The Effect of Cut-fin Array Arrangement onHeat Transfer and Friction Characteristics
Kazuya Tatsumi, Kensei Noda & Kazuyoshi Nakabe
Department of Energy Systems Engineering, Osaka Prefecture University, Osaka, Japane-mail address: tatsumi@energy.osakafu-u.ac.jp

Keywords: Densely-mounted cut-fins, fin arrangement effects, laminar flow, numerical simulation
Abstract: Notches have been applied to the densely mounted parallel fin array in order to increase the fluid mixing
and to enhance the heat transfer performance. The effects of the notch size and its arrangement have beeninvestigated from a three-dimensional numerical approach. In the first half of this paper, discussion iscarried out on the performance of the fins, which are periodically placed in both streamwise and spanwise
directions. In this case, although the heat transfer surface area is reduced, a comparable heat transfer
performance to the notch-less continuous fin case is obtained. Reduction of the friction loss is alsoachieved in this case. Therefore, consequently the overall performance is improved. In the remaining half,
performance of cut-fin arrays mounted in a channel with sidewalls is discussed. When the notches are
obliquely arranged, longitudinal vortex-like secondary flow is generated, and this enhances the fluid
mixing between the fin area and the clearance. This effectively increases the heat transfer coefficient at
the fin walls.
Typical miniature size heat exchangers and heatsinks provided today are comprised of highly dense
plate-fin arrays or micro channels using the walls as
fins. In these channels, a serious trade-off problem
takes place between the friction loss and heat transfer
coefficient especially when a clearance at the fin topedge exists (Sparrow, 1978, Matsubara, 1996, Min,2004). Therefore, development of an effective but
applicable and affordable fins or heat sinks for smaller
application is still required. In the present study, a finwith square shape notches, referred to as ‘cut-fin’, isinvestigated from a numerical approach using an FVM
based code developed by the authors. The expectedmajor effects of the cut-fin are threefold: to reduce thepressure loss penalty; to increase heat transfer rate at
the fin sidewalls by increasing the mass flow between
the fins; to enhance the mixing between the fluid
passing the fin tip clearance and the fluid in between
the fins. In the present paper, two types of channels inwhich the fins are embedded are discussed. In the firstchannel the fins are mounted periodically in the
spanwise direction, namely there is no sidewall. The
second one is a channel with sidewalls.
Figure 1 shows the computational domain for the
first channel case where the fins are attached at thechannel bottom wall periodically in the streamwise andspanwise directions. The geometric parameters changedin the present study are tabulated in Table 1. The othervalues such as the fin height Hf, fin pitch WP, fin widthw 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 Reynolds
number, that is calculated by the channel double height,
is fixed at a constant value at Re=200. As for thethermal boundary conditions, adiabatic and isothermal
conditions are respectively applied to the top andbottom walls.

HnHHfLnLWPwOz∆LxL

Fig. 1 Computational domain.
Table 1 Geometric parametersNotation
Hn/Hf
Ln/L
∆L/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
Figure 2 shows the friction factor, f and thermal
resistance, R. R is calculated as (Tw-Tin)/q where Tw,
Tin and q are the channel bottom wall temperature,bulk mean temperature of the inlet flow and theaveraged heat flux provided at the bottom wall,
respectively. Each value is normalized by the value ofthe Plain case, namely a case of simple parallel finswithout notches. f in all cases is smaller than unity
which indicates that friction loss reduction is obtainedby apply the notch to the fins. On the other hand, R is

also smaller than unity. Considering that the heattransfer surface area is also decreased in the cut-fin
cases (45% for case Cut-c), this shows that higher heattransfer efficiency is achieved by the cut-fins. Amongthe cut-fins, case O-cut shows the best performance.
This is due to the inclination of the notch array which
produces a spanwise flow. A redevelopment of thethermal boundary layer is induced at the side surface ofthe leading edge of the protruded part of the fin thatresults in an increase of the local heat transfer.
1.0

f/fp

0.6
0.4
R/Rp

0.2
0.0

Cut-a

Cut-b

Cut-c

Inline

O-Cut

R/Rp

f/fp

0.8

2.0
1.8
1.6
1.4
1.2
1.0
0.8
0.6
0.0

Fig. 2 Friction factor f and thermal resistance R.
Figure 3 shows the computational domain of thecase of the fin array inside a channel with sidewalls. In
this case, five identical fins are attached to the channelbottom wall equally spaced in the spanwise direction.
Three types of fin shape are tested here, i.e. a simple
parallel fin array without notches (Plain-5), cut-finsarranged in a parallel (Cut-P5) and oblique (Cut-O5)
forms. The fin geometry is identical to that of theaforementioned Cut-a case except that the notch pitch
and notch length are enlarged and are L/H=4.63 and
Ln/L=0.67. The phase displacement for case Cut-O5 is∆L/L=0.067. The Reynolds number is set as Re=200
which is based on the channel hydraulic diameter.
Isothermal condition is applied to the channel bottom
wall and adiabatic condition is applied to the remainingwalls.

Fig. 3 Computational domain.
Table 2 Friction factor f and thermal resistance R
R/Rp
Notation
f/fp
Cut-P50.74
0.91
Cut-O50.82
0.35
Table 2 illustrates the f and R of cases Cut-P5 andCut-O5 both normalized by the values of case Plain-5.
Same as in Fig. 2, introducing a notch reduces thepressure loss penalty compared to the plain-fin case.
For case Cut-P5, 10% reduction of R is attained eventhough the heat transfer surface area is decreases by
34%. Furthermore, R is improved by 65% for case CutO5 by slightly changing the fin arrangement.

Fig. 4 Nusselt number distributions.
Figure 4 illustrates the local Nusselt number, Nu
distribution at the fin surface. In both cases, Nu takes alarge value at the leading edge of the protruded part of
the fin due to the incoming flow from the clearance andto the redevelopment of the thermal boundary layer.
As mentioned above, the displacement of the fin’s
streamwise arrangement accompanies a considerable
spanwise flow motion. When the channel sidewall
exists, this spanwise flow develops to a secondary flow
similar to a longitudinal vortex and enhances the fluid
mixing between the notch area and the fin tip clearance.
Figure 5 displays the dimensionless temperature atseveral cross sectional planes. The black arrow roughlyshows the flow direction of the secondary flow. The
fluid of large dimensionless temperature (representedby the white area) is brought deeply into the notcheven at its leading part (third sliced plane). This results
in an increase of the heat transfer coefficient at thenotch top surfaces and especially at the leading edge ofthe protruded part of the fin as shown in Fig. 4.
Consequently, a cut-fin of an arrangement withstreamwise displacement requires a moderate increaseof the friction factor, however, produces a noticeableenhancement in the heat transfer performance.

Fig. 5 Cross sectional view of the dimensionless temperature distribution (case Cut-O5).
Matsubara, K., Nakabe, K. & Suzuki, K., 1996, A threedimensional numerical study on heat transfer characteristicsof flow in a channel with fins attached to one wall, Heat
Transfer Science and Technology, Higher Education Press,Beijing, pp. 156-161.
Min, J.Y., Jang, S.P. & Kim S.J., 2 0 0 4 ,Effect of tip clearance on the cooling performance of a microchannel heat sink, Int. J. Heat Mass Transfer, V
ol. 47, pp. 1099-1103.
Sparrow, E.M., Baliga, B.R. & Patankar, S.V., 1978 ,Forced convection heat transfer for shrouded fin array with and without tip clearance, ASME J. Heat Transfer, V
ol. 100, pp. 572-579.
The first author would like to acknowledge the Japanese
Ministry of Science and Technology and JAXA for theirsupport on this research.