A comprehensive analysis of the flow and heat transfer for a nanofluid over an unsteady stretching flat plate

In the present paper, the unsteady flow and the related heat transfer of a nanofluid caused by linear motion of a horizontal flat plate has been analyzed and the nonlinear differential equations governing on the presented system have been reduced to a set of ordinary differential equations and obtained equations have been solved by Differential Transformation Method. Comparisons have been made between the obtained results and Runge–Kutta Numerical Solution, and the outcomes have been revealed that DTM is applicable in this case study. Furthermore, the relevant errors of the achieved solutions have been depicted graphically and these results indicate that the obtained analysis is trustable and applicable. It is necessary to mention that the effects of unsteadiness parameter S, Prandtl Number and finally volume fraction of the nanoparticles, ϕ on the temperature and velocity profile have been investigated. As a main outcome, the velocity profile is increased by enlarging the S parameter. Also, by increasing the ϕ, temperature profile has risen a lot which means the heat transfer properties can be enhanced by selecting appropriate nanoparticles sizes.