sec13-heat-exch-theory

# sec13-heat-exch-theory - ChE 120B Heat Exchanges/Theory The...

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ChE 120B 13 - 1 Heat Exchanges/Theory The double-pipe heat exchanger Call the hot stream h and the cold stream c and determine all coefficients w.r.t the outside diameter of inside pipe. Usually, we need to figure out the required heat transfer area for a given job, given a flowrate and a temperature difference.

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ChE 120B 13 - 2 Performing an energy balance on each stream separately, we get 0 2 rdz   00 || | cc c hh h hc zz z dq w Cp dt w Cp dt U t t dA   temp & position temp & position temp & position position Usually, 0 ,, wC pwC pU are temperature and position dependent. To simplify, assume mass flow, and c Cp , are independent of temperature hence, position. Then integrate inside equations.    ,2 ,1 ,2 c c h h wCp T T T Q and c wCpd t = Ut td A h t = A c dt tt = UdA wCp h dt  = if we add these two dt t    = 11 This equation relates the ' ts to position for U 0 independent of position, integrate from inlet (1) to outlet (2) ,2 n = UA 1 = ,1 Q 1 = ,1 Q Hence   n = ,2 ,2 Q  = ,1 ,1 Q 
ChE 120B 13 - 3  ,2 ,1 ,1 00 ,1 hc m tt UA Q UA t n   ,1 ,1 m t n  Linear Temperature Dependence of U 0 on Temperature Let 0 Ua b t  and insert this in the balance equation cc c wCpd t = Ut td A h t = A c dt = 0 0 U dA wCp c dt = 0 0 hh U dA dt t = 11 UdA    0 Ut t = 0 dA 21 Q  Let   0 b t t t   2 1 0 t t dt A ab t t Q    2 1 1 | t t t n aa b t     = 2 1 0 1 | t t t n aU   12 1 and Ut n t 1 2 02 0 01 1 nA aUt Q in which,   ; b t t b t t 1 abt ; 2 b t

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ChE 120B 13 - 4 1 02 2 12 Ut a tb t t  2 01 1 Uta t b t t subtract  02 01 2 1 UtUtat t
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sec13-heat-exch-theory - ChE 120B Heat Exchanges/Theory The...

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