Effects of partial slip on entropy generation and MHD combined
convection in a lid-driven porous enclosure saturated with a Cu–water
nanofluid
A. J. Chamkha
1,2
·
A. M. Rashad
3
·
T. Armaghani
4
·
M. A. Mansour
5
Received: 24 August 2017 / Accepted: 9 December 2017 / Published online: 22 December 2017
© Akadémiai Kiadó, Budapest, Hungary 2017
Abstract
In this work, the influences of heat generation/absorption and nanofluid volume fraction on the entropy generation and
MHD combined convection heat transfer in a porous enclosure filled with a Cu–water nanofluid are studied numerically
with of partial slip effect. The finite volume technique is utilized to solve the dimensionless equations governing the
problem. A comparison with already published studies is conducted, and the data are found to be in an excellent agreement.
The minimization of entropy generation and the local heat transfer according to various values of the controlling
parameters are reported in detail. The outcome indicates that an augmentation in the heat generation/absorption parameter
decreases the Nusselt number. Also, when the volume fraction is raised, the Nusselt number and entropy generation are
reduced. The impact of Hartmann number on heat transfer and the Richardson number on the entropy generation and the
thermal rendering criteria are also presented and discussed.
Keywords Heat generation/absorption · Entropy generation · Nanofluid · Partial slip · Nusselt number
List of symbols
B Dimensionless of heat source/sink length
B
0
Magnetic field strength (T)
Be Bejan number
b Length of heat source (m)
C
p Specific heat at constant pressure ðJ kg K
1
Þ
D Dimensionless heat source position
Da Darcy number
d Location of heat sink and source (m)
H Length of cavity (m)
Ha
Hartmann number, B
0
L
ffiffiffiffiffiffiffiffiffiffiffiffiffiffi
r
f
=q
f
m
f
p
Gr Grashof number, gb
f
H
3
DT =t
2
f
g Acceleration due to gravity (m s
-2
)
K Permeability of porous medium (m
2
)
k Thermal conductivity (W m
-1
K
-1
)
Nu Local Nusselt number
Nu
m
Average Nusselt number of heat source
p Fluid pressure (Pa)
P Dimensionless pressure, pH=q
nf
a
2
f
Pr Prandtl number, t
f
=a
f
Re Reynolds number, V
0
H=t
f
S Entropy generation (W K
-1
m
-3
)
T Temperature (K)
T
c
Cold wall temperature (K)
T
h
Heated wall temperature (K)
u,v Velocity components in x, y directions (m s
-1
)
U; V Dimensionless velocity components, u/V
0
, v/V
0
x; y Cartesian coordinates (m)
X; Y Dimensionless coordinates, x/L, y/L
Greek symbols
a Thermal diffusivity, m
2
s
1
; k=qc
p
b Thermal expansion coefficient, K
-1
& T. Armaghani
armaghani.taher@yahoo.com
1
Mechanical Engineering Department, Prince Sultan
Endowment for Energy and Environment Prince Mohammad
Bin Fahd University, Al-Khobar 31952, Kingdom of Saudi
Arabia
2
Rak Research and Innovation Center, American University of
Ras Al Khaimah, Ras Al Khaimah, United Arab Emirates
3
Department of Mathematics, Faculty of Science, Aswan
University, Aswa ˆn 81528, Egypt
4
Department of Engineering, Mahdishahr Branch, Islamic
Azad University, Mahdishahr, Iran
5
Department of Mathematics, Faculty of Science, Assuit
University, Assuit, Egypt
123
Journal of Thermal Analysis and Calorimetry (2018) 132:1291–1306
https://doi.org/10.1007/s10973-017-6918-8