Semi-analytic solutions and sensitivity analysis for an unsteady squeezing MHD Casson nanoliquid flow between two parallel disks

The transport phenomena of Casson nanofluid flow between two parallel disks subject to convective boundary conditions are analyzed in this paper. The mathematical model incorporates the impact of thermophoresis and Brownian motion since the Buongiorno's nanoliquid model is adopted to characterize the nanoliquid's transport features. The appropriate similarity transformations are applied to obtain the resulting nondimensional ordinary differential equations from the basic governing equations. The resulting ordinary differential equations and the associated boundary conditions are solved analytically by adopting the homotopy perturbation technique. Further, a statistical experiment is conducted to identify notable flow parameters which cause significant impact on the heat transfer rate. The characteristics of critical pertinent parameters on the flow field are graphically manifested. It is worth noting that the Casson nanofluid velocity escalates by augmenting the magnetic field parameter in the case of injection near the disks. Nanoparticle concentration is considerably diminished with an increment in thermophoresis parameter. In the cases of equal and unequal Biot numbers, the heat transfer rate is promoted with higher values of the Brownian motion parameter. Among the Casson fluid parameter, squeezing parameter and magnetic field parameter, the heat transfer rate discloses the highest positive sensitivity with the lowest value of the Casson fluid parameter.