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 |