Question

3 - (50 pts.) A fluid flow in a circular pipe is heated with a constant surface temperature. The pipe diameter is set to D (in m) and the length of the pipe to L -2.5m. The inlet temperature is 300 K and the inlet velocity is uniform. Use the following air properties: p=1 kg/m', u=2x10* Pa-s, k=0.03 W/m-K. The Reynolds number to Rep - 200 and the Prandt number to Pr=1.75. A section of the pipe is heated with a constant surface temperature of T, as it is showed in the figure. The surface temperature is 7,-450 K. Note: P-6 D = 0.035 m. a) (5 pts.) Is the flow hydrodynamically fully developed in the heated region. b) (5 pts.) Is the flow thermally fully developed at the end of the heated region? c) (20 pts.) Which will be the mean temperature at the end of the heated region? d) (20 pts.) Which will be the heat transfer rate to the pipe in Watts? 1 - 450K ID 1.- 450K L1 m L-10 m L-0.5m

Answer 1

Solution to question is through empirical relations which are found out experimentaly I cannot post the results directly because of HomeworkLib policy, but I tried to explain it . U can use Google to check these empirical relations also if you have doubt you can use comment section.

given - L = 2.5m D=1035m T = 3ook T = 450 P= 1 kg/m3 M= axiory pas K = .03 w/mk Re Por 1.75 se g+ 1056 Re as for fly dronomically developed flow using empircally bwrlopol yatalion, 4 2 L b 59 7.056*2w •035 19.79 035 = 41265 m / =) Entry Lingth is greater than 41265 m flow is developed b) for themally fully develop Emperical relation is os Re Pr L р =) L 03) s.Os xacox [125] =) / L = .6125m 3) Entrance length is less than total dength at End 2. flow is Thermally developed of heated region

I y Now For Constant wall Temprature Nussult No = 366 constant 3.66 Ô Tw2450k =) hle 'T til 300k = Ti Le = YAG 4x (02) *D *L: 035m Substituting Le in o → h (.035), 3:66 03 =) ha 3.137 w/mk

Also PY : ищо 7) 1.75 = 2x107x म "o 3 How wing (p = 262,5 I kyk relation for Const. kall temprature -Chis do] e Т- Ти Ti - Tw m up 3.137 X XPL e w TYSO 300-450 8 x Volume x 262.5 T-450 3.137 X ADXL - ) el 2625 -120 IX 0%x2 *262,5 é- [ 318 =) T-YDO 3.13 7 X Y 0358 2 6215 w a Touro -1.3657 e -150 TayTO ==38.277 >> T= 411.78?k d) q = mlp dT > q = px Vol x Cpx dT IX D2 x 1 x 262.5 x 7411•722-30)
q=28.01 watts/