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030810 sec14-basic-desig

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

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ChE 120B 14 - 1 Basic Design Equations Steady state 2 2 1 p z T T T C u k r z r r r z ( ) only z z u u r ~ T T O z L 2 2 2 2 2 2 ~ / T T d T d T L O r R dr dz R So….. In most instances 2 2 1 T T T r z r r r p z T C u z So….. p z T k T C u r z r r r 1 @ 0 T T z @ R T T r R 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 0 0 0 2 2 2 R R z z R z u rdr T u rdr T T Q u rdr This is the mixing-cup temp or the mass-averaged T . We can radially average the differential equation above: 0 0 1 R R p z T T C u rdr k r rdr z r r r ; 0 0 B.C 0 . | | R R p z R dT dT C u T rdr k r kR z dr dr
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