Analysis of fractional derivatives in thermal and solutal transfer equations of second‐grade non‐Newtonian fluids: A numerical study

Abstract

A numerical analysis is carried out using Atangana–Baleanu and Caputo–Fabrizio time‐fractional derivatives to study the mixed convective unsteady flow of a second‐grade fluid past an infinite vertical porous plate under the influence of a uniform transverse magnetic field. As finding the exact solutions of fluid equations presents huge difficulties due to the vagueness or uncertainty associated with the fluid parameters, fuzzy theoretic concepts are used rather than the classical crisp theoretic ones. Governing partial differential equations are made dimensionless and are then subject to fuzzification. The finite‐difference scheme is used to discretize the equations, and hence suitable programming codes are developed in PYTHON for AB and CF fractional derivatives. The results are obtained and plotted graphically. Interpretations based on these physical parameters imply that both AB and CF methods agreed well.

Parameter Identification of the Fractional-Order Mathematical Model for Convective Mass Transfer in a Porous Medium

“…Borah et al [15] numerically analyzed thermal transfer equations for non-Newtonian fluids. Based on Atangana-Baleanu and Caputo-Fabrizio fractional derivatives, the mixed convective unsteady flow through an infinite vertical porous plate was investigated for a uniform field.…”