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Numerical Heat Transfer, Part A: Applications
An International Journal of Computation and Methodology
Volume 71, 2017 - Issue 4
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Original Articles

Role of various moving walls on entropy generation during mixed convection within entrapped porous triangular cavities

, , &
Pages 423-447 | Received 08 Aug 2016, Accepted 28 Nov 2016, Published online: 09 Mar 2017
 

ABSTRACT

The aim of the present investigation is to analyze the effect of the motion of horizontal walls on the entropy generation and heat transfer rates in an entrapped triangular porous cavity during mixed convection. Two different thermal boundary conditions are considered as follows: (i) hot inclined walls and cold horizontal walls and (ii) cold inclined walls and hot horizontal walls. Overall, Re = 100 may be recommended at Prm = 0.026, 7.2, Gr = 105, and Dam = 10−4 to 10−2 within the upper and lower cavities for cases 1 and 2.

Nomenclature

Be=

Bejan number

Dam=

modified Darcy number

g=

acceleration due to gravity, m/s2

Gr=

Grashof number

K=

medium permeability

L=

base of the triangular cavity, m

=

average Nusselt number

P=

dimensionless pressure

Pem=

modified Peclet number

Prm=

modified Prandtl number

Re=

Reynolds number

Ri=

Richardson number

Sθ, Sψ=

dimensionless entropy generation due to heat transfer and fluid friction

T=

temperature of the fluid, K

Tc, Th=

temperature of cold wall and hot wall, K

u, v=

x and y components of velocity, m/s

U, V=

x and y components of dimensionless velocity

x, y=

distances along x and y coordinates, m

X, Y=

dimensionless distances along x and y coordinates

Greek Symbols=
α=

thermal diffusivity, m2/s

β=

volume expansion coefficient, K−1

γ=

penalty parameter

θ=

dimensionless temperature

ν=

kinematic viscosity, m2/s

ρ=

density, kg/m3

Φ=

basis function

ψ=

dimensionless streamfunction

µ=

dynamic viscosity, kg/m/s

Ω=

two-dimensional domain

ϵ=

porosity of the medium

Subscripts=
av=

spatial average

b, t, l, r=

bottom, top, left, and right walls

eff, f=

effective and fluid properties

i, k=

global and local node numbers

total=

total

Superscript=
e=

element

Nomenclature

Be=

Bejan number

Dam=

modified Darcy number

g=

acceleration due to gravity, m/s2

Gr=

Grashof number

K=

medium permeability

L=

base of the triangular cavity, m

=

average Nusselt number

P=

dimensionless pressure

Pem=

modified Peclet number

Prm=

modified Prandtl number

Re=

Reynolds number

Ri=

Richardson number

Sθ, Sψ=

dimensionless entropy generation due to heat transfer and fluid friction

T=

temperature of the fluid, K

Tc, Th=

temperature of cold wall and hot wall, K

u, v=

x and y components of velocity, m/s

U, V=

x and y components of dimensionless velocity

x, y=

distances along x and y coordinates, m

X, Y=

dimensionless distances along x and y coordinates

Greek Symbols=
α=

thermal diffusivity, m2/s

β=

volume expansion coefficient, K−1

γ=

penalty parameter

θ=

dimensionless temperature

ν=

kinematic viscosity, m2/s

ρ=

density, kg/m3

Φ=

basis function

ψ=

dimensionless streamfunction

µ=

dynamic viscosity, kg/m/s

Ω=

two-dimensional domain

ϵ=

porosity of the medium

Subscripts=
av=

spatial average

b, t, l, r=

bottom, top, left, and right walls

eff, f=

effective and fluid properties

i, k=

global and local node numbers

total=

total

Superscript=
e=

element

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