Analytical solutions for unsteady electrohydrodynamics flows of Maxwell fluids in microchannels with circular cross section
Nehad Ali Shah, Yasir Mahsud, M. Ghazian Rahman Aziz, Iskander Tlili
Abstract
Unsteady electrohydrodynamic flow of Maxwell fluids through a microchannel with a circular cross section under the influence of a time-dependent external electric field is studied in the Debye–Hückel approximation. Analytical solutions for electric potential of charge distribution, fluid velocity, and the components of a shear stress tensor are determined by using a suitable integral transform regarding the azimuthal variable, the Laplace transform with respect to the time variable, and the finite Hankel transform regarding the radial coordinate. Flows caused by an oscillating electric field have been studied as a particular case of the general model. The analytical solutions corresponding to the flow of Newtonian fluids have also been obtained as particular cases of analytical solutions of the Maxwell fluid flow. Numerical values of the analytical solutions are obtained using the MathCAD15 software. The profiles of electric potential and fluid velocity are presented in two/three-dimensional graphical illustrations.