Analytical solution of Graetz problem in pipe flow with periodic inlet temperature

The paper reports an analytical solution for the temperature field in a fully developed pipe flow subject to
periodic (of any shape) inlet temperature variation. The solution is given in term of a series of Kummer
functions for the cases of uniform and constant wall temperature and wall heat flux, thus comprising also
the adiabatic wall case. A ‘‘fully developed” region for the fluctuating component of the fluid temperature
is also evidenced and closed-form solutions are given. An interpretation of the temperature field as superposition
of travelling thermal waves is presented and discussed