GS5-13
Paper No.

Proceedings
ofthe
theProceeding of
1stInternational
International Forum
Forum onon HeatHeatTransfer
Transfer
1stNovember
Kyoto, JapanJapan
November24-26,24-26, 2004,2004, Kyoto,

NUMERICAL STUDY ON HEAT TRANSFER CHARACTERISTICS OFA CHANNEL WITH DENSELY-MOUNTED CUT-FINS
Kazuya Tatsumi*, Kensei Noda* and Kazuyoshi Nakabe** Osaka Prefecture University, Sakai, Osaka 599-8531, Japan
E-mail : tatsumi@energy.osakafu-u.ac.jp
Keywords : Cut-fin, Heat sinks, Heat exchangers, Laminar flow, Numerical simulation
ABSTRACTThe present study reports the results of the three-dimensional
numerical simulation on heat transfer characteristics of a channel
having densely-mounted ‘cut-fins’. The effects of the length, depth
and geometrical phase shift of the notch of the fins on heat transfer
and friction loss have been examined. From the results, it is shownthat by applying a notch to the fin, both friction factor and thermal
resistance decreases compared to a continuous plain-fin. Thistendency appears more clearly for larger notch length and depth.
Furthermore, higher heat transfer performance is obtained for thecut-fins with obliquely arranged notches due to the induced
secondary flow motion.
1. INTRODUCTION
Micro fin array is an effective cooling technique and is widelyused in various small applications such as compact heat exchangers
and electronic devise cooling. In such micro fin arrays, high heattransfer coefficient is available, whereas unfavorable pressure loss
takes place. On the other hand, when a clearance exists between thefin top edge and the channel top wall, improvement of the pressure
loss is obtained at the cost of a considerable decrease of the heattransfer coefficient at the fin sidewalls due to the reduction of themass flow rate in those areas. Thus, a serious trade-off problem
takes place (Sparrow, 1978, Matsubara, 1996, Min, 2004).
Considering this background, a fin with square shape notches,
referred to as ‘cut-fin’, is proposed and investigated in the present
study from a three-dimensional numerical approach. The expected
effectiveness of the cut-fin is threefold: to reduce the pressure loss
penalty; to increase heat transfer rate at the fin sidewalls byincreasing the mass flow in between the fins; to enhance the mixing
between the fluid passing the fin tip clearance and the fluid in
between the fins.
2. COMPUTATIONAL PROCEDURE
2.1 Numerical conditions
The computational domain is illustrated in Fig. 1. Periodical
boundary conditions are applied in the streamwise and spanwise
boundaries representing a continuous fin arrangement. Constant heat
flux condition and adiabatic wall condition are applied at thechannel bottom and top walls, respectively. At the fin surface,harmonic mean value of the fluid and solid thermal conductivity isused to solve the heat flux at the interface. The working fluid is air
and the material of the fin is stainless steel.
In the present computation, the fin height Hf, fin pitch WP, finwidth w and notch pitch L are kept constant, i.e. Hf/H=0.75,
WP/H=0.075, w/H=0.025, L/H=3.125. The notch length Ln and__depth Hn, streamwise geometrical phase shift ǻL are varied whose
actual values are tabularized in Table 1. The Reynolds number,which is based on the channel hydraulic diameter and thestreamwise mean velocity, is fixed at a constant value as Re=200.

HnHHfLnLWPw
Oz'L

xLFig. 1 Computational domain.
2.2 Numerical method
The governing equations solved in the present computation are
three-dimensional, incompressible, time-dependent continuous,
Navier-Stokes and energy equations. The present numerical method
is based on Finite Volume Method. The Navier-Stokes equation is
discretized by applying the 5th-order upwind scheme and 4th-order
central-difference scheme to the convection and diffusion terms,respectively. Fully implicit method is adopted for the temporal
discretization and SIMPLE is used to solve the pressure correction.
Table 1 Geometric parameters
Notation
Hn/HfLn/L
ǻL/L
Plain
Cut-a
0.5
0.6
0
Cut-b
0.5
0.32
0
Cut-c
0.75
0.60Inline
1.0
0.6
0O-Cut0.5
0.6
0.1
3. RESULTS AND DISCUSSION
Figure 2 shows the friction factor f and the thermal resistance R.
R is calculated as (Tw  Tin ) / q where Tw , Tin and q are theaveraged channel bottom wall temperature, bulk mean temperatureof the inlet flow and the heat flux provided at the bottom wall,respectively. Both values are normalized by the value of the Plaincase, a fin without notches. In all cases, f/fp is smaller than unity
which indicates that adding a notch to the fin reduces the pressureloss. Comparing cases Cut-a~c, we can see that larger pressure loss
reduction is attained by increasing the notch length Ln, and also that

237 __

Proceeding of the
1st International Forum on Heat Transfer
November 24-26, 2004, Kyoto, Japan

Paper No.

the effect of the notch depth Hn is virtually negligible. For O-Cutcase, f/fp shows a much smaller value compared to the other cases.
This is due to the fact that large amount of flow passes in theoblique direction along the notch.
For the Inline case, in which the notch depth and fin height areequal, a much larger R is obtained compared to the other cases. Thisis ascribable to the salient increase of the fluid temperature observedin the area where no fin exists. On the other hand, only a small
difference is found in R for cases Cut-a~c. This indicates that theinfluence of the notch length and depth on R is small within theexamined cases and that equal heat transfer performance is obtainedin spite of the reduced heat transfer area for the cut-fins compared tothe Plain case.
㪈㪅㪇2.4

㪇㪅㪏

2.2

f/fp

2.0
1.0

㪇㪅㪋

R/RP

㪇㪅㪉

W/U m

10.5

R/Rp

f/fp

㪇㪅㪍

the same manner as Fig. 3 on which the contour maps of thespanwise velocity W at z/WP=0.5 is superimposed. A strong
spanwise flow motion exists inside the notch and no circulation isgenerated. This spanwise flow produces flow impingement andredevelopment of the thermal boundary layer at the leading andtrailing edges of the fin entailing an increase of the heat transfer
coefficient. Since the Reynolds number is based on the streamwise
velocity without considering the spanwise flow, the total mass flowrate is not identical between case O-Cut and the other cases. Thus,
direct comparison is difficult. However, from Figs. 2 and 4, it isbelieved that better heat transfer and pressure loss performances canbe obtained by the O-Cut case.

00.8

00.2

0.4

x/L

0.6

0.8

1W
0.8
0.8
0.685714
0.571429
0.457143
0.342857
0.228571
0.114286
0 0.0-0.114286-0.228571-0.342857-0.457143-0.571429-0.685714
-0.8
-0.8

Fig. 4 Fluid-particle tracking lines and spanwise velocity contours ofcase O-Cut.

0.6

㪇㪅㪇
Cut-a

Cut-b

Cut-c

InlineO-Cut

REFERENCES
Sparrow, E.M., Baliga, B.R., and Patankar, S.V., Forced
convection heat transfer for shrouded fin array with and without tip
clearance, ASME J. Heat Transfer, vol. 100, pp. 572-579, 1978.
Matsubara, K., Nakabe, K., and Suzuki, K., A three-dimensional
numerical study on heat transfer characteristics of flow in a channel
with fins attached to one wall, Heat Transfer Science andTechnology, Higher Education Press, Beijing, pp. 156-161, 1996.
Min, J.Y., Jang, S.P., and Kim S.J., Effect of tip clearance on thecooling performance of a microchannel heat sink, Int. J. Heat Mass
Transfer, vol. 47, pp. 1099-1103, 2004.

Fig. 2 Friction factor and thermal resistance.
10.5
000.2

0.4x/L

0.6

0.8

1(a) Case Cut-a1K. Tatsumi received M.E. (1999) and PhD(2003) in Kyoto Univ. Dept. Mech. Eng. He
is now a Research Assistant of Dept. ofEnergy Systems Eng., Osaka Prefecture
Univ. His current interests include Compact
heat exchangers, hydrogen fuel reformer andMicro energy supply systems.

0.5
000.2

0.4x/L

0.60.81(b) Case Inline
Fig. 3 Fluid-particle tracking lines.
Figure 3 shows the side-view of the fluid-particle tracking linesof cases Cut-a and Inline. The initial locations of the tracking lines
are z/W=1.0 at the domain inlet boundary. A circulation is formed inthe region of 0.2x/L0.8 and upward and downward flows areobserved at x/L=0.3 and x/L=0.8, respectively. For case Inline, asmentioned before, the existence of this circulation and the lack of
the fin in this area incur a temperature increase and impair the heattransfer performance at the bottom wall. At the downstream side of
the notch, the downwash flow induces the fluid located at the upperside of the channel into the space between the fins. Although notshown here, the mass flow rate in between the fins increased by therate of 2~5 time larger than the Plain case. Thus, thermal boundary
layer is redeveloped and large heat transfer coefficient is obtained inthis area, which is the reason why the cut fin case provides high heattransfer performance.
Figure 4 shows the fluid-particle tracking lines of case O-Cut in__K. Noda received the B.E. (2002) and M.E.
(2004) in Osaka Prefecture Univ.
He is currently working at Toshibaindustrial and power systems & services
company.

K. Nakabe received M.E. (1983) in Kyoto
Univ. Dept. Mech. Eng and PhD (1991) inOsaka University. He is now Prof. of Dept.
of energy Systems Eng., Osaka Prefecture
Univ. His current interests are in the fieldsof turbulent mixing, micro mixer, heattransfer and combustion.

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