Question

The roof of a refrigerated truck compartment consists of a layer of foamed urethane insulation (t2 = 21 mm, ki = 0.026 W/m K) between aluminum alloy panels (t1 = 9 mm, kp = 180 W/m K). The length of the roof is L = 13 m. The net solar radiation into the roof is 107 W/m2. The temperature of the inner surface is Ts,i = -4 oC and the air temperature is T[infinity] = 29 oC. The convective heat transfer coefficient for the top surface of the truck is h = 47 W/m2 K. Find Ts,o in oC.

Answer 1

Answer:

Tso = 28.15°C

Explanation:

given data

t2 = 21 mm

ki = 0.026 W/m K

t1 = 9 mm

kp = 180 W/m K

length of the roof is L = 13 m

net solar radiation into the roof = 107 W/m²

temperature of the inner surface Ts,i = -4°C

air temperature is T[infinity] = 29°C

convective heat transfer coefficient h = 47 W/m² K

solution

As when energy on the outer surface at roof of a refrigerated truck that is balance as

Q = $\frac{T \infty - T si }{\frac{1}{hA}+\frac{t1}{AKp}+\frac{t2}{AKi}+\frac{t1}{aKp}}$       .....................1

Q = $\frac{T \infty - Tso}{\frac{1}{hA}}$                         .....................2

now we compare both equation 1 and 2 and put here value

$\frac{29-(-4)}{\frac{1}{47}+\frac{2\times0.009}{180}+\frac{0.021}{0.026}} = \frac{29-Tso}{\frac{1}{47}}$            

solve it and we get

Tso = 28.153113

so Tso = 28.15°C