There is an intense worldwide activity in the development of instrumentation for medical diagnosis and bioscreening based on biological labeling and detection of nanoparticles. Based on this profound observation, Hall and ion slip effects on magnetohydrodynamic (MHD) free convective rotating flow of nanofluids in a porous medium past a moving vertical semi-infinite flat plate are investigated. The equations for governing flow are solved analytically by perturbation approximation. The effects of various parameters on the flow are discussed through graphs and tables. The velocity increases with Hall and ion slip parameters. An increase in the convective parameter led to amplify the thermal boundary layer thickness, but when the heat generation parameter is taken into consideration, an opposite effect occurs. The skin friction coefficient increases with an increase in nanoparticle volume fraction and it reduces with increase in Hall and ion slip parameters. Outcomes disclose that the impact of thermal convection of nanoparticles has increased the temperature distribution, which helps in destroying the cancer cells during the drug delivery process.

The effects of radiation and Hall current on an unsteady magnetohydrodynamic free convective flow in a vertical channel filled with a porous medium have been studied. We consider an incompressible viscous and electrically conducting incompressible viscous second grade fluid bounded by a loosely packed porous medium. The fluid is driven by an oscillating pressure gradient parallel to the channel plates, and the entire flow field is subjected to a uniform inclined magnetic field of strength H_o inclined at an angle of inclination α with the normal to the boundaries in the transverse xy-plane. The temperature of one of the plates varies periodically, and the temperature difference of the plates is high enough to induce the radiative heat transfer. The effects of various parameters on the velocity profiles, the skin friction, temperature field, rate of heat transfer in terms of their amplitude, and phase angles are shown graphically.

The heat generation/absorption and thermo-diffusion on an unsteady free convective MHD flow of radiating and chemically reactive second grade fluid near an infinite vertical plate through a porous medium and taking the Hall current into account have been studied. Assume that the bounding plate has a ramped temperature with a ramped surface concentration and isothermal temperature with a ramped surface concentration. The analytical solutions for the governing equations are obtained by making use of the Laplace transforms technique. The velocity, temperature, and concentration profiles are discussed through graphs. We also found that velocity, temperature, and concentration profiles in the case of ramped temperature with ramped surface concentrations are less than those of isothermal temperature with ramped surface concentrations. Also, the expressions of the skin friction, Nusselt number, and Sherwood number are obtained and represented computationally through a tabular form.