**1. Introduction**

The progressive thermal patterns of nanoparticles have an extensive range of exploitations in the engineering, industrial, technical, and biomedical fields. Many thermal engineering and industrial processes employ nanofluids to increase their thermal efficiency. In recent decades, dynamic scientists have shown interest in nanoparticles with a small size (1–100 nm). Nanofluids are nanoparticle suspensions in base fluids. It is noted that these particles do not change the reaction process, but they do improve the fundamental thermal processes of base liquids at the peak level. Nanoparticles are used in sophisticated thermal extrusion systems, engineering heating devices, biomedical applications, cancer treatments, the chemotherapy process, energy resources, heat exchangers, manufacturing processes, thermal management equipment, and many other applications. Usually, these nanoparticles undergo aggregation so that a fluid can flow through a porous medium as a completely interconnected network (ideal porous pipe), formed by the constricted channel between each pore. Choi [1] proposed a ground-breaking study on the thermal characteristics of nanofluids, prompting other researchers to pay attention to the subject.

**Citation:** Shah, Z.; Vrinceanu, N.; Rooman, M.; Deebani, W.; Shutaywi, M. Mathematical Modelling of Ree-Eyring Nanofluid Using Koo-Kleinstreuer and Cattaneo-Christov Models on Chemically Reactive *AA*7072-*AA*7075 Alloys over a Magnetic Dipole Stretching Surface. *Coatings* **2022**, *12*, 391. https://doi.org/10.3390/ coatings12030391

Academic Editor: Eduardo Guzmán

Received: 15 February 2022 Accepted: 6 March 2022 Published: 15 March 2022

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Here, we briefly highlight certain contributions due to innovative research on the subject. Kishan and Deepa [2] studied the immersion of nanoparticles in micropolar liquid and the stagnation point flow in a porous region. In a nanofluid material flow constrained by a vertical surface, Alim et al. [3] used the Joule heating process. Sheikholeslami et al. [4] conducted research on CuO nanoparticles contained in a heated chamber with a sensodial wall. The heat process in nanomaterial within a micro-channel with a sinusoidal double layer was studied by He et al. [5]. Mahdavi et al. [6] used nanoparticles to identify cooling applications in a hot jet surface. Abdelsalam et al. [7] addressed the thermal repercussions of hybrid nanofluids in blood flow when electro-osmotic forces are present. Nadeem et al. [8] used dual solution simulations to visualise the slip characteristics of nanofluid flow. Khan et al. [9] concentrated on the thermal characteristics of hybrid nanofluids in unsteady flow. Abbas et al. [10] investigated the influence of time-dependent viscosity on nanofluid flow over the Riga surface. Awais et al. [11] used the KKL model to investigate heat transfer in a suspension of nanomaterials containing (CuO and Al2O3).

Nanomaterials are important because of their high thermal and mechanical properties. The characteristics of the nanoliquids formed by each nanomaterial are considerably altered by these materials. Among nanomaterials, there is a substance known as aluminium alloy, in which aluminium plays a major role. Heat treatable and non-heat treatable alloys are the two main types of aluminium alloys. Aluminium alloys are widely utilised in the construction, testing, and production of spacecraft, aircraft parts, and other structures. Researchers have investigated numerous flow models consisting of aluminium alloys and discovered remarkable thermal transport behaviour due to the improved heat transport features of *AA*7072 and *AA*7075 aluminium alloys. Sandeep and Animasaun [12] reported an examination of heat transfer in nanoliquids consisting of *AA*7072 and *AA*7075 aluminium alloys while considering the impact of varying Lorentz forces. They discovered that nanoliquid made of *AA*7075 alloy is superior in terms of heat transmission to nanoliquid made of *AA*7072. Kandasamy at al. [13] considered the electric field strength for the analysis of heat transport in magnetised *AA*7075 alloys. Tlili et al. [14] investigated three-dimensional heat transfer characteristics in the hybrid colloidal model *AA*7072-*AA*7075/*Methanol* under various velocity conditions. They used a numerical approach to the model and described the results in terms of flow regimes.

Since MHD is commonly used in numerous fields, such as the polymer and petroleum industries, a significant amount of thought has been given to the approach of magnetic fields in liquid flow in recent decades. As we know that the pace of cooling is even more essential than in the standard processes, numerous fabrication processes have been used to regulate the rate of cooling for magneto-hydrodynamic liquids. Unifying metals in electric heaters, metal casting, and gem creating are some of the other functions of magnetohydrodynamics. It also assists in the cooling of the atomic reactor's internal dividers. Magneto-hydrodynamic flows were first sculpted and highly valued in biodesign because they are used in a variety of symptomatic kinds of sickness. In this approach, studying magneto-hydrodynamic flow has a significant impact on several scientific fields. The convective circumstances for MHD Jeffrey flow on an elaborated sheet were examined by Ahmad et al. [15]. Khan et al. [16] studied MHD Falknar-Skan flow through a permeable material with a convective boundary condition. Malik et al. [17] explored MHD hyperbolic flow through an expanded cylinder via numerical methodology, the Kellor-Box method. By assuming magnetic field-dependent viscosity effects, Sheikholeslami et al. [18] described MHD nanofluid flow. The finite element method was used to address this problem.

Flow due to a stretchy surface has risen in prominence among researchers in recent years, owing to its widespread application in industry. Hot rolling, paper production, glass blowing, polymer extrusion, metal extrusion, and crystal growth are only a few of these uses. Crane [19] started flow research with an enlarged sheet. The fluid stream in an enlarged channel was examined by Brady and Acrivos [20]. Researchers discovered that there is a solution for a two-dimensional flow for any given Reynolds number. The movement of fluid past a stretchable cylinder was studied by Wang [21]. By changing the

heat flux, Elbashbeshy [22] investigated heat transfer across a stretchy surface. By using a viscous fluid created by a stretchable surface, Nadeem et al. [23] examined a stagnationpoint stream. Different fluid flow over stretched surfaces was inspected by Awan et al. [24]. The production of entropy for MHD Maxwell fluid across a stretchable and penetrable surface was investigated by Jawad et al. [25].

Because of its vast industrial use in nuclear reactor cooling, chemical engineering, geothermal reservoirs, and thermal oil recovery, the chemical reaction effect has gained a tremendous response. Generally, the relationship between mass transfer and chemical reaction is very important, and it can be studied in terms of reactant species deployment and creation at various speeds during nanofluid mass transfer. Bestman et al. [26] conducted ground-breaking work in defining these influences. Mustafa et al. [27] examined a hydromagnetic flow past a radial surface caused by chemical reaction and Arrhenius activation energy. They found that the concentration of a species rises as the activation energy of a chemical process rises. Mohyud-Din et al. [28] looked at how chemical reactions affected convergent/divergent channels. Aleem et al. [29] instigated alternative forms of water based nanofluids, such as titanium-oxide, aluminium-oxide, and copper-oxide, that arose in a porous media after a chemical reaction and Newtonian heating.

The majority of industrial applications necessitate non-Newtonian nanofluids with non-linearly related shear rates and shear stresses. The shear rate is heavily influenced by the timeframe of the shear stress. Thus, coefficients such as viscosity do not fully describe shear stress in such nanofluids. As a result, numerous mathematicians have debated the class of non-Newtonian models, one of which is the Ree-Eyring nanofluid model. Inks, molten polymers, adhesives, paints, organic materials, and other non-Newtonian fluids are some examples. These are used in food industries, drilling rigs, cooling systems, adhesive industries, and so on. Hayat et al. [30] conducted an entropy examination in the flow of Ree-Eyring nanofluid in this respect. Tanveer and Malik [31] investigated the thermal effectiveness of Ree-Eyring nanofluid peristaltic flow. Khan et al. [32] investigated the effect of Lorentz force on the velocity of a Ree-Eyring nanofluid flow past a paraboloid surface. Al-Mdallal et al. [33] investigated the thermal properties of *Cu*-*Water* nanofluid under the sway of radiation. Purna et al. [34] used the Darcy-Frochheimer law to examine the flow of Ree-Eyring nanofluid on a porous plate inclined at an angle, as well as the impact of the chemical reaction. Some recent studies about nanofluids and heat transfer properties are mentioned in Refs. [35–38].

The main goal of this article is to study the existence of a magnetic dipole and the Koo-Kleinstreuer model using different alloys over a stretching sheet. The Cattaneo-Christov model is used to calculate heat transfer in a two-dimensional flow of Ree-Eyring nanofluid across a stretching sheet. The mathematical formulation is created in the following section, utilising fluid flow assumptions. By applying appropriate similarity transformations, the physical flow phenomenon is represented and then translated into a non-dimensional form. The HAM is used to arrive at a solution. Through graphical demonstrations, the influences of a few key parameters on the temperature, velocity fields, and concentration profile are highlighted.
