Unsteady flow of magnetohydrodynamic hybrid nanofluid over a stretching/shrinking sheet: Multiple solutions

The main goal of this article is to perform a heat transfer analysis of unsteady magnetohydrodynamic hybrid nanofluid flow over a stretching/shrinking sheet. The hybrid nanofluid is synthesized by adding two kinds of nano-sized particles. In this examination, TiO2 and Cu nano-sized particles are taken with water as a base fluid. Using an appropriate similarity transformation approach, a set of nonlinear equations is obtained from the governing equations of the current study. To solve the changed system, the Runge-Kutta-Fehlberg approach is applied combined with the shooting method. The obtained data is presented in graphs and tables. Here, dual solutions can be seen utilizing upper and lower division solutions particularly aimed at a specific domain of unsteadiness parameter. The skin friction coefficient parameter shows a considerable improvement. Whereas in the case of the shrinking sheet, larger values of the magnetic parameter and solid volume fraction results in a significant drop in the local heat transfer rate for the upper branch case, while the lower branch case shows a different pattern.

Automated summary

The main objective of this article is to analyze the heat transfer characteristics of unsteady magnetohydrodynamic hybrid nanofluid flow over a stretching/shrinking sheet. The study synthesizes a hybrid nanofluid by incorporating TiO2 and Cu nanoparticles into water. Nonlinear equations are obtained using a similarity transformation approach and solved using the Runge-Kutta-Fehlberg method combined with the shooting method. The results indicate the existence of dual solutions in a specific parameter range and demonstrate improved heat transfer performance with the use of hybrid nanofluids.