I am currently in the process of designing a section of pipe in which a fluid will flow within, and would like to determine the specific heat transfer which may occur once the fluid enters the pipe, until it exits. The fluid will be flowing at a constant velocity "V" at a Temperature "T1" at the entrance of a pipe with length "L". In other terms, I want to find the length of pipe it would take for a fluid to be heated to a certain temperature when it is being passed through a pipe which is placed in specified external conditions. I think this must be done by deriving a differential equation which includes convective and conductive heat resistance terms both in radial and axial coordinate systems. The differential equation must then be solved in order to calulate the time the fluid must spend in the pipe, and from there calculate the length of pipe required using the selecting fluid flow velocity in the pipe.