The current article examines a nonlinear axisymmetric streaming flow obeying the Rivlin–Ericksen viscoelastic model and overloaded by suspended dust particles. The fluids are separated by an infinite vertical cylindrical interface. A uniform axial magnetic field as well as mass and heat transmission (MHT) act everywhere the cylindrical flows. For the sake of simplicity, the viscous potential theory (VPT) is adopted to ease the analysis. The study finds its significance in wastewater treatment, petroleum transport as well as various practical engineering applications. The methodology of the nonlinear approach is conditional primarily on utilizing the linear fundamental equations of motion along with the appropriate nonlinear applicable boundary conditions (BCs). A dimensionless procedure reveals a group of physical dimensionless numerals. The linear stability requirements are estimated by means of the Routh–Hurwitz statement. The application of Taylor’s theory with the multiple time scales provides a Ginzburg–Landau equation, which regulates the nonlinear stability criterion. Therefore, the theoretical nonlinear stability standards are determined. A collection of graphs is drawn throughout the linear as well as the nonlinear approaches. In light of the Homotopy perturbation method (HPM), an estimated uniform solution to the surface displacement is anticipated. This solution is verified by means of a numerical approach. The influence of different natural factors on the stability configuration is addressed. When the density number of the suspended inner dust particles is less than the density number of the suspended outer dust particles, and vice versa, it is found that the structure is reflected to be stable. Furthermore, as the pure outer viscosity of the liquid increases, the stable range contracts, this means that this parameter has a destabilizing effect. Additionally, the magnetic field and the transfer of heat don’t affect the nature of viscoelasticity.

In this paper, the couple influence of axial magnetic field and the heat and mass transfer on two rotating cylinders of Walter’s viscoelastic fluids by using the potential flow theory of viscoelastic fluid has been investigated. The normal mode method is used to compute the growth rate of disturbance. The influence of gravity is ignored at the interface, while the effect of surface tension is present in the analysis. The effect of the parameters on the stability is studied. It is found that the rotation of the inner cylinder induces stability. Furthermore, the viscoelastic ratio of fluids has a stabilizing influence. The heat and mass transfer, magnetic permeability ratio, and Ohnesorge number have a stabilized influence, while viscosity ratio of fluids, density ratio of fluids, and axial magnetic field have destabilizing influence on the considered system.