Abstract
Peristaltic flow of viscoelastic fluid through a uniform channel is considered under the assumptions of long wavelength and low Reynolds number. The fractional Oldroyd-B constitutive viscoelastic law is employed. Based on models for peristaltic viscoelastic flows given in a series of papers by Tripathi et al. (e.g. Appl Math Comput. 215 (2010) 3645–3654; Math Biosci. 233 (2011) 90–97) we present a detailed analytical and numerical study of the evolution in time of the pressure gradient across one wavelength. An analytical expression for the pressure gradient is obtained in terms of Mittag-Leffler functions and its behavior is analyzed. For numerical computation the fractional Adams method is used. The influence of the different material parameters is discussed, as well as constraints on the parameters under which the model is physically meaningful.
Highlights
Fractional Calculus has gained considerable popularity mainly due to its numerous applications in diverse fields of science and engineering
In [24], [25], [26], [27] two semi-numerical techniques are used for the solution of Eq (27): Adomian decomposition method (ADM) and homotopy analysis method (HAM)
These two methods give a series of functions, which first terms are used for the numerical computation of y(t). It appears that the obtained approximations of y(t) by these two methods are the same as if we take the first terms of the series in (34)
Summary
Fractional Calculus has gained considerable popularity mainly due to its numerous applications in diverse fields of science and engineering. Fractional Calculus allows integration and differentiation of arbitrary order, not necessarily integer. It deals with integrodifferential operators, where the integrals are of convolution type with weakly singular power-law kernels. Unlike the classical models which exhibit exponential relaxation, the models of fractional order show power-law behavior which is widely observed in a variety of experiments. They provide a higher level of adequacy preserving linearity and give the possibility for relatively simple description of the complex behavior of non-Newtonian viscoelastic fluids
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