The core is at 37C , skin-fat layer thermal conductivity k_s = 0.3 W/m-K, skin emissivity E_s = 0.95, skin-fat thickness l_s = 3 mm, and convection coefficient ℎ_air = 2 W/m2 -K. The jacket has thermal conductivity of k_j = 0.5 W/m-K, jacket emissivity E_j = 0.02, and jacket thickness l_j = 2 cm.
a) Write two energy balances, one at the skin-jacket interface and another at the jacket-air interface. Can any of the terms in your energy balances be ignored?
b) Using your two energy balances, write a new equation that does not depend on the core temperature. You need not simplify this equation.
c) Solve for the skin temperature using your equation from part (b).
d) Calculate the heat flux through the skin using T_s calculated in part
(c). Also, calculate the ratio of the heat fluxes through the skin with and without the jacket on.
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