With the following materials:~Paper cup~Black Paper~Bubble Wrap~Aluminum FoilYOU DO NOT NEED ALL THE INGREDIENTS USED
First wrap the bubble wrap around the cup, then cover it with aluminum foil. Explanation: You have to mechanisms of heat transfer - heat conduction from liquid the through the wall to the outer surface of the cup - heat transfer to the surrounding by convection and radiation at the surface of the wall. Since material choice does hardly affect convective heat transfer don't bother with this aspect. The radiative heat transfer mainly depends on the emissivity/absorptivity of the material. From the offered materials aluminum foil has the lowest emissivity. If i remember right ε = 0.04 for a polished aluminum and ε = 0.1 oxidized aluminum surfaces .However the emissivity of the aluminum foil is much lower than the emissivity of the other materials. Unfortunately aluminum has a pretty high heat conductivity. So we need another material for insulation between the foil and the cup. The best for this is IMHO the bubble wrap. The reason is not the heat conductivity of the plastic of the bubble wrap. By wrapping it around the cup you add layer of air between the cup and the aluminum foil. And the heat conductivity of air is lower than the heat conductivity of all solids.
