Analysis of arrhenius kinetics on multiphase flow between a pair of rotating circular plates

In this study, we aim to deal with the flow behavior betwixt a pair of rotating circular plates filled with Carreau fluid under the suspension of nanoparticles and motile gyrotactic microorganisms in the presence of generalized magnetic Reynolds number. The activation energy is also contemplated with the nanoparticle concentration equation. The appropriate similarity transformations are used to formulate the proposed mathematical modeling in the three dimensions. The outcomes of the torque on both plates, i.e., the fix and the moving plate, are also contemplated. A well-known differential transform method (DTM) with a combination of Padé approximation will be implemented to get solutions to the coupled nonlinear ordinary differential equations (ODEs). The impact of different nondimensional physical aspects on velocity profile, temperature, concentration, and motile gyrotactic microorganism functions is discussed. The shear-thinning fluid viscosity decreases with shear strain due to its high velocity compared to the Newtonian and shear-thickening case. The impact of Carreau fluid velocity for shear-thinning (n < 1), Newtonian case (n = 0), and shear-thickening (n > 1) cases on axial velocity distribution f′(λ) has been discussed in tabular form and graphical figures. For the validation of the current methodology, a comparison is made between DTM-Padé and the numerical shooting scheme.