LMTD stands for Logarithmic Mean Temperature Difference, which is a method of calculating the arithmetic mean temperature difference in a heat exchanger. The LMTD is calculated using the following formula:
Formula of LMTD
LMTD = (ΔT1-ΔT2) / ln (ΔT1/ΔT2)
Here, ΔT1 is the temperature difference between the hot and cold fluids on one side of the heat exchanger, and ΔT2 is the temperature difference on the other side. This formula is used to calculate the heat transfer surface area of a heat exchanger.
There are two types of heat exchangers such as parallel-flow and counter-flow heat exchangers that differ in the direction of fluid flow. In a parallel-flow heat exchanger, the hot and cold fluids enter at the same end, flow in the same direction, and leave at the same end. In contrast, in a counter-flow heat exchanger, the fluids enter at opposite ends, flow in opposite directions, and leave at opposite ends.
The counter-flow heat exchanger is more efficient than the parallel-flow heat exchanger because it allows for a greater temperature difference between the hot and cold fluids. This results in a higher rate of heat transfer and a smaller heat exchanger size.
For parallel flow in tubular heat exchangers
LMTD = ((Thi-Tci)-(Tho-Tco))/ln((Thi-Tci)/(Tho-Tco))
For counterflow in tubular heat exchangers
LMTD = ((Tho-Tci)-(Thi-Tco))/ln((Tho-Tci)/(Thi-Tco))
Where,
LMTD = log mean temperature difference (degC or degF)
Thi = inlet temperature of the hot fluid (degC or degF)
Tho = outlet temperature of the hot fluid (degC or degF)
Tci = inlet temperature of the cold fluid (degC or degF)
Tco = outlet temperature of the cold fluid (degC or degF)
LMTD = log mean temperature difference (degC or degF)
Thi = inlet temperature of the hot fluid (degC or degF)
Tho = outlet temperature of the hot fluid (degC or degF)
Tci = inlet temperature of the cold fluid (degC or degF)
Tco = outlet temperature of the cold fluid (degC or degF)
Python code
LMTD calculation in the heat exchanger is coded in Python as follows.
import math
def lmtd(Thi, Tho, Tci, Tco):
if min(Thi, Tho) > max(Tci, Tco):
dt = (Thi-Tci) if (Thi-Tci) == (Tho-Tco) else ((Thi-Tci)-(Tho-Tco))/math.log((Thi-Tci)/(Tho-Tco))
else:
dt = (Thi-Tci) if (Tho-Tci) == (Thi-Tco) else ((Tho-Tci)-(Thi-Tco))/math.log((Tho-Tci)/(Thi-Tco))
return dt
print("parallel flow case = ", lmtd(150, 120, 50, 80))
print("counter flow case = ", lmtd(180, 130, 100, 120))
Here, Thi, Tho, Tci and Tco are the temperatures of the hot and cold fluids at the inlet and outlet of the heat exchanger. The function lmtd calculates the LMTD using the formula (ΔT1-ΔT2)/ln(ΔT1/ΔT2) and returns the result.
parallel flow case = 65.48
counter flow case = 33.66
