Investigation of magnetized convection for second-grade nanofluids via Prabhakar differentiation

Abstract The application of nanoparticles in the base fluids strongly influences the presentation of cooling as well as heating techniques. The nanoparticles improve thermal conductivity by fluctuating the heat characteristics in the base fluid. The expertise of nanoparticles in increasing heat transference has captivated several investigators to more evaluate the working fluid. This study disputes the investigation of convection flow for magnetohydrodynamics second-grade nanofluid with an infinite upright heated flat plate. The fractional model is obtained through Fourier law by exploiting Prabhakar fractional approach along with graphene oxide ( GO ) ({\rm{GO}}) and molybdenum disulfide ( Mo S 2 ) ({\rm{Mo}}{{\rm{S}}}_{2}) nanoparticles and engine oil is considered as the base fluid. The equations are solved analytically via the Laplace approach. The temperature and momentum profiles show the dual behavior of the fractional parameters ( α , β , γ ) (\alpha ,\beta ,\gamma ) at different times. The velocity increases as Grashof number {\rm{Grashof\; number}} increases and declines for greater values of magnetic parameter and Prandtl number. In the comparison of different numerical methods, the curves are overlapped, signifying that our attained results are authentic. The numerical investigation of governed profiles comparison shows that our obtained results in percentages of 0.2 0.2 ≤ temperature ≤ 4.36 4.36 and velocity 0.48 ≤ 7.53 0.48\le 7.53 are better than those of Basit et al. The development in temperature and momentum profile, due to engine oil–GO is more progressive, than engine oil–MoS2.