HTE-15

HEAT TRANSFER AND PRESSURE LOSS CHARACTERISTICS
OF OBLIQUELY-ARRANGED CUT-FINS
K Tatsumi, M Yamaguchi, Y Nishio, K Nakabe
Osaka Prefecture University, Sakai, Osaka, Japan

Abstract
Notches have been applied to a parallel fin array, referred to as “cut-fin”, for the purpose ofenhancing the fluid mixing and heat transfer, and also reducing the pressure loss penalty. To
evaluate the effects of the notch size, the notch arrangement and the spanwise fin-pitch on the heattransfer and pressure loss characteristics, experimental and numerical studies were carried out for achannel with cut-fins mounted on the bottom wall. Velocity fields were measured by the PIV systemand heat transfer coefficients were obtained by applying the modified single-blow method.
Three-dimensional numerical simulation was conducted to calculate the flow and thermal fields
including the heat conduction inside the fin. In the first half of this paper, the results of thepreliminary test cases of parallel plates and cut-fin arrays are introduced to evaluate theexperimental setup and numerical code. In the test case, an excellent agreement was obtained
between the numerical and experimental results.
In the case of cut-fin array arranged in parallel, although the heat transfer surface area is reduced,
a comparable heat transfer performance to the notch-less plain-fin case is obtained. The notch size
does not largely affect the overall heat transfer performance due to the existence of the trade-off
problem between the increase of the heat transfer coefficient and the decrease of the heat transfer
area. Reduction of the friction loss is also achieved in this case indicating an increase of the total
performance. An optimum value of the fin pitch exists for minimizing the fin thermal resistance andis smaller than that of the plain-fin case. When the notches are obliquely arranged, a larger heattransfer coefficient is obtained compared to the parallel arrangement case. This is believed to be
attributed to the spanwise flow produced by the notch flowing along the inclined notch array.

1. Introduction
Plate-fins are one of the most fundamental but effective ways of improving the heat transfer
between the solid surface and adjacent fluids in terms of the surface extension, and are used innumerous applications such as heat exchangers and heat sinks. Research works have keenly been
carried out in the past, and high efficiency fins of various shapes have been developed (Incropera(1988), Knight et al. (1991), Ledezman and Bejan (1996), Leon et al. (2002), Morega et al. (1995),
Wirtz et al. (1994)). Nowadays, the fin size becomes remarkably smaller due to the progress of thehigh fabrication technology. A typical example is the micro heat sinks provided by using microchannels as the flow passages and walls as fins (Min et al. (2004), Qu and Mudawar (2002), Zhao
and Lu (2002)). In such micro channels, high heat transfer coefficient is available due to the small
characteristics length of the channel, whereas unfavorable pressure loss penalty is incurred.
Furthermore, when a clearance exists between the fin tip and the channel top wall, an improvementof the pressure loss penalty is obtained at the cost of a considerable decrease of the heat transfer
coefficient at the fin sidewalls that leads to a serious trade-off problem (Matsubara et al. (1996),
Min et al. (2004), Sparrow et al. (1978)). Thus, the development of an effective but applicable andaffordable fins or heat sinks for smaller scale application is required.
To tackle these problems, a fin with rectangular shape notches, as shown in Figure 1 and referred
to as “cut-fin”, is investigated in the present study. The expected major effectiveness of the cut-fin

Figure 1: Schematic view of a cut-fin array and the geometrical parameters.
is threefold: to reduce the pressure loss penalty, to increase heat transfer rate at the fin sidewalls by
increasing the mass flow in between the fins, and to enhance the mixing between the flow passing
the fin tip clearance and the flow in between the fins. Three-dimensional numerical simulation, PIV(Particle Image Velocimetry) measurement and heat transfer experiment applying a modified
single-blow method are carried out to discuss the flow and heat transfer characteristics of a channel
with cut-fins densely-mounted on the bottom wall. The effects of the notch’s length (Ln), its depth(Hn), fin spanwise pitch (WP), the notch arrangement (ΔL) and the main flow Reynolds number onheat transfer and friction loss characteristics are examined.

2. Numerical Procedure
Finite-Volume Method (FVM) is adopted in the present three-dimensional numerical computation.
The governing equations of the flow solved in this study are continuity, Navier-Stokes and energy
equations. These equations are described in time-dependent, incompressible form and are shown as
follows:
∂U i
=0
∂xi
Dρ f U i
Dt

=−

(1)
∂P
∂ ⎛⎜ ∂U i ⎞⎟+μ
∂xi ∂x j ⎜⎝ ∂x j ⎟⎠Dρ f θ∂ ⎛ μ ∂θ ⎞⎜⎟=Dt∂xi ⎜⎝ Pr ∂xi ⎟⎠

(2)
(3)

where U i is the velocity of xi direction and θ is the temperature. ρ f , μ and Pr are the fluid
density, viscosity and Prandtl number, respectively. The temperature field inside the fin is also
solved in the present study, i.e. the thermal conduction inside the solid and the heat transfer at thefin surface are both considered, and the energy equation of the solid part solved simultaneously inthe computation is as follows:dρ sθ∂ ⎛ λs ∂θ ⎞
⎜⎜
⎟⎟
=
(4)
dt

∂xi ⎝ Cs ∂xi ⎠here ρ s , λs and C s are the density, thermal conductivity and thermal capacity of the solid part,respectively.
For the boundary conditions at the channel wall and fin surfaces, no-slip condition is employed forthe flow fields while a method proposed by Patankar et al. (1980) is adopted for solving the local
heat flux at wall boundaries. This approach solves the wall heat flux passing through the solid/fluidinterface of the two components by using the temperature gradients at walls as follows:∂θ
q w = − λh(5)∂nwhere ∂θ / ∂n is the gradient of θ normal to the wall surface. λh is the harmonic thermal

conductivity to be calculated using the thermal conductivities of the fluid part, λ f , and solid part,
λs , defined as follows:λh =2
1 / λ f + 1 / λs

(6)Isothermal wall condition is applied at the channel bottom wall while the channel top wall is treatedas adiabatic. The fin array considered in the present study is the one in which the single unit shownin Figure 1 continues periodically in both streamwise and spanwise directions. The test section isconsiderably wide and is located at a sufficiently large distance downstream of the inlet. Therefore,
periodic boundary conditions are applied in each direction for the flow and thermal fields. The
method proposed by Patankar et al. (1977) is applied to the present computation to solve the flow
fields having the periodic boundaries in the streamwise direction. As for the thermal field, thefollowing condition is applied at the streamwise direction:
θ inlet − θ w θ oulet − θ w=(7)θ binlet − θ w θ boutlet − θ w
θ w and θ b are the wall and bulk mean temperatures respectively, and the superscript in the above
equation denotes the location of each boundary, inlet or outlet. The properties of air and stainlesssteel have been used for the fluid and solid parts, respectively. The Prandtl number is fixed as
Pr=0.7.
In the discretization method, 4th-order central-difference scheme is employed for the diffusion
terms and the 5th-order upwind scheme is employed for the convective terms. These higher orderschemes are applied in the present code to reduce the discretization errors particularly numerical
diffusion errors. However, since the heat diffusivity of the solid side is much larger than that of thefluid side, the iteration number necessary in the numerical algorithm is considerably large.
Therefore, in solving the energy equation (3) and (4), 1st-order upwind scheme and second order
central-difference scheme are respectively applied to the convective and diffusion terms to reducethe computational load. Semi-Implicit Method for Pressure-Linked Equations (SIMPLE) algorithm
is applied to solve the pressure correction. To solve the discretized equations, a linear-iterative
method using the modified Tri-Diagonal Matrix Algorithm (TDMA) combined with an Alternating
Direction Implicit Method (ADI) is employed. More detail of the scheme applied to the present
code can be referred to the paper of Iwai et al. (2003).

3. Experimental Setup
PIV measurements and heat transfer experiments based on the modified single-blow method
proposed by Liang and Yang (1975) are conducted in the present study. Figures 2 and 3 show theexperimental apparatus of both measurements. The air pressurized by a compressor is supplied
through a regulator, a flow meter and a settling chamber to the test section. A particle generator (TSI,
model 9306) is installed in the upstream of the chamber by which a small amount of oil mist
(Di-Ethyl-Hexyl-Sebacate, 1.0μm in nominal diameter) is produced and mixed into the air for the
PIV measurements. The mass flow rate for the air supplied into the test section is measured by theflow meter and the mean velocity for calculating the Reynolds number is obtained using this flow
rate. A 500mm-long channel is installed in the upstream of the test section and a flow conditioner
consisted of 1mm pitch parallel thin plate is inserted at the inlet of this channel. The test section, in
which a fin array is attached to the bottom wall, is made of Acrylic and is 245mm in length, 150mm
in width and 10mm in height, respectively. Three types of fin array were examined in theFigure 2: Experimental apparatus.

Double pulsed YAG laser

FlowHigh resolution CCD camera(a) Schematic view of PIV measurement(b) Apparatus of heat transfer measurement
Figure 3: Experimental apparatus for flow and heat transfer measurements.
experiments. The first one is a parallel plain-fin without notches but having a clearance between the
fin tip and channel top wall. Second is a parallel cut fin whose notches are arranged perpendicularly
to the main flow. And third is an oblique cut fin array whose attack angle of the notch row against
the main flow is set as 45°.
The PIV system is composed of a double pulse Nd:YAG laser (New wave Solo3: wave length
532nm) and high resolution CCD camera (TSI, PIVCAM 13-8: 12-bit monochrome, 4M pixels).
The frame rate is 15 frames/s and a sufficient number of frames of instantaneous particle image istaken to calculate the time mean velocity field.
The single-blow method estimates the heat transfer coefficient by considering the unsteady
temperature profile at the inlet of the test section and its response at the outlet. The time history of
the outlet temperature mainly depends on the temporal profile of the inlet temperature, flow heat
capacity of the fluid, and the heat transfer coefficients and heat capacities of the fin and channel
walls, in other words NTU (Number of Transfer Units, Kays and London (1964)). If the energy
equation in the test section is formulated correctly and the inlet temperature profile is known, theheat transfer coefficient can be predicted by finding the exact value that adjusts the calculated
temperature distribution to the one obtained from the experiment. The governing equations appliedin the analysis are as follows:∂θ s*= θ f* − θ s*
(8)
*
∂t
∂θ w*
= b1 (θ f* − θ w* )∂t *∂θ *f ∂θ f*+= b2 (θ s* − θ f* ) + b3 (θ w* − θ *f )∂t * ∂x *

(9)
(10)

where θ * is the dimensionless temperature defined by the initial temperature, θ 0 , as
θ * = (θ * − θ 0 ) / θ 0 . t * and x * are the dimensionless time and distance respectively defined ast * = ms C s t / hA and x * = hAx / m f C f L . Here m , m , C and L are the mass, mass flow rate, specificheat and length of the test section, respectively. h and A are the heat transfer coefficient and the heatFigure 4: Nusselt number for parallel plate case.
transfer area of the fin surface. The values b1, b2 and b3 are defined as follows:hw Aw ms Cs
×hA mwCwmC
b2 = s s
mf Cf

(11)

b1 =

b3 =

(12)

hw Aw ms Cs
×hA m f C f(13)

The subscripts s, w and f represent the solid, channel wall and fluid parts, respectively. Theseequations are discretized by using a second order central differential scheme in space and using
fully implicit method in time. To solve the algebraic equations, TDMA is applied to the iteration
process.
As shown in Figure 3 (b), thermocouples are attached at the inlet and outlet of the test section tomeasure the temperature of the flow at each location. 15 thermocouples are used in total, placed
spanwisely in five rows at equal intervals. In each row, 3 thermocouples are located respectively at
different heights at equal intervals. To calculate the bulk mean temperature more accurately, apreliminary velocity measurement using the PIV was carried out to obtain the velocity at the point
where the thermocouples are located. A wire mesh heater made of stainless wires of 0.3mm indiameter is attached in the upstream of the thermocouples, and is operated by energizing it using acircuit switch and a voltage slider (Yamabishi V-130-3).

4. Preliminary Test Cases
Here is shortly discussed some of the results obtained in the preliminary tests made for parallel
plates and parallel cut-fins. In the former case, heat transfer measurements are conducted in order toevaluate the experimental setup and analytical method. In the latter case, velocity measurement iscarried out by using the PIV system, and the results are compared with those obtained from thenumerical computation for the purpose of validating the present numerical code.
In the parallel plate case, cupper fins of the length of 100mm and thickness of 1mm are attachedto the channel bottom and top walls. Reynolds number, Re, is based on the double height of thespace between the fins and is in the range from 400 to 3,000. Figure 4 shows the relation between
the Reynolds number and Colburn j-factor, j. The results of the single-blow method experimentcarried out by Liang and Yang (1975) are shown for comparison. The lines in the figure present theresults of parallel plate cases under the uniform wall temperature and uniform wall heat flux
conditions, i.e. Nusselt number are Nu=6.7 and 7.47, respectively. An excellent agreement between

Hn/Hf0.5

Table 1: Geometric parameters for preliminary test case.
Ln/L
Hf/H
L/H
wf/H
0.5
0.8
3.5
0.025

Wp/H
0.075

Figure 5: Cross-sectional distributions of streamwise velocities, U (Re=200).
the present results and the experiment of Liang and Yang is obtained. j shows a linear profile atlower Re indicating Nu is constant in this region, while for Re larger than 2,000, the j profile
deviates from the linear profile showing that Nu starts to slightly increase. The reason why j of thepresent study increases in larger Re might be attributed to the area in the upstream end of the test
section, in which the thermal boundary layer is not fully developed. Since the plate length tochannel height ratio is 12.5 and is not sufficiently large, the large heat transfer coefficient obtainedin this area raises the averaged Nu resulting in larger j. Nevertheless, the result sufficiently showsthat the heat transfer coefficient obtained from the present experimental analysis is reasonable andcan be discussed in a qualitative manner.
Table 1 tabulates the geometric conditions of the cut-fin tested in the preliminary PIV
measurements. Figure 5 shows the distributions of the streamwise velocities, U, at several
streamwise locations, x/H=0.9, 1.3, 1.75, 2.2 and 2.6. The symbols and lines present the results
obtained from the experiment and computation, respectively. Here, U is normalized by thestreamwise mean velocity, Um. Note that due to the optical specification of the present PIV system,
there is a limitation for narrowing down the laser sheet thickness, and the minimum spatial
resolution in the spanwise direction is about equivalent to the fin thickness. The velocity results
obtained from the PIV measurements are the averaged value in this region, and the computational
results are, therefore, averaged in the spanwise direction across the computational domain. The two
results show an excellent correspondence and the validation of each method is ascertained. The
basic characteristics of the flow field will be briefly discussed here to help the discussion carried out
in Section 5. Under this spanwise fin-pitch condition, the flow passing over the leading edge of thenotch accompanies a downwash flow toward the notch that produces a strong shear stress with thefluid inside the notch. By this, a circulation is generated in the notch as can be seen by the reverse
flow located at 0.4≤y/H≤0.5 of x/H=1.75 and 2.2.
On the other hand, since U is small inside the notch at x/H=1.3, the mass flow between thefins is also small. This is due to the condition of Wp/H =0.075, indicating that the fin pitch isrelatively small compared to the fin tip clearance which entails a larger pressure loss in the area
between the fins. The notch existence is not effective enough to increase the mass flow rate between
the fins. The generation of the circulation and the flow rate between the fins are considered to beTable 2 Geometric parameters for cut-fin array.
Notation
Hn/Hf
Ln/L
ΔL/L
Plain
Cut-a
0.5
0.6
0
Cut-b
0.5
0.32
0
Cut-c
0.75
0.6
0
Inline1.0
0.60(a) Friction factor, f(b) Thermal resistance, R
Figure 6: Fiction factor and thermal resistance (Notch size effect).
strongly related to fin pitch and will be discussed in Section 5.2.

5. Results and Discussion
5.1 Effect of notch shape
The geometric specifications of the fins discussed in the present section are compiled in Table 2.
The rest of the specification such as the fin height Hf, fin pitch Wp, fin width wf and notchstreamwise pitch Ln are kept constant, i.e. Hf/H=0.75, Wp/H=0.075, wf/H=0.025 and Ln/H=3.125.
The Reynolds number, based on the channel double height, is fixed at a constant value, Re=200.
Figure 6 shows the friction factor, f, and thermal resistance, R. R is calculated as ( θ w - θ binlet )/q
where θ w , θ binlet and q are the channel bottom wall temperature, bulk mean temperature of the inlet
flow and the averaged heat flux provided at the bottom wall, respectively. Each value is normalized
by the value of the plain-fin case, namely a case of simple parallel fins without notches. f/fp in allcases is smaller than unity which indicates that friction loss reduction is obtained by applying thenotch to the fins. R is obtained to be also smaller than unity. Considering that the heat transfer
surface area is decreased in the cut-fin cases (45% of the case plain-fin for the case Cut-c), thisshows that higher heat transfer efficiency is achieved by the cut-fins. Not much effect of the notch
size appears in R while a smaller friction loss is obtained for larger notch size. The reason for theformer result is believed to be related to the trade-off problem of the notch size between the heattransfer enhancement rate and the friction loss reduction.
5.2 Effect of fin pitch
The effect of the fin spanwise pitch, Wp, on the heat transfer enhancement rate and pressure loss
reduction is discussed with the case Cut-a which was introduced in Section 5.1. Wp is varied in therange from Wp/wf=3.0 to 9.0. Figure 7 shows the friction factor, f, and the thermal resistance, R, of
the cut-fin arrays. The value normalized by the plain-fin case against Wp/wf is also depicted in thesame figure for the comparison where the labels are shown in the right hand side ordinates.

(a) Friction factor, f(b) Thermal resistance, R
Figure 7: Fiction factor and thermal resistance (fin pitch effect).
In Figure 7(b), R decreases as Wp increases for both cases. For the cut-fin case, a minimum peakis observed approximately at Wp/wf=7.5. Although not shown here, for the plain-fin case also, aminimum peak appears if Wp is further increased. This is attributed to the trade-off problem
between the increase of the heat transfer coefficient at the fin sidewalls and the reduction of the finheat transfer area per channel bottom wall area. The former effect results from the increase of mass
flow rate between the fins for larger Wp, and the latter is due to the fact that the fin number
decreases as the fin pitch increases. R/Rp is smaller than unity at Wp/wf<7.5, which indicates that
cut-fins achieve a better heat transfer performance compared to the plain-fin in this region. This is
ascribable to the increase of the heat transfer coefficient at the trailing edge of the notch. At thislocation, the thermal boundary layer is redeveloped due to the downwash flow from the fin tip
clearance mentioned before in Section 4. However, the notch effect decreases as Wp increases. The
mass flow rate ratio of the flows passing the tip clearance and the area between the fins decreases as
Wp increases since the pressure loss between the fins decreases. Consequently, the heat transfer
coefficient at the sidewalls increases and is more significant than that of the notch effect. Therefore,
under this condition of Wp/wf>7.5, an increase of the heat transfer area, i.e. the reduction of thenotch size, is more effective to enhance the heat transfer performance.
In Figure 7 (a), friction factor for the cut-fin case is smaller than the plain-fin case, and f/fp isnearly constant, approximately 0.6, against Wp/wf. This shows that the pressure loss reduction effectproduced by introducing the notch to the fin is still notable even at large Wp. In the case of Wp/wf
1/ 3=9.0, where R/Rp is larger than unity, 1 /[(R / Rp )( f / f p )] and 1 / [(R / R p )( f / f p ) ] are 1.5 and 1.1,
respectively. Although these values do not precisely describe the overall performance considering
the pumping power, we still can assume that even in large Wp conditions, the cut-fin arrays has acomparable or larger potential compared with the plain-fin case.
5.3 Notch arrangement effect
Here is discussed the heat transfer performance of a cut-fin array where ΔL is changed so thatthe notch is arranged in parallel and oblique manners. Since a spanwise velocity component is
expected to be produced in the oblique notch arrangement case as shown by Tatsumi et al. (2005)
and hence the flow is affected also by the channel sidewalls, it is not appropriate to apply a periodic
boundary condition at the spanwise computational domain, and it is difficult to discuss this problem
from a numerical approach. The effect of the notch arrangement is, therefore, investigated by heattransfer experiments. Table 3 shows the geometric parameters of the cut-fin array. The values are
Hn/Hf
0.5

Table 3: Geometrical parameters of cut-fin array.
Ln/L
Hf/H
L/H
wf/H
0.5
0.8
3.5
0.05

Wp/H
0.35

Figure 8: Nusselt number of cut-fins with different notch arrangements.
identical with those of the cut-fin discussed in Section 4 as shown in Table 1, except that fin width,
wf, to channel height, H, ratio is changed. This is due to the limitation in the fabrication process.
The fin pitch, Wp, to H ratio is also changed by considering the results obtained in Section 5.2, in
which a smaller thermal resistance is attained by the condition of Wp/wf=7 than Wp/wf=3. Two cases
are investigated here for ΔL, i.e. ΔL=0 (parallel notch arrangement case) and ΔL=Wp (oblique notcharrangement case). The attack angle of the notch array to the main flow is, therefore, 45° for theoblique case. In addition to these cases, a fin without notches, referred to as plain-fin case, is also
examined for comparison. Reynolds number is varied from Re=1,000 to 2,000. Measurements forlower Re was difficult to carry out since the outlet temperature was too small at the period of theinitial rising, and that the heat loss from the channel wall to the ambient was not negligible.
Figure 8 shows the overall Nusselt numbers of the three cases. In the cut-fin cases, Nu
increases as Re increases. On the contrary, Nu is nearly constant for the plain-fin case. The reason
for this difference might be as follows. Since the examined Reynolds number in the measurements
is small the flow between the fins is assumed to be in laminar flow regime. The thermal boundary
layer in between the fins can, therefore, assumed to be fully developed and the heat transfer
coefficient at the fin sidewalls is nearly constant. On the other hand, in the cut-fin cases, the thermalboundary layer is interrupted by the notches. In this area, Reynolds number effect on heat transfer
becomes noticeable and larger heat transfer coefficient is obtained when Re is increased.
Comparing the results of the three cases, Nu of the cut-fin cases is larger than the plain-fin casefor all examined Re, indicating a higher heat transfer performance is attained. This tendency
becomes more noticeable for larger Re. In other words, for smaller Re, Nu of the three cases areshown to be similar, that is, 8% difference between the oblique cut-fin and plain-fin cases. This
characteristic is similar to that of the results obtained by the numerical computation described in theprevious sections.
The largest Nu is obtained for the oblique cut-fin case among the above three cases. This isbelieved to be ascribable to the spanwise flow produced by the inclination of the notch
configuration. A portion of the main flow flows in the spanwise direction along the notch and theheat transfer coefficient at the fin sidewall is effectively increased by the flow impingement andredevelopment of the thermal boundary layer.
In order to have a rough view of the flow and thermal fields in such oblique cut-fin arrays, anumerical computation was carried out for a rectangular channel in which five cut-fins are attached
in an oblique manner onto the channel bottom wall. The fin number is much smaller than that of theexperiment and a larger sidewall effect is expected. However, it is believed that the oblique(a) Streamwise center of the non-notched area(b) At the notch center of the middle cut-fin
Figure 9: Cross-sectional view of the velocity vectors and U contours.

(a) Streamwise center of the non-notched area(b) At the notch center of the middle cut-fin
Figure 10: Cross-sectional view of the dimensionless temperature, (θ-θw)/( θb-θw).
arrangement effect on the flow and heat transfer can be obtained. The fin shape specifications are
identical to those applied in the experiment as shown in Table 3. The space between the channel
sidewalls and the adjacent fin is 3wf and is equal to the gap width between each fin. Thus thechannel aspect ratio, Wd/H, is 2.05. At the channel top wall and sidewalls, adiabatic wall condition
is applied. Note that the Reynolds number is based on the channel double height, 2H, and is set as
Re=200 which is smaller than that of the experimental conditions, but is the same as the conditionsof the numerical computations previously discussed shown in Sections 5.1 and 5.2.
Figures 9 and 10 are the cross-sectional distributions of the streamwise velocity, U, velocity
vectors and dimensionless temperature, (θ-θw)/(θb-θw). The streamwise location of each figure islocated at (a) the middle of the area where no notch exists and (b) the middle of the notch of thecenterline-located fin, respectively. As shown in Figure 9(a), the maximum peaks of U are locatedin the area between the fins and the tip clearance. In the notch area shown in Figure 9(b), downwash
flow from the tip clearance and upwash flow from the gap between the fins appear. Due to theexistence of the notch trailing edge blocking the flow in the downstream side, the flow will be
driven to the clearance and the gap. However, since the notches are located in a oblique manner, alarger amount of flow flows in the direction along the notch and a spanwise flow is generated inside
the notch area. At the sidewall located at the end of the notch array, the spanwise flow becomes as
an upwash flow and then flows in the z positive direction which is the opposite direction of the flowin the notch. This can be seen at the tip clearance shown in Figure 9(a). As shown in Figure 10, thislongitudinal vortex like secondary flow motion enhances the fluid mixing between the notch and thefin tip clearance.

(a) z positive side(b) z negative side
Figure 11: Nusselt number distribution at fin sidewalls (centerline-located fin).
Figure 11 shows the local Nusselt number, Nu, on the sidewall surfaces of the centerline-locatedfin. Nu shown here is based on the flow bulk mean temperature. Large Nu is obtained at the areaadjacent to the fin tip. As shown in Figure 9, this is the area where the streamwise velocity takes its
maximum peak, and a strong sweeping effect of the flow is obtained at the fin sidewalls. Large Nu
also appears at the trailing edge of the notch. As discussed above, the flow from the tip clearance
and the gap between the fins sweeps the fin surface at this area. Furthermore, the spanwise flow in
the notch also impinges on this area. The thermal boundary layer is thus interrupted which
contributes to an increase of the heat transfer coefficient. These might be the main reasons why alarger overall heat transfer coefficient was achieved by the oblique cut-fin array than the parallelone.

6. Conclusions
Flow and heat transfer characteristics of a cut-fin array have been studied by conducting PIV
measurements, heat transfer experiment based on the modified single-blow method andthree-dimensional numerical simulations. The notch size, fin spanwise pitch and notch arrangement
effects on the heat transfer and pressure loss performance were examined. The main conclusions
drawn from this study is as follows:(1) Under the condition of Re=200, an excellent agreement of the velocity field of the cut-fin case
was obtained between the numerical and experimental results.
(2) A downwash flow was observed at the notch by which a portion of the flow passing the fin tip
clearance was brought inside the notch. This enhanced the heat transfer of the fin surface at thenotch trailing edge. If the fin pitch was small, a shear layer was generated by this flow and acirculation was produced accompanied by a reverse flow at the bottom side of the fin.
(3) The thermal resistance, R, was not significantly affected by the notch size due to the trade-off
problem between the increase of the heat transfer coefficient and the decrease of the heat transfer
area. On the other hand, a larger pressure loss reduction was obtained by the fin with larger notch
size.
(4) An optimum fin pitch existed where R takes a minimum value. This is related to the balance
between the increase of the heat transfer coefficient at the fin sidewalls, which is attributed to theincrease of the mass flow between the fins, and the decrease of the fin number. Comparing theperformance with the plain-fin case without notches, a cut-fin case showed a better performance
when the fin pitch was small. As the fin pitch exceeds a certain value, smaller R is obtained by theplain-fin case.
(5) The results of the heat transfer experiment for fin arrays showed that the overall Nusselt number,
Nu , is nearly constant in the examined Re range, i.e. 1,000<Re<2,000. However, Nu of both
oblique and parallel cut-fin cases increased as Re increased and a higher heat transfer performance
was obtained than the plain-fin case. This is believed to be due to the interruption of the thermalboundary layer at the notch edges, which becomes more effective in larger Re.
(6) Comparing the cases of parallel and oblique notch arrangements, larger heat transfer coefficient
was achieved by the oblique case. This is believed to be attributed to the spanwise flow flowing
along the inclined notch array. This flow enhances the mixing between the fluids located at the fin
tip clearance and the notch area, and also impinges and sweeps the fin sidewalls resulting in anincrease of the wall heat transfer coefficient.

Acknowledgement
This work was financially supported by the Japanese Ministry of Science and Technology and by
The MIKIYA Science and Technology Foundation. The authors would also like to acknowledge theJapan Aerospace Exploration Agency (JAXA) for providing their super-computer resources for thepresent numerical simulations.

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