An electrically heated glove consists of a flat thin-sheet electrode embedded within a 0.01 m layer of an insulating material with a thermal conductivity of 0.02 W/m K, which is directly in contact with the skin.

Blood vessels, 0.004 m below the skin surface, keep the temperature at 37°C. The external air temperature is −10°C and the external heat transfer coefficient is 5.0 W/m² K. The electrode temperature is 60°C. For this problem, assume that the thermal conductivity of skin is 0.20 W/m K. (a)

Sketch the temperature profiles for this problem assuming a flat wall geometry with the thin-sheet electrode located at a distance x from the outer glove surface. Note that the temperature is maximum at the electrode. (b)

Write explicit expressions for the heat transfer fluxes to the surrounding air and to the skin in terms of known temperatures only, when the thin-sheet electrode is located at a distance x from the outer glove surface. (c)

Determine a distance from the outer glove surface where the thin-sheet electrode should be located if the power generated is 250 W/m².

(d) For the conditions in part

c, determine the temperature at the inner glove surface in contact with the skin.