3-D magnetohydrodynamic AA7072-AA7075/methanol hybrid nanofluid flow above an uneven thickness surface with slip effect

A 3-D magnetohydrodynamic flow of hybrid nanofluid across a stretched plane of non-uniform thickness with slip effects is studied. We pondered aluminum alloys of AA7072 and AA7072 + AA7075 in methanol liquid. The aluminum alloys amalgamated in this study are uniquely manufactured materials, possessing enhanced heat transfer features. AA7072 alloy is a composite mixture of Aluminum & Zinc in the ratio 98 & 1 respectively with added metals Silicon, ferrous and Copper. Equally, AA7075 is a mixture of Aluminum, Zinc, Magnesium, and Copper in the ratio of ~90, ~6, ~3 and ~1 respectively with added metals Silicon ferrous and Magnesium. Numerical solutions are attained using R-K based shooting scheme. Role of physical factors on the flow phenomenon are analyzed and reflected by plots and numerical interpretations. Results ascertain that heat transfer rate of the hybrid nanoliquid is considerably large as matched by the nanofluid. The impact of Lorentz force is less on hybrid nanofluid when equated with nanofluid. Also, the wall thickness parameter tends to improve the Nusselt number of both the solutions.


Scientific RepoRtS |
(2020) 10:4265 | https://doi.org/10.1038/s41598-020-61215-8 www.nature.com/scientificreports www.nature.com/scientificreports/ Benos et al. 16 . They noticed that variation in the shape of the nanomaterials tends to enhance heat transfer performance. Moreover, Chamkha 17 discussed numerically the impression of magnetic properties over the nano liquid flow caused due cylinder in a three-dimensional enclosure by the aid of the finite element method. Meanwhile, the joint response of Prandtl number and magnetic properties over the 2D steady motion of nanofluid past a stretched membrane was numerically explored by Ganesh et al. 18 . As per the available literature, several researchers ( [19][20][21][22][23] ) did the outstanding work on applying MHD concept in their analysis.
Radiative thermal emission found vital applications in industrial engineering as the construction of gas turbines, design of fin and missiles, etc. Khan et al. 24 deliberated the 2-D flow of nano liquid through melting plane under the response of radiative heat flux 24 . They revealed that hike in thermal radiation results in the improvement of heat transfer performance of the liquid. Seth et al. 25 examined semi analytically with the aid of OHAM to study the flow of nanofluid through an elongated plane by the implication of magnetic properties and also examined the entropy generation. Further, the researchers 26-31 made noticeable results their analysis in convective heat transfer. Acharya et al. 32 explored a computational work for analyzing the multiple slip effects on chemically reacting Williamson fluid flow in permeable medium. A hybrid approach for investigating the thermal radiation and hall current effects on nanoliquid flow over a spinning disk was proposed by Acharya et al. 33 . The effect of aligned magnetic field on the slippery flow of nanofluid was numerically studied by Acharya et al. 34 . The researchers 35,36 investigated the convective heat transport in different nanofluids using NDM and Lie group approaches. Effect of internal heat source and radiation on 3-D flow of nanofluid past a shrinking sheet was theoretically studied by Sharma et al. 37 . The researchers 38,39 investigated the natural convection in magnetohydrodynamic flow under various physical effects. Thermal radiation effect on magnetohydrodynamic flow in the presence of heat generation was numerically studied by the researchers 40,41 . Boling et al. 42 proposed a stability solution for the MHD equation. The researchers 43,44 studied the magnetohydrodynamic flow of Power-Law fluid by considering the various flow geometries. Recently, Tlili et al. 45,46 premeditated the magnetohydrodynamic flow of nanofluid by considering the various physical effects and flow geometries.
Recent days, variety of nanomaterial are discovered in literature, among these aluminum alloy nanoparticles AA7075 and AA7072 are of special featured nanomaterial with greater thermal, chemical and physical properties. Aluminum alloy plays a prominent role in aerospace industries, especially, aluminum alloys AA7072 and AA7075 are of abundant significance in the production of transport appliances namely, glider aircraft, rocket climbing frame, etc. 29 . It is evident that very less work has found in the study of hybrid nanofluids. This article reports the 3-D magnetohydrodynamic flow of hybrid nanofluid across a stretched plane of non-uniform thickness with slip effects. We pondered aluminum alloys of AA7072 and AA7072 + AA7075 in methanol liquid. The numerical solutions are attained, and the role of physical factors on the flow phenomenon is analyzed and reflected by plots and numerical interpretations.

Formulation
3D MHD, steady flow of hybrid nanofluid past a stretched plane of non-uniform thickness with slip effect is considered. The hybrid nanofluid is composed of alloy nanoparticles of AA7072 and AA7072 + AA7075 suspended in methanol liquid.
The sheet of non-uniform thickness is considered as z A x y c n , , 1 we have chosen A is small. It is also presumed, the sheet temperature as . The induced magnetic field is ignored in this study. Here B 0 is the magnetic field applied in parallel with the z− axis as revealed in Fig. 1. With conventions made above, the governing equations in vector form can be expressed as 30 : www.nature.com/scientificreports www.nature.com/scientificreports/ p hnf hnf 2 the linked boundary restrictions are The hybrid nanofluid parameters k , , , nf nf nf nf ρ µ σ represent the density, dynamic viscosity, electrical conductivity, thermal conductivity can be used as 26 : ( following similarity transformations are used for non-dimensionalisation             are the magnetic field parameter, Prandtl number and wall thickness parameters respectively. For engineering curiosity the C f and Nu x are defined as

Results and Discussion
The system of ODE's (10-12) along the boundary restrictions (13) are resolved numerically using R-K based shooting procedure 14   www.nature.com/scientificreports www.nature.com/scientificreports/ to attain the required results. Above quantities are reserved for the complete study, unless they specified in respective graphs and tables. Symbols used in figures f ( ) η ′ , g ( ) η ′ and θ(η) describes the flow common quantities as velocity and temperature respectively. Simultaneous solutions are noticed for Methanol+AA7075 nanofluid and Methanol+AA7075 + AA7072 nanofluid. We treat Methanol+AA7075 nanofluid as first solution and Methanol+AA7075 + AA7072 nanofluid as second solution. Figures 2-4 exhibits the impact of (φ) on f ( ) η ′ , η ′ g ( ) and θ(η) we detect a hike in η ′ f ( ), g ( ) η ′ and θ(η) for improvement in volume of (φ). The methanol+AA7075 nanofluid flow is highly influenced for rise in (φ) than Methanol+AA7075 + AA7072 nanofluid. Physically, rising the nanoparticle volume fraction leads to enhance the thermal conductivity of the fluid. Figures 5-7 depicted to witness the effect of Lorentz force on η ′ f ( ), η ′ g ( ) and θ(η). We conclude that, increase in M upshots the reduction of η ′ f ( ) and η ′ g ( ). And a reverse trend is detected for θ(η). Physically, improvement in M leads to develop Lorentz force which in turn causes to resist the fluid motion, hence, we notice upswing in   Table 1. Physio-thermal properties 29 .     It is clear that, rise in n improves the distributions for η ′ f ( ), g ( ) η ′ and θ(η). Actually, boosting n helps in slendering of the sheet. It leads to, weaken the thickness of the sheet and in turn it enhances the thermal boundary layers. Figures 11-13 outlined to witness the consequences of Λ on f ( ) η ′ , η ′ g ( ) and θ(η). We found that, η ′ f ( ), g ( ) η ′ and θ(η) are decreasing function of Λ. This concur the physical nature of the wall thickness parameter. Figures 14-16 are portrayed to witness the changes in f ( ) η ′ , g ( ) η ′ and θ(η) for diverse values of h 1 . It is evident that, escalating values of h 1 improves θ(η), but reverse nature is observed for η ′ f ( ) and η ′ g ( ). Finally, Fig. 17 exhibits the impact of h 2 on θ(η). It is obvious that, temperature distributions are diminishing functions of h 2 . Table 1 Table 2. The following observations are made, improved values of M and n results in declination of both skin friction coefficient and rate of heat transfer. It also worth noting that, the values ″ f (0) and (0) θ − ′ of methanol+AA7072 + AA7075 nanofluid are more influenced by the varied values of M and n when compared with methanol+AA7075 nanofluid. Rate of heat transfer is a rising function of Λ, and (0) θ − ′ of metha-nol+AA7072 + AA7075 solution is high as equated with methanol+AA7075 solution. They are intensifying the values of φ and h 1 , both the parameters ″ f (0) and (0) θ − ′ decelerates. Thermal transport rate of the nanofluids diminishes for improved vales of h 2 . The validation of the present results is depicted in Table 3.

Conclusions
A 3D MHD flow of hybrid nanofluid over a surface of non-uniform thickness with slip effects is studied numerically. We pondered aluminum alloys of AA7072 and AA7072 + AA7075 in methanol liquid and presented simultaneous solutions. The significant outcomes are as follows: • Momentum and thermal distributions are increasing functions of n.
• Flow field is diminished by magnetic field parameter, M and a reverse trend is observed for the temperature field. • The hike in wall thickness parameter results in a lessening in the flow and energy fields.
• The impact of Lorentz force is less on hybrid nanofluid when equated with nanofluid.
• The rate of thermal transport of the hybrid nanofluid is higher than the nanofluid.
• Wall thickness parameter regulates the Nusselt number for both the nanoliquids.
• The major application of the present study can be found in aerospace manufacturing industries.