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S2017_ME454_Exam02_Key.pdf - ME 454 Spring 2017 Name h”...

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Unformatted text preview: ME 454 Spring 2017 Name h” «W06 Scott Exam #2 Total Points: 100 pts The points for each problem are listed. Be sure to include the symbolic version of the equation when you are solving a problem. ifyou find yourself running short oftime, explain how you would finish the problem if you had time (for partial credit). 1. 36 points. The top surface of the passenger car of a train moving at a velocity of 70 km/h is 2.8 m wide and 8 m long. The top surface is absorbing solar radiation at a rate of 200 W/mz, and the temperature of the ambient air is 30 °C. Assuming the roof of the car to be perfectly insulated and the radiation heat exchange from the surface to the surroundings is negligible, determine the average temperature of the top surface of the car. You do not need to list your assumptions. qusolar = 200 W/m2 be = 30 0C Air Properties: k = 0.03 W/m-K v = 1.6 x 10 ‘5 mZ/s p = 0.6 kg/m3 Pr=0.7 4———————————> L=8m \\ Solution: Th5 pirdolrewx ‘6 Cked—MUY Q. "wmmdfinn Vrch a Qkh ?lu\"€ QUICM alum kw. “mum Must c.1u o.\ M klasar cl snkr‘ (WC? , Wei—om. h .IQQQEA=HHM/S M \n 300mm KM ‘0 sa \i—is i—w‘a. plow at“ Rem." \ivl; : m'qm/S (ng -— 37'wa motsmce wwisvw’rfiiwsm. M» x ro’gMz/s' valcw $*¢{U\(“\‘r flood“ ‘motutmi 'lurwlmcc, we‘ll “Sum? waist-(Al ‘ /3 Flow 93/ Rae‘s—X”). __ 4/5- IL E ~43?“ Nuf‘ (0'03? REL “8143?? 2 I ‘t 4,? V3 \ 70.0w (tam em} (7+3 = rm -— Cl ("3.63531g TV Nut “ ': “EL/“A: : 4411‘? fiat-K L 8M 72:" J 0 Rd l e ms+ Le (zed—E Naif: M steely gird—fi, 9K“ M atlas r h icjf: ragga/'Z‘fi'zwi 32 4 2 f” aw u t .' 3* v m We» comieLHM “a? Eur-3‘} BM‘MCQ ¥ i—A‘7—7/{77‘7F—77E3. 249i r .‘wasols’nafi a. ME 454 Spring 2017 Name Frowkcié Suffi- 2. 38 points. Two long copper rods of diameter D = 10 mm are soldered together end to end, with solder having a melting point of 650 “C. The rods are in air at 25 °C with an air velocity of l 0.4 m/s. Assume the ends of the rods are long enough that the tip is in equilibrium with the l surroundings. What is the minimumI steady state power input needed at the solder ioint to just start melting the solder? List your assumptions Air Properties: k = 0.04 W/m-K ' Fl :»=25°C;V=0. i Air 0W T 4m/S v=5.0X10 >5 mZ/S i llll ‘lllM’ Copper Properties: D = 10 mm I Copper Rod Copper ROd k = 380 W/va Ttip = Tm I 0 Trip = °° SolderJoint Tmelt = 650 0C q=? Assumptions: Sl-gmk/ Sled-Q) lob QavaxLQX-‘K'OVK ‘iv\ (1045 (LE. ad- like g'wx5\, (,oWS'l‘Owk‘\‘ Fmper‘i-“pes/ No Hoe-\- (nng/kiegiobiiole malla‘rim losses Solution: We rotLfi odd MKEmfl—«Lk/ [13va ¥‘\(\S. TLngr-L tl-0 V‘lflo‘ 1‘ we ¢N~ egg ‘WL eiox‘r'me-er \«ex‘rl-rkvLSS-xf (Paw; 7‘4~< Rn _ ‘ Alia. MQH‘l \x/ i: Ly Z b/L chr-1 8: Ru - z lwséu ‘St W p; MS OM” Netok Jrs‘ V44 \"\ . W‘xs "S c‘ fivllMLtf—‘WK Lrufié" Q’I‘Q'JQ SB) Rtktfl: O,HM/$(.O\M\_ 80 v _ T 1 — 5k M _ 09*: 51:ng => Nut-t CR1» r u/ egg—~30 M‘OALDQ ME 454 Spring 2017 Name l’rowms Scfii 3. 8 points. What do the Biot and Fourier numbers represent physically? The Blot number is the ratio of conduction resistance of the solid to the convective resistance. The Fourier number is a dimensionless time. 4. 6 points. What is the main difference between implicit and explicit numerical techniques? In solving the nodal temperatures, the implicit method uses the current temperature of the surrounding nodes, while explicit uses the Qast temperatures of the surrounding nodes. 5. 4 points. Name one way you can verify your numerical solution and state whether it is an internal or external check. There are a number of possible answers. For example: Compare the solution to analytical or experimental date — external Check that the solution is mesh independent — internal Check to make sure the solution is free of any non-physical discontinuities — internal 6. 8 points. Using one of the empirical Nu correlations from the textbook, an engineer in your facility does a quick calculation for the convection heat rejection for one of your process comparing the current set-up with a proposed new set-up. She determines that by increasing the velocity of the cooling fluid with the new set—up, you can increase the heat transfer by 5% compared the current set up and slightly increase productivity. However, it requires down time to replace the blower. Do you follow through on her recommendation? Why or Why not? Not without some additional analysis. The empirical Nusselt correlations can have a high degree of uncertainty (1 10 — 25%). So the 5% bump is probably not statistically relevant and therefore doesn’t warrant the investment. The additional analysis could include an uncertainty analysis and a test for statistical relevance to try to show that it is a statistically relevant increase in heat transfer. ...
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