An industrial cold room has four $200$ mm thick walls made of co ncrete. The walls are insulated on the outside with a layer of foam $60$ mm thick. Cladding with a thickness of $15$ mm protects the foam on the outside from the elements. The composite wall surface temperatures are $3\backslash$deg C on the inside and $18\backslash$deg C on the outside of the room respectively. The thermal conductivities of concrete, foam and cladding are $0\mathrm{.}75,0\mathrm{.}35$ and $0\mathrm{.}5$ W$/$m K

respectively.

a$)$ Assuming perfect thermal contact between the layers of the composite walls, draw the typical temperature distribution across the layers and determine the heat energy gained per hour through all $4$ walls of the room with a total surface area of $20$ m$2.$

What does this heat energy represent in terms of the refrigeration system of the cold room?