Basic Viscoelastic Fluid Flow Problems Under Harmonic Fluctuating Driving Force

Analytical solutions are obtained for five basic viscoelastic fluid flow problems under harmonic fluctuating driving forces. Jeffrey's model is adopted in the study. The five fundamental problems are the fluctuating Couette flow, fluctuating wind-driven flow over finite and infinite fluid domains, fluctuating Stokes' first problem and the fluctuating Poiseuille flow. It is shown that the effect of the relaxation lambda (1) and retardation lambda (2) times on the flow behavior becomes more significant at large fluctuation frequencies (omega). It is found that increasing lambda (1) in velocity-type driving force problems causes a lag in the flow response and an increase in the fluctuation amplitude, while increasing lambda (2) in this type causes a lead in the flow response and an increase in the fluctuation amplitude. However, increasing lambda (1) in shear-type driving force problems causes a lead in the flow response and an increase in the amplitude, while increasing lambda (2) in this type causes a lag in the response and a decrease in the fluctuation amplitudes.