A New Fourth-Order Predictor–Corrector Numerical Scheme for Heat Transfer by Darcy–Forchheimer Flow of Micropolar Fluid with Homogeneous–Heterogeneous Reactions

This paper proposes a numerical scheme for solving linear and nonlinear differential equations obtained from the mathematical modeling of a flow phenomenon. The scheme is constructed on two grid points. It is a two-stage, or predictor–corrector type, scheme whose first stage (the predictor stage) comprises a forward Euler scheme. The stability region of the proposed scheme is larger than that of the first-order forward Euler scheme. A problem is constructed, comprised of a mathematical model for the Darcy–Forchheimer flow of micropolar fluid over a stretching sheet, and is modified using partial differential equations (PDEs) by incorporating the effects of homogeneous–heterogeneous reactions. A set of PDEs is further reduced into ordinary differential equations (ODEs) by several transformations and is solved using the proposed numerical scheme. By comparing the results obtained using the proposed scheme with those obtained using the existing forward Euler scheme, it can be observed that the proposed scheme achieved a smaller absolute error. The obtained results show that the angular velocity profile displayed dual behavior according to increases in the values of the microrotation and coupling constant parameters. As part of our research, we conducted a comparison with other existing schemes. The findings of this study can serve as a helpful guide for future investigations into fluid flow in closed-off industrial settings.