Analytical solution of convective heat transfer of oscillating flow subject to a triangular pressure waveform

The analytical solutions of velocity and temperature distributions of a laminar viscoelastic fully developed pipe flow subject to a triangular pressure waveform are presented. The solution for the velocity field is given in terms of a series of Bessel functions during the solution for temperature distribution in term of a series of Kummer function. The velocity and temperature distributions for a triangular pressure waveform are significant from the sinusoidal pressure waveform. The fluid temperature depends upon the Prandtl number in the case of large values of time where it does not depend on this parameter in the case of small values of time. The trend of larger temperature rises with triangular pressure waveform in comparison with the corresponding temperature rise due to a sinusoidal waveform.