$(2)$ Consider a person with a skin $/$ fat layer of thickness $3$ mm and effective thermal conductivity $0\mathrm{.}3\frac{W}{m}K.$

The person has a surface area $1\mathrm{.}8m^2$ and wears snow suit made from silica aerogel insulation with very

low thermal conductivity of $0\mathrm{.}014\frac{W}{m}K.$ The outer surface of skin$/$fat layer is exposed to the environment

$($air or water$)$ at $10C,$ and its inner surface is at a temperature $35C.$ The emissivity of the outer surface of

the snow suit is $0\mathrm{.}95.$ What thickness of aerogel insulation is needed to reduce the rate of heat loss to $100$ W

in air and water? What are the resulting skin temperatures?

Convection heat transfer coefficient $($Air$)$ : $2\frac{W}{m^2}K$

Convection heat transfer coefficient $($Water$)$ : $200\frac{W}{m^2}K.$