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<p>This study explores the combined effects of a chemical reaction, heat source, and Joule heating on the unsteady, two-dimensional flow of an incompressible, viscous, magnetohydrodynamic (MHD) fluid over a vertically stretched surface within a Darcy-Forchheimer porous medium. The system of coupled partial differential equations governing the flow is simplified into a set of nonlinear ordinary differential equations using similarity transformations. These equations are then solved using the bvp4c numerical method. Graphs are used to illustrate and analyze how various physical parameters namely, Hartmann number, Forchheimer number, Joule heating parameter, Prandtl number, heat source parameter, Soret number, Schmidt number, and chemical reaction parameter etc. affect the fluid’s velocity, temperature, and concentration. Numerical values for skin friction, the Sherwood number, and the Nusselt number are presented in tables. To verify the accuracy of the method, the results are compared with previously published studies and show strong agreement. The results indicate that increasing the Forchheimer number leads to a decrease in fluid velocity, while the temperature increases. Moreover, higher Hartmann numbers and unsteadiness parameters result in reduced skin friction.</p>

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Unsteady MHD Flow Over a Stretching Sheet in a Darcy-Forchheimer Porous Medium: Influence of Joule Heating, Soret Effect, and Chemical Reaction

  • 期刊论文

  • 发表日期：

    2025年8月1日

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  • Saleem Jabed Al Khayer,
  • Shyamanta Chakraborty

摘要

This study explores the combined effects of a chemical reaction, heat source, and Joule heating on the unsteady, two-dimensional flow of an incompressible, viscous, magnetohydrodynamic (MHD) fluid over a vertically stretched surface within a Darcy-Forchheimer porous medium. The system of coupled partial differential equations governing the flow is simplified into a set of nonlinear ordinary differential equations using similarity transformations. These equations are then solved using the bvp4c numerical method. Graphs are used to illustrate and analyze how various physical parameters namely, Hartmann number, Forchheimer number, Joule heating parameter, Prandtl number, heat source parameter, Soret number, Schmidt number, and chemical reaction parameter etc. affect the fluid’s velocity, temperature, and concentration. Numerical values for skin friction, the Sherwood number, and the Nusselt number are presented in tables. To verify the accuracy of the method, the results are compared with previously published studies and show strong agreement. The results indicate that increasing the Forchheimer number leads to a decrease in fluid velocity, while the temperature increases. Moreover, higher Hartmann numbers and unsteadiness parameters result in reduced skin friction.