The formula to calculate the Log Mean Temperature Difference (LMTD) is:
\[ \text{LMTD} = \frac{(\text{Tho} - \text{Tco}) - (\text{Thi} - \text{Tci})}{\ln \left( \frac{\text{Tho} - \text{Tco}}{\text{Thi} - \text{Tci}} \right)} \]
The Log Mean Temperature Difference (LMTD) is a logarithmic average of the temperature difference between the hot and cold streams at each end of the exchanger. Outlet Temperature of Hot Fluid is the temperature at which the hot fluid exits the heat exchanger. Outlet Temperature of Cold Fluid is the temperature at which the cold fluid exits the heat exchanger. Inlet Temperature of Hot Fluid is the temperature at which the hot fluid enters the heat exchanger. Inlet Temperature of Cold Fluid is the temperature at which the cold fluid enters the heat exchanger.
Let's assume the following values:
Using the formula:
\[ \text{LMTD} = \frac{(20 - 10) - (35 - 5)}{\ln \left( \frac{20 - 10}{35 - 5} \right)} \approx 18.2047845325367 \]
The Log Mean Temperature Difference is approximately 18.2047845325367 Kelvin.
| Outlet Temperature of Hot Fluid (Kelvin) | Outlet Temperature of Cold Fluid (Kelvin) | Inlet Temperature of Hot Fluid (Kelvin) | Inlet Temperature of Cold Fluid (Kelvin) | LMTD (Kelvin) |
|---|---|---|---|---|
| 15 | 10 | 35 | 5 | 13.952765663781182 |
| 16 | 10 | 35 | 5 | 14.912038429430684 |
| 17 | 10 | 35 | 5 | 15.804440171443215 |
| 18 | 10 | 35 | 5 | 16.644526420472850 |
| 19 | 10 | 35 | 5 | 17.442254446733283 |
| 20 | 10 | 35 | 5 | 18.204784532536745 |
| 21 | 10 | 35 | 5 | 18.937466424262816 |
| 22 | 10 | 35 | 5 | 19.644420022871248 |
| 23 | 10 | 35 | 5 | 20.328897059279203 |
| 24 | 10 | 35 | 5 | 20.993516817582858 |
| 25 | 10 | 35 | 5 | 21.640425613334450 |