Typically, satellites contain electronic devices which often operate at cryogenic temperatures to reduce the signal to noise ratio. In order to operate, these devices require electrical power delivered to the cooled electronic device through an electrical conductor connected to the device at one end while the other end is connected to the source of electricity at ambient temperature at the other end. Unfortunately, normal conductors, such as copper, transport to the cold end of the conductor not only the desired electrons from the power source, but also unwanted energy and entropy. Thus, the electrical current lead becomes a heat leak, and the greater the heat leak, the faster the coolant (cryogen) is consumed. In addition, the conductor has an electrical resistance; consequently, the moving electrons also generate entropy via Joule heating (IR dissipation) in the conductor which is also ultimately transported to the coolant. Since coolant is not considered part of the satellite payload and since a limited supply of coolant is available, it is desirable to reduce these sources of entropy. One possible solution is to employ superconducting current leads. When materials undergo a transition from the normal state to the superconducting state, both their electrical resistivity and their thermal conductivity are reduced substantially. As a consequence, Joule heating, as well as energy and entropy transfer through the conductor into the cryogenic region of a satellite, can be significantly reduced by employing superconducting current leads for electronic devices. If properly designed, this reduced heat leak can extend the lifetime of the cryogen and/or decrease the amount of cryogen needed for a mission by a substantial amount. Unfortunately, metallic superconductors undergo the superconducting phase transition at very low temperatures, typically Te < 10 K, which is below the temperatures usually found in these systems. Ceramic materials, on the other hand, undergo the superconducting phase transition at significantly higher temperatures, sometimes as high as 100 K. However, these superconductors, known as high Te superconductors, are brittle and lack the structural integrity of metals; hence, they cannot be used alone as superconducting current leads. Typically, thermalfluid engineers design these current leads as composite structures with a high T, material as the core and a superconducting metal as the sheath. As shown in the sketch below, NASA satellite ASTRO-E2 employs such composite current leads with magnesium diboride, MgB2, as the core material and pure niobium as the structural sheath. The superconducting transition temperature for the magnesium diboride is (T)MgB2 = 39 K while that of the niobium is (T)Nb = 9.2 K. (Niobium has the highest value of T. of all pure metals.) The leads in question have a length of R = 25 cm with end point temperatures of TL = 1.3 K and TH = 17 K. The outer surface of the leads is adiabatic due to the ultra-high vacuum conditions of outer space. Because of the temperature gradient in the leads, the niobium is superconducting with a concomitant reduction in thermal conductivity for only a portion of its length while the magnesium diboride is superconducting throughout its length. Thus, the MGB2 functions as the electrical current carrier with essentially no current flowing in the niobium sheath, NOTE: The temperatures in the core and sheath can be assumed equal at any given axial location within the lead. (b) Determine the heat leak Q for a current lead of this design. NOTE: The following data for the thermal conductivity are average values representative of the true values and merely serve to illustrate the design concept presented here. Actual thermal conductivity data in this temperature range are a very strong function of the temperature and would require numerical methods for their use in the design process. MgB, in the superconducting state: ko = 0.847 W/m K Nb in the normal state: k, = 67.3 W/m K Nb in the superconducting state: k,= 18.2 W/m K Current lead T = 9.2 K , - 1.3 T,-17K Power supply Electronic device - 25 cm LNiobium superconducting over this length Niobium normal conducting over this length Section A- A MgB, D- 100 um Nh A-7.854 x 10" m D- 175 um Ae-1.62 x 10 m NOTE: Ium - 10 m