In this endeavor thin‐film flow of magneto hydrodynamic (MHD) fluid in the presence of thermal conductivity and variable viscosity over a porous steady stretching surface with a magnetic field and radioactive heat fluctuation is studied. In this phenomenon the viscosity vary inversely and thermal conductivity directly with temperature. The nonlinear coupled differential equations for the velocity and temperature profiles are achieved and solved by using a new analytical approach, called 3rd form of Optimal Homotopy Asymptotic Method (OHAM‐3). The proposed technique consists of initial guess, embedding parameter, optimal convergence control parameters, auxiliary functions and homotopy. Numerical (ND‐Solve Method) solutions are also achieved and compared with the results gained by the proposed method. The fast convergence of the applied new method and the influence of different physical nondimensional parameters on the velocity and temperature profiles are mainly focused in this research.

An easy and efficient technique is applied to get a reliable analytic approximate solution of linear and nonlinear integral and integro‐differential equations arising in the phenomena of everyday life. The proposed technique consists of a series only in which the unknown constants are determined in the usual way. The obtained results by this technique are in good agreement with the exact solution and it is proved that this technique is effective and easy to apply. Some problems are solved to prove the above claims and also the results are compared with exact solutions as well as with the results obtained by already existing different techniques.

This study presents mechanisms for the investigation of an unsteady magnetohydrodynamic second‐grade fluid flow between two periodically oscillating plates. The flow characterization is given in three forms, that is, Couette flow, Poiseuille flow, and a combination flow of both of them. A mathematical system is generated to design the problems, which are solved in an analytical way with two novel procedures, namely Adomian decomposition method (ADM) and optimal homotopy asymptotic method (OHAM). The numerical comparison, absolute errors, and residuals of OHAM and ADM solutions are evaluated. Results obtained from these two methods are studied comparatively in the form of numbers and graphs. A good agreement between the respective data is obtained. The influences of flow parameters like frequency parameter, non‐Newtonian fluid parameter, magnetic field parameter, pressure gradient parameter, and time variable on velocity scriptv(y,t) have been analyzed.

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.