Analytical and Numerical Solutions of Oscillating Flow at a Trapezoidal Pressurewaveform

Abstract

This study aimed to develop a mathematical model of an unsteady Burgers’ fluid in a circular cylinder with a trapezoidal pressure waveform described by an infinite Fourier series. An analytical solution was obtained for the governing equation using the Bessel transform method together with similarity arguments. The validity of the solution was verified using a numerical inversion method based on Stehfest’s method. Limiting cases were considered to examine the fluid flow performance of different fluids. Our results show that the Newtonian and Oldroyd-B fluids performed similar velocity time variation for the trapezoidal waveform of oscillating motion, whereas the velocity time variation was different for Maxwell and Burger’s fluids. Moreover, it is evident that the material constant of a Burgers’ fluid is another important factor that affects flow performance in an oscillating flow.