Question

Question 1 [40 Points] Liquid mercury at 300 K flows over a flat surface at a free stream velocity 0.15 m/s. The flat plate is smooth with a width of 0.25 m and length 0.5 m and is kept at a uniform temperature of 400 K. The flow is parallel to the longer dimension of the plate. Find out: 1. MINIMUM LOCAL convective heat flux, q min and its location (60%) 2. Total convective heat transfer rate, q (40%) Use appropriate correlations from the diagram here (A better resolution picture is in your announcement. Also, Re = Reynolds number, Pr = Prandtl number, Pe = RexPr (Peclet number): To Nu= 0.332RE PUP306

Answer 1

o=15m/s Too-Book TS= 4wok 0.5m Using Regnold's No. Re=fvx = vr at x=2=0.5m REL= 0.15% 0. 5 - 7684 42.623758103 0.0976x106 Hence its a case of mixed flow. Let at xir, transition from laminar to turbulent becaps, 5x105 = 0.15xxer xcr=0.3253m 00976 x 166 We know that, as flow progresses during lamingo flow upto transition Point ha decreases continously. As tromstion occurs, there is sudden rise in bx amd then again starrts decreasing. So minimum hn rom occupat Иy Ин ри x=xer or x=L the ha ha ha ha ACY at x-HR lamingy zone (Just before tromsition) Mux = 0.564 Red (follorquid melals) for Mercury Pv=V_0,0976X166 a 4,915x15 = 0.0196 Pex - 62 442 623 0.0196 =+5075=3709 - 9800 5X165 -0.504 +507503769 9800 hux xos = 69 29 89 55.83 Kf hx6989894 9.12 - 1994:21 W/m2K 0.3253 1575.62 heat flux, q" (X-Men)= 1994-61(400-300) 195421 ka! 157561-74 m2 0.0196 n

at x=L, Ren= 7684 42. 623 using Nur= 0.0296 Real5p 3 495 hx0.5 9.18 .1983 = 0.029667 624 42.623 x 0.0196 buz 8003.66 W/m2K which is greater than that at transition point hence minimum feux occurs cet x= x=0.3253m and minimum value Poin =157561.14 like 2 Total convective heat fromsfer rate. for flat plate, constant Tomd mixed flow, averege Nu niamber Tue=[0.037 R420.037 Rees to. 664 Reser P =1010374.762442.62.3.0.027x15x185) 40664x(6415)]*0.012 hx0.5 9.18 h = 274. 96 x 9.18 - 5642.27 W/m2K Total convective heat fromsfer rate ( assuming Heat Transfer from one side only a = h A (Ts-Too) 048 27x(0.2580+5)×(400-300) Q = 63103.41K1
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