LMTD Calculator with correction factor for Heat Exchanger Design

The LMTD calculator is commonly used in the heat exchanger design optimization. It evaluates the heat transfer efficiency between the hot and cold fluid across the heat exchangers. LMTD directly affects the heat exchanger’s size and performance.

LMTD Calculator for heat Exchanger

This LMTD (Log Mean Temperature Difference) calculator helps users to compute the temperature differences in heat exchangers with both counterflow and parallel flow configurations.

The advanced web tool calculates the LMTD, correction factor, and corrected LMTD based on options given for Shell & Tube heat exchanger types (1-1, 1-2, 2-4 pass) and a user-provided correction factor.

Note: For “Other Shell and Tube TEMA E Type” heat exchangers use LMTD correction factor charts.

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Note: In real applictions exchangers are used in counter flow type as they are more efficent. We have provided calculation for both counter and parallel flow for better understanding

LMTD Formula and Calculation

Logarithmic Mean Temperature Difference (LMTD) is the average temperature driving force for heat transfer in a heat exchanger. LMTD is calculated logarithmically to account for the varying temperature differences between the hot and cold fluids along the length of the exchanger.

The formula for LMTD is given as:

\[\text{LMTD} = \frac{\Delta T_1 – \Delta T_2}{\ln\left(\frac{\Delta T_1}{\Delta T_2}\right)}\]

where:

• \(\Delta T_1 \) is the temperature difference at inlet
• \(\Delta T_2\) is the temperature difference at outlet

For parallel flow, the LMTD is given as:

LMTD_parallel= (ΔT₁ – ΔT₂) / ln(ΔT₁ / ΔT₂)

where:

• ΔT₁ = T_h,in – T_c,in
• ΔT₂ = T_h,out – T_c,out

In parallel flow, the temperature difference reduces significantly along the exchanger which leads to lower efficiency.

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For counter flow, the LMTD is given as:

LMTD_counter= (ΔT₁ – ΔT₂) / ln(ΔT₁ / ΔT₂)

where:

• ΔT₁ = T_h,in – T_c,out
• ΔT₂ = T_h,out – T_c,in

In counterflow, the temperature difference is maintained better, hence results in higher efficiency.

Note: The LMTD is used because it accurately represents the varying temperature difference across the heat exchanger length. It helps in calculating the correct heat transfer and efficient designs.

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Also Read: Nusselt Number Calculator – Significance and Calculation

How to find LMTD Correction Factor

In Heat Exchangers, LMTD is key parameter for calculating heat transfer, this LMTD assume Ideal flow conditions, such as perfect parallel and counter flow.

In real application, correction factor is required to adjust the ideal LMTD to account factors like multiple passes, crossflow or mixed flow patterns. Therefore, corrected LMTD is calculated by multiplying the correction factor with ideal LMTD value.

LMTD_corrected =F x LMTD

where, F is the correction factor.

Steps to Calculate Correction Factor:

Step 1. Identify the Heat Exchanger configuration

Select a type of heat exchanger such as Crossflow, Single-shell-pass / multiple-tube-pass. For each configuration there is a chart for F based on specific parameters (R & P)

Step 2. Determine the dimensionless parameters P and R

To calculate P, use formula given below:

\[P = \frac{T_{h,\text{out}} – T_{h,\text{in}}}{T_{c,\text{in}} – T_{h,\text{in}}}\]

To calculate R, use formula given below:

\[R = \frac{T_{c,\text{in}} – T_{c,\text{out}}}{T_{h,\text{out}} – T_{h,\text{in}}}\]

Step 3. Locate the F on Chart

Using the selected type of heat exchanger configuration (e.g., single-shell-pass, two-shell-pass), refer to the corresponding chart or empirical correlations for the correction factor (F). These charts are specific to the configuration and show F as a function of P and R.

Note: Here in the above calculator we have used the correlation provided in the paper – Bowman, R. A., Mueller, A. C., & Nagle, W. M. Mean Temperature Difference in Design.

User may refer charts from the link given here:

• LMTD correction Factor – Perry’s Handbook for Chemical Engineers
• LMTD correction Factor – Industrial Chemical Process Design, 2nd Edition

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Step 4. Determine F Using the Chart

1. Locate the calculated R value on the horizontal axis.
2. Locate the P value on the vertical axis.
3. Find the intersection point of R and P on the chart to read the correction factor F.

After determing the value of F from the chart, caluclate the corrected LMTD.

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Python Code for LMTD Calculation

This Python code calculates the Log Mean Temperature Difference (LMTD) for both parallel and counterflow heat exchangers taking the temperatures at the hot and cold fluid inlets and outlets.

User can input the correct value from the reference given LMTD correction factor charts based on the values of R and P for the desired type of heat exchanger.

import math
from tabulate import tabulate

def calculate_lmtd(T_hot_in, T_hot_out, T_cold_in, T_cold_out, flow_type):
    # Calculate LMTD for both parallel and counterflow
    if flow_type == "parallel":
        lmtd = ((T_hot_in - T_cold_out) - (T_hot_out - T_cold_in)) / math.log((T_hot_in - T_cold_out) / (T_hot_out - T_cold_in))
    elif flow_type == "counterflow":
        lmtd = ((T_hot_in - T_cold_in) - (T_hot_out - T_cold_out)) / math.log((T_hot_in - T_cold_in) / (T_hot_out - T_cold_out))
    else:
        raise ValueError("Invalid flow type. Choose 'parallel' or 'counterflow'.")
    return lmtd

def calculate_temperature_ratios(T_hot_in, T_hot_out, T_cold_in, T_cold_out):
    # Calculate temperature ratios R and P
    R = (T_hot_in - T_cold_in) / (T_hot_out - T_cold_out)
    P = (T_hot_in - T_cold_out) / (T_hot_out - T_cold_in)
    return R, P

def corrected_lmtd(lmtd, F):
    # Calculate corrected LMTD
    return lmtd * F

# Example Inputs (in Celsius)
T_hot_in = 150
T_hot_out = 100
T_cold_in = 30
T_cold_out = 50

# Calculate LMTD for Parallel Flow
lmtd_parallel = calculate_lmtd(T_hot_in, T_hot_out, T_cold_in, T_cold_out, "parallel")

# Calculate LMTD for Counterflow
lmtd_counterflow = calculate_lmtd(T_hot_in, T_hot_out, T_cold_in, T_cold_out, "counterflow")

# Calculate Temperature Ratios R and P
R, P = calculate_temperature_ratios(T_hot_in, T_hot_out, T_cold_in, T_cold_out)

# Assume Correction Factor F (example value)
# User should get the right correction factor value based on type of heat exchanger
F = 0.99

# Calculate Corrected LMTD for Parallel Flow
corrected_parallel = corrected_lmtd(lmtd_parallel, F)

# Calculate Corrected LMTD for Counterflow
corrected_counterflow = corrected_lmtd(lmtd_counterflow, F)

# Prepare the results for vertical column display
table_data = [
    ["Parameter", "Parallel Flow", "Counterflow"],
    ["LMTD (°C)", f"{lmtd_parallel:.2f}", f"{lmtd_counterflow:.2f}"],
    ["Temperature Ratio R", f"{R:.2f}", f"{R:.2f}"],
    ["Temperature Ratio P", f"{P:.2f}", f"{P:.2f}"],
    ["Corrected LMTD (°C)", f"{corrected_parallel:.2f}", f"{corrected_counterflow:.2f}"]
]

# Print the table using tabulate
print(tabulate(table_data, headers="firstrow", tablefmt="grid"))

Output:

+---------------------+-----------------+---------------+
| Parameter           |   Parallel Flow |   Counterflow |
+=====================+=================+===============+
| LMTD (°C)           |           84.11 |         79.96 |
+---------------------+-----------------+---------------+
| Temperature Ratio R |            2.4  |          2.4  |
+---------------------+-----------------+---------------+
| Temperature Ratio P |            1.43 |          1.43 |
+---------------------+-----------------+---------------+
| Corrected LMTD (°C) |           83.27 |         79.16 |
+---------------------+-----------------+---------------+

Resources

• Heat Transfer a Practical Approach – Book by Yunus A Çengel
• Bowman, R. A., Mueller, A. C., & Nagle, W. M. Mean Temperature Difference in Design.
• Industrial Chemical Process Design, 2nd Edition – Douglas L. Erwin, P.E
• “Heat Transfer Book” by David W. Hahn.
• “Introduction to Heat Transfer” by Frank P. Incropera, David P. DeWitt, Theodore L. Bergman, and Adrienne S. Lavine.

Disclaimer: The content provided here is for educational purposes. While efforts ensure accuracy, results may not always reflect real-world scenarios. Verify results with other sources and consult professionals for critical applications. Contact us for any suggestions or corrections.