Question

3. (20 pts) Preferred air duct shape: You are trying to decide whether to use a square or a round air duct to cool the air inlet temperature is 50 °C) through the duct. a) (5 pts) Write the expression for the convective heat transfer rate on the interior of the round duct (expand fully in terms of properties, not just non-dimensional terms, but do not calculate), b) (5 pts) Write the expression for the convective heat transfer rate on the interior exterior of the square duct (expand fully in terms of properties, not just non-dimensional terms, but do not calculate), c) (10 pts) Calculate the ratio of heat transfer rate of the square duct to that of the round duct. Which duct shape would you use? Assume that both ducts have same cross-sectional area (for apples-to-apples comparison), that side of the square duct is 0.3 m long, and the flow is laminar. The duct surface is isothermal.

Please help with the following problem and show work thank you

Answer 1

for square duct Isothermal Too Constant s 'Ts Constance Ti-soc flow is laminar a=0.3m long 46 dc =402 DH- Hydraulic dia = POP 4a a = 0.3m DHE laminar the As the flow is 3.66 N 니 h ob Keluid 3.66 kf 3.66 x kg 11 b = 0.3 Db To tuua Ida. ńcdTma hpla (Ts-Tm Surface maintain at Canst Temp =) T-c

Is Ts ATI Atz To Tomi mean Ihlet Tenip X-L y=0 h pa mc Tmo-mean Outlet Tem Timo Ts - e 3.66 y PXL (LMTD). h As @ Talal 0.3 Tmi TS ATI-AT2 InCATI ATZ. 72] = 4a92 (LMTD) xkg 12.27 a total 14.64 2(LMTD) * kg a total duct for round II g2=a2 22 = (0.3)? T 4. к 0.33851 m

(6) Nu = bob 3.66 к ha 8.664 kg bh b= 10.82kf h - Heat transfer air. kg - The oral Conductivity q Q Total = h AS LMTD 10.82 2 kg 4. TT YOL (LMTD) 10.82% kefy T X 0.33851 Y L (LMTD) 11.5066CL) (LMTD) Q.1040 Dround duct a total sau 14.64(4) LMTDTG 11.5066 (L) x kf & LMTD2 atofal Round ((MID), (LMD). a total sa 102723 a total Roured from this Square duct is better to use More Heat from of es sale.