Question

4) Air at 101 kPa and 360 K flows at 15 m/s over a flat plate maintained at 300 K Assume that the transition Reynolds number is 5x10 (0.332R 12Pr1/3 Re < 5 x 105 0.029Repr0:43 5 x 105 < Re <3 x 107 Assume that k-0.03 W/( mK), 20x10* m?ls, Pr-0.7.p=1.16 kg/m a) If the plate is 2 m long, sketch the local heat transfer coefficient over the plate. Specify the functional form of h with respect tox b) For the 2 m long plate, sketch the local wall shear stress over the plate. c) For a case where the plate length is variable, sketch the total heat transfer rate per unit width to the plate as a function of plate length. Specify the approximate functional dependence of Q' with respect to plate length d) Calculate the heat total heat transfer rate per unit width to the plate for a 1.0 m long plate e) For a laminar boundary layer, using a scaling perspective, how does Nu, vary with 8x)? 1) Is this scaling valid for a turbulent boundary layer? Answer yes or no. h(x)

Answer 1

In the given zuestion we have to Plot the graph between different parameter with respect to the length of the Plate. As All Parameter related to Reynolds yumber so rest find out Reynolds Number along the length. * Here Length of the plate (4= rm. I am dividing this into a earts as 0.5m, im, 1.5m and 2m. you com divided into many parts for getting enact on graph. pe = out. Whe UL Ren = in U= 15 mis. v=20x10-6 m2/s. calculate Regnolds number for different Just put the values and section. Plate Length u=0.5 Wol n=01.5 non corresponding 3.75x105 7.50X105 1.125x06 1.50X106 Reynolds number so from this we are getting ; at Length toom to na the frow is turbulent. To get enact point from where turbulent how start. put Rez 5x105 [ As it is critical point] 1 5X105 - 15 m noxorb Ina 0.66m That means before the length of Dobb m, the flow is miner and after 0.66m the flow is turbulent. According to the frow we have to use Nun formula

* to sketch † the local heat tromster Coettinent non We know Wuna K. = 0.332 Ren/2 pr % - for = 0.029 Rens pro:43 - Laminer - 0.332 Re% prie turbulen for Laminer 0.029 Penis pro:43 - turbulent, Just put the values and make the table of blu) and m. Į k20,oo, wine, pr=oiz. ç. 120.5 na 1.5 Apy I hu= 10.83 hun = 37.40 Laminer/ W/m2u 34.49 32.56 pe 5x105 . APPLZ turbulent As Rey 5x105 . you can find different Consideration of different hn length according to the 37.40 wind 34.49 32.56 • 10.83 0.5 1 1.5 2 m m ). graph will be linear as & is raring linearly with respect to n.

(b). To sketch graph b/w Local wall shear stress us n. ble know the formule for local wall shear stress 17. = Gux Pu2 p= 66 1116 kg/m3. to 15 mis. Where Can= 0.664 = Local friction coest pe I Reme V Ren Just make a table for better understand to draw graph. w 1321.5 nur 2 can I 1.DBX103 7.6604 6.26410-4 5.42x10-4 To 0.140 10.099 To.o81 0.070. 0-144 YoLM) 0.099 0.081 0.081 • 0.070 0.067 0.04 Take proper scale for drawing enact graph 0.027 1.5 2n (6) To Skeck the is variable, graph between heat transfer rate us length. formula is d= 5 A (Torte). b= Average heat transfer Coeftinent, Ingeneral (5= 2ha. V premember for your mo 97 know leage and To=3604 and Too = 300k.

Ensim Lyr1.5 Luram Techin 21.66 54.8 68.98 65.12 Consider 0ทร์- wiath. 649.8 w/ 4468 6208.2 78 14.4 Froo. 07814.4 w OLL) Groo 6208.2 Stoof 44B8 4000 3000 2000 1boo & 649.8W 0 0.5 1 1.5 2 m Note. I have drawn the graph roughing Just to show you wh How it is varing with respect to given parameter. you please learn the concept and a draw yourself and you com increase the wee of Number of finding parameter, to get more onas graph you com tame total length into 6 or 8 divisible part. * (d). To Calculate total heat transter rate per unit width to the plate for a Im Long Plate 0 - TAAT & (+ 4.8) (1+1) (360-300) [5= 2 bu] do - 4488 w. Ans.

For Laminer Boundar Nur= 0.332 Rena pris. and boundary layer thicknen p Sim sy men le s(m) x (Renya and Win a Renta 7 Hona Ren in » Hona S (4) * (Ren) [as vai This is the reauired relation between Nusselet Number and boundary Layer thickness. The scaling is valid for turbulent boundary layer also as all parameter as variable with respect to w as well as pegnolds Number, Thoml