Heat and Mass Transfer Enhancement of MHDHybrid Nanofluid Flow in the Presence of Activation Energy

In this study, water is apprehended as conventional fluid with the suspension of two types of hybrid nanoparticles, namely, singlewalled CNTs (SWCNTs) and multiwalled CNTs (MWCNTs). )e influence of a magnetic field, thermal radiation, and activation energy with binary chemical reaction has been added to better examine the fine point of hybrid nanofluid flow.)e mathematical structure regarding the physical model for hybrid nanofluid is established and then the similarity variables are induced to transmute the leading PDEs into nonlinear ODEs.)ese equations were solved using the shooting technique together with RKF 45 order for various values of the governing parameters numerically. )e results of prominent parameters were manifested through graphs and tables.)e results indicate that the hybrid nanofluid SWCNT − (MWCNT/water) is fully adequate in cooling and heating compared to other hybrid nanofluids. In addition, the rise in the value of activation energy (E) upsurges the nanoparticle transfer rate of hybrid nanofluid.


Introduction
Hybrid nanofluids are a new kind of working fluid that is made by suspension of two different types of nanoparticles with sizes (under 100 nm) into the conventional fluid (water, oils, ethylene glycol, biological fluids, etc.). is new form of nanofiluid is having higher thermal conductivity and thermo-physical properties than conventional fluids. In recent years, these hybrid nanofluids were used in various heat transfer applications such as heat pipe, solar energy, refrigeration as well as heating, heat exchanger, ventilation, air conditioning system, coolant in machining and manufacturing, biomedical, space, ships, defense, etc. A comprehensive review on hybrid nanofluids in heat transfer applications is given in Sarkar et al. [1]; Sidik et al. [2]; Sundar et al. [3]; and Sajid and Ali [4]. Khashi'ie et al. [5] presented analytical and numerical solutions of MHD flow of Cu − Al 2 O 3 /water hybrid nanofluid towards a shrinking cylinder. e effect of velocity and thermal slips and chemical and thermal radiation on TiO 2 /Al 2 O 3 -water-based hybrid nanoliquid over a stretching sheet in both steady and unsteady was examined by Santhi et al. [6]. Khan  Carbon nanotubes (CNTs) are the cylindrical structures of carbons atoms (graphene). CNTs are classified into three groups depending on the number of graphene layers: singlewalled CNTs (SWCNT) consisting of one graphene layer with a diameter of 0.5-1.5 nm, double-walled carbon nanotube (DWCNT), and multiwalled CNTs (MWCNTs) dwelling of many graphene layers interlinked nanotubes, with diameters of ranges between 10 and 100 nm. Due to the unique properties such as high mechanical strength, rigidity, hardness, adhesion, high dimensional ratio, chemical stability and high thermal and electrical conductivity, they provide many applications in nanotechnology, chemical and biochemical sensors, catalytic, conductive plastics, structural composite materials, etc. Prabhavathi et al. [10] analyzed the slip effects of SWCNTs and MWCNTs based Maxwell nanofluid flow and identified that the temperature of both nanofluids intensifies as the values of Maxwell parameter rises. Sreedevi and Sudarsana Reddy [11] deliberated the impact of radiation on MWCNT-kerosene-dependent nanofluid over a wedge. Recently, several authors (Tassaddiq et al. [12]; Esfe et al. [13]; Al-Hanaya et al. [14]; Upreti et al. [15,16]) studied heat and mass transfer analysis of CNTbased hybrid nanofluid over different geometries.
Activation energy is a term introduced in 1889 by Svante Arrhenius that is defined the minimum energy attained through the atoms or molecules required to start a chemical reaction. Activation energy along with binary chemical reaction existing in mass transfer has numerous applications in chemical and geothermal engineering, oil reservoirs, water and oil emulsions, food processing, etc. Initially, this concept was introduced by Bestman [17]. Some researchers reported the impact of activation energy in binary chemically reactive flow of hybrid nanofluids under numerous features (Ijaz Khan et al. [18]; Ahmad and Nadeem [19]; Zaib et al. [20]; Khan et al. [21]). e research regarding the boundary layer flow with heat and mass transfer, involving hybrid nanofluid, has revealed to be realistically significant in engineering processes. However, a cautious review of the current literature reveals that the flow over a moving wedge embedded in the hybrid nanofluid was not taken into account. Due to broad fascinating in energy sector, the present work investigate the impact of activation energy with binary chemical reaction on mass and heat transport characteristics of magnetohydrodynamic (MHD) flow of a SWCNT − (MWCNT/water) hybrid nanofluid induced by moving wedge. e resultant equations were solved using shooting technique along with RKF 4-5 th order. Results for velocity, temperature, concentration profiles, skin friction coefficient, heat transfer rate, and nanoparticle transfer rate are graphically displayed and debated briefly.

Physical Description.
e steady two-dimensional MHD boundary layer flow of a SWCNT − (MWCNT/water) hybrid nanofluid induced by moving wedge was investigated. It is assumed that the wedge is moving with the velocity is the Hartree pressure gradient in which β � (2m/(1 + m)) is the wedge angle parameter which can be symbolized as Ω * � πβ 1 (see Figure 1). Temperature and concentration hybrid nanofluids at the wall are T w and C w , respectively, while T ⟶ T fs and C ⟶ C fs are ambient temperature and concentration.

Flow Analysis.
e modeled equations based on the above assumptions are stated as follows [6]: with In (4), k 2 r (T/T fs ) n 0 e (− E a /κT fs ) exemplify the modifies Arrhenius equation in which k r is the rate of chemical reaction rate, n 0 is fitted rate constant, and E a is the modified Arrhenius function.

Transformation.
In order to transform the modeled equations, the following transformations are established [22]: with the components of velocity (u, v) and stream function (ψ) as

ermophysical Properties of SWCNT − (MWCNT/ water)-Based Hybrid Nanofluid.
e dynamic viscosity μ hnf , the effective dynamic density ρ hnf , the specific heat or heat capacitance(ρC p ) hnf , and the thermal conductivity k hnf of the hybrid nanofluid are specified as where . φ 1 and φ 2 are used for the solid volume fraction of MWCNT and SWCNT respectively, ρ f , (ρC p ) f and k f are the respective densities, specific heat, and thermal conductivity of the conventional fluid. e thermophysical properties of the present flow modeled are listed in Table 1.

Computational Scheme
A shooting technique together with RKF 4-5 th order integration scheme is adopted to establish the computational results of nonlinear differential equations (9)- (11) with the boundary restrictions represented in equation (12). Following the basic methodology of shooting technique, we reduce this dimensionless boundary value flow system into first-order system by using the pursuing procedure: with
e ranges of constraints in this research are considered as Figures 2-7, given the impact of φ 1 and φ 2 on f ′ (ζ), θ(ζ) and φ(ζ). e intensification of φ 1 and φ 2 reduces the thickness of the boundary layer flow, which arises in an increase of fluid velocity. We boost the quantity of both CNT s in H 2 O, the heat absorbing capacity of the fluid intensifies. As a result, the temperature profile is enhanced. Additionally, the higher values of φ 1 and φ 2 decay the mass transfer rate. Figures 8 and 9 demonstrate the effects of m (Hartree pressure gradient parameter) on f ′ (ζ) and θ(ζ). e augmented values of maugmented the      International Journal of Chemical Engineering surface drag force and f ′ (ζ) increases. A reverse configuration is grasped for growing values of min θ(ζ). e variation of f ′ (ζ) on M (magnetic parameter) is shown in Figures 10 and 11. An increment in magnetic strength strengthens the velocity and weakens the temperature. is is due to the fact that with growing values of M, the Lorentz forces enhances, which raises the resistive force to the hybrid nanofluid motion.
e response of f ′ (ζ) and θ(ζ) to the variation of c (moving wedge parameter) are illustrated in Figures 12 and 13. Rising of c increases the velocity distribution and diminishes the temperature distribution. Furthermore, the thickness of the hydrodynamic boundary layer depreciation and thermal boundary layer are upgraded. Figure  14 demonstrates the effect of R(Radiation parameter) on θ(ζ). It explains that, due to the increment of R, depreciate k * (the mean absorption coefficient), consequently increases (zq r /zy) (heat flux radiation) and the radiative heat transfer rate into the hybrid nanofluid that caused an increase in θ(ζ). Figures 15 and 16 Figure 19 reveals that an elevation in Le (Lewis number) diminishes the mass diffusion and φ(ζ); this is because that Le inversely related to the mass diffusion. Figure 20 illustrates the φ(ζ) profiles decline due to the intensification of σ (dimensionless reaction rate) in the entire flow region. Physically, growing values of σ causes an increment in the term σ(1 + δθ) n 0 exp(− E/(1 + δθ)), it helps to calamitous k r (chemical reaction rate) that decreases φ(ζ). Figure 21 shows the abating phenomena of hybrid nanoparticle concentration φ(ζ) due to the fluctuation of δ. e portrayal of E (activation energy) in distribution of φ(ζ) is shown in Figure 22. It is found that φ(ζ) attained a maximum level when E is assigned the maximum value. Physically, due to involvement of E afford some extra energy to system, which enhances the chemical reaction rate and hence φ(ζ) increases with higher values of E.
e current results of the present problem are compared with the available literature and divulged in Table 2.  Tables 3-5 show the computational results of skin friction, heat transfer rate, and nanoparticle transfer rate against certain physical parameters. ese tables shows that S fx Re 0.5