A CHEBYSHEV SPECTRAL METHOD FOR HEAT AND MASS TRANSFER IN MHD NANOFLUID FLOW WITH SPACE FRACTIONAL CONSTITUTIVE MODEL

In some recent studies, it has been suggested that non–Newtonian fluid flow can be modeled by a spatially non–local velocity, whose dynamics are described by a fractional derivative. In this study, we use the space fractional constitutive relation to model heat and mass transfer in a nanofluid. We present a numerically accurate algorithm for approximating solutions of the system of fractional ordinary differential equations describing the nanofluid flow. We present numerically stable differentiation matrices for both integer and fractional order derivatives defined by the one–sided Caputo derivative. The differentiation matrices are based on the series expansion of the unknown functions using a truncated Chebyshev polynomial of the first kind and interpolation using Gauss–Lobatto quadrature. We show that the proposed technique is highly effective for solving the fractional model equations.