The aim of this article is to study time dependent rotating single-wall electrically conducting carbon nanotubes with aqueous suspensions under the influence of nonlinear thermal radiation in a permeable medium. The impact of viscous dissipation is taken into account. The basic governing equations, which are in the form of partial differential equations (PDEs), are transformed to a set of ordinary differential equations (ODEs) suitable for transformations. The homotopy analysis method (HAM) is applied for the solution. The effect of numerous parameters on the temperature and velocity fields is explanation by graphs. Furthermore, the action of significant parameters on the mass transportation and the rates of fiction factor are determined and discussed by plots in detail. The boundary layer thickness was reduced by a greater rotation rate parameter in our established simulations. Moreover, velocity and temperature profiles decreased with increases of the unsteadiness parameter. The action of radiation phenomena acts as a source of energy to the fluid system. For a greater rotation parameter value, the thickness of the thermal boundary layer decreases. The unsteadiness parameter rises with velocity and the temperature profile decreases. Higher value of $\varphi$ augments the strength of frictional force within a liquid motion. For greater $R$ and $\theta w$ ; the heat transfer rate rises. Temperature profile reduces by rising values of $\mathrm{Pr}$ .

The capability to stock energy and manage consumption in the future is one of the keys to retrieving huge quantities of renewable energy on the grid. There are numerous techniques to stock energy, such as mechanical, electrical, chemical, electrochemical, and thermal. The q-rung orthopair fuzzy soft set (q-ROFSS) is a precise parametrization tool with fuzzy and uncertain contractions. In several environments, the attributes need to be further categorized because the attribute values are not disjointed. The existing q-rung orthopair fuzzy soft set configurations cannot resolve this state. Hypersoft sets are a leeway of soft sets (SSs) that use multi-parameter approximation functions to overcome the inadequacies of prevailing SS structures. The significance of this investigation lies in anticipating Einstein-ordered weighted aggregation operators (AOs) for q-rung orthopair fuzzy hypersoft sets (q-ROFHSSs), such as the q-rung orthopair fuzzy hypersoft Einstein-ordered weighted average (q-ROFHSEOWA) and the q-rung orthopair fuzzy hypersoft Einstein-ordered weighted geometric (q-ROFHSEOWG) operators, using the Einstein operational laws, with their requisite properties. Mathematical interpretations of decision-making constrictions are considered able to ensure the symmetry of the utilized methodology. Einstein-ordered aggregation operators, based on prospects, enable a dynamic multi-criteria group decision-making (MCGDM) approach with the most significant consequences with the predominant multi-criteria group decision techniques. Furthermore, we present the solicitation of Einstein-ordered weighted aggregation operators for selecting thermal energy-storing technology. Moreover, a numerical example is described to determine the effective use of a decision-making pattern. The output of the suggested algorithm is more authentic than existing models and the most reliable to regulate the favorable features of the planned study.