Electroosmotic flow of a fractional second‐grade fluid with interfacial slip and heat transfer in the microchannel when exposed to a magnetic field

We investigated the time‐dependent viscoelastic fluid flow through a parallel‐plate microchannel under the influence of a transversely applied magnetic field and an axially imposed electric field. We performed the analysis by employing the Poisson‐Boltzmann equation under the Debye‐Huckel approximation. The generalized second‐grade fluid model with a fractional‐order time derivative is used to observe the non‐Newtonian and fractional behavior rates of deformation employing the Riemann‐Liouville fractional operator. We considered the asymmetric zeta potentials and different slip effects at the walls to study the flow behavior near the vicinity of the channel. We obtained an analytical solution in terms of Mittag‐Leffler function, applying Fourier and Laplace transformations. We imposed the heat transfer phenomena with the dissipation of energy and Joule heating effects on the model. The governing equations were also solved numerically by employing an implicit finite difference scheme. The numerical solution was compared with the analytical results, considering the influence of the pertinent parameters involved in the problem. The study delineates that the flow rate decreases with a rise in the fractional‐order parameter, while the opposite trend is observed with the electroosmotic parameter. Due to the application of sufficient strength of the magnetic field and the Joule heating effects, the temperature increases within the channel.