Unconditionally Stable Numerical Scheme for Heat Transfer of Mixed Convective Darcy-Forchheimer Flow of Micropolar Fluid Over Oscillatory Moving Sheet

A third-order numerical scheme is proposed for the time discretization of time-dependent partial differential equations (PDEs). This third-order proposed scheme is further modified, and the new scheme is obtained with second-order accuracy in time and is unconditionally stable. The stability of the new scheme is proved by employing von Neumann stability analysis. For spatial discretization, a compact fourth-order scheme is adopted. Moreover, a mathematical model for heat transfer of Darcy-Forchheimer flow of Micropolar fluid is modified with an oscillatory sheet, nonlinear mixed convection, thermal radiation and viscous dissipation. The suitable transformations are considered to transform the dimensional system of PDEs into dimensionless PDEs and further solve this system using the proposed numerical scheme. It is found that velocity and angular velocity have dual behaviour by incrementing coupling parameters. The proposed second-order accurate in-time scheme is compared with the existing Crank-Nicolson scheme. The proposed scheme is shown to have faster convergence than the existing scheme with the same accuracy. We anticipated this would help investigators address outstanding challenges in industrial and engineering enclosures.