Analysis of the delay hot/cold water problem

We have analysed the delay hot/cold water problem in a fluid-pipe system. Our simplified model has been used to evaluate variations of pipe and fluid temperatures with time at different locations when the fluid-pipe system is subjected to a sudden increase in fluid temperature at the pipe entrance. The analysis shows a slow increase in pipe temperature with time and an increase of the fluid temperature at every pipe location. Temperature variations with time move at a velocity less than the fluid velocity.