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Received: 14 June 2020 Accepted: 5 September 2020 We focused on developing an accurate numerical scheme for the flow of a fractionalorder Oldroyd–B fluid model with the non-isothermal property. In many cases, the direct application of the Chebyshev tau method using the operational matrix of the Chebyshev polynomials usually leads to an accurate solution. However, in some cases, dealing with non–linearity and coupling can be tedious. In this study, we present a numerical method based on Chebyshev polynomials of the first kind and interpolation using Gauss–Lobatto quadrature. The coefficients of the series expansion of the pseudospectral method are obtained through integration of the Chebyshev polynomials orthogonality condition. The numerical results show that the scheme is accurate and reliable. The effects of the fractional-order objective stress rate of the Oldroyd–B fluid on the velocity and shear stress are also presented. The error bound theorems presented in this study support the findings of the numerical computations.

A Chebyshev Based Spectral Method for Solving Boundary Layer Flow of a Fractional-Order Oldroyd-B Fluid