Dusty hybrid nanofluid flow over a shrinking sheet with magnetic field effects

Purpose This paper aims to examine the Cu-Al2O3/water hybrid nanofluid flow over a shrinking sheet in the presence of the magnetic field and dust particles. Design/methodology/approach The governing partial differential equations for the two-phase flow of the hybrid nanofluid and the dust particles are reduced to ordinary differential equations using a similarity transformation. Then, these equations are solved using bvp4c in MATLAB software. The bvp4c solver is a finite-difference code that implements the three-stage Lobatto IIIa formula. The numerical results are gained for several values of the physical parameters. The effects of these parameters on the flow and the thermal characteristics of the hybrid nanofluid and the dust particles are analyzed and discussed. Later, the temporal stability analysis is used to determine the stability of the dual solutions obtained as time evolves. Findings The outcome shows that the flow is unlikely to exist unless satisfactory suction strength is imposed on the shrinking sheet. Besides, the heat transfer rate on the shrinking sheet decreases with the increase of . However, the increase in and lead to enhance the heat transfer rate. Two solutions are found, where the domain of the solutions is expanded with the rising of, and. Consequently, the boundary layer separation on the surface is delayed in the presence of these parameters. Implementing the temporal stability analysis, it is found that only one of the solutions is stable as time evolves. Originality/value The dusty fluid problem has been widely studied for the flow over a stretching sheet, but only limited findings can be found for the shrinking counterpart. Therefore, this study considers the problem of the dusty fluid flow over a shrinking sheet containing Cu-Al2O3/water hybrid nanofluid with the effect of the magnetic field. In fact, this is the first study to discover the dual solutions of the dusty hybrid nanofluid flow over a shrinking sheet. Also, further analysis shows that only one of the solutions is stable as time evolves.

Automated summary

The study investigates the flow of Cu-Al2O3/water hybrid nanofluid over a shrinking sheet in the presence of the magnetic field and dust particles. Two solutions are found for the dual solutions, with the stability of only one solution proven as time evolves. The impact of physical parameters on flow and thermal characteristics are analyzed, showing the importance of suction strength, and on the heat transfer rate on the shrinking sheet.