Calculation and Significance of Log Mean Temperature Difference

Understanding the concept of log mean temperature difference or LMTD is very important for heat exchanger design especially for the heat exchangers with no phase change.

LMTD is the logarithmic mean of temperature difference of the fluids at both the sides of the heat exchangers.

Say, “A” and “B” are the two sides of a heat exchanger, in which fluid “1” and “2” are flowing. Also, let’s assume the temperature of the fluid “1” at side “A” and “B” are “Ta1” and “Tb1” respectively and that of fluid “2” are “Ta2” and “Tb2”. Then the LMTD (LM) can be calculated as:

LM = [ABS(T_a1 - T_a2) - ABS(T_b1 – T_b2)] / [LN{ ABS(T_a1 - T_a2) / ABS(T_b1 – T_b2)}]…………..eqn1.1

“ABS(Ta1 – Ta2)” signifies the absolute temperature difference between Ta1 and Ta2.

The LMTD is a single value for the whole heat exchanger.

The LMTD is the driven force for the heat exchange between the two fluids. As the LMTD value increases, the amounts of heat transfer between the two fluids also increase. The LMTD value is used for calculating the heat duty of the heat exchanger. The formula is:

Q = U * A * LMTD…………eqn1.1

Where,

Q – Heat duty of the heat exchanger (in watts)

U – Heat transfer co-efficient (in watts/Kelvin/Meter­­­­­ square)

A – Heat transfer area (in meter square)

From the above equation (eqn1.1) it is clear that the amount of the exchanged heat (Q) is directly proportional to the value of LMTD.

Log Mean Temperature Difference or LMTD is the driving force for the amount of exchanged heat by a heat exchanger. LMTD approach is quite straight forward and simple. But this approach cannot be used for the cases, where phase change occurs in the heat exchanger. Also, if the specific heats of the fluids change then the LMTD approach cannot be used.