Question

A 5-cm-diameter shaft rotates at 4500 rpm in a 15-cm long, 8-cm-outer-diameter cast iron bearing (k =70 W/m.K) with a uniform clearance of 0.6 mm filled wwith tubricating oil (u 0.03 N.s/m2 and k 0.14 W/m.K). The bearing is cooled externally by a liquid, and its outer surface is maintained at 40°C. Disregarding heat conduction through the shaft and assuming one- dimensional heat transfer, determine (a) the rate of heat transfer to the coolant, (b) the sutacs temperature of the shaft, and (c) the mechanical power wasted by the viscous dissipation in o. ( the properties of oil k0.14 W/m.K, u-0.03 N.s/m2. The thermal conductivity of bearing is given to be k 70 W/m.k) 450m 1 cm 15 om Engine oll at 80°C flows over a 6-m-long flat plate whose temperature is 30°C with a

Answer 1

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Ths a scrend oden Gdinasy difeantial auatu,oud Audegrate rho tusee Euatuen uy)Y Tnde gateieng enstant The feuid velohi ot gurtacmut be £aualt plte The veloutu of Tho Padeg beau c The no.- Slip endikuBn Thu The boundasy (endihieng ar as follous velouy disibutue Apply The tounday Cenditieng gi a V The veloulty raud LJh clasna Calaulate The Vebuty TIDN 60 Ar J Tthe Speed hure,D i ha dlamulen, aud Us00 PM f&M N 5 Cm fe D, aud Substatule 7(sum x 16 m)Cuso) o.uToo) 66 1.78 m/s

The Pates au disecfuen, aud Thuythe temoraturr depends woute he Erusgygatem aedufld uih visceug diasifutiem au 0 K Substitude fo ay2 K aud ntepade tuice dauide EanD bothu idus by k SK 2 K APPly Tha bounchy (enditden aj folbu At 4o C30 At L TIL)70 uv2

Substltute o fer C3 ad To t Vte Cy du Euatdon (2) 2 K 2 :(본v) TI) 2K 2 K To t 2 2 K temperatune gradit by differantiatiy Defeomine the TCY uh espect to y, TCY) To t v 2K Differantiate TheEquatuen (2) uth suPect to y uv2 To t d Y 2 dT dy kL2 Calculate The hiat flux at The UPper wrface L- dy y ki f dT dy Substutute KL2 9ute e het Tamsfe Calauate he Inene A J he atla ehe shaft, aud q di Th hoaf flu al Thu UPper wiface

TIDW fe A, aud Substulute fe ) () (7IDW w The wdth, Daj dlameter, u i dynamic viscakfy L j cleatanc , V J^ velouty &ubstutute 5 Cm for D, 15 Cm fen w 11-78 m/s fe v,a03 . fen u, aud a.6 mm fen L 0.03 15 Cm x Icm Cam ww 0.D3 I.78 (0.o5 Co.15) 0.0006 163 SW Threfore The srate 2wTo-T) 63-5u w-15Cm Do SCm D 5 Cm )CTo -uo 2 T (63.S-o) To uot116S To Eu65 fewpenture The Shaft d

The MechamialPower wasted by The viscou4 diximbusy Euivalent to h grade e huf Jmurotn n ouil Mechamdcal Powen wasled b visceu diihi Glaulade The Wut Thurufere, The Mecamlal Powen wasted by visroug disaitin 63-5 W