The thickness of polystyrene, t = 0.02m
Inner dimensions of the box, l*b*h =0.5m * 0.3m * 0.3m
Outer dimensions of the box = (l+2t) * (b+2t) * (c+2t)
= (0.5+2(0.02))m * (0.3+2(0.02))m * (0.3+2(0.02))m
= 0.54m * 0.34m * 0.34m
Ambient temperature, Ta = 30 C = 303K
Inner wall temperature, Ti = temperature of ice-water = 4 C = 277K
Let outer wall temperature be To
Conductivity of polystyrene, k = 0.021 W/mK
Assuming free convection of air to the exposed surface of the cooler, h ~ 5 to 25 W/m2K
Heat transfer coefficient of air at 30C, h = 10 W/m2K -- assumed, for stagnant air
Area for heat transfer, A = 5 faces of the cooler exposed to air
Assuming that no heat transfer occurs at the bottom face of cooler.
Heat flux through cooler by conduction = Heat flux from cooler to air by convection
So heat flux through cooler, q:
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