(1) If one adds insulating material to the outside of a hot wire (circular cross section with a very small diameter) that is exposed to air, the total steady-state heat loss out of the wire will increase with additional insulation until a critical thickness is achieved; any additional insulation thickness added beyond this amount will decrease the heat loss out. Briefly show mathematically that if one adds insulation thickness to the surface of a plane wall at constant temperature Tv (1D heat transfer in the x-direction) exposed to cold air at T. (Ty>T..). no such critical thickness exists adding additional insulation decreases heat rate out. See diagram below. Assume steady state. H Wall kw constant TW h Add insulation to this surface w