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Numerical Heat Transfer, Part A: Applications
An International Journal of Computation and Methodology
Volume 69, 2016 - Issue 12
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Original Articles

Analysis of entropy generation during natural convection in tilted triangular enclosures with various base angles

, &
Pages 1332-1354 | Received 06 Aug 2015, Accepted 03 Dec 2015, Published online: 02 May 2016
 

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

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