A description for magnetohydrodynamic effects on the transient rotational flow of Oldroyd-B nanofluids is considered. The temperature and concentration distributions are associated with Cattaneo-Christove double diffusion, Brownian motion, thermophoresis, Soret, and Dufour. The governing equations in the three-dimensional form are transmuted into dimensionless two-dimensional form with the implementation of suitable scaling transformations. The variational finite element procedure is harnessed and coded in Matlab script to obtain the numerical solution of the coupled non-linear partial differential problem. The varying patterns of velocities, skin friction coefficients, Nusselt number, Sherwood number, fluid temperature, and concentration functions are computed to reveal the physical nature of this study. It is observed that higher inputs of the parameters for magnetic force, Deborah number, rotational fluid, and cause to slow the primary as well as secondary velocities but they raise the temperature like thermophoresis and Brownian motion does. However, thermal relaxation parameter reduces the nanofluid temperature. The local heat transfer rate reduces against Nt, rotational, and Nb parameters, and it is higher for Prandtl number. The current FEM (finite element method) solutions have been approved widely with the recent published results, showing an excellent correlation. The examination has significant applications in the food industry and relevance to energy systems, biomedical, and modern technologies of aerospace systems. (C) 2020 Published by Elsevier B.V.