Question

Water ( ρ= 1000 kg/m3; Cp= 4.2 kJ/kg.K) at 1,488 kg/hr and 13oC enters a 10-mm-diameter smooth tube whose wall temperature is maintained at 56oC. If the convection heat transfer coefficient is 11,496 W/m2.K, calculate the tube length, in m, necessary to heat the water to 40oC.

Answer 1

the concept of condensor type heat exchanger is used to calculate heat transfer from tube wall to the cold water. As the tube wall is maintained at constant temperature and temperature of water will increase continuosly, so the temperature difference between water and tube wall will change continuously. Hence we considered mean temperature difference i.e, logarithmic temperature difference. First of all total heat energy required to increase the temperature of water from initial temperature to final temperature is calculated from its specific heat and mass flow rate. Then this is equated with convective heat transfer from tube wall to water. From this convective heat transfer area of tube is calculated, with the use of which the total length of the tube is calculated as 4.752367m. Last four images in the answer are provided from my handwritten notes of the subject for extra information on heat exchangers and logarithmic mean temperature difference. I hope you will like this answer. If you really do, then please provide positive ratings, which will motivate me and boost my confidence further to provide quality answers. Thank you!