The design of an astronaut’s glove requires that you select the thickness of insulation needed to keep the skin surface temperature at 25°C for long periods of time when the outer surface of the insulation is at

−271°C. The skin and insulation are separated by a 1-mm-thick polymer membrane with k = 0.35 W/m K. Blood vessels 3.0 mm below the skin surface keep the temperature there at a constant 37°C. Neglecting heat transfer by radiation:

(a) Determine the thickness of insulation required if its thermal conductivity is 0.07 W/m K.

(b) For the thickness you have selected, what temperature would be sensed by nerve endings located 1.5 mm from the skin surface?