Question

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.

Answer 1

Answer:

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

$A=2(lb+bh+hl)$

Put the value into the formula

$A=2(0.3\times0.5+0.25\times0.5+0.5\times0.3)$

$A=0.85\ m^2$

Inner surface temperature of freezer

$T_{i}=-10°C=263\ K$

Outer surface temperature of freezer

$T_{o}=33+273=306\ K$

We need to calculate the thickness of Styrofoam insulation

Using Fourier law,

$q=\dfrac{kA}{L}(T_{o}-T_{i})$

$L=\dfrac{kA}{q}(T_{o}-T_{i})$

Put the value into the formula

$L=\dfrac{0.30\times0.85}{400}(306-263)$

$L=0.02741\ m$

Hence, Thickness of Styrofoam insulation is 0.02741 m.