Log Mean Temperature Difference in Counter Flow Heat Exchangers

Log mean temperature difference (LMTD) in the logarithmic average between the hot and cold flows at each end of a heat exchanger. The LMTD is used in heat exchangers to determine the temperature-driving force of heat transfer.
CalculationInputs﻿﻿THO
:70K​
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﻿﻿TCO
:25K​
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﻿﻿THI
:90K​
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﻿﻿TCI
:20K​
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Output﻿﻿LMTD
:57.1724203K​
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ExplanationIn counter flow heat exchangers the hot and cold fluids enter at opposite ends, and flow in opposing directions through the heat exchanger. This helps to maintain a large temperature difference between the hot and cold liquids throughout the length of the exchanger. Log mean temperature difference is is used to describe this difference using the following the equation.
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Cold & Hot Counter Flow Heat Exchangers
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Cold & Hot Counter Flow Heat Exchangers
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ΔTLM=(THo−TCi)−(THi−TCo)ln(THo−TCiTHi−TCo)\Delta T_{LM} = \frac {(T_{H_o} - T_{C_i})-(T_{H_i} - T_{C_o})}{ln(\frac {T_{H_o} - T_{C_i}}{T_{H_i} - T_{C_o}})}ΔTLM​=ln(THi​​−TCo​​THo​​−TCi​​​)(THo​​−TCi​​)−(THi​​−TCo​​)​
Where:
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ΔTLM=Log Mean Temperature Difference (K)THO= Outlet Temperature of the Hot Fluid (K)TCO= Outlet Temperature of the Cold Fluid (K)THi= Inlet Temperature of the Hot Fluid (K)TCi= Inlet Temperature of the Cold Fluid (K)\Delta T_{LM} = Log \: Mean \: Temperature \: Difference \: (K) \\ T_{H_O} = \: Outlet \: Temperature \: of \: the \: Hot \: Fluid \:(K) \\ T_{C_O} = \: Outlet \: Temperature \: of \: the \: Cold \: Fluid \: (K) \\ T_{H_i} = \: Inlet \: Temperature \: of \: the \: Hot \: Fluid \:(K) \\ T_{C_i} = \: Inlet \: Temperature \: of \: the \: Cold \: Fluid \: (K) \\ΔTLM​=LogMeanTemperatureDifference(K)THO​​=OutletTemperatureoftheHotFluid(K)TCO​​=OutletTemperatureoftheColdFluid(K)THi​​=InletTemperatureoftheHotFluid(K)TCi​​=InletTemperatureoftheColdFluid(K)
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Log Mean Temperature Difference (lmtd) Calculator
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