Unsteady stagnation-point flow of a hybrid nanofluid over a spinning disk: analysis of dual solutions

This paper is concerned about the characteristics of the dual solutions of an unsteady stagnation-point flow of a hybrid nanofluid over a rotating disk with the effect of Hall current. The governing equations are non-dimensionalized using the appropriate similarity transformations. The resulting equations are solved numerically by employing the bvp4c method. A comparison between the present solutions with the available solutions is presented which shows an excellent agreement. The solution exists in the upper branch for all values of the hybrid nanofluid phi(1), phi(2), the swirl parameter Omega(A), and impinging parameter beta(A). However, the breakdown is observed in the lower branch solution at some moderate values of beta(A). In addition, the radial velocity increases due to hybrid nanofluid, while the azimuthal velocity decreases. However, the temperature increases due to hybrid nanofluid. Moreover, the results also indicate that the swirl parameter augments the velocity in both directions but declines the temperature. Also, it is perceived that the azimuthal velocity and temperature decrease in the upper branch solution as the magnetic parameter increases, while the lower branch solution initially increases and then decreases for the transverse component of velocity but the temperature monotonically increases.

Automated summary

This paper investigates the characteristics of dual solutions for an unsteady stagnation-point flow of a hybrid nanofluid over a rotating disk, considering the effect of Hall current. The governing equations are made dimensionless and solved numerically. The obtained solutions are compared with existing ones, showing good agreement. The solutions exist in the upper branch for all values of the hybrid nanofluid and certain parameters, while breakdown occurs in the lower branch solution at moderate values of one parameter. The radial velocity increases, while the azimuthal velocity decreases and the temperature increases due to the hybrid nanofluid. The swirl parameter enhances velocity in both directions but decreases temperature. Moreover, the azimuthal velocity and temperature decrease in the upper branch solution as the magnetic parameter increases, while the lower branch solution exhibits different behaviors.