The fundamental concern of the present study is to analyze the magnetohydrodynamics (MHD) hybrid nanofluid (Carbon-nanotubes and ferrous oxide-water)$ CNT-Fe_{3}O_{4}/H_{2}O$ flow through a horizontal parallel channel having squeezing and dilating porous walls along with thermal radiation. The porous walls of the channel cause the parting motion. The fluid flow is laminar and time-dependent. The channel is asymmetric and the temperature and porosity of the upper and lower walls are different. The concept of hybrid nanofluid is exploited with the combination of nanoparticles of $Fe_{3}O_{4}$ and single and multi-wall carbon nanotubes. The set of partial differential equations (PDEs) of this mathematical model, governed from momentum and energy equations, are reduced to respective ordinary differential equations (ODEs) by using the similarity transformation. To achieve the solutions of governing ODEs, a very common numerical approach called, Runge-Kutta method of order four along with shooting technique is utilized. A computing software MATLAB is used to construct the graphs of temperature and velocity profiles for different emerging parameters. The main findings are summarized at the end of the manuscript.

This study emphasized the computational aspects of the electromagnetohydrodynamic (EMHD) flow of Williamson nanofluid with variable viscosity and dissipation effects over a nonlinearly expanding sheet. The viscosity of the fluid depends upon temperature and thermal diffusion. Due to nonlinear expansion of sheet, a solutal and thermal stratification phenomenon are also incorporated. A uitable transformation is applied to the basic mathematical problem to convert the system of partial differential equations (PDEs) into nonlinear ordinary differential equations (ODEs). An efficient analytical approach known as HAM (homotopy analysis method) is used to achieve the local similar solutions. The attributes of commanding variables, such as the viscosity parameter, Hartman number, Lewis number, Weissenberg number, Brownian motion parameter, stretching index, and stratification parameters are related to velocity, temperature, and concentration profiles through graphs and tables. Convergence table and h-curves are drawn for the optimal solution through HAM. Numerical values are well tabulated for the study of skin-friction and Sherwood numbers against the different parameters.