Numerical study of diffusion-thermo phenomena in Darcy medium using fractional calculus
Mumtaz Khan, Amer Rasheed
Abstract
In the current article, we mainly focus on evaluating the behavior of Joule heated viscoelastic fluid in the presence of Soret and Dufour effects over the moving surface filled with porous structures. In the newly introduced model, we have minutely described the Joule heating where fractional memory term, relaxation, and retardation time are also considered. We have used the fractional calculus approach to develop a constitutive coupling model of a viscoelastic fluid. To compute the numerical solution of the nonlinear coupled problem, finite element method and finite difference method, together with the L1 algorithm technique, are utilized, i.e. developed in MATLAB. Further, we have performed the stability and convergence analysis of the presented model and conveyed suitable error estimates. Efficient numerical simulations are carried out to have a detailed overview of the supremacy of characteristic flow parameters of velocity, temperature, and concentration fields. All coupling effects that can occur are considered, and accordingly, their impact on numerical simulations is precisely evaluated.