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ABSTRACT
This paper presents a study of entropy generation during natural convection in a triangular enclosure with various configurations (cases 1 and 2 symmetric about Y-axis, and case 3 symmetric about X-axis) for the linearly heated inclined walls. The detailed analysis and comparison for the various base angles (φ = 45° and 60°) of the triangular enclosures have been carried out for Pr = 0.015 − 1,000 and Ra = 103 − 105. The results show that, case 3 configuration with the tilt angle φ = 60° may be the optimal shape based on the minimum total entropy generation (Stotal) with the high heat transfer rate at Ra = 105, irrespective of Pr.
Nomenclature
| Be | = | Bejan number |
| g | = | acceleration due to gravity, m s−2 |
| H | = | height of the isosceles triangular cavity, m |
| k | = | thermal conductivity, W m−1 K−1 |
| n | = | normal vector to the plane |
| p | = | pressure, Pa |
| P | = | dimensionless pressure |
| Pr | = | Prandtl number |
| Ra | = | Rayleigh number |
| Sθ | = | dimensionless entropy generation due to heat transfer |
| Sψ | = | dimensionless entropy generation due to fluid friction |
| T | = | temperature of the fluid, K |
| U | = | x component of dimensionless velocity |
| V | = | y component of dimensionless velocity |
| X | = | dimensionless distance along x coordinate |
| Y | = | dimensionless distance along y coordinate |
| α | = | thermal diffusivity, m2 s−1 |
| β | = | volume expansion coefficient, K−1 |
| γ | = | penalty parameter |
| θ | = | dimensionless temperature |
| ν | = | kinematic viscosity, m2 s−1 |
| ρ | = | density, kg m−3 |
| Φ | = | basis functions |
| φ | = | base angle |
| ψ | = | dimensionless streamfunction |
| μ | = | dynamic viscosity, kg m−1 s−1 |
| Ω | = | two dimensional domain |
| subscripts | = | |
| av | = | spatial average |
| i | = | global node number |
| k | = | local node number |
| superscripts | = | |
| e | = | element |
Nomenclature
| Be | = | Bejan number |
| g | = | acceleration due to gravity, m s−2 |
| H | = | height of the isosceles triangular cavity, m |
| k | = | thermal conductivity, W m−1 K−1 |
| n | = | normal vector to the plane |
| p | = | pressure, Pa |
| P | = | dimensionless pressure |
| Pr | = | Prandtl number |
| Ra | = | Rayleigh number |
| Sθ | = | dimensionless entropy generation due to heat transfer |
| Sψ | = | dimensionless entropy generation due to fluid friction |
| T | = | temperature of the fluid, K |
| U | = | x component of dimensionless velocity |
| V | = | y component of dimensionless velocity |
| X | = | dimensionless distance along x coordinate |
| Y | = | dimensionless distance along y coordinate |
| α | = | thermal diffusivity, m2 s−1 |
| β | = | volume expansion coefficient, K−1 |
| γ | = | penalty parameter |
| θ | = | dimensionless temperature |
| ν | = | kinematic viscosity, m2 s−1 |
| ρ | = | density, kg m−3 |
| Φ | = | basis functions |
| φ | = | base angle |
| ψ | = | dimensionless streamfunction |
| μ | = | dynamic viscosity, kg m−1 s−1 |
| Ω | = | two dimensional domain |
| subscripts | = | |
| av | = | spatial average |
| i | = | global node number |
| k | = | local node number |
| superscripts | = | |
| e | = | element |