A comparative analysis of multiple fractional solutions of generalized Couette flow of couple stress fluid in a channel

Abstract

AbstractThis study provides the exact solutions of couple stress fluid (CSF) in a channel. The CSF is bounded by two plates in which the lower plate is moving with constant velocity Uo and the upper plate is fixed. The influence of the external pressure gradient is considered on the CSF fluid. To transform the classical CSF model, we have introduced three approaches to fractional derivatives, (a) Caputo (b) Caputo–Fabrizio (CF), and (c) Atangana–Baleanu (AB) fractional definitions. Exact solutions have been obtained using the Laplace and finite Fourier sine transforms jointly. Furthermore, the effect of different fractional derivatives is compared, and the results are shown in graphs. Moreover, parameters that affect the CSF motion are discussed in the graphs using the computational software MATHCAD. The most important outcome of the given study is the comparison of Caputo, CF, and AB fractional models with the classical CSF model. From the comparison, it can be noticed that AB fractional model discusses the dynamics of the CSF with a good memory effect as compared to Caputo and CF fractional operators. The CSF model can be reduced to Newtonian fluid as a limiting case and also investigated solutions in the absence of external pressure. Finally, Skin friction is evaluated for lower and upper plates, and the obtained results presented in tabular form.