The flow in the heat exchanger is considered under steady-state and fully insulated at the outer surface. Consider an infinitesimal part of the heat exchanging tube of area dA, where temperatures of hot and cold fluid are T_{h} and T_{c}, respectively. The figure below shows the temperature profile along the direction of flow in parallel flow and counter flow heat exchangers.

The profile of temperature variation depends upon the heat capacity of the fluid. The profiles are different for both types of heat exchangers, therefore, expressions of LMTD are also different, derived as follows. heat exchange from infinitesimal area dA at any point of the heat exchanger is given by

_{h}– T

_{c})

Where ‘U’ is the overall heat exchanger coefficient and ‘A’ is the heat transfer area of the heat exchanger. this heat is taken from hot fluid and given to cold fluid. the temperature of hot fluid reduces, while that of the cold fluid increases.

There are two types of problems associated with designing of heat exchangers:

**Designing Heat Exchanger:**When the desired temperature at inlets and outlets of both the fluids is known and a number of tubes required in the heat exchanger are to be calculated, then logarithmic mean temperature difference LMTD method is used.**Determining the Capacity:**When the heat exchanger is given and one wants to know the heat exchange capacity, so this is a reverse problem. then, effectiveness-number of transfer units (NTU) method is used.