Flow of Maxwell Fluid with Heat Transfer through Porous Medium with Thermophoresis Particle Deposition and Soret–Dufour Effects: Numerical Solution

In this paper, we study the magnetohydrodynamics of Darcy flow in a non-Newtonian liquid. The influence of thermophoresis on particle deposition is examined in the Darcy flow of a Maxwell nanofluid. In our model, the temperature distribution is generated by the Fourier law of heat conduction with nonlinear thermal radiation and heat sink/source. We also examine the Soret–Dufour effects in the mass concentration equations. The Brownian and thermophoretic diffusions are assumed to be generated by nanoparticle dispersion in the fluid. The similarity method is used to transform the partial differential equations into nonlinear ordinary differential equations. The transformed flow equations were solved numerically using the BVP Midrich scheme. The results of the computation are displayed graphically and in tabular form. The results obtained show that increasing the Deborah number leads to a decline in radial and angular motion and a decrease in the magnitude of axial flow. As expected, the strength of the heat source and the values of the thermal radiation parameters determine the temperature of the liquid. We also found that as the Soret number rises (or the Dufour number falls), so does the mass transfer rate.