In the present study, laminar forced convective nanofluid flow over a backward-facing step was numerically investigated. The bottom wall downstream of the step was flexible, and finite element method was used to solve the governing equations. The numerical simulation was performed for a range of Reynolds number (between 25 and 250), elastic modulus of the flexible wall (between 104 and 106), and solid particle volume fraction (between 0 and 0.035). It was observed that the flexibility of the bottom wall results in the variation of the fluid flow and heat transfer characteristics for the backward-facing step problem. As the value of Reynolds number and solid particle volume fraction enhances, local and average heat transfer rates increase. At the highest value of Reynolds number, heat transfer rate is higher for the case with the wall having lowest value of elastic modulus whereas the situation is reversed for other value of Reynolds number. Average Nusselt number reduces by about 9.21% and increases by about 6.1% for the flexible wall with the lowest elastic modulus as compared to a rigid bottom wall for Reynolds number of 25 and 250. Adding nano-additives to the base fluid results in higher heat transfer enhancements. Average heat transfer rates enhance by about 35.72% and 35.32% at the highest solid particle volume fraction as compared to nanofluid with solid volume fraction of 0.01 for the case with wall at the lowest and highest elastic modulus. A polynomial type correlation for the average Nusselt number along the flexible hot wall was proposed, which is dependent on the elastic modulus and solid particle volume fraction. The results of this study are useful for many thermal engineering problems where flow separation and reattachment coupled with heat transfer occur. Control of convective heat transfer for such configurations with wall flexibility and nanoparticle inclusion to the base fluid was aimed in this study to find the effects of various pertinent parameters for heat transfer enhancement.

References

References
1.
Stuer
,
H.
,
Gyr
,
A.
, and
Kinzelbach
,
W.
,
1999
, “
Laminar Separation on a Forward Facing Step
,”
Eur. J. Mech. B
,
18
(
4
), pp.
675
692
.
2.
Abu-Mulaweh
,
H.
,
2005
, “
Turbulent Mixed Convection Flow Over a Forward-Facing Step—The Effect of Step Heights
,”
Int. J. Therm. Sci.
,
44
(
2
), pp.
155
162
.
3.
Selimefendigil
,
F.
, and
Oztop
,
H. F.
,
2014
, “
Control of Laminar Pulsating Flow and Heat Transfer in Backward-Facing Step by Using a Square Obstacle
,”
ASME J. Heat Transfer
,
136
(
8
), p.
081701
.
4.
Selimefendigil
,
F.
, and
Oztop
,
H. F.
,
2013
, “
Numerical Analysis of Laminar Pulsating Flow at a Backward Facing Step With an Upper Wall Mounted Adiabatic Thin Fin
,”
Comput. Fluids
,
88
, pp.
93
107
.
5.
Armaly
,
B. F.
,
Durst
,
F.
,
Pereier
,
J. C. F.
, and
Schonung
,
B.
,
1983
, “
Experimental and Theoretical Investigation of Backward-Facing Step Flow
,”
J. Fluid Mech.
,
127
, pp.
473
496
.
6.
Sherry
,
M.
,
LoJacono
,
D.
, and
Sheridan
,
J.
,
2010
, “
An Experimental Investigation of the Recirculation Zone Formed Downstream of a Forward Facing Step
,”
J. Wind Eng. Ind. Aerodyn.
,
98
(
12
), pp.
888
894
.
7.
Barkley
,
D.
,
Gomes
,
M. G. M.
, and
Henderson
,
R. D.
,
2002
, “
Three-Dimensional Instability in Flow Over a Backward-Facing Step
,”
J. Fluid Mech.
,
473
, pp.
167
190
.
8.
Erturk
,
E.
,
2008
, “
Numerical Solutions of 2-D Steady Incompressible Flow Over a Backward-Facing Step—Part 1: High Reynolds Number Solutions
,”
Comput. Fluids
,
37
(
6
), pp.
633
655
.
9.
Barbosa-Saldana
,
J. G.
, and
Anand
,
N. K.
,
2007
, “
Flow Over a Three-Dimensional Horizontal Forward-Facing Step
,”
Numer. Heat Transfer, Part A
,
53
(
1
), pp.
1
17
.
10.
Saldana
,
J. G. B.
,
Anand
,
N. K.
, and
Sarin
,
V.
,
2005
, “
Numerical Simulation of Mixed Convective Flow Over a Three-Dimensional Horizontal Backward Facing Step
,”
ASME J. Heat Transfer
,
127
(
9
), pp.
1027
1036
.
11.
Iwai
,
H.
,
Nakabe
,
K.
, and
Suzuki
,
K.
,
2000
, “
Flow and Heat Transfer Characteristics of Backward-Facing Step Laminar Flow in a Rectangular Duct
,”
Int. J. Heat Mass Transfer
,
43
(
3
), pp.
457
471
.
12.
Nie
,
J.
, and
Armaly
,
B.
,
2004
, “
Convection in Laminar Three-Dimensional Separated Flow
,”
Int. J. Heat Mass Transfer
,
47
(
25
), pp.
5407
5416
.
13.
Batenko
,
S. R.
, and
Terekhov
,
V. I.
,
2006
, “
Friction and Heat Transfer in a Laminar Separated Flow behind a Rectangular Step With Porous Injection or Suction
,”
J. Appl. Mech. Tech. Phys.
,
47
(
1
), pp.
12
21
.
14.
Abu-Nada
,
E.
,
Al-Sarkhi
,
A.
,
Akash
,
B.
, and
Al-Hinti
,
I.
,
2007
, “
Heat Transfer and Fluid Flow Characteristics of Separated Flows Encountered in a Backward-Facing Step Under the Effect of Suction and Blowing
,”
ASME J. Heat Transfer
,
129
(
11
), pp.
1517
1528
.
15.
Oztop
,
H. F.
,
Mushatet
,
K. S.
, and
Yılmaz
,
I.
,
2012
, “
Analysis of Turbulent Flow and Heat Transfer Over a Double Forward Facing Step With Obstacles
,”
Int. Commun. Heat Mass Transfer
,
39
(
9
), pp.
1395
1403
.
16.
Selimefendigil
,
F.
, and
Oztop
,
H. F.
,
2017
, “
Conjugate Natural Convection in a Nanofluid Filled Partitioned Horizontal Annulus Formed by Two Isothermal Cylinder Surfaces Under Magnetic Field
,”
Int. J. Heat Mass Transfer
,
108
(
Pt. A
), pp.
156
171
.
17.
Abu-Nada
,
E.
,
2008
, “
Application of Nanofluids for Heat Transfer Enhancement of Separated Flows Encountered in a Backward Facing Step
,”
Int. J. Heat Fluid Flow
,
29
(
1
), pp.
242
249
.
18.
Selimefendigil
,
F.
, and
Oztop
,
H. F.
,
2013
, “
Identification of Forced Convection in Pulsating Flow at a Backward Facing Step With a Stationary Cylinder Subjected to Nanofluid
,”
Int. Commun. Heat Mass Transfer
,
45
, pp. 111–121.
19.
Amiri
,
A.
,
Arzani
,
H. K.
,
Kazi
,
S.
,
Chew
,
B.
, and
Badarudin
,
A.
,
2016
, “
Backward-Facing Step Heat Transfer of the Turbulent Regime for Functionalized Graphene Nanoplatelets Based Water-Ethylene Glycol Nanofluids
,”
Int. J. Heat Mass Transfer
,
97
, pp.
538
546
.
20.
Mohammed
,
K. A.
,
Talib
,
A. A.
,
Nuraini
,
A.
, and
Ahmed
,
K.
,
2017
, “
Review of Forced Convection Nanofluids Through Corrugated Facing Step
,”
Renewable Sustainable Energy Rev.
,
75
, pp.
234
241
.
21.
Khanafer
,
K.
,
2014
, “
Comparison of Flow and Heat Transfer Characteristics in a Lid-Driven Cavity Between Flexible and Modified Geometry of a Heated Bottom Wall
,”
Int. J. Heat Mass Transfer
,
78
, pp.
1032
1041
.
22.
Al-Amiri
,
A.
, and
Khanafer
,
K.
,
2011
, “
Fluid-Structure Interaction Analysis of Mixed Convection Heat Transfer in a Lid-Driven Cavity With a Flexible Bottom Wall
,”
Int. J. Heat Mass Transfer
,
54
(
17–18
), pp.
3826
3836
.
23.
Selimefendigil
,
F.
,
Oztop
,
H. F.
, and
Chamkha
,
A. J.
,
2017
, “
Fluid–Structure-Magnetic Field Interaction in a Nanofluid Filled Lid-Driven Cavity With Flexible Side Wall
,”
Eur. J. Mech. B
,
61
(
Pt. 1
), pp.
77
85
.
24.
Selimefendigil
,
F.
, and
Oztop
,
H. F.
,
2017
, “
Mixed Convection in a Partially Heated Triangular Cavity Filled With Nanofluid Having a Partially Flexible Wall and Internal Heat Generation
,”
J. Taiwan Inst. Chem. Eng.
,
70
, pp.
168
178
.
25.
Ghalambaz
,
M.
,
Jamesahar
,
E.
,
Ismael
,
M. A.
, and
Chamkha
,
A. J.
,
2017
, “
Fluid-Structure Interaction Study of Natural Convection Heat Transfer Over a Flexible Oscillating Fin in a Square Cavity
,”
Int. J. Therm. Sci.
,
111
, pp.
256
273
.
26.
Chon
,
C. H.
,
Kihm
,
K. D.
,
Lee
,
S. P.
, and
Choi
,
S. U.
,
2005
, “
Empirical Correlation Finding the Role of Temperature and Particle Size for Nanofluid (Al2O3) Thermal Conductivity Enhancement
,”
Appl. Phys. Lett.
,
87
(
15
), p.
153107
.
27.
Abu-Nada
,
E.
,
2009
, “
Effects of Variable Viscosity and Thermal Conductivity of Al2O3-Water Nanofluid on Heat Transfer Enhancement in Natural Convection
,”
Int. J. Heat Fluid Flow
,
30
(
4
), pp.
679
690
.
28.
Brinkman
,
H.
,
1952
, “
The Viscosity of Concentrated Suspensions and Solutions
,”
J. Chem. Phys.
,
20
(
4
), pp.
571
581
.
29.
Mahmoudi
,
A. H.
,
Pop
,
I.
, and
Shahi
,
M.
,
2012
, “
Effect of Magnetic Field on Natural Convection in a Triangular Enclosure Filled With Nanofluid
,”
Int. J. Therm. Sci.
,
59
, pp.
126
140
.
30.
Acharya
,
S.
,
Dixit
,
G.
, and
Hou
,
Q.
,
1993
, “
Laminar Mixed Convection in a Vertical Channel With a Backstep: A Benchmark Study
,”
ASME
Winter Annual Meeting, New Orleans, LA, Nov. 28–Dec. 3, pp.
11
20
.
31.
Lin
,
J.
,
Armaly
,
B.
, and
Chen
,
T.
,
1990
, “
Mixed Convection in Buoyancy-Assisted Vertical Backward-Facing Step Flows
,”
Int. J. Heat Mass Transfer
,
33
(
10
), pp.
2121
2132
.
32.
Cochran
,
R.
,
Horstman
,
R.
,
Sun
,
Y.
, and
Emery
,
A.
,
1993
, “
Benchmark Solution for a Vertical Buoyancy-Assisted Laminar Backward-Facing Step Flow Using Finite Element, Finite Volume and Finite Difference Methods
,”
ASME
Winter Annual Meeting, New Orleans, LA, Nov. 28–Dec. 3, pp.
37
47
.
33.
El-Refaee
,
M.
,
El-Sayed
,
M.
,
Al-Najem
,
N.
, and
Megahid
,
I.
,
1996
, “
Steady-State Solutions of Buoyancy-Assisted Internal Flows Using a Fast False Implicit Transient Scheme (Fits)
,”
Int. J. Numer. Methods Heat Fluid Flow
,
6
, pp.
3
23
.
34.
Khandelwal
,
V.
,
Dhiman
,
A.
, and
Baranyi
,
L.
,
2015
, “
Laminar Flow of Non-Newtonian Shear-Thinning Fluids in a T-Channel
,”
Comput. Fluids
,
108
, pp.
79
91
.
35.
Chiang
,
T. P.
, and
Sheu
,
T. W. H.
,
1999
, “
A Numerical Revisit of Backward-Facing Step Flow Problem
,”
Phys. Fluids
,
11
(
4
), pp.
862
874
.
36.
Williams
,
P. T.
, and
Baker
,
A. J.
,
1997
, “
Numerical Simulations of Laminar Flow Over a 3D Backward-Facing Step
,”
Int. J. Numer. Methods Fluids
,
24
(
11
), pp.
1159
1183
.
You do not currently have access to this content.