Legendre wavelet integration operational matrix method for the numerical solution of unsteady MHD nanofluid flow between moving parallel plates

This study proposes a novel method based on Legendre wavelet integration operational matrix for solving a system of nonlinear ODE's to model the two-phase, unsteady nanofluid flow and heat transfer between parallel plates in presence of magnetic field. To validate the applicability of proposed method, system of nonlinear BVP with exact solutions is employed as a test problem. Test problem results are compared with exact solution, and other numerical methods. The governing equations were then changed using similarity transformation into a set of nonlinear ODE's. . Following this, the LWOMM is applied for the proposed problem. Findings demonstrated that, for a constant Reynolds number, skin friction coefficient value increases with rising Hartmann and squeezing numbers. Furthermore, it is demonstrated that Eckert number is a reducing function of the squeeze number and Nusselt number is an increasing function of Hartmann number.