Question
Download Solution PDFIn a counter flow heat exchanger, if the hot and cold fluids enter at T1 and T2, respectively, whereas cold fluid leaves at T3 and hot fluid leaves at T4, then LMTD is given by:
Answer (Detailed Solution Below)
Detailed Solution
Download Solution PDFConcept:
For counterflow heat exchanger:
Log mean temperature difference is given by:
\(LMTD = \frac{{{\rm{Δ }}{T_i}\; - \;{\rm{Δ }}{T_e}}}{{\ln \left( {\frac{{{\rm{Δ }}Ti}}{{{\rm{Δ }}Te}}} \right)}}\)
Where ΔTi = Thi – Tce
ΔTe = The - Tci
Thi & Tci = Temperature at which hot or and cold water enters respectively
The & Tce = Temperature at which hot air & cold water exits respectively
In the case of the balanced counter flow heat exchanger,
ṁhch = ṁccc = C
ṁh and ṁc are mass flow rates of hot and cold fluid, and ch and cc specific heat capacity of hot and cold fluid.
LMTD for counter-flow heat exchanger, ΔTi = ΔTe
Explanation:
Given:
Tci = T2, Tce = T4, Thi = T1, The = T4
ΔTi = T1 – T3
ΔTe = T4 – T2
\(LMTD = \frac{{{\rm{Δ }}{T_i}\; - \;{\rm{Δ }}{T_e}}}{{\ln \left( {\frac{{{\rm{Δ }}Ti}}{{{\rm{Δ }}Te}}} \right)}}\)
\(LMTD = \rm \frac{(T_1-T_3)-(T_4-T_2)}{In\frac{(T_1-T_3)}{(T_4-T_2)}}\)
Last updated on Jun 2, 2025
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