Exact solutions for Two-dimensional flow of Fractional NTNN fluid within an oscillatory rectangular enclosure

In this paper, we present an analysis for the unsteady two-dimensional flow of incompressible fractional NTNN model. The purpose of this research is to detect exact solutions for the cosine oscillation inside an oscillating rectangular duct having fractional fluid. The mixed initial-boundary value problem is simplified by using Laplace and double finite Fourier sine transform. The impacts of pertinent parameters on the velocity profile and the corresponding shear stresses are analyzed through graphical illustrations for cosine oscillation. Our results indicate that the fluid's flow rises in correlation with fractional and rheological factors, such as α,N,ω, and t. As limiting cases of exact solution, the results can also be obtained for the ordinary NTNN and Newtonian fluid.