THE FIRST SOLUTION FOR THE HELICAL FLOWS OF GENERALIZED MAXWELL FLUID WITH LONGITUDINAL TIME DEPENDENT SHEAR STRESSES ON THE BOUNDARY

Helical flows of generalized Maxwell fluid is researched between two infinite coaxial circular cylinders. The velocity field and the adequate shear stress corresponding to the flow of a Maxwell fluid with fractional derivative model, between two infinite coaxial cylinders, are determined by means of the Laplace and finite Hankel transforms. The first solutions that have been obtained, presented under integral and series form in terms of the generalized G- and R-functions, satisfy all imposed initial and boundary conditions. The similar solutions for ordinary Maxwell and Newtonian fluid can be also obtained as the limit of the solution of generalized Maxwell fluid.

Automated summary

The helical flows of generalized Maxwell fluid between two infinite coaxial circular cylinders were studied, and the velocity field and shear stress were determined using Laplace and finite Hankel transforms. The obtained solutions, presented in terms of generalized G- and R-functions, satisfy all imposed initial and boundary conditions. Similar solutions for ordinary Maxwell and Newtonian fluids can also be obtained as a limit of the solution for generalized Maxwell fluid.