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