Heat exchanger analysis/ LMTD method with example

There are two important methods for the analysis of heat exchangers. The first one is the LMTD method and the second one is the NTU method. In this problem, we will discuss the LMTD method with an example.
In a heat exchanger, the heat is transferred from hot to cold fluid. In a shell and tube heat exchanger, the heat is first transferred from hot fluid to the wall of the tube by convection, then the heat will transfer through the tube by conduction process. At last, the heat will transfer from the wall to the cold fluid by convection again. Sometimes the scale of calcium, magnesium, or other ions present in hard water can deposit on the inside and outside surface of the tube wall and increase resistance to the heat transfer. The algae or other microorganisms can grow in water and can accumulate on the tube walls which is called fouling. We should remove fouling by washing, chemical to increase the overall heat transfer coefficient.