Which of the following statement is incorrect in case of assumption made while deriving LMTD (Logarithmic Mean Temperature Difference) expression?

Explanation:

Logarithmic Mean Temperature Difference (LMTD)

• The Logarithmic Mean Temperature Difference (LMTD) is a logarithmic average of the temperature difference between the hot and cold fluids at each end of the heat exchanger.
• It is used to determine the temperature driving force for heat transfer in flow systems, most notably in heat exchangers.
• LMTD is used in the design and analysis of heat exchangers because it simplifies the heat transfer calculations.
• It assumes that the temperature difference between the hot and cold fluids changes logarithmically along the length of the heat exchanger.
• The LMTD method provides an accurate measure of the average temperature difference when the temperatures of the fluids vary linearly.

Advantages:

• Provides a more accurate representation of the temperature driving force for heat exchangers.
• Useful in the design and analysis of various types of heat exchangers, including shell and tube, plate, and finned tube heat exchangers.

Disadvantages:

• Assumes steady-state conditions, which may not be valid in all practical scenarios.
• Requires knowledge of the inlet and outlet temperatures of both hot and cold fluids, which may not always be available.

Applications: LMTD is widely used in the design, analysis, and performance evaluation of heat exchangers in various industries, including power generation, chemical processing, HVAC, and refrigeration.

Additional InformationLMTD calculation for Parallel flow heat exchanger:

The formula for calculation of LMTD (Log Mean Temperature Difference) for a parallel flow heat exchanger is given by-

\(LMTD_{parallel}=\frac{{{θ _1} - {θ _2}}}{{\ln \left( {\frac{{{θ _1}}}{{{θ _2}}}} \right)}}=\frac{{{θ _2} - {θ _1}}}{{\ln \left( {\frac{{{θ _2}}}{{{θ _1}}}} \right)}}\)

where θ1 = Th1 - Tc1 and θ2 = Th2 - Tc2
LMTD calculation for Counterflow heat exchanger:

\(LMTD_{counter}=\frac{{{θ _1} - {θ _2}}}{{\ln \left( {\frac{{{θ _1}}}{{{θ _2}}}} \right)}}=\frac{{{θ _2} - {θ _1}}}{{\ln \left( {\frac{{{θ _2}}}{{{θ _1}}}} \right)}}\)

where θ1 = Th1 - Tc2 and θ2 = Th2 - Tc1