# Logarithmic mean temperature difference for heat transfer

• amrmohammed
In summary, the question is about calculating the logarithmic mean temperature difference (LMTD) for heating water through a tube with a fixed temperature. The equation used is LMTD = (Ti - Te)/(ln[(Ts-Te)/(Ts-Ti)]). The attempt at a solution resulted in a LMTD of 12.1 C, which is incorrect as it should be greater than the initial temperature of 21 C. The poster is unsure if they are missing something in their calculation.
amrmohammed

## Homework Statement

[Update: just realized that the LMTD is a temperature difference, so my question was not valid] :P

Calculate the logarithmic mean temperature difference (LMTD) to heat water flowing through a tube from 21 C (Ti) to 40 C (Te) if the tube has a fixed temperature of 45 C (Ts).
I should then calculate the length needed, which I can do. I am stuck with calculating the logarithmic mean temperature difference as I get a number that is less than the initial temperature of the water, which I know should be wrong!

## Homework Equations

LMTD = (Ti - Te)/(ln[(Ts-Te)/(Ts-Ti)])

## The Attempt at a Solution

For the given parameters:
LMTD = (21-40)/(ln[(45-40)/(45-21)]) = 12.1 C

Last edited:
This is obviously wrong as the LMTD should be greater than the initial temperature of the water, 21 C. Is there something that I am missing?

## 1. What is the logarithmic mean temperature difference (LMTD) formula?

The LMTD formula is used to calculate the average temperature difference between two fluids in a heat exchanger. It is given by LMTD = (ΔT1 - ΔT2) / ln(ΔT1/ΔT2), where ΔT1 and ΔT2 are the temperature differences at the hot and cold ends of the heat exchanger, respectively.

## 2. How is the LMTD used in heat transfer calculations?

The LMTD is used in heat transfer calculations to determine the rate of heat transfer between two fluids in a heat exchanger. It takes into account the temperature difference between the two fluids and the logarithmic average of their temperatures, allowing for a more accurate calculation of the overall heat transfer coefficient.

## 3. What is the significance of the LMTD in heat exchanger design?

The LMTD is an important parameter in heat exchanger design as it helps to determine the required surface area for effective heat transfer. By using the LMTD formula, engineers can optimize the design of heat exchangers to achieve the desired heat transfer rate.

## 4. What factors affect the LMTD?

The LMTD is affected by many factors, including the type of heat exchanger, the flow rate and properties of the fluids, and the inlet and outlet temperatures. Additionally, any variation in flow direction, fluid properties, or heat transfer coefficients can also impact the LMTD.

## 5. How is the LMTD different from the arithmetic mean temperature difference (AMTD)?

The LMTD and AMTD are both used to calculate the average temperature difference between two fluids in a heat exchanger. However, the LMTD takes into account the logarithmic average of the temperatures, which is more accurate for non-linear temperature profiles. The AMTD, on the other hand, assumes a constant temperature difference between the two fluids, which may lead to less accurate results.

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