Thermal stability of composite superconducting tape under the effect of a two-dimensional dual-phase-lag heat conduction model

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.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) - g_max Ohmic heat generation with the whole current in the stabilizer, (W m^–3) - G_max 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 (_T/2_q) - t rime, (s) - T temperature, (K) - T_c critical temperature, (K) - T_c1 current sharing temperature, (K) - T_i initial temperature, (K) - T_o ambient temperature, (K) - x, y co-ordinate defined in Fig. 1, (m) - thermal diffusivity (m² s^–1) - dimensionless time - _i dimensionless duration time - dimensionless y-variable - _o superconductor dimensionless thickness - dimensionless temperature - _c1 dimensionless current sharing temperature - 1 dimensionless maximum temperature - dimensionless disturbance energy - numerical tolerance - x width of conductor subjected to heat disturbances, (m) - y thickness of conductor subjected to heat disturbances, (m) - dimensionless x-variable - _o superconductor dimensionless width - stabilizer electrical resistivity, () - _q relaxation time of heat flux, (s) - _T relaxation time of temperature gradient, (s) - i initial - sc current sharing - max maximum - o ambient