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**Unformatted text preview: **Fin Design Total heat loss: q f =Mtanh(mL) for an adiabatic fin, or q f =Mtanh(mL C ) if there is convective heat transfer at the tip C C C , , hP where = , and M= hPkA hPkA ( ) Use the thermal resistance concept: ( ) hPkA tanh( )( ) where is the thermal resistance of the fin. For a fin with an adiabatic tip, the fin b b c b f b t f t f m T T kA T T q mL T T R R θ ∞ ∞ ∞ =-- =- = , C resistance can be expressed as ( ) 1 hPkA [tanh( )] b t f f T T R q mL ∞- = = T b T ∞ Fin Effectiveness How effective a fin can enhance heat transfer is characterized by the fin effectiveness ε f : Ratio of fin heat transfer and the heat transfer without the fin. For an adiabatic fin: C hPkA tanh( ) tanh( ) ( ) If the fin is long enough, mL>2, tanh(mL) 1, it can be considered an infinite fin (case D of table3.4) In order to enhance heat tra f f f C b C C f C C q q mL kP mL q hA T T hA hA kP k P hA h A ε ε ∞ = = = =- → → = nsfer, 1. However, 2 will be considered justifiable If <1 then we have an insulator instead of a heat fin f f f ε ε ε ≥ C A P h k Fin Effectiveness (cont.)Fin Effectiveness (cont....

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