A novel numerical method to evaluate the heat transfer characteristics of complicated CICC structures

In this article, we propose a numerical model for calculating the external heat transfer coefficient between the bundle region and its wall for cables in conduit conductor (CICC). With the assumption of local thermal equilibrium, one macro equation describing the steady heat transfer on the cross section of the CICC can be obtained. A key parameter, the effective transverse thermal conductivity $k_{\text{eff}}$, which takes the contribution of both strands and flowing fluid into consideration, is introduced. To calculate the effective transverse thermal conductivity $k_{\text{eff}}$, we first obtain the true distribution of different phases (fluid, copper and superconducting material) on a cross section of CICC with the help of the image recognition technique. Based on this, the value of the effective transverse thermal conductivity $k_{\text{eff}}$ can be calculated numerically. Due to the large difference among the component thermal conductivities (at 4.5 K, typical values of the thermal conductivity of liquid helium, superconducting material and copper are $k_{\text{He}}=0.024W{m}^{-1}{K}^{-1}$, $k_{N{b}_3\text{Sn}}=0.04W{m}^{-1}{K}^{-1}$ and $k_{\text{Cu}}=708W{m}^{-1}{K}^{-1}$; and the maximal ratio of thermal conductivity can be as high as about 30,000), the high-performance finite analytical method (FAM) is recommended to calculate $k_{\text{eff}}$. After obtaining the effective transverse thermal conductivity $k_{\text{eff}}$ of the bundle region, the heat transfer coefficient can be calculated directly by solving a simple Poisson equation under proper boundary conditions. Two case studies are performed, including the JT-60 Super Advanced (JT-60SA) CICC and the dual channel International Thermonuclear Experimental Reactor, Toroidal Field Performance Sample (ITER-TFPS). The calculated values of heat transfer coefficient are consistent with the experimental results, which verifies our proposed model.