y | = | Cartesian coordinates |
| Greek symbols | = | |
| ω | = | angular velocity |
| Θ | = | dimensionless temperature |
| η | = | aspect ratio |
| ϕ | = | a general scalar variable |
| Subscripts | = | |
| 0 | = | reference value |
| C | = | cold |
| F | = | fluid |
| H | = | hot |
| I | = | inner |
| max | = | maximum |
| o | = | outer |
| rms | = | root mean square |
| u | = | up |
| w | = | wall |
| Superscripts | = | |
| Num | = | numerical |
Nomenclature
| g | = | gravitational acceleration |
| = | Grashof number | |
| H | = | grid size, heat transfer coefficient |
| K | = | conductivity |
| L | = | length |
| N | = | number of nodes |
| N | = | normal direction |
| Nu | = | Nusselt number |
| P | = | dimensionless pressure |
| P | = | pressure |
| = | Peclet number | |
| = | Prandtl number | |
| Q | = | heat flux |
| r | = | radius |
| = | Rayleigh number | |
| = | Reynolds number | |
| Res | = | residual |
| = | Richardson number | |
| T | = | temperature |
| U, V | = | dimensionless velocity components |
| u, v | = | velocity components |
| X, Y | = | dimensionless Cartesian coordinates |
| x, y | = | Cartesian coordinates |
| Greek symbols | = | |
| ω | = | angular velocity |
| Θ | = | dimensionless temperature |
| η | = | aspect ratio |
| ϕ | = | a general scalar variable |
| Subscripts | = | |
| 0 | = | reference value |
| C | = | cold |
| F | = | fluid |
| H | = | hot |
| I | = | inner |
| max | = | maximum |
| o | = | outer |
| rms | = | root mean square |
| u | = | up |
| w | = | wall |
| Superscripts | = | |
| Num | = | numerical |