030810 sec14-basic-desig

030810 sec14-basic-desig - ChE 120B Basic Design Equations...

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ChE 120B 14 - 1 Basic Design Equations T T Z L h = ? R T = ? ± R Steady state 2 2 1         pz TT T Cu k r zr r rz ( ) only zz uu r ~ O zL  22 2 222 ~ / T T dT dT L O r R dr dz R So…. . In most instances 2 2 1 T r r r T z So…. . Tk T r r r 1 @0  TT z @ R TT rR 0@ 0 T r r While this can be solved by separation of variables for some u ( r ) we are interested in an average temperature, not detailed profiles: Define 00 0 2  RR R z ur d r T d r T T Q d r  This is the mixing-cup temp or the mass-averaged T . We can radially average the differential equation above: 1 r d r k r r d r r r ; 0 0 B.C 0 . ||  R R R dT dT T r d r k rk R zd r d r
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ChE 120B 14 - 2 from definitions, 0 2 R z Q uTrd r T 2 | p rR dQ d T CT k R dz dr    mass flowrate w constant Q  2 | p dT T wC k R dz r By continuity  |  R T kh T T r So  pR Dh T T dz R p R T Dh dz TT 1 exp exp 4 R Rp Dhz z St w C D 1 exp 4 LR R L St D ic±-wat±r ² ft T =? L wat±r 75 F o 32 F o ² ft 2 mm i.d. steel capillary Gravity driven water cooler 4 32 2 gr cm 30.48 cm dyn (1) (980 )(2ft) 5.9 10 cm s ft cm 
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This note was uploaded on 03/22/2011 for the course CHE 120B taught by Professor Zasadinski during the Winter '10 term at UCSB.

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030810 sec14-basic-desig - ChE 120B Basic Design Equations...

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