LMTD Calculator
Calculate Log Mean Temperature Difference for heat exchangers with parallel flow, counter flow, and shell-tube configurations
Calculate LMTD
Select the type of heat exchanger configuration
Hot Fluid Temperatures
Cold Fluid Temperatures
LMTD Results
Formula used: LMTD = (ΔT₁ - ΔT₂) / ln(ΔT₁/ΔT₂)
ΔT₁: 0.00°C, ΔT₂: 0.00°C
Configuration: Counter Flow
Configuration Analysis
Example Calculation
Shell and Tube Heat Exchanger
Given: Shell and tube heat exchanger with 2 shell passes and 4 tube passes
Hot fluid (shell): Inlet = 80°C, Outlet = 40°C
Cold fluid (tube): Inlet = 20°C, Outlet = 50°C
Solution:
1. Calculate for counter flow: ΔT₁ = 80-50 = 30°C, ΔT₂ = 40-20 = 20°C
2. LMTD = (30-20)/ln(30/20) = 24.66°C
3. Calculate P and R parameters for correction factor
4. Apply correction factor: LMTD_corrected = F × 24.66°C
Counter Flow Example
Hot fluid: 100°C → 60°C
Cold fluid: 30°C → 70°C
Solution: ΔT₁ = 100-70 = 30°C, ΔT₂ = 60-30 = 30°C
LMTD = 30°C (equal temperature differences)
Heat Exchanger Types
Counter Flow
Fluids flow in opposite directions
Highest heat transfer efficiency
Parallel Flow
Fluids flow in same direction
Lower efficiency, simpler design
Shell & Tube
Complex multi-pass design
Requires correction factor
LMTD Key Facts
Used in Q = U × A × LMTD heat transfer equation
More accurate than arithmetic mean for exponential temperature profiles
Counter flow gives highest LMTD for same conditions
Shell and tube require correction factors from charts
Alternative to effectiveness-NTU method
Understanding LMTD
What is LMTD?
The Log Mean Temperature Difference (LMTD) is the logarithmic average of the temperature differences at the inlet and outlet of a heat exchanger. It accounts for the exponential temperature profile that occurs during heat transfer processes.
Why Use LMTD?
- •Temperature varies exponentially along heat exchanger length
- •Arithmetic mean overestimates heat transfer
- •Provides accurate driving force for heat transfer
- •Essential for heat exchanger design and analysis
LMTD Formula
LMTD = (ΔT₁ - ΔT₂) / ln(ΔT₁/ΔT₂)
Counter Flow:
ΔT₁ = Thi - Tco, ΔT₂ = Tho - Tci
Parallel Flow:
ΔT₁ = Thi - Tci, ΔT₂ = Tho - Tco
Special Case: When ΔT₁ = ΔT₂, LMTD equals the temperature difference (avoiding ln(1) = 0)
Shell and Tube Correction Factor
For complex heat exchangers like shell-and-tube or cross-flow configurations, the LMTD calculated for counter flow must be corrected using a correction factor F:
LMTD_actual = F × LMTD_counter_flow
P Parameter
P = (Ts2 - Ts1) / (Tc1 - Ts1)
Temperature rise effectiveness
R Parameter
R = (Tc1 - Tc2) / (Ts2 - Ts1)
Heat capacity rate ratio
Correction Factor
F is read from charts using P and R values
Typically 0.8 to 1.0