The helical flows of couple-stress fluids in a straight circular cylinder are studied in the framework of the newly developed, fully\ndeterminate linear couple-stress theory. The fluid flow is generated by the helical motion of the cylinder with time-dependent\nvelocity. Also, the couple-stress vector is given on the cylindrical surface and the nonslip condition is considered. Using the integral\ntransformmethod, analytical solutions to the axial velocity, azimuthal velocity, nonsymmetric force-stress tensor, and couple-stress\nvector are obtained.The obtained solutions incorporate the characteristic material length scale, which is essential to understand the\nfluid behavior at microscales. If characteristic length of the couple-stress fluid is zero, the results to the classical fluid are recovered.\nThe influence of the scale parameter on the fluid velocity, axial flow rate, force-stress tensor, and couple-stress vector is analyzed by\nnumerical calculus and graphical illustrations. It is found that the small values of the scale parameter have a significant influence\non the flow parameters.
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