Analysis of unsteady MHD fluid flow across two parallel discs with uniform fluctuation subject to modified Hall and activation energy

This study intends to examine the consequences of the externally applied magnetic field and modified Hall effect on nanofluid flow across two symmetrically spinning and extending discs, where continuously the upper disc moves upward and downward. The lower disc is vertically fixed. The discs rotate and move vertically, generating a 3D flow. The mass density, heat transfer and flow motion have been evaluated and modeled in the form of the system of partial differential equations (PDEs) with an additional influence of activation energy, heat source and chemical reaction. The system of PDEs is modified to an ordinary set of differential equations by employing the resemblance substitution method. The obtained system of ODEs is further solved through the numerical approach (bvp4c). The results are compared to the bvp4c package and published work for validity purposes. In the case of downward displacement of the upper disc, magnetic and Hall characteristics have a significant impact on the velocity curve. The energy curve elevates with the upward movement of the disc, while it reduces with the downward fluctuation. Furthermore, the mass transmission rate enhances with the influence of hall current, while diminishing with the impact of chemical reaction rate.