Physica C 470 (2010) 1397–1400

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Physica C
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Anisotropic thermal transport in double-pancake coil wound with DI-BSCCOÒ tape
T. Naito a,*, H. Fujishiro a, Y. Yamada bab

Faculty of Engineering, Iwate University, Morioka 020-8551, Japan
Sumitomo Electric Industries, Ltd., Osaka 554-0024, Japana r t i c l e

i n f oArticle history:
Available online 16 May 2010
Keywords:
DI-BSCCO
Bi2223/Ag tape
Double-pancake coil
Thermal resistanceHeat current circuita b s t r a c tWe have measured the temperature dependence of the thermal resistances Rr(T) and Rz(T) of the parallelepiped samples cut from a double-pancake coil along the radial (r) and the thickness (z) directions,respectively. The double-pancake coil was wound with DI-BSCCOÒ tape fabricated by Sumitomo ElectricIndustries, Ltd. DI-BSCCO is a (Bi, Pb)2Sr2Ca2Cu3O10+x tape sheathed with silver. Both Rr(T) and Rz(T)increase monotonically with decreasing temperature. We analyze the thermal transport in the coil byuse of the parallel and series heat current circuit of DI-BSCCO tapes and insulators.
Ó 2010 Elsevier B.V. All rights reserved.

1. Introduction
DI-BSCCOÒ is a silver sheathed (Bi, Pb)2Sr2Ca2Cu3O10+x (Bi2223)
superconductive tape [1]. It has a high critical current density over
200 A at 77 K in the self-ﬁeld [2] and a high mechanical strength[3] in comparison with other conventional Bi2223/Ag tapes. Because of the thermal stability in the superconducting apparatus,
the thermal conductivity, j(T), is one of the most important physical properties [4]. It is well known that the absolute value andtemperature dependence of j for the Bi2223/Ag tapes strongly depend on the j of the sheath material, the volume ratio of thesheath to the Bi2223 and fabrication processes [5]. We have measured j(T) for various types of DI-BSCCO [6]. j(T) of the stacked
bundle, in which six DI-BSCCO tapes were soldered, was also measured [7]. Furthermore, j(T) of the sandwiched sample, in which
the single DI-BSCCO tape was laminated from both sides by thethin alloy tapes (20–100 lm in thickness) was measured [8]. The
obtained j(T) for the composite samples can be successfully described by the parallel circuit of the heat current using the j(T)’sfor the single DI-BSCCO tape, solder and alloy tape. A superconducting coil has a composite structure which consists of a superconducting tape and the insulators. In this paper, we investigate theanisotropic thermal transport along the radial and the thickness
directions of the double-pancake coil wound with the DI-BSCCO
tape using the thermal resistance measurement.
2. Experimental
Using the DI-BSCCO tape (type H) wrapt by an insulating
Kapton tape, a double-pancake coil was prepared by a winding* Corresponding author. Tel./fax: +81 19 621 6362.
E-mail address: tnaito@iwate-u.ac.jp (T. Naito).
0921-4534/$ - see front matter Ó 2010 Elsevier B.V. All rights reserved.
doi:10.1016/j.physc.2010.05.122

and react process and completed by epoxy impregnation. We measured the r- and z-samples cut from the coil along the radial andthe thickness directions, as shown in the center of Fig. 1. The rsample was cut from the upper pancake coil. The dimensions ofthe samples are shown in Table 1. The DI-BSCCO (type H) tape,which is a standard type, was fabricated by a powder in tube(PIT) method with the controlled overpressure (CT-OP) sintering
technique [9].
Thermal resistance, R(T), was measured by a steady-state heat
ﬂow method [10]. The experimental setup is schematically illustrated in Fig. 1. One end of the sample was adhered to the copper
block using a silver paste (H20E). A small metal chip resistor (1 kX)
which was used as a heater was adhered to the other end of thesample using GE7031 varnish. R is calculated by the relation:

R¼DT;
Q

ð1Þ

where Q is the applied heat ﬂow and DT the temperature difference
between two chromel-constantan thermocouples (76 lm in diameter). DT was maintained to be approximately 1 K by controlling theheater power. The temperature of the sample stage was controlledusing a Gifford–McMahon cycle helium refrigerator. To eliminate
the radiation loss, R was measured below 250 K.
3. Results
Fig. 2a and b show the temperature dependence of the thermalresistance, R(T), for the r- and z-samples, respectively. R(T) for bothsamples increases monotonically with decreasing temperature. Inset of Fig. 2a shows the thermal conductivity, j(T), for the DIBSCCO tape (type H) along the tape surface, jkSC [6], the epoxy resin, jE [11], and the Kapton tape, jK [11], all of which are used in
the analysis for the thermal transport in the next section.

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T. Naito et al. / Physica C 470 (2010) 1397–1400

Fig. 1. (Center) Schematic view of the double-pancake coil. (Left and right) Experimental setup for the thermal conductivity measurement along the r- and z-direction.

4. Discussion
Table 1
Dimensions of the samples.

r-samplez-sample

4.1. Analysis for thermal transport along the r-direction
Length (mm)Cross section (mm2)

15.1
9.1

16(= 4.0  4.0)
16(= 4.0  4.0)(a)

As shown in the left of Fig. 3a, the DI-BSCCO tape and the Kapton sheets were stacked one after the other in the r-sample. For
simplicity, all the pieces for DI-BSCCO tapes and Kapton sheets
were virtually collected and stacked as shown in the middle ofFig. 3a. As a result, the equivalent heat current circuit can be represented in the right of Fig. 3a, where R?
SC is the thermal resistanceof the DI-BSCCO tape perpendicular to the tape surface, i.e., along
the c-axis of the Bi2223 ﬁlament and RK is that of the Kapton sheet.
Furthermore, Rcon is the total thermal contact resistance at theinterfaces between the DI-BSCCO tape and the Kapton sheet andbetween the Kapton sheets. The measured DTr for the r-sample isgiven as:DT r ¼ DT ?SC þ DT K þ DT con ¼ R?SC þ RK þ Rcon  Q ;(b)Fig. 2. Temperature dependence of the thermal resistance, R(T), for (a) the r-sampleand (b) z-sample. Inset of (a) shows the thermal conductivity, j(T), for the DI-BSCCO
tape (type H) [6], the resin [11], and the Kapton tape [11].

where DT ?
SC ; DT K and DTcon are the temperature difference in the
DI-BSCCO part, the Kapton part and the contact resistance part,respectively. At 77 K, the measured DTr was 1.03 K and the applied
heat ﬂow Q was 0.0016 W. Using the reported value of jK =0.22 W m1 K1 [11], SK = 16 mm2 and LK = 1.33 mm, DTK(= RKQ =[LK/(jK  SK)]Q) was estimated to be 0.64 K, where SK is the crosssection and LK the total thickness of the Kapton part, respectively.
For the DI-BSCCO part in the r-sample, the applied heat current
ﬂows perpendicular to the tape surface.
Fig. 3b shows the photograph of the cross section of the DIBSCCO tape. Black and white regions represent the Bi2223 ﬁlamentand Ag region, respectively. Since the Bi2223 ﬁlaments separately
distribute in the Ag region, the path of the heat current is quitecomplicated. To determine R?
SC analytically, we consider the simple
parallel circuit as shown in Fig. 3c. Here, RAg and Rkc
Bi2223 are thethermal resistance of Ag and the Bi2223 ﬁlament along the c-axis,respectively. j(T) of the Bi2223 single crystal along the c-axis has
not been reported. Only the j value for the Bi2223 polycrystal
was reported to be about 3 W m1 K1 at 77 K [10], which was
two orders of magnitude smaller than that for Ag(360 W m1 K1 at 77 K) [12]. In this situation, the heat current
ﬂows
through
onlytheAg
parts[13],andtheDT ?SC ð¼ RAg Q ¼ ½LAg =ðjAg  S Ag ÞQ Þ was estimated to be 0.002 K.
SAg(= 2.8  4 mm2) is the effective cross section of the Ag partwhich is estimated using the volume ratio ð¼ 1:8Þ of Ag to the

T. Naito et al. / Physica C 470 (2010) 1397–1400

1399

(a)

(b)
(c)

Fig. 3. (a) Equivalent heat current circuit for the r-sample. (b) Photograph of the cross section of DI-BSCCO tape. Black and white regions represent the Bi2223 ﬁlament and Agregion, respectively. (c) Equivalent heat current circuit perpendicular to the tape surface in the DI-BSCCO tape.

Bi2223 and LAg(= 4.4 mm) is the total thickness of the DI-BSCCO
tape. The sum of DTK and DT ?
SC (’0.64 K) cannot reproduce themeasured DTr = 1.03 K, indicating that a large thermal contact
resistance, Rcon, exists and is estimated to be 260 K W1 at theinterfaces. Rcon prevents greatly the ﬂow of the heat current. It isnoteworthy that the estimated Rcon is not a universal value; Rcon
depends on the number and thickness of both DI-BSCCO tapes
and Kapton sheets. We note that R?
SC obtained by the simple model
mentioned above gives the lower limit. Since the thermal carriers
are scattered at the surface of the Bi2223 ﬁlaments, R?SC must beenhanced. To discuss more precisely the thermal transport along

the r-direction, the thermal conductivity, j?
SC , perpendicular to
the tape surface should be directly measured.
4.2. Analysis for thermal transport along the z-direction
As shown in the left of Fig. 4, two bundles, which consist of
fourteen sheets of DI-BSCCO tapes and thirteen Kapton layers,
are adhered by the epoxy resin in the z-sample. In each bundle,
the applied heat current ﬂows in parallel along the surface of theDI-BSCCO tape (i.e., the ab-plane of the Bi2223 ﬁlament) and theKapton sheet. The equivalent heat current circuit in the z-sample

Fig. 4. Equivalent heat current circuit for the z-sample.

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T. Naito et al. / Physica C 470 (2010) 1397–1400
kcan be depicted in the right of Fig. 4, where RSC and RE are the thermal resistance for the DI-BSCCO tape along the tape surface andthat for the epoxy resin, respectively. The measured DTz for thez-sample is given as2DT z ¼ DT kSC þ DT E þ DT con ¼ 4hi’ RkSC þ RE þ Rcon  Q;

11
þ
RkSC RK!13þ RE þ Rcon 5  Q

where DT kSC and DTE are the temperature difference in the bundles
and the epoxy resin, respectively. At 77 K, the measured DTz was1.05 K and the applied heater power Q was 0.0094 W. The reported
jE is about 0.6 W m1 K1 at 77 K [11] and gives DTE = 0.19 K using
SE = 16 mm2 and LE = 0.2 mm, where SE and LE are the cross section
and the length of the epoxy resin part.
We can neglect the contribution of the Kapton layers to the heatktransport because of RK  RSC . Using j = 230 W m1 K1 of the DIBSCCO (type H) tape along the tape surface at 77 K [6],kkk
S SC = 12 mm2 and LSC = 3.4 mm, the DT SC was estimated to bekk
0.16 K. SSC is the cross section and L SC is the total thickness ofkthe DI-BSCCO tapes. The sum of the DTE and DT SC is approximately
0.35 K. We cannot reproduce the measured DTz = 1.05 K. These results indicate that DTcon is as large as 0.74 K and the large Rcon of79 K W1 exists at the interface between the bundle and the epoxy
resin and suppresses the heat transport in the z-sample. The Rconvalue
 in the z-sample changes depending on the length of the bunkdle L SC and the thickness of the epoxy resin part (LE).
A double-pancake coil might be cooled along the z-direction
using the helium refrigerator. If a hot-spot creates in the upper
pancake coil, the generated heat cannot be immediately exhausted
to the cold stage because of the large Rcon value, causing the temperature rise in the coil. Therefore, a cooling path for the upper coilshould be considered.
5. Summary
We have measured the temperature dependence of the thermal
resistance, R(T), in the double-pancake coil wound with the DI-BSCCO tapes (type H) along the radial and the thickness directions
using the parallelepiped samples cut from the coil. The thermaltransport was analyzed using the equivalent heat current circuitand the thermal contact resistance, Rcon, at the interface between
the DI-BSCCO tape and the insulating separator was estimated.
The Rcon value affects strongly the thermal transport along both
directions in the coil. Note that the obtained value of the thermal
contact resistance is not a universal one, which depends on thecondition of the interface between the materials. Using the results,
the temperature rise in the coil can be estimated when a hot-spotcreates. These analysis might play an important role in the designof the cooling system.
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