Dual solutions of aqueous Ti-alloy & MWCNT hybrid nanofluid: A stability test

The flow and heat transfer induced by an exponentially shrinking sheet with Ti-alloy & MWCNT hybrid nanofluid are investigated in this paper. Additionally, this investigation focuses on the flow separation of hybrid nanofluid with an inclined magnetic field, thermal buoyancy force, and Joule heating effect. The Tiwari and Das model is used to formulate the hybrid nanofluid mathematical model. Suitable similarity transformations convert partial differential equations (PDEs) into a system of ordinary differential equations (ODEs). The resultant system is numerically solved by implementing the shooting approach along with the RK-4 technique. Multiple solutions are found for this current problem, and intriguingly, the velocity and temperature profiles of these two solution branches exhibit opposing characteristics. In conclusion, conducting a stability study on these two alternative solutions is worthwhile to determine which solution is more realistic and stable. The temporal stability test reveals that only the first solution is stable or physically valid. The important outcomes of this study, based on the stable solutions, are as follows: (i) velocity (temperature) is found to be higher (lower) when thermal buoyancy is absent and it is found to be lower (higher) for opposing thermal buoyancy; (ii) the skin friction coefficient and rate of heat transfer are found to be better for aiding thermal buoyancy and lower for opposing thermal buoyancy; and (iii) the thickness of momentum and thermal boundary layers is thinner for the first solution than the second solution. Furthermore, in this work, the flow patterns (streamlines) are investigated. The flow separation point is finally located. This current study revealed strong consistency with previous research. These types of studies are very useful in the areas of medical and aerodynamic science.

Automated summary

This paper investigates the flow and heat transfer induced by an exponentially shrinking sheet with Ti-alloy & MWCNT hybrid nanofluid. It focuses on the flow separation of the hybrid nanofluid with an inclined magnetic field, thermal buoyancy force, and Joule heating effect. The mathematical model for the hybrid nanofluid is formulated using the Tiwari and Das model. Multiple solutions are found for the problem, and the stability test reveals that only the first solution is stable. The study provides important findings regarding the velocity, temperature, skin friction coefficient, rate of heat transfer, and thickness of momentum and thermal boundary layers.