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

Abstract

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.

Analysis of Joule heating and chemical reaction effects in electroosmosis peristaltic transport of couple‐stress and micropolar fluids

“…Furthermore, Misra et al 41 and Chaube et al 42 conducted various theoretical analyses of micropolar fluids on peristaltic flows with the principle of electroosmosis mechanism. Some new studies have been described here in ref 43–51 …”

“…Some new studies have been described here in ref. [43][44][45][46][47][48][49][50][51] An analysis of relevant literature presents that none of the earlier researchers have calculated the peristaltic flow of fluids of micropolar. In view of the above, it has been our effort here to present a mathematical study that takes into account electroosmosis of couple-stress micropolar fluid and the effects of thermal radiation.…”

Electroosmotic flow of fractional Oldroyd‐B fluid through a vertical microchannel filled with a homogeneous porous medium: Numerical and semianalytical solutions

“…Important contributions regarding electroosmotic flow (EOF) for various types of fluids with time-fractional derivatives have been discussed in Wang and colleagues. [22][23][24][25][26][27][28][29] Fluid flow through porous media has grown increasingly relevant in the chemical and petroleum industries in recent years. Due to the high demands of such different disciplines, the interest in fluid flows across porous surfaces has developed significantly.…”

“…Caputo‐Fabrizio fractional‐order derivatives come in handy by using the Laplace transform. Important contributions regarding electroosmotic flow (EOF) for various types of fluids with time‐fractional derivatives have been discussed in Wang and colleagues 22–29 …”

Heat transfer analysis for particle–fluid suspension thermomagnetohydrodynamic peristaltic flow with Darcy–Forchheimer medium

“…They also incorporated the Soret number and Dufour number effects in the transport. Dey and Shit 29 examined the electromagnetic flow of a fractional viscoelastic fluid in a microchannel. They examined the unsteady second‐grade fractional model numerically via the FDM.…”