*1.1. Literature Review*

Nanofluid, characterized by a significant increase in the heat and mass transfer rate compared to conventional engineered fluid (oils, lubricants, water, ethylene glycol, etc.) [1], is found to serve in a number of engineering applications, for instance, the solar energy system [2], fuel-cell industry [3], petroleum engineering [4–6], materials science [7,8], etc. Choi [9] was the first person who introduced the concept of a dilute suspension of nanoparticles with a dimension less than 100 nm (Cu, TiO2, Al2O3, Ag, Fe) and their oxides in conventional fluids (oils, lubricants, water, ethylene glycol), which enhances the thermal performance of conventional fluids. Recent applications of nanofluids in the biomechanical field, such as cancer therapy, drug delivery and medicines, have produced a lot of interest in the investigation of nanofluid flows and heat transport. In view of these various applications, researchers have focused their attention on nanofluid flows. Ellahi [10] examined the impact of MHD and thermal viscosity on the flow of non-Newtonian nanoliquid over a tube. Alshomrani and Gul [11] computed the analytical solution of magneto-hydrodynamics thin film spray of water base Al2O3 and CuO nanofluids on a horizontal stretchable cylinder. Asadi et al. [12,13] investigated the experimental and theoretical influence of adding MWCNTs, ZnO nanoparticles, and MgO-MWCNT hybrid nanofluids in thermal oil. Gul et al. [14] discussed the impact of an effective Prandtl number on water and ethylene glycol-based alumina nanofluid spray along a stretching cylinder.

CNTs (carbon nanotubes) have a long cylindrical profile, such as frames of carbon atoms with a diameter ranging from 0.7 nm to 50 nm. Carbon nanotubes have a specific importance in nanotechnology, conductive plastics, hardwater, air purification mechanisms, structural composite materials, sensors, display of flat panels, storage of gas, biosensors, extra-long fibers, and many other areas of science and engineering. The idea of CNTs was first discovered in 1991 by Lijima [15]. Carbon nanotubes are further classified as single wall carbon nanotubes (SWCNTs) and multi wall carbon nanotubes (MWCNTs), depending on the number of concentric layers of rolled graphene sheets. Furthermore, carbon nanotubes are predictable inventive material of the 21st century due to their special morphology; new physicochemical features; and unique thermal, electrical, and mechanical characteristics. Additionally, the existence of carbon chains in carbon nanotubes does not pose any danger to the atmosphere. Keeping the above applications, Haq et al. [16] investigated the impact of the thermal conductivity and viscosity of CNTs nanoparticles within three different base fluids (water, engine oil, and ethylene glycol) in nanofluid flowing over a stretching surface. Khan et al. [17] considered the analysis of flow and heat transport of nanofluids containing carbon nanotubes along a flat plate in the presence of the Navier slip boundary condition. Aman et al. [18] examined the effect of MHD on the flow of non-Newtonian CNTs nanofluid. They used three kinds of base liquid. Similarly, the exact solution of Maxwell nanofluid containing CNTs in four types of base fluid was investigated in [19]. Asadi et al. [20–23] conducted some experimental study on the dynamic viscosity of different nanofluids. They found that the viscosity of MWCNTs nanofluids is considerably higher than that of the base fluids. Various other important studies that have been conducted on CNTs base nanofluid can be seen via [24,25].

After the development of nanoliquids, scholars and engineers focused their concentration on examining the motion of nanofluids from various circumstances, such as stretching cylinders and sheets, rotating disks or cylinders, and parallel plates with various flow conditions. The flow problem of magneto-nanofluid through a stretching/extending surface has several practical applications in manufacturing progressions due to the mechanical property of electrically conducting liquids. A stretching surface has gained the extensive attention of scholars due to many manufacturing and technological applications, such as the fabrication and removal of polymer slips from dye, freezing of continuing filaments, lead crystal blowing, manufacture of paper, production of meals, and sketching of wires. Khan et al. [26] explored the phenomena of MHD spray scattering on a stretching cylinder using nanoparticles Al2O3 and CuO water-based nanoliquids. Recently, some more useful explorations of the subject associated with thin film flow have been presented in [27–30].

Non-Newtonian liquids like toothpaste, food stuff, and plastic have various uses in biochemical, pharmacological, and cosmetic industries. It is very problematic to handle this kind of liquid because the extra nonlinear term originates in the equation of motion. Thus, various liquid models are presented to describe the performance of the said materials. In the present analysis, we select the Casson model. Initially, this model was presented by [31]. It is a shear thinning fluid which is thought of as the zero-shear rate of immeasurable viscosity [32], but is the infinite shear rate at zero viscosity. Human blood, honey, jelly, and soup are examples of Casson fluid. The influence of thermal radiation on Casson fluid flow and the rate of heat exchange on a permeable extending surface have been reported [33]. Asma et al. [34] have explored the MHD flow of Casson liquid on a permeable upright plate. The impact of MHD on Casson nanofliquid flow with thermal radiation over a cylinder was studied in [35].

Among the various models of non-Newtonian time independent fluids models, one of the distinct features and a quite famous Casson model [31,36] known as the most approved is the rheological model for characterizing human blood flow [24,37,38].

In the present work, the thin film Casson nanofluid (human blood) flow comprising CNTs nanoparticles is analyzed with uniform MHD over a stretching upright cylinder. Human blood is used as the base liquid, with two varieties of SWCNTs and MWCNTs nanoparticles inside. The HAM technique [11,39–43] is performed to find the series solution of velocity and the thermal field. The physical performance of each model's parameters for SWCNTs and MWCNTs nanoparticles is presented graphically for velocity, temperature, and pressure fields. Conclusions have been established on the basis of the results.
