Dear Auroshis Rout
In this case your LMTD is 50 C.
If you have same temperature difference in both ends then your LMTD is temperature difference between the two fluids.
When Thi-Tco=Tho-Tci the LMTD is equal to Thi-Tco=Tho-Tci.
In such cases Gh*cph=Gc*cpc and temperature profiles are straight lines.
In the above analysis we assume that cph and cpc are constant.
LMTD is originally is the change of temperature difference between cold and hot fluid.. Here temperature difference between cold and hot fluids are constant and then equal (150 - 100) = (90-40) = 50 degree.
I think that this does not happen in the real case. If you observe these temperature results in an apparatus, I think that you have to take into account another heat transfer other than the heat transfer at the main part of the heat exchanger including heat loss.
This case is very rare. The LMTD is limited to coaxial exchangers in which the two flows are perfectly against or co-current. If this happens it is better to use the UTN method, it is more general
When Th,i - Tc,o = Th,o - Tc,i, this means that Th,i-Th,o = Tc,o - Tc,i and that the temperature differences in both sides of the exchanger are the same. Temperature differences in both sides are the same if and only if the two fluids of the exchanger have the same Heat capacity rate (kg/s)*(J/kg.K). Actually the two fluids cannot have exactly the same heat capacity rate. Therefore, this does not happen in the real case. However, for calculation purposes, the LMTD can be considered equal to the temperature difference.
The albegraic limit of the LMTD formula as the two end temperature differences tend to the same value is that same temperature difference i.e. 50 C
When the difference in temperature is constant throughout , then there is no meaning to find the log mean value. The difference 50 C itself the LMTD in this case.
LMTD comparison between counter-current and co-current arrangement
Dear Auroshis Rout
In this case your LMTD is 50 C.
If you have same temperature difference in both ends then your LMTD is temperature difference between the two fluids.
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