Question

The roof of a refrigerated truck compartment consists of a layer of foamed urethane insulation (t2 = 62 mm, ki = 0.026 W/m K) between aluminum alloy panels (t1 = 6 mm, kp = 180 W/m K). The length of the roof is L = 9 m. The net solar radiation into the roof is 131 W/m2. The temperature of the inner surface is Ts,i = -3 °C and the air temperature is T. = 30 °C. The convective heat transfer coefficient for the top surface of the truck is h = 32 W/m2K. Find Ts, in °C. Frank & Dave's Frozen Desserts for Those Who Don't Count Calories TOT

Answer 1

datai = criven → Thickness of Aluminum alloy plates, ti 6 mm - Thermal Conductivity of Aluminum Alloy, Kp = 180 W/m - Thickness of layer of foamed urethane tz= 60 mm. -> Thermal Conductivity of foamed Urethane Ki=0.026 - Net solat radication on Roof, oo 99 = 131 W/m² - Temperature of inner surface ts, i = 93°C - Aiz Temperature Too = 30°C - Convective heat Transfer coefficient , h = 32 x v Ts,o KP a t Now, Torell Heelt Transfer on Truck Roof Surfence, Q = Solar radication & Convection Hecet Transfet - Ist ac Ki nákfot Ts, i t - Convective Heat Tremsfer, och uc = h (Too - Tso) of (Cross-section of roof refrigerated tema) Q = 9s + Vc = 131+ 324 (30-Tso] ----- Tremsfer Through the Roof can also be => Noce, Heat given by Q = Too - - Toi Tsi W/m2 {Rth cię and El Erth = Total Thermal Resistance between inneę surfacce h+ the + thit te Elth = ħ + + 1+ 2+1 KP K KP

..enth- 32 ' 0.026 180 Elena tot 0.062 + 2X 0.006 Ehin = 2. 4159 km² 2= Too - Tsi - 30-63) 2.4159 Q-13.659 C/m2) Efth Now From equation , R = 131 + 32% (30 – Ts,o). 1:13:659 = 131 + 32%C30- Ts,o) 82 (30-T3,0) = -117.341 30 - T5,0 = -3.667 ... Ts,o=30+3.667 1. Ts,o = 33.667 °C
So, Temperature of Outer surface of refrigerated truck will be 33.667 oC.