Two-phase nanofluid flow exhibiting Brownian motion and thermophoretic diffusion via a horizontal circular pipe: numerical simulation

The present study investigates the impact of an unsteady internal flow of a particulate nanofluid within a porous material on the heat and mass transfer along a circular horizontal conduit. It is assumed that both the carrier nanofluid and the dust particles have a high viscosity and are hence incompressible. To kick off this two-phase flow, a constant pressure gradient is applied along the axial direction of the circular pipe. The porous medium’s drag is explained by Darcy’s law and the energy calculations account for the Darcy limit of porous dissipation. A set of nonlinear partial differential equations (PDEs) is used to characterize the nanofluid and dust particle phases, as well as the concentration of suspended nanoparticles. These PDEs were numerically solved using the methodology of finite differences. Coefficients of skin friction and flow rates regarding both phases were also calculated. The novelty lies in the ability of numerical simulation to capture the intricate interplay between Brownian motion, thermophoretic diffusion, and fluid flow within nanofluids. This approach allows for detailed analysis of the complex phenomena involved, which may not be easily achieved through experimental investigations alone. These profiles are formed as a result of the regulating physical factors. Graphs and tabular data are utilized to visually represent the impact of different parameters on solutions. Ultimately, an evaluation of the current solutions for some special cases with previously published findings demonstrates the precision and reliability of the present results.