Unsteady Helical Flows of a Size-Dependent Couple-Stress Fluid

Abstract EN

The helical flows of couple-stress fluids in a straight circular cylinder are studied in the framework of the newly developed, fully determinate linear couple-stress theory.

The fluid flow is generated by the helical motion of the cylinder with time-dependent velocity.

Also, the couple-stress vector is given on the cylindrical surface and the nonslip condition is considered.

Using the integral transform method, analytical solutions to the axial velocity, azimuthal velocity, nonsymmetric force-stress tensor, and couple-stress vector are obtained.

The obtained solutions incorporate the characteristic material length scale, which is essential to understand the fluid behavior at microscales.

If characteristic length of the couple-stress fluid is zero, the results to the classical fluid are recovered.

The influence of the scale parameter on the fluid velocity, axial flow rate, force-stress tensor, and couple-stress vector is analyzed by numerical calculus and graphical illustrations.

It is found that the small values of the scale parameter have a significant influence on the flow parameters.