On the Thermal Dynamics of Metallic and Superconducting Wires. Bifurcations, Quench, the Destruction of Bistability and Temperature Blowup
Abstract
:1. Introduction
2. Analysis
2.1. Metallic Wire
2.2. Steady State
2.3. Wave Fronts
2.4. Stability
2.5. Superconducting Composite Wire
3. Results, Applications and Discussion
3.1. Metallic Wires
3.2. Quench, the Destruction of Bistability and Thermal Runaway
3.3. Stability
3.4. Superconducting Composites
4. Conclusions
Funding
Conflicts of Interest
Nomenclature
cross sectional area | [m2] | |
Bi | Biot number | [-] |
reduced specific heat capacity | [-] | |
specific heat capacity | [J/(kgK)] | |
disturbance strength | [-] | |
volume fraction of normal metal | [-] | |
generation number | [-] | |
reduced heat transfer coefficient | [-] | |
heat transfer coefficient | [W/(m2K)] | |
applied current | [A] | |
current density | [A/m2] | |
reduced thermal conductivity | [-] | |
K | thermal conductivity | [W/(mK)] |
conductor length | [m] | |
perimetry | [m] | |
internal heat generation rate per unit volume | [W/m3] | |
reduced internal heat generation rate | [-] | |
reduced boiling heat flux | [-] | |
time | [sec] | |
temperature | [K] | |
dimensionless distance along wire | [-] | |
distance along wire | [m] | |
conduction-convection parameter | [-] | |
dimensionless front velocity | [-] | |
disturbance width parameter | [-] | |
longitudinal co-ordinate | [-] | |
Greek Symbols | ||
thermal diffusivity | [m2/s] | |
reduced heat flux difference | [-] | |
temperature difference | [K] | |
dimensionless temperature | [-] | |
critical temperature at | [-] | |
temperature where current sharing starts | [-] | |
knot temperature connecting nucleate and transition regimes | [-] | |
knot temperature connecting transition and film regimes | [-] | |
eigenvalue | [-] | |
dimensionless co-ordinate | [-] | |
reduced electrical resistivity | [-] | |
electrical resistivity | [Ω m] | |
dimensionless time | [-] | |
reduced electric potential | [-] | |
electric potential | [V] | |
Subscripts | ||
b | base | b |
e | tip | e |
LP | reference to limit points | LP |
ref | reference value | ref |
s | steady state | s |
u | reference to uniform solutions | u |
∞ | ambient boiling liquid | ∞ |
Superscripts | ||
derivative with respect to x or to ξ | ||
Abbreviations | ||
CCP | Conduction-Convection Parameter |
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Krikkis, R.N. On the Thermal Dynamics of Metallic and Superconducting Wires. Bifurcations, Quench, the Destruction of Bistability and Temperature Blowup. J 2021, 4, 803-823. https://doi.org/10.3390/j4040055
Krikkis RN. On the Thermal Dynamics of Metallic and Superconducting Wires. Bifurcations, Quench, the Destruction of Bistability and Temperature Blowup. J. 2021; 4(4):803-823. https://doi.org/10.3390/j4040055
Chicago/Turabian StyleKrikkis, Rizos N. 2021. "On the Thermal Dynamics of Metallic and Superconducting Wires. Bifurcations, Quench, the Destruction of Bistability and Temperature Blowup" J 4, no. 4: 803-823. https://doi.org/10.3390/j4040055