Abstract
This paper investigates the steady, two dimensional, and magnetohydrodynamic flow of copper and alumina/water hybrid nanofluid on a permeable exponentially shrinking surface in the presence of Joule heating, velocity slip, and thermal slip parameters. Adopting the model of Tiwari and Das, the mathematical formulation of governing partial differential equations was constructed, which was then transformed into the equivalent system of non-linear ordinary differential equations by employing exponential similarity transformation variables. The resultant system was solved numerically using the BVP4C solver in the MATLAB software. For validation purposes, the obtained numerical results were compared graphically with those in previous studies, and found to be in good agreement, as the critical points are the same up to three decimal points. Based on the numerical results, it was revealed that dual solutions exist within specific ranges of the suction and magnetic parameters. Stability analysis was performed on both solutions in order to determine which solution(s) is/are stable. The analysis indicated that only the first solution is stable. Furthermore, it was also found that the temperature increases in both solutions when the magnetic parameter and Eckert number are increased, while it reduces as the thermal slip parameter rises. Furthermore, the coefficient of skin friction and the heat transfer rate increase for the first solution when the magnetic and the suction parameters are increased. Meanwhile, no change is noticed in the boundary layer separation for the various values of the Eckert number in the heat transfer rate.
Highlights
Previous studies have proven that fluids play a vital role in enhancing the heat transfer rate in many engineering and industrial systems
It can be concluded that the thermophysical properties of Devi and Devi have been used broadly, as these properties match with the experimental results. Taking advantage of this situation, in this study, we considered the thermophysical properties of Devi and Devi [23,24] in dealing with hybrid nanofluid, and anticipated that our results would help in understanding hybrid nanofluid effectively without having to conduct costly experimental studies
There have been considered the incompressible 2D, MHD, and steady boundary layer flow of hybrid nanofluid with the effects of Joule heating, velocity, and thermal slip conditions over the exponentially shrinking surface without the viscous dissipation effect
Summary
Previous studies have proven that fluids play a vital role in enhancing the heat transfer rate in many engineering and industrial systems. This idea was initiated by Suresh et al [15,16] by considering alumina and copper as the solid particles with a base fluid of water They claimed that the rate of heat transfer of hybrid nanofluid is higher at the surface compared to that of simple fluid and nanofluid. Waini et al [33] considered the unsteady flow of hybrid nanofluid, by mixing copper and alumina (nanoparticles) with water (base fluid) They noticed that double solutions appeared in specific ranges of the unsteadiness parameter. Hybrid nanofluid flow on the stretching/shrinking surface, with the effects of transpiration, was explored by Waini et al [42] It is noticed from the previous literature that regular fluids, such as water, ethylene glycol, etc., must keep thermal conductivity low in order to improve the heat transfer rate [43,44]. It is expected that the current studies will provide good benefits to the researchers who are working on the hybrid nanofluid experimentally, and it is expected that these results will reduce the cost of the experimental work in the future
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