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Study on the intrinsic thermal stability of thin-film superconductors due to a point heat source

Untersuchung der inhärenten thermischen Stabilität von Dünnfilm-Supraleitern unter der Wirkung einer punktförmigen Wärmequelle

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Abstract

Intrinsic thermal stability denotes a situation where a superconductor can carry the operating current without Joule heating at all times after the occurrence of a localized release of thermal disturbance. The present work deals with the intrinsic thermal stability of an anisotropic thin-film superconductor under a localized release of thermal energy. A three-dimensional analysis is introduced to consider an instantaneous release of energy in the form of a point source at different locations. Through the transformation of coordinate, an exact solution is obtained by the method of separation of variables. Results from this study indicate that the thermal stability parameter of highly oriented films of superconductors is strongly under the influence of anisotropy. The stability parameter also depends on the location of point source, the amount of disturbance energy, the Biot number, and the aspect ratio in the plane of thin film and normal to it.

Zusammenfassung

Inhärente thermische Stabilität bezeichnet einen Zustand, in dem ein Supraleiter den Betriebsstrom zu allen, einer örtlich begrenzten thermischen Störung folgenden Zeiten ohne Joulesche Erwärmung transportieren kann. Die vorliegende Arbeit befaßt sich mit der inhärenten Stabilität eines anisotropen Dünnfilm-Supraleiters bei örtlich begrenzter Freisetzung thermischer Energie. Um die plötzliche Energiefreisetzung in Form einer Punktquelle an verschiedenen Stellen aufprägen zu können, wird die Untersuchung dreidimensional durchgeführt. Nach einer Koordinaten-transformation erhält man die exakte Lösung mittels der Methode der Variablentrennung. Die Ergebnisse dieser Studie zeigen, daß der thermische Stabilitätsparameter hochorientierter Supraleitfilme stark von Anisotropieeinflüssen abhängt, ferner von der Lokalisation der Punktquelle, dem Betrag der Störenergie, der Biot-Zahl sowie dem Seitenverhältnis in der Dünnfilm-Ebene und normal dazu.

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Abbreviations

a :

half length of superconductor parallel to current

b :

half width of cross section normal to current

c :

specific heat

d :

thickness of thin film

e 0 :

disturbance energy

E 0 :

dimensionless disturbance energy

h :

heat transfer coefficient

I :

current

J c :

critical current density

J co :

critical current density atT o

k :

thermal conductivity

K 1 :

thermal conductivity ratio,k x/kz

K 2 :

thermal conductivity ratio,k y/kz

K :

thermal conductivity tensor

r :

transformed aspect ratio

t :

time

T :

temperature

x, y, z :

Cartesian coordinate

x 0,y 0,z 0 :

location of the occurrence of point source

X, Y, Z :

transformed dimensionless coordinate

X 0,Y 0,Z 0 :

dimensionless location of the point source

θ :

dimensionless temperature, (T−T 0)/(T c−T0)

ϱ :

density

Φ :

stability parameter

δ :

Dirac delta function

μ, ν,γ,λ :

eigenvalues

c:

critical

o:

evaluated at operating temperature

max:

maximum value for all timest

x, y, z :

x, y, z directions respectively

l :

thel-th eigenfunction ofX direction

m :

them-th eigenfunction ofY direction

n :

then-th eigenfunction ofZ direction

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Authors and Affiliations

  1. Department of Mechanical Engineering, National Chiao Tung University, Hsinchu, Taiwan 30049, R.O.C.

    Hsin-Sen Chu & Rong-Chang Chen

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  1. Hsin-Sen Chu
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  2. Rong-Chang Chen
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Chu, HS., Chen, RC. Study on the intrinsic thermal stability of thin-film superconductors due to a point heat source. Wärme- und Stoffübertragung 27, 413–419 (1992). https://doi.org/10.1007/BF01637055

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  • DOI: https://doi.org/10.1007/BF01637055

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