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In the present research article, modeling and computations are presented to introduce the novel concept of relaxation-retardation viscous dissipation and hyperbolic time variation boundary conditions on the magnetohydrodynamic transient flow of Oldroyd-B nanofluid past a vertical stretched plate for the first time. In the present work, firstly we implement Buongiorno’s model to illustrate Brownian motion and thermophoretic diffusion which take vital role in heat and mass transportation process. Nonlinear non-dimensional governing equations are solved by fourth order Runge-Kutta method along with shooting technique. We investigate the behavior of influential variables on the velocity, thermal and solutal fields through graphical illustrations. Our results indicate that relaxation and retardation Deborah numbers exhibit completely reverse trend in the flow field. Especially, augmented relaxation-retardation viscous dissipation invigorates the temperature gradient. The results of the current theoretical study may be instrumental for worthful practical applications.

Flow and heat transfer of Oldroyd-B nanofluid with relaxation-retardation viscous dissipation and hyperbolic boundary conditions