In the example in class we calculated the heat loss rate from a human body in air and water

environments $($Example $1\mathrm{.}6$ or $1\mathrm{.}7$ depending on edition$).$ Now we consider the same conditions

except that the surroundings $($air or water$)$ are at $10C.$ To reduce the heat loss rate, the person

wears special sporting gear $($snow suit and wet suit$)$ made from a nanostructured silica aerogel

insulation with an extremely low thermal conductivity of $0\mathrm{.}014\frac{W}{m}K.$ The emissivity of the

outer surface of the snow and wet suits is $0\mathrm{.}95.$ Person surface area is $1\mathrm{.}8m^2.$ What thickness

of aerogel insulation is needed to reduce the heat loss rate to $100$ W $($a typical metabolic heat

generation rate$)$ in air and water? What is the resulting outer insulation temperature $(Ts,o)$ and

the skin temperature $($Ts$)?$