<p>In this study, the problem of bi-convective heat and mass transfer in two-dimensional steady Powell–Eyring nanofluid flow from a nonlinear stretched sheet in a porous medium is explored. The convective conditions for temperature and concentration are modeled using Biot numbers. Additionally, the influence of the magnetic field, porous medium resistance, Joule heating, viscous dissipation, velocity slip, Brownian motion, thermophoresis, chemical reaction, and Soret-Dufour cross-diffusion is taken into account. Using appropriate similar variables, the governing PDEs are fully transformed into a set of coupled ODEs, which are then solved using a collocation method based on piecewise polynomial interpolations in the fourth order. The results are validated by matching them with known models in limiting conditions. The findings show that the Soret effect has remarkable effects in increasing mass transfer by causing species diffusion because of temperature gradients, and that the Dufour effect has substantial effects in increasing the temperature field by causing heat flux because of concentration gradients. Their highly nonlinear coupling shows substantial effects in varying Nusselt and Sherwood number profiles, especially as Soret number and section location increase. Beyond evaluating the individual effects of the governing parameters, the study clarifies how magnetic damping, porous resistance, and cross-diffusion mechanisms collectively regulate the coupled momentum, thermal, and concentration transport processes. The results provide physical insight into the multiscale interaction among these transport mechanisms, thereby extending the understanding of heat and mass transfer beyond conventional parameter-by-parameter analyses.</p>

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Bi-convective Analysis of Powell–Eyring Nanofluid Flow: Combined Effects of Joule Heating, and Viscous Dissipation over a Porous Sheet

  • Dipta Roy,
  • Kajal Chandra Saha

摘要

In this study, the problem of bi-convective heat and mass transfer in two-dimensional steady Powell–Eyring nanofluid flow from a nonlinear stretched sheet in a porous medium is explored. The convective conditions for temperature and concentration are modeled using Biot numbers. Additionally, the influence of the magnetic field, porous medium resistance, Joule heating, viscous dissipation, velocity slip, Brownian motion, thermophoresis, chemical reaction, and Soret-Dufour cross-diffusion is taken into account. Using appropriate similar variables, the governing PDEs are fully transformed into a set of coupled ODEs, which are then solved using a collocation method based on piecewise polynomial interpolations in the fourth order. The results are validated by matching them with known models in limiting conditions. The findings show that the Soret effect has remarkable effects in increasing mass transfer by causing species diffusion because of temperature gradients, and that the Dufour effect has substantial effects in increasing the temperature field by causing heat flux because of concentration gradients. Their highly nonlinear coupling shows substantial effects in varying Nusselt and Sherwood number profiles, especially as Soret number and section location increase. Beyond evaluating the individual effects of the governing parameters, the study clarifies how magnetic damping, porous resistance, and cross-diffusion mechanisms collectively regulate the coupled momentum, thermal, and concentration transport processes. The results provide physical insight into the multiscale interaction among these transport mechanisms, thereby extending the understanding of heat and mass transfer beyond conventional parameter-by-parameter analyses.