Thermal stability of composite superconducting tape under the effect of a two-dimensional dual-phase-lag heat conduction model
- 83 Downloads
- 3 Citations
Abstract.
Thermal stability of composite superconducting tape subjected to a thermal disturbance is numerically investigated under the effect of a two-dimensional dual-phase-lag heat conduction model. It is found that the dual-phase-lag model predicts a wider stable region as compared to the predictions of the parabolic and the hyperbolic heat conduction models. The effects of different design, geometrical and operating conditions on superconducting tape thermal stability were also studied.
Keywords.
Composite superconductors Tape-type superconductors Thermal stability Dual-phase-lag model Stability under non-Fourier conduction model- a
conductor width, (m)
- A
conductor cross sectional area of, (m2)
- As
conductor aspect ratio, (a/b)
- b
conductor thickness, (m)
- Bi
Biot number
- B
dimensionless disturbance Intensity
- C
heat capacity, (J m–3 K–1)
- D
disturbance energy density, (W m–3)
- f
volume fraction of the stabilizer in the conductor
- g(T)
steady capacity of the Ohmic heat source, (W m–3)
- gmax
Ohmic heat generation with the whole current in the stabilizer, (W m–3)
- Gmax
dimensionless maximum Joule heating
- h
convective heat transfer coefficient, (W m–2 K–1)
- J
current density, (A m–2)
- k
thermal conductivity of conductor, (W m–1 K–1)
- q
conduction heat flux vector, (W m–2)
- Q
dimensionless Joule heating
- R
relaxation times ratio (τT/2τq)
- t
rime, (s)
- T
temperature, (K)
- Tc
critical temperature, (K)
- Tc1
current sharing temperature, (K)
- Ti
initial temperature, (K)
- To
ambient temperature, (K)
- x, y
co-ordinate defined in Fig. 1, (m)
- α
thermal diffusivity (m2 s–1)
- β
dimensionless time
- βi
dimensionless duration time
- η
dimensionless y-variable
- ηo
superconductor dimensionless thickness
- θ
dimensionless temperature
- θc1
dimensionless current sharing temperature
- θ1
dimensionless maximum temperature
- φ
dimensionless disturbance energy
- ɛ
numerical tolerance
- Δx
width of conductor subjected to heat disturbances, (m)
- Δy
thickness of conductor subjected to heat disturbances, (m)
- ξ
dimensionless x-variable
- ξo
superconductor dimensionless width
- ρ
stabilizer electrical resistivity, (Ω)
- τq
relaxation time of heat flux, (s)
- τT
relaxation time of temperature gradient, (s)
- i
initial
- sc
current sharing
- max
maximum
- o
ambient
References
- 1.Abeln A; Klemt E; Riess H (1993) Stability consideration for design of a high temperature superconductor. Cryogenics 32(3): 269–278CrossRefGoogle Scholar
- 2.Bejan A; Tien CL (1978) Effect of axial conduction and metal helium heat transfer on the local thermal stability of superconducting composite media. Cryogenics 18: 433–441Google Scholar
- 3.Bellis RH; Iwasa Y (1994) Quench propagation in high-Tc superconductor. Cryogenics 34(2): 129–144Google Scholar
- 4.Maddock BJ; James GB; Norris WT (1969) Superconductive composites: heat transfer and steady-state stabilization. Cryogenics 9: 261–273Google Scholar
- 5.Malinowski L (1991) Critical energy of thermally insulated composite. Cryogenics 31(6): 444–449CrossRefGoogle Scholar
- 6.Malinowski L (1999) Explicit expression for critical energy of uncooled superconductor considering transient heat conduction. Cryogenics 33(7): 724–728CrossRefGoogle Scholar
- 7.Pradhan S; Romanovskii VR (1999) Thermal stability of superconducting multifilamentray wire with multiply connected stabilizing regions. Cryogenics 39: 339–350CrossRefGoogle Scholar
- 8.Seol SY; Chyu MC (1994) Stability criterion for composite super-conductors of large aspect ratio. Cryogenics 37(6): 513–519CrossRefGoogle Scholar
- 9.Ünal A; Chyu MC; Kuzay TM (1993) Stability and recovery behavior of tape/film-type Superconductors. J Heat Transfer 115: 467–469Google Scholar
- 10.Flik MI; Tien CL (1990) Intrinsic thermal stability of anisotropic thin-film superconductors. J Heat Transfer 112: 10–15Google Scholar
- 11.Ünal A; Chyu MC (1994) Quenching recovery of Tape/Film-type superconductors. Cryogenics 34(2): 123–128CrossRefGoogle Scholar
- 12.Ünal A; Chyu MC (1995) Instability behavior of superconductor wires/cylinders under finite linear thermal disturbance. Cryogenics 35(2): 87–92CrossRefGoogle Scholar
- 13.Malinowski L (1993) Novel model for evolution of normal zones in composite superconductor. Cryogenics 33(7): 724–728Google Scholar
- 14.Al-Nimr MA; Odat MQ; Hamdan M (2002) Superconductor thermal stability under the effect of hyperbolic heat conduction model. JSME Int J series B 45(2): 432–438Google Scholar
- 15.Al-Odat MQ; Al-Nimr MA; Hamdan M (2002) Thermal stability of superconductors under the effect of a two-dimensional hyperbolic heat conduction Model. Int J Numer Meth Heat Fluid Flow 12(2): 163–177Google Scholar
- 16.Lewandowska M; Malinowski L (2001) Analytical method for determining critical energies of uncooled superconductors based on the hyperbolic model of heat conduction. Cryogenics 41(4): 267–273CrossRefGoogle Scholar
- 17.Al-Odat MQ; Al-Nimr M; Hamdan M (2002) Superconductors thermal stability under the effect of the dual-phase-lag heat conduction model. Int J Thermophys 23(3): 855–868CrossRefGoogle Scholar
- 18.Al-Nimr MA; Naji M (2000) On the phase-lag effect on the non-equilibrium entropy production. Microscale Thermophys Eng l4: 281–287Google Scholar
- 19.Al-Nimr MA; Al-Huniti NS (2000) Transient thermal stresses in a thin under due to a rapid dual-phase-lag heating. J Thermal Stresses 23: 731–746CrossRefGoogle Scholar
- 20.Al-Nimr MA; Naji M; Arpaci VS (2000) Non-equilibrium entropy production under the effect of dual-phase-lag heat conduction model. J Heat Transfer 22: 217–223CrossRefGoogle Scholar
- 21.Al-Nimr MA; Haddad OM; Arpaci VS (1999) Thermal behavior of metal films – a hyperbolic two-step model. Heat Mass Transfer 36: 459–464CrossRefGoogle Scholar
- 22.Patankar SV (1980) Numerical heat transfer and fluid flow. Hemisphere, New York, USAGoogle Scholar