The exploration of thin liquid film flow under the influences of various physical parameters by a new analytical innovation

Abstract

A new analytical innovation is utilized to explore the thin liquid film flow of magnetohydrodynamic (MHD) fluid over an unsteady porous stretching surface. Here magnetic field, thermal radiation, and variable viscosity are taken. The self‐similarity variables have been used to transform the modeled partial differential equations into a set of non‐linear coupled differential equations. These non‐linear differential equations for the velocity and temperature profiles have been tackled through an innovation containing homotopy, auxiliary functions, and convergence control parameters. This method is called the second configuration of the Optimal Homotopy Asymptotic Method and is denoted by (OHAM‐2). Galerkin's process is chosen for the optimizations of parameters. The achieved coupled equations are also solved numerically (ND‐Solve Method), and the obtained outcomes are compared with the results elaborated by the suggested algorithm. Here the utmost attention is on the rapid convergence of the proposed algorithm and the consequences of various tangible variables on the velocity and temperature profiles. This straightforward algorithm consists of a few steps but gives better outcomes. The technique can be applied to solve partial differential equations and their systems forming in various disciplines. This technique can also solve Integro differential equations. The residuals achieved by the proposed method for the velocity and temperature fields are shown graphically. The errors and residuals are also taught in Table 1 and Table 2. The effects of parameters are inculcated in Table 3 and Table 4. The results are validated with the published work as shown in Table 5. Nomenclature is indicated in the text below.