The present article deals with the MHD flow of a Casson nanofluid between two disks. The lower disk was fixed as well as permeable. The upper disk was not permeable, but it could move perpendicularly up and down toward the lower disk. Titanium dioxide was selected as nanoparticles and water as a base fluid. The governing higher-order nonlinear partial differential equations were transformed into a set of nonlinear ordinary differential equations by using similarity transformation. The differential transform method (DTM) was applied to solve the nonlinear ODEs. The nature of the velocity profiles for the different values of the suction injection parameter, the squeeze number, the Casson fluid parameter, and the volume fraction parameter of the nanofluid are pictorially discussed in this paper. The coefficient of skin friction was tabulated for the novelty of the research. The comparison of the results was determined by the DTM and the numerical methods. The profile values were also compared with the literature work and found to agree. This comparative study proves the accuracy and efficiency of the method. It is concluded from this research that the flow properties behave oppositely for all parameters during suction and injection.

The present article addresses the steady and laminar magnetohydrodynamics (MHD) flow of a micropolar nanofluid between two porous disks. The fluid is flowing uniformly in the inward and upward directions from both disks. The microrotation of the nanoparticles acts an important role in the flow regime. To show its significance, a comparative study of the analytical results and numerical results is presented. Titanium dioxide is chosen as nanoparticles in the water-based fluid. An appropriate transformation is used for transforming PDEs into ODEs. These nonlinear ODEs are computed by the differential transform method (DTM). The consequences of the Reynolds number, material parameter, and magnetic parameter on the radial velocity, axial velocity, and microrotation profile are graphically presented and discussed. The results calculated by DTM and the results calculated numerically are compared and tabulated. This comparison shows the accuracy and validity of DTM. The coefficient of skin friction is also tabulated and compared with the numerical result. At the end of this study, it is concluded that the behavior of the radial and the axial velocities and the microrotation profile are almost the same in the case of the Reynolds number and the magnetic field parameters.

The model of temperature profile in the flow of non-Newtonian second-order fluid, flowing in an annulus, is investigated. The boundary of annulus is considered porous. Appropriate similarity transformation is used to convert non-linear PDEs into non-linear ODEs. The obtained differential equations are solved numerically. The nature of the temperature profile is presented graphically for the various physical parameters.