Dual solutions of magnetohydrodynamic mixed convection flow of an Oldroyd-B nanofluid over a shrinking sheet with heat source/sink

Abstract

In this study, the dual solutions for mixed convection flow of an Oldroyd-B fluid containing alumina nanoparticles over a shrinking sheet are investigated taking into account the effects of magnetic field and heat source/sink. By utilizing the similarity transformations, the governing equations are reduced to ordinary differential equations which have been solved by the well-known shooting method. The present investigation reveals that some published results are not realistic. It is remarkable that for higher Deborah numbers for relaxation and retardation times, suction parameter and magnetic field parameter, the domain of the occurrence of dual solutions becomes wider and the local skin friction coefficient and local Nusselt number are found to increase. On the other hand, dual solutions exist in a broader domain as long as the volume fraction of alumina nanoparticles is less than or equal to 0.05 and after that it decreases. The critical values of the shrinking parameter relating to the existence of dual solutions are rendered in approximate functions. These characteristics of an Oldroyd-B nanofluid are not reported yet and might be useful in the development of the existing technology.