*Corresponding Author

Abstract: - Carbon nanotubes (CNTs) and graphenes possess the properties that make them the future of armory

in the military. Bullet-proof vests, for instance, are indispensable components of any military arsenal whose

maintenance cost and weight can be drastically reduced if the materials are changed to CNT and graphenes.

The purpose of this study is to investigate heat and mass transport phenomena in the hydromagnetic flow of

Casson fluid suspending carbon nanotubes and graphene nanoparticles in armory production. An appropriate

model is developed, taking into account the Buongiorno model and the effect of heat radiation. Using similarity

variables, the model is reformulated into a dimensionless form. The numerical solution to the dimensionless

model is obtained using the three-stage Lobatto IIIa finite difference approach, which is programmed into the

Received: November 18, 2022. Revised: August 27, 2023. Accepted: October 6, 2023. Published: November 8, 2023.

Most natural and engineered fluids do not obey the

Newtonian law of viscosity, [1], [2], [3], [4]. These

diverse properties of the fluids led to the

formulation of fluid models such as the Casson fluid

model, the Carreau fluid model, and the Williamson

fluid model, [5], [6], [7], [8], [9]. The Casson fluid

when he added millimetre-scale solid particles to a

fluid. The study, [13], however, improved on the

work by proposing nanoparticles in place of the

suspension of nanoparticles in a base fluid is now

[23], reiterated that heat transmission is drastically

improved in hybrid nanofluid when compared with

the ordinary base fluid or a nanofluid of similar

individual nanoparticles. The study, [24], explored

the semi-analytical solutions of an unsteady flow of

a hybrid nanofluid and their results showed the

existence of one stable solution and one unstable

solution. The study, [25], explained the existence of

the two solutions by showing that only one of the

solutions is significant for the research study. The

nanoparticles like Carbon nanotubes greatly

improve the heat transfer rate than many others. The

study, [27], elucidated the significance of magnetic

field strength and heat source on the flow of hybrid

nanofluid over an exponential stretching Surface

(ESS). More recently, [28], studied heat and mass

transfer flow in the flow of Casson nanofluid in a

mixed-convective double diffusive flow with

convective boundary conditions. The result

indicated that skin friction, heat transfer rate, and

laminated securely in layers. The fabric material

absorbs the energy of the impacting bullet by

stretching the fibers, and the stiff fibers guarantee

that the load is distributed across a vast area within

the material. This mechanism slows the bullet and

eventually prevents it from hitting the body. The

ability of a fiber to deform in polymer matrix

composites (PMCs) is severely limited as a result of

surrounding resin, and therefore the energy

absorption capacity is diminished. Under ballistic

strength, and low thermal expansion coefficient,

contribute to their potential ability to replace current

materials used in the production of armories.

Furthermore, graphenes and carbon nanotubes

Casson hybrid nanofluid over an ESS in the

presence of thermal

The dimensionless form of the quantities of interest

are

 󰇡

 󰇛󰇜

󰇛󰇜

employed to convert the dimensionless boundary

some initial guesses for  and the results are

compared with the three free stream conditions

found in the comparison. The process is repeated

until a tolerable error is achieved. Once the

equivalent initial value ordinary differential

equation has been obtained, then the 3-stage Loabtto

IIIa is executed to solve the problem (Other methods

of solution can be found in, [35]). The Lobatto IIIa

method is a symmetric and nonstiff A-stable method

whose stability function 󰇛󰇜 is 󰇛󰇜-Pade

explains why the temperature profile increases with

increasing Casson fluid parameters as shown in

Figure 6. Figure 7 shows that increasing the

Magnetic field parameter increases the temperature

profile. This observation can be traced to the fact

that the Lorentz force generated from the magnetic

field creates a lot of internal friction between the

fluid molecules within the thermal boundary layer.

Additional internal energy is created in the form of

heat which raises the flow temperature profiles as

temperature profile in Figure 9 is a result of the

increasing thermal radiation.

4.3 Effects of Various Parameters on the

Figure 10, Figure 11 and Figure 12 illustrate the

effects of the dimensionless parameters on the

concentration. As the Casson parameter γ increases,

the concentration profile increases due to the

increase in the concentration at the boundary layer

(as shown in Figure 10). Increasing the magnetic

concentration profile. This is because, as the

Radiation parameter increases, heat is generated in

the flow. An increase in the flow temperature

enhances the migration of nanoparticles from the

boundary layer and consequently reduces the

particle concentration within the boundary layer.

Fig. 5: Primary velocity with Radiation parameter

Fig. 6: Temperature with Casson parameter

Fig. 7: Temperature with Magnetic parameter

Fig. 12: Concentration with Radiation parameter