Chapter 13.5, Problem 8P

Water at ${100}^{°}$ is flowing through a long pipe of radius 1 rapidly enough so that we may assume that the temperature is ${100}^{°}$ at all points. At $t=0,$ the water is turned off and the surface of the pipe is maintained at 40 from then on (neglect the wallthickness of the pipe). Find the temperature distribution in the water as a function of $r$ and t .Note that you need only consider a cross section of the pipe.