The aim of this research work is to investigate the innovative concept of magnetohydrodynamic (MHD) three-dimensional rotational flow of nanoparticles (single-walled carbon nanotubes and multi-walled carbon nanotubes). This flow occurs in the presence of non-linear thermal radiation along with heat generation or absorption based on the Casson fluid model over a stretching sheet. Three common types of liquids (water, engine oil, and kerosene oil) are proposed as a base liquid for these carbon nanotubes (CNTs). The formulation of the problem is based upon the basic equation of the Casson fluid model to describe the non-Newtonian behavior. By implementing the suitable non-dimensional conditions, the model system of equations is altered to provide an appropriate non-dimensional nature. The extremely productive Homotopy Asymptotic Method (HAM) is developed to solve the model equations for velocity and temperature distributions, and a graphical presentation is provided. The influences of conspicuous physical variables on the velocity and temperature distributions are described and discussed using graphs. Moreover, skin fraction coefficient and heat transfer rate (Nusselt number) are tabulated for several values of relevant variables. For ease of comprehension, physical representations of embedded parameters such as radiation parameter $\left(Rd\right)$ , magnetic parameter $\left(M\right)$ , rotation parameter ( $K$ ), Prandtl number ( $Pr$ ), Biot number $\left(\lambda \right)$ , and heat generation or absorption parameter $\left(Q_h\right)$ are plotted and deliberated graphically.

In this article, flow of Casson fluid on permeable exponential stretching exterior in the existence of dust and fluid phase with thermal radiation are presented. The basic governing equations of fluid velocity and thermal energy has converted to differential equations with the help of suitable variables of similarity which are coupled and nonlinear. An analytical methodology have been applied to obtain solution of the model equations. The effect of different emerging parameters, radiation parameter (Rd), concentration of mass of the dust particles (γ), volume fraction of dust particles (φ _d ), unsteadiness parameter (S), fluid particle interaction parameter (λ), volume fraction of nanoparticles (φ), and porosity parameter (κ), on different profiles like temperature, velocity and concentration has been studied. The influence of skin friction, Nusslet number and Sherwood number has been illustrated. Comparison is provided for the validation of our results with prevailing works and is found in decent settlement. It has been seen that fluid particle interaction is direct proportionate to the temperature transfer rate and is in inverse relation to wall friction. Further, the heat profile of dusty nanofluid is raised efficiently with radiation parameter.

In this paper, investigation of three-dimensional squeezing flow of carbon nanotubes (CNTs) based on water (H₂O) in a rotating channel with the permeable fixed bottom wall has been presented. The walls of the channel are kept porous. Appropriate transformations correspond to strong nonlinear ordinary differential system is solved by Homotopy analysis method (HAM) with the help of similarity variables. The influences of conspicuous physical variables on the velocity and temperature distributions are described and discussed using graphs. Moreover, skin fraction coefficient and heat transfer rate (Nusselt number) are tabulated for several values of relevant variables. The most important result of this investigation is to study the different behaviors of emerging parameters on carbon nanotubes (CNTs) based on the water (H₂O) with changes in squeezing parameter and to see the impacts of these emerging parameters.