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Appendix E: Psychrometrics and Sensible Heat Ratio E.1 Sensible heat ratio in terms of log-mean differences The sensible heat ratio is defined as: SHR = qsensible (E.1) qsensible + qlatent For sensible heat transfer, based a resistance network and the log-mean difference is: 1=α+1 (E.2) UA href Aair hairAair qsensible = href hair Aair ⋅ LMTD (E.3) href +αhair Localized mass transfer is given by: qlatent = hmass A(ωair − ωsat )h fg (E.4) As a result, incorporating the heat/mass transfer analogy, the overall latent heat transfer based on log-mean difference is: hmass = 1 UA hheat cp,mLe2/3 1 (E.5) (E.6) (E.7) (E.8) (E.9) From the expression for sensible heat ratio it is evident that this is independent of capacity, which can be explained based on psychrometric considerations. Since the latent and sensible heat transfer is a function of the = qlatent = hairAair ⋅LMωD⋅hfg = c p,m Le2 /3 cp,mLe2/3 hair Aair h A ⇒UA= air air hmass A cp,mLe2/3 Combining the above, the sensible heat ratio is determined by: SHR = 1 1+ LMωD⋅hfg ⋅(href +αhair) LMTD ⋅cp,m ⋅Le2/3 ⋅href Based on the previous equations the required heat exchanger area can be calculated by: Aair = qtotal h LMTD LMωD⋅h hair ref + fg h+αh cLe2/3 ref air p,m E.2 Psychrometric relationship 73PDF Image | Comparison of R744 and R410A
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