# Chebyshev polynomials for generalized Couette flow of fractional Jeffrey nanofluid subjected to several thermochemical effects

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## Abstract

The generalized Couette flow of Jeffrey nanofluid through porous medium, subjected to the oscillating pressure gradient and mixed convection, is numerically simulated using variable-order fractional calculus. The effect of several involving parameters such as chemical reactions, heat generation, thermophoresis, radiation, channel inclination, and Soret effect is also considered. To the best of the authors’ knowledge, the described general form of the Couette flow problem is not tackled by the researchers yet. The non-dimensional form of heat, mass, and momentum equations is solved as a coupled set. The effect of several parameters such as Grashof, Hartmann, Prandtl, Soret, and Schmidt numbers in addition to oscillation frequency, retardation time, radiation, heat absorption, and reaction rate are determined and presented graphically. An operational matrix method based on the second kind shifted Chebyshev polynomials is proposed to investigate the behavior of the interested problem. In fact, regarding the established method, the unknown solutions are expanded by the mentioned basis polynomials. Then, the operational matrix of the variable-order fractional derivative is utilized to transfer the problem into solving an algebraic system of equations. According to the obtained results, the growth of fractional order from 0 to 1 changes the skin friction coefficient, *Nu* and flow rate by \(-18.1\), 35.5, and \(10\%\), respectively.

## Keywords

Shifted Chebyshev polynomials (SCPs) Jeffrey nanofluid Mixed convection heat transfer Memory-dependent material Couette flow## Notes

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