Two-layered electroosmotic flow through a vertical microchannel with fractional Cattaneo heat flux

The unsteady electroosmotic flow (EOF) of two layers of immiscible fluids through a vertical microchannel with heat transfer will be investigated. The channel is subjected to an alternating current (AC) electric field. The channel has two fluid layers: layer (I) is filled with Newtonian fluid, while layer (II) is filled with fractional Jeffreys fluid. The fractional derivatives will be replaced by the well-known Caputo-Fabrizio fractional derivatives. The Laplace and finite Fourier sine transforms and their numerical inverses have been used to get the semi-analytical solutions for the current problem. It has been found that the electroosmosis velocity and the flow rate are higher in the Newtonian layer compared with the non-Newtonian layer. Moreover, the heat transfer delays by elevating the value of the heat relaxation time in the two layers.