The freezer compartment in a conventional refrigerator can be modeled as a rectangular cavity 0.3 m high and 0.25 m wide with a depth of 0.5 m. determine the thickness of styrofoam insulation (k = 0.30 w/m⋅k) needed to limit the heat loss to 400 w if the inner and outer surface temperatures are −10 and 33°c, respectively.

Thickness of Styrofoam insulation is 0.02741 m.

Explanation:

Given that,

Height = 0.25 m

Depth = 0.5 m

Power = 400 W

Temperature = 33°C

We need to calculate the area of Styrofoam

Using formula of area

Put the value into the formula

Inner surface temperature of freezer

Outer surface temperature of freezer

We need to calculate the thickness of Styrofoam insulation

Using Fourier law,

Put the value into the formula

Hence, Thickness of Styrofoam insulation is 0.02741 m.

t = 1/400 h   ⇔ 0.0025 h ⇔ 9s ⇔ 0.15 m

any of the answers are correct.