Analytical solution of convective oscillating flow at a sinusoidal pressure waveform

Abstract

The flow of an oscillating motion of viscoelastic fluid in a capillary tube is modelled to determine a sinusoidal waveform effect on the heat transfer performance. Analytical technique based on finite Hankel transformation, incorporating Laplace transformation and combined with confluent hypergeometric function (Kummer’s function) is implemented in time and space with the constitutive model for the viscoelastic fluid. Explicit analytical expressions for the steady, permanent and transient solutions for both the velocity and temperature fields describing the flow at small and large times have been derived. The results are displayed graphically, and the influence of the Prandtl number Pr and transient amplitude B_{1} is discussed.