Magnetohydrodynamic electroosmotic flow of Maxwell fluids with Caputo–Fabrizio derivatives through circular tubes

Abstract

Unsteady flows of an incompressible Maxwell fluid with Caputo–Fabrizio time-fractional derivatives through a circular tube are studied. Flows are generated by an axial oscillating pressure gradient. The influence of a magnetic field, perpendicular on the flow direction, and of an axial electric field are considered. Solutions for the velocity and temperature fields are obtained by combining the Laplace transform with respect to the time variable t, and the finite Hankel transform with respect to the radial variable r. Influences of the order of Caputo–Fabrizio fractional time-derivative and the pertinent system parameters on the fluid flow and heat transfer performance were analyzed numerically by using the Mathcad software. Results show that the fluid velocity and the associated heat transfer modeled by fractional derivatives are quite distinct from those of the ordinary fluids. The fluid velocity and the thermal performance in cylindrical tubes can be controlled by regulating the fractional derivative parameter.