In this paper, we show how the design of a microdevice manifold should be tapered for uniform flow rate distribution. The designs based on the tree-branching rule of Leonardo da Vinci and the Hess–Murray rule were considered in addition to the constructal design. Both da Vinci and Hess–Murray designs are insensitive to the inlet velocity, and they provide better flow uniformity than the base (not tapered) design. However, the results of this paper uncover that not only pressure drop but also velocity distribution in the microdevice play an integral role in the flow uniformity. Therefore, an iterative approach was adopted with five degrees-of-freedom (inclined wall positions) and one constraint (constant distribution channel thickness) in order to uncover the constructal design which conforms the uniform flow rate distribution. In addition, the effect of slenderness of the microchannels (Svelteness) and inlet velocity on the flow rate distribution to the microchannels has been documented. This paper also uncovers that the design of a manifold should be designed with not only the consideration of pressure distribution but also dynamic pressure distribution especially for non-Svelte microdevices.

References

1.
Tonomura
,
O.
,
Tanaka
,
S.
,
Noda
,
M.
,
Kano
,
M.
,
Hasebe
,
S.
, and
Hashimoto
,
I.
,
2004
, “
CFD-Based Optimal Design of Manifold in Plate-Fin Microdevices
,”
Chem. Eng. J.
,
101
(
1–3
), pp.
397
402
.
2.
Lagally
,
E. T.
,
Medintz
,
I.
, and
Mathies
,
R. A.
,
2001
, “
Single-Molecule DNA Amplification and Analysis in an Integrated Microfluidic Device
,”
Anal. Chem.
,
73
(
3
), pp.
565
570
.
3.
Sanders
,
G. H. W.
, and
Manz
,
A.
,
2000
, “
Chip-Based Microsystems for Genomic and Proteomic Analysis
,”
TrAC
,
19
(
6
), pp.
364
378
.
4.
Lee
,
D.
,
Kim
,
Y. T.
,
Jee
,
J. W.
,
Kim
,
D. H.
, and
Seo
,
T. S.
,
2016
, “
An Integrated Direct Loop-Mediated Isothermal Amplification Microdevice Incorporated With an Immunochromatographic Strip for Bacteria Detection in Human Whole Blood and Milk Without Sample Preparation Step
,”
Biosens. Bioelectron.
,
79
, pp.
273
279
.
5.
Sweeney
,
J.
,
Whitney
,
C.
, and
Wilson
,
C. G.
,
2009
, “
A Plasma Spectroscopic Microdevice for On-Site Water Monitoring
,”
IEEE Sensors
, Vol.
1–3
, pp.
2005
2008
.
6.
Sanchez
,
Z.
,
Tani
,
A.
,
Suzuki
,
N.
,
Kariyama
,
R.
,
Kumon
,
H.
, and
Kimbara
,
K.
,
2013
, “
Assessment of Change in Biofilm Architecture by Nutrient Concentration Using a Multichannel Microdevice Flow System
,”
J. Biosci. Bioeng.
,
115
(
3
), pp.
326
331
.
7.
Xie
,
Y.
,
Shen
,
Z.
,
Zhang
,
D.
, and
Lan
,
J.
,
2014
, “
Thermal Performance of a Water-Cooled Microchannel Heat Sink With Grooves and Obstacles
,”
ASME J. Electron. Packag.
,
136
(
2
), p.
021001
.
8.
Wibel
,
W.
,
Schygulla
,
U.
, and
Brandner
,
J. J.
,
2011
, “
Micro Device for Liquid Cooling by Evaporation of R134a
,”
Chem. Eng. J.
,
167
(
2–3
), pp.
705
712
.
9.
Xia
,
G. D.
,
Jiang
,
J.
,
Zhai
,
Y. L.
, and
Ma
,
D. D.
,
2015
, “
Effects of Different Geometric Structures on Fluid Flow and Heat Transfer Performance in Microchannel Heat Sinks
,”
Int. J. Heat Mass Transfer
,
80
, pp.
439
447
.
10.
Bello-Ochende
,
T.
,
Liebenberg
,
L.
, and
Meyer
,
J. P.
,
2007
, “
Constructal Cooling Channels for Micro-Channel Heat Sinks
,”
Int. J. Heat Mass Transfer
,
50
(
21–22
), pp.
4141
4150
.
11.
Kosar
,
A.
, and
Peles
,
Y.
,
2005
, “
Thermal-Hydraulic Performance of MEMS-Based Pin Fin Heat Sink
,”
ASME J. Heat Transfer
,
128
(
2
), pp.
121
131
.
12.
Lee
,
Y. J.
,
Lee
,
P. S.
, and
Chou
,
S. K.
,
2013
, “
Numerical Study of Fluid Flow and Heat Transfer in the Enhanced Microchannel With Oblique Fins
,”
ASME J. Heat Transfer
,
135
(
4
), p.
041901
.
13.
Khan
,
M. G.
, and
Fartaj
,
A.
,
2011
, “
Heat Exchanger: A Review on Microchannel Heat Exchangers and Potential Applications
,”
Int. J. Energy Res.
,
35
(
7
), pp.
553
582
.
14.
Wei
,
X.
,
Joshi
,
Y.
, and
Patterson
,
M. K.
,
2007
, “
Experimental and Numerical Study of a Stacked Microchannel Heat Sink for Liquid Cooling of Microelectronic Devices
,”
ASME J. Heat Transfer
,
129
(
10
), pp.
1432
1444
.
15.
Toohey
,
K. S.
,
Sottos
,
N. R.
,
Lewis
,
J. A.
,
Moore
,
J. S.
, and
White
,
S. R.
,
2007
, “
Self-Healing Materials With Microvascular Networks
,”
Nat. Mater.
,
6
(
8
), pp.
581
585
.
16.
White
,
S. R.
,
Sottos
,
N. R.
,
Geubelle
,
P. H.
,
Moore
,
J. S.
,
Kessler
,
M. R.
,
Sriram
,
S. R.
,
Brown
,
E. N.
, and
Viswanathan
,
S.
,
2001
, “
Autonomic Healing of Polymer Composites
,”
Nature
,
409
(
6822
), pp.
794
797
.
17.
Cetkin
,
E.
,
2015
, “
Constructal Vascular Structures With High-Conductivity Inserts for Self-Cooling
,”
ASME J. Heat Transfer
,
137
(
11
), p.
111901
.
18.
Yenigun
,
O.
, and
Cetkin
,
E.
,
2016
, “
Experimental and Numerical Investigation of Constructal Vascular Channels for Self-Cooling: Parallel Channels, Tree-Shaped and Hybrid Designs
,”
Int. J. Heat Mass Transfer
,
103
, pp.
1155
1165
.
19.
Cetkin
,
E.
,
Lorente
,
S.
, and
Bejan
,
A.
,
2010
, “
Natural Constructal Emergence of Vascular Design With Turbulent Flow
,”
J. Appl. Phys.
,
107
(
11
), p.
114901
.
20.
Cetkin
,
E.
,
2014
, “
Emergence of Tapered Ducts in Vascular Designs With Laminar and Turbulent Flows
,”
J. Porous Media
,
17
(
8
), pp.
715
722
.
21.
Huang
,
C.-H.
,
Wang
,
C.-H.
, and
Kim
,
S.
,
2016
, “
A Manifold Design Problem for a Plate-Fin Microdevice to Maximize the Flow Uniformity of System
,”
Int. J. Heat Mass Transfer
,
95
, pp.
22
34
.
22.
Bejan
,
A.
,
1997
,
Advanced Engineering Thermodynamics
, 2nd ed.,
Wiley
,
New York
.
23.
Lorenzini
,
G.
,
Machado
,
B. S.
,
Isoldi
,
L. A.
,
dos Santos
,
E. D.
, and
Rocha
,
L. A. O.
,
2016
, “
Constructal Design of Rectangular Fin Intruded Into Mixed Convective Lid-Driven Cavity Flows
,”
ASME J. Heat Transfer
,
138
(
10
), p.
102501
.
24.
Bejan
,
A.
,
2015
, “
Constructal Law: Optimization as Design Evolution
,”
ASME J. Heat Transfer
,
137
(
6
), p.
061003
.
25.
Rocha
,
L. A. O.
,
Lorente
,
S.
, and
Bejan
,
A.
,
2002
, “
Constructal Design for Cooling a Disc-Shaped Area by Conduction
,”
Int. J. Heat Mass Transfer
,
45
(
8
), pp.
1643
1652
.
26.
Muzychka
,
Y. S.
,
2005
, “
Constructal Design of Forced Convection Cooled Microchannel Heat Sinks and Heat Exchangers
,”
Int. J. Heat Mass Transfer
,
48
(
15
), pp.
3119
3127
.
27.
Azoumah
,
Y.
,
Neveu
,
P.
, and
Mazet
,
N.
,
2007
, “
Optimal Design of Thermochemical Reactors Based on Constructal Approach
,”
AIChe J.
,
53
(
5
), pp.
1257
1266
.
28.
Miguel
,
A. F.
,
2006
, “
Constructal Pattern Formation in Stony Corals, Bacterial Colonies and Plant Roots Under Different Hydrodynamics Conditions
,”
J. Theor. Biol.
,
242
(
4
), pp.
954
961
.
29.
Bejan
,
A.
,
Lorente
,
S.
, and
Lee
,
J.
,
2008
, “
Unifying Constructal Theory of Tree Roots, Canopies and Forests
,”
J. Theor. Biol.
,
254
(
3
), pp.
529
540
.
30.
Lucia
,
U.
,
Ponzetto
,
A.
, and
Deisboeck
,
T. S.
,
2014
, “
A Thermo-Physical Analysis of the Proton Pump Vacuolar-ATPase: The Constructal Approach
,”
Sci. Rep.
,
4
, p.
6763
.
31.
Reis
,
A. H.
,
2006
, “
Constructal View of Scaling Laws of River Basins
,”
Geomorphology
,
78
(
3–4
), pp.
201
206
.
32.
Bejan
,
A.
,
2007
, “
Constructal Theory of Pattern Formation
,”
Hydrol. Earth Syst. Sci.
,
11
(
2
), pp.
753
768
.
33.
Bejan
,
A.
, and
Merkx
,
G. W.
,
2007
,
Constructal Theory of Social Dynamics
,
Springer
,
New York
.
34.
Lui
,
C. H.
,
Fong
,
N. K.
,
Lorente
,
S.
,
Bejan
,
A.
, and
Chow
,
W. K.
,
2012
, “
Constructal Design for Pedestrian Movement in Living Spaces: Evacuation Configurations
,”
J. Appl. Phys.
,
111
(
5
), p.
054903
.
35.
Reis
,
A. H.
,
Miguel
,
A. F.
, and
Aydin
,
M.
,
2004
, “
Constructal Theory of Flow Architectures of the Lungs
,”
Med. Phys.
,
31
(
5
), pp.
1135
1140
.
36.
Bejan
,
A.
, and
Zane
,
J. P.
,
2013
,
Design in Nature
,
Anchor Books
,
New York
.
37.
Bejan
,
A.
,
2016
,
Physics of Life
,
St. Martin's Press
,
New York
.
38.
Cetkin
,
E.
, and
Oliani
,
A.
,
2015
, “
The Natural Emergence of Asymmetric Tree-Shaped Pathways for Cooling of a Non-Uniformly Heated Domain
,”
J. Appl. Phys.
,
118
(
2
), p.
024902
.
39.
COMSOL
,
2014
, “
COMSOL Multiphysics 5.0
,” COMSOL Inc.,
Burlington, MA
.
40.
Bejan
,
A.
, and
Lorente
,
S.
,
2008
,
Design With Constructal Theory
,
Wiley
,
Hoboken, NJ
.
41.
Richter
,
J.
,
1970
,
The Notebooks of Leonardo da Vinci
,
Dover
,
New York
.
42.
Minamino
,
R.
, and
Tateno
,
M.
,
2014
, “
Tree Branching: Leonardo da Vinci`s Rule Versus Biomechanical Models
,”
PLoS One
,
9
(
4
), p.
e93535
.
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