How is heat exchanger performance calculated?

Sanda Heat exchanger design starts looking just as simple, but it gets much more interesting!  Heat exchangers are machines that get fluids to transfer their heat.  Most heat exchangers work with two fluids flowing through separate passages, for example cold water flowing inside a tube and warm air flowing outside the tube.  When this happens, the cold fluid warms up and the hot fluid cools off.  The key relationship here is:

Where:
A is the required amount of surface area in ft2
Q is duty in BTU/hr
U is the performance of the heat exchanger in BTU/hr-ft2-°F
LMTD is the mean temperature difference throughout the heat exchanger in deg F

Q. How is mean temperature difference calculated?
The LMTD is a computation that takes the inlet and outlet temperatures of both fluids and reduces them to one number, which is the average temperature difference:

T1 = Hot Stream Inlet Temp.
T2 = Hot Stream Outlet Temp.
t1 = Cold Stream Inlet Temp.
t2 = Cold Stream Outlet Temp.