You are working for a consultancy and need to give advice on the required length of a tube in the shell counter flow heat exchanger. The customer wants to place the heat exchanger in a factory to heat up water. The water is heated by steam condensing in the shell at 120C with a latent heat of evaporation of 2203 kJ/kg. The water needs to be heated from 13 to 80C in the heat exchanger and flows at 1.7 kg/s. The cp of the water is 4187 J/kgK. The diameter of the water pipe is 3 cm and the overall heat transfer coefficient is 700 W/m2 K.

Calculate the required length of the pipe for the water to reach 80C. You need to use the calculation method of Log Mean Temperature Difference (LMTD). Use the known, assumptions (minimum of two), find, and analysis method.