The present study deals with the swimming of gyrotactic microorganisms in a nanofluid past a stretched surface. The combined effects of magnetohydrodynamics and porosity are taken into account. The mathematical modeling is based on momentum, energy, nanoparticle concentration, and microorganisms’ equation. A new computational technique, namely successive local linearization method (SLLM), is used to solve nonlinear coupled differential equations. The SLLM algorithm is smooth to establish and employ because this method is based on a simple univariate linearization of nonlinear functions. The numerical efficiency of SLLM is much powerful as it develops a series of equations which can be subsequently solved by reutilizing the data from the solution of one equation in the next one. The convergence was improved through relaxation parameters in the study. The accuracy of SLLM was assured through known methods and convergence analysis. A comparison of the proposed method with the existing literature has also been made and found an excellent agreement. It is worth mentioning that the successive local linearization method was found to be very stable and flexible for resolving the issues of nonlinear magnetic materials processing transport phenomena.

In this article, the effects of swimming gyrotactic microorganisms for magnetohydrodynamics nanofluid using Darcy law are investigated. The numerical results of nonlinear coupled mathematical model are obtained by means of Successive Local Linearization Method. This technique is based on a simple notion of the decoupling systems of equations utilizing the linearization of the unknown functions sequentially according to the order of classifying the system of governing equations. The linearized equations, that developed a sequence of linear differential equations along with variable coefficients, were solved by employing the Chebyshev spectral collocation method. The convergence speed of the SLLM technique can be willingly upgraded by successive applying over relaxation method. The comparison of current study with available published literature has been made for the validation of obtained results. It is found that the reported numerical method is in perfect accord with the said similar methods. The results are displayed through tables and graphs.

In this article, stagnation point flow of a Maxwell fluid over a shrinking porous sheet is considered. The governing partial differential equations are reduced to ordinary differential equations by using similarity transformations. The solution of the resulting nonlinear boundary value problem is calculated with the help of Successive linearization method (SLM) using computational software Matlab. The present analysis confirmed the existence of dual solution for shrinking sheet, while for stretching case the solution is unique. The effects of suction parameter S on the velocity profiles are shown through graphs and analyzed in detail