The Additive Approximation for Heat Transfer and for Stability Calculations in a Multi-filamentary Superconductor - part A

Abstract

This paper addresses the applicability of the “additive approximation” of total thermal conductivity in heat transfer and in superconductor stability calculations. If cases (a), (b) and (c) denote total (conductive plus radiative), or only conductive or only radiative heat flux, respectively, each flux $\dot{q}$ calculated with Fourier’s conduction law using the corresponding thermal conductivity (λ_a, λ_b, λ_c), the additive approximation would be confirmed if the heat flux difference Δ$\dot{\mathrm{q}}$ = ${\dot{\mathrm{q}}}_{\mathrm{a}}-$${\dot{\mathrm{q}}}_{\mathrm{b}}-$${\dot{\mathrm{q}}}_{\mathrm{c}}$, at any position of an investigated object, and at any time, converges to zero. This is not trivial because of the strong, non-linear temperature dependence of the radiation component. Heat transfer calculations including radiative transfer are presented in this paper, first for simple, homogeneous, thin film test samples and later for a multi-filamentary BSCCO 2223 superconductor. The simulated heat sources either result from a sudden increase of conductor boundary temperature or from flux flow and Ohmic resistances in the superconductor under a disturbance (like transport current exceeding critcal current density). The conductors, though very thin, are non-transparent to mid-IR radiation. Validity of the additive approximation is critical for superconductor stability against quench. Based on the applied numerical scheme, a hypothesis is suggested concerning correlation of the results of the simulation (the “numerical space”) with the experimental situation (the “physical reality”): Non-convergence of the numerical scheme might tightly be correlated with occurrence of a quench in the simulated superconductor.