Free convective couette flow analysis of viscoelastic dusty fluid along with Newtonian heating in a rotating frame

Applications in daily life heavily rely on the viscoelastic fluid's response to Newtonian heating. The importance of viscoelastic fluid rotation in engineering and the production of goods is also varied. Nuclear reactors, gas cooling systems, system temperature control, centrifugal separators, and other systems can all benefit from viscoelastic dusty fluids and Newtonian heating. In light of this inspiration, the current study describes the Newtonian heating effect on a viscoelastic fluid that contains dust particles. In addition, a uniformly applied magnetic field and a free convective heat transfer are taken into account for Couette flow in a rotating frame. Because the dust particles have complex velocities due to rotation, the primary and secondary velocities are combined. Poincare-Light Hill technique has been used for the solution of the system of partial differential equations. The velocity and temperature profile for dust particles and fluid are discussed in this article. The influence of different parameters on the Nusselt number is also discussed thoroughly.