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In this paper, transversal flow field of nonlinear viscoelastic fluids abiding by the modified-Phan-Thien-Tanner (MPTT) constitutive model in straight tubes of eccentric-annular cross-section is investigated. An analytical solution is developed based on an asymptotic expansion in terms of the Weissenberg number coupled with the shape factor method a one-to-one mapping taking the circular cross-section into the eccentric annular cross section. The analysis reveals the formation of transversal flows due to elasticity and to the eccentricity parameter. The number of vortices in the cross-section depends on the ratio of the diameters in addition to the eccentricity parameter. The effect of these parameters on the vortical structure is explored for different values of the material parameters.

The relaxation response of viscoelastic fluids associated with the natural frequencies of oscillation that arise as a consequence of the structure of the constitutive equation is explored for the case of pulsating flow. The matching of the forcing frequency to the fluid’s natural frequencies induces a multiple resonance phenomenon. In this paper, the resonance phenomenon is investigated in pulsating flow in straight circular tubes when the fluid is characterized by the Johnson-Segalman constitutive model. An analytical solution is developed based on an asymptotic expansion in terms of a material parameter. The analysis reveals that the forcing frequency associated with the pressure gradient can generate a sequence of resonances of decaying intensity dependent on the material parameter and other fluid constitutive constants. The effects of resonance on the rate of flow and oscillating velocity field are explored for several values of the relevant parameters.