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The purpose of this paper is to examine the electro-magnetohydrodynamic behavior of a third-grade non-Newtonian fluid, flowing between a pair of parallel plates in the presence of electric and magnetic fields. The flow medium between the plates is porous. The effects of Joule heating and viscous energy dissipation are studied in the present study.

A semi-analytical/numerical method, the differential transform method, is used to obtain solutions for the system of the nonlinear differential governing equations. This solution technique is efficient and may be adapted to solve a variety of nonlinear problems in simple geometries, as it was confirmed by comparisons between the results using this method and those of a fully numerical scheme.

The results of the computations show that the Darcy–Brinkman–Forchheimer parameter and the third-grade fluid model parameter retards, whereas both parameters have an inverse effect on the temperature profile because the viscous dissipation increases. The presence of the magnetic field also enhances the temperature profile between the two plates but retards the velocity profile because it generates the opposing Lorenz force. A graphical comparison with previously published results is also presented as a special case of this study.

The obtained results are new and presented for the first time in the literature.

The flow and heat transfer of a hybrid nanofluid composed of kerosene and ZnO-Al2O3 nanoparticles (NPs) is investigated. The flow occurs over complex surfaces with stretching and shrinking features. The base fluid is electrically conducting, and an external magnetic field is added so that the nanofluid and the electric field are in equilibrium. Irrotational flow with viscous dissipation effects is considered.

The governing equations of the system are formulated, and a similarity transformation is used to convert the system of equations into ordinary differential equations, which are solved numerically. The friction coefficient of the flow and the Nusselt number are calculated for a wide range of parameters, and the results are presented in graphical form. In addition, dual solutions of the problem were noticed to occur for a certain range of the unsteadiness parameter. A stability analysis has been performed and presented to elucidate the behavior of these dual solutions.

For the solution of the upper branch, the velocity and temperature profiles of the nanofluid are enhanced by increasing the magnetic field parameter M, but the same variables decrease in the solution of the lower branch. The same trend is detected for the velocity of the fluid with the suction parameter. The temperature of the nanofluid decreases in both branches of the solution by increasing the Prandtl number. Similarly, they decrease with the suction parameter. The temperature of the nanofluid slightly increases in both branches of the solution by increasing the Eckert number. With the stability analysis the authors performed, it was determined that the solution is stable in the upper branch, but unstable in the lower branch.

The kerosene nanofluid with hybrid Zinc/Aluminum-oxide is presented for the first time in the literature.