A study in nonlinear mechanical sciences on modelling has been carried out to analyse the combined effect of rotation and Darcy parameter with forced convective heat transfer on the steady flow of magnetic nanofluid over a rotating disk. The basic idea of the Neuringer–Rosensweig (NR) model has been used for the equations of motion and the governing nonlinear time-independent coupled partial differential equations together with the boundary conditions in cylindrical coordinates are transformed to a system of ordinary differential equations, via appropriate transformations. Further, the modelled system is solved by the MATLAB routine bvp4c solver package with suitable initial guesses. Besides calculating numerically, the velocity and temperature profiles with the variation of similarity parameter $\eta$, the effects of several non-dimensional motivating parameters, such as Prandtl number $Pr$, Darcy parameter $\beta$ and ferrohydrodynamic (FHD) interaction parameter $B$, the heat transfer rate from the surface of the disk and skin frictions are also discussed. The results for these emerging parameters are found numerically and discussed with plots.

In this manuscript, the heat transport phenomena have been studied on time-dependent Bodewadt flow of magnetic nanofluids in the porous medium under the effect of thermal radiation. The governed modelled equations are solved using a finite difference scheme followed by the shooting techniques. To cover a wide range of nanofluids, we took the Prandtl number from 12.3 to 176.4. The impacts of geothermal viscosity, permeability parameter, ferrohydrodynamics (FHD) interaction parameter and thermal radiation on flow behaviour have beendiscussed. It is observed that the heat transport rate enhanced significantly due to the thinner thermal boundary layer thickness for higher radiation parameter. Also, an enhancement of 268% in heat dissipation is noted for themagnetic nanofluids with high Prandtl values.