Semi-spectral computational algorithm for fractional characterization of time-dependent fluid model with convergence and stability analysis

Abstract

The current study is carried out to analyze the unsteady MHD flow of fractional-order Oldroyd-B nanofluid and heat transfer via a semi-spectral computational method. The governing model for MHD naturally convective fractional-order Oldroyd-B is expressed in terms of a coupled PDE system. To analyze the numerical solution novel scheme is suggested, where finite difference is used to approximate the temporal derivative whereas spatial variable is approximated via operational matrices which are computed using Chelyshkov polynomials. The proposed scheme transforms the nonlinear system of PDEs into a system of linear algebraic equations. Relevant theorems are presented to support the mathematical justification of the operational matrices-based method whereas stability analysis is being made for the proposed computational algorithm. The impact of involved physical parameters on velocity temperature, skin friction, and Nusselt number profiles are studied numerically. The impact of the magnetic field drops the velocity behavior whilst the effect of buoyancy forces on velocity is the opposite. The radiation pass through the nanofluid transmits the energy to the fluid particles and eventually causes an increase in the temperature of the fluid whereas similar behavior is noticed in heat generation. The substantial effect of the fractional parameter is noted for smaller values.