Answer to Question #207487 in Mechanical Engineering for amam

Question #207487

Air is heated in a 4cmu 4cm square duct at uniform surface flux of 590 The mean air velocity is 0.32 m/s. At a section far away from the inlet the mean temperature is 40 . The mean outlet temperature is 120 . Determine the required length and maximum surface temperature.


1
Expert's answer
2021-06-17T07:37:24-0400

Mean temperature "\\bar{T_m}=\\frac{T_{mi+T_{mo}}}{2}=\\frac{40+120}{2}=80^oC"

"L=\\frac{\\rho s \\bar{u}c_p(T_{mo}-T_{mi})}{4q''_s} = \\frac{0.9996*0.04*0.32*1009.2(120-40)}{4*590}=0.4378 m"

Reynold's number, "Re= \\frac{\\bar{u}De}{v}= \\frac{0.32*0.04}{20.92*10^{-6}}=611.9"

The flow is laminar, hence the Nusslet number , "Nu=\\frac{h}{k}=3.608* \\frac{0.02991}{0.04}=2.7 W\/m^{2 \\space \\space\\space 0}C"

"T_s (L)=T_{mi}+q''_s[\\frac{4L}{\\rho s \\bar{u}c_p}+\\frac{1}{h(L)}]= 40+590[\\frac{4*0.4378}{0.9996*0.04*0.32*1009.5}+\\frac{1}{2.7}]=338.5^0 C"


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