considered to be hazards at the workplace. Consider a machine surface that is made of a $5-$mm$-$thick aluminum with a thermal conductivity of $237\frac{W}{m}-K.$ During operation the machine dissipates about $300\frac{W}{m^2}$ of heat to the surroundings, and the inner aluminum surface is at $190C.$ To prevent machine operators from thermal burns, the machine surface can be covered with insulation. The aluminum$/$insulation interface has a thermal contact conductance of $3000\frac{W}{m^2}*K.$What is the thickness $($in mm$)$ required for the insulation layer with a thermal conductivity of $0\mathrm{.}06\frac{W}{m}K$ in order to maintain the surface temperature at $45C$ or lower?