Abstract
In this paper, the unsteady magnetohydrodynamic (MHD) flow of hybrid nanofluid (HNF) composed of C u − A l 2 O 3 /water in the presence of a thermal radiation effect over the stretching/shrinking sheet is investigated. Using similarity transformation, the governing partial differential equations (PDEs) are transformed into a system of ordinary differential equations (ODEs), which are then solved by using a shooting method. In order to validate the obtained numerical results, the comparison of the results with the published literature is made numerically as well as graphically and is found in good agreements. In addition, the effects of many emerging physical governing parameters on the profiles of velocity, temperature, skin friction coefficient, and heat transfer rate are demonstrated graphically and are elucidated theoretically. Based on the numerical results, dual solutions exist in a specific range of magnetic, suction, and unsteadiness parameters. It was also found that the values of f ″ ( 0 ) rise in the first solution and reduce in the second solution when the solid volume fraction ϕ C u is increased. Finally, the temporal stability analysis of the solutions is conducted, and it is concluded that only the first solution is stable.
Highlights
Researchers are interested in studying the enhancement of heat transfer due to its significant applications in engineering and industries
The shooting method has been employed by many researchers [41,42,43,44]
The solid volume fraction φCu is added in order to make the Cu − Al2 O3 / water hybrid nanofluid
Summary
Researchers are interested in studying the enhancement of heat transfer due to its significant applications in engineering and industries. The heat transfer of convectional fluids such as ethylene glycol, water, and oil can be utilized in various apparatus of engineering, for instance, devices of electrons and heat exchangers These base liquids keep limited thermal conductivity or, in other words, they have low thermal conductivity. Engineers, mathematicians, and researchers of various fields attempt to improve thermal conductivity of previously mentioned liquids by including a solitary kind of nanosized particles to form a mixture called ‘nanofluid’, which was initially presented by Choi and Eastman [1] It is shown from the previous studies that solid nanoparticles possess the ability increase thermal conductivity and the rate of heat transfer of convectional base fluids. The examination of the single-phase models of Symmetry 2020, 12, 276; doi:10.3390/sym12020276 www.mdpi.com/journal/symmetry
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