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

Tso = 28.15°C

Step-by-step 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 =
`(T \infty - T si )/((1)/(hA)+(t1)/(AKp)+(t2)/(AKi)+(t1)/(aKp))` .....................1

Q =
`(T \infty - Tso)/((1)/(hA))` .....................2

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

`(29-(-4))/((1)/(47)+(2*0.009)/(180)+(0.021)/(0.026)) = (29-Tso)/((1)/(47))`

solve it and we get

Tso = 28.153113

so Tso = 28.15°C