A Radiative Chemical Process for the Methylene Blue Degradation by Natural Convective Nanofluid Flow over an Upright Cone

An upstraight cone with nonisothermal surface velocity, temperature, and concentration was investigated using a numerical solution approach to simulate MHD, MB dye, and various nanofluid flows. Numerical evaluation of the flow field equation was carried out using an excellent finite difference method after it has been converted into a dimensionless form. Different heat transfer occurrences were observed depending on temperature, velocity, and concentration when using several types of nanofluids (TiO, Ag, Cu, and Al2O3Z3). The amount of MB dye that was degraded by the synthesized nanofluids under the influence of sunlight irradiation was 81.40 percent as a catalyst (carbon nanodots). The parametric analysis of various features of flow fields has been shown using graphs. It was observed that heat is generated from the cone during the sun light irradiation reaction, heat is transferred to MB dye containing nanofluids, and heat interacts with nanofluids and is involved in the chemical reaction with the assistance of electrons. As MB dye degrades in the absence of catalysts (carbon nanodots), it is only 52 percent effective. MB dye is degraded at 81.40 percent, then becomes stable, and takes 120 minutes to degrade in nanofluids containing MB dye with catalysts (carbon nanodots).


Introduction
Te textile, medicine, dyeing, printing, pharmaceutical, paint, paper, and food industries could all beneft from MB dye. Te dye used in textiles is the most common and is considered to be one of the most popular clothing dyes. Te adhesive properties of MB allow it to be securely attached to cotton fbers and to fabrics used in textile production. Furthermore, it has the potential to be employed in dyesensitized solar cells, sensors, microbial fuel cells, capacitors, and other devices. Sambath et al. [1] derived numerical solutions based on Crank-Nicholson methods for the transient radiative MHD heat and mass transfer fow past an upstraight cone when a chemical reaction is occurring. Te numerical analysis done by Hanif et al. [2] included a magnetic feld and radiative heat fux to account for variable viscosities in water-based hybrid nanofuid fows in a cone with an inverted permeable. Te fow of twodimensional water-based nanofuid containing a nonspherical CdTe nanoparticle solution has been investigated by Hanif et al. [3]. Te chemical reaction of nanofuids in diferent geometries was studied by Tameem Basha et al. [4] based on electrohydromagnetic as well as nonuniform heat absorbs/supplies. Tameem Basha et al. [5] used two different confgurations of chemically reacting nanofuids to study how the Lorentz force afects fuid transport. Radiative MHD evaluation of a third-grade viscoelastic non-Newtonian fuid external to an isothermal vertical cone at a low temperature was carried out by Gafer et al. [6]. Sulochana et al. [7] investigated thermal as well as mass transference across a cone with radiation as well as chemical processes through magnetohydrodynamic streams. Reddy et al. [8] explored heat as well as species transmission properties using an upright cone fow in a porous nanofuid. Te work by Sreedevi et al. [9] includes both heat and mass transfer studies of nanoparticles that are constituted of single and multiwall carbon nanotubes near the surface of porous media showing convectional boundary conditions caused by chemical reactions as well as by suction or injection. Hydromagnetic nanofuid fow accompanied by nonuniform heat sources/sinks is described by Basha et al. [10] using two diferent types of confgurations. Using a vertical cone as a testbed, Sambath et al. [11] investigated the laminar free convection of inviscid viscosity electrically conducting fuid. Te impact of thermic radiation/chemical processes on thermal and species transport in a fow of nanofuids upon a plumb cone was investigated by Reddy et al. [12]. Te plain convective periphery layer heat and mass transport properties of nanofuids around a vertical cone were demonstrated by Sudarsana Reddy and Chamkha [13]. A mathematical model developed by Sandeep and Reddy [14] assessed the heat transfer characteristics of electrically conducting MHD nanofuid fow over a cone and wedge by taking into account nonlinear thermal radiation and heat source/sink efects. Te mixed convection fow of a Newtonian fuid through a revolving vertical cone immersed in porous media was carried out by Mallikarjuna et al. [15] while associated thermal and mass transit were also examined. Te peripheral layer current of such MHD Eyring-Powell nanofuid was proposed by Babu et al. [16] in terms of buoyancy efects and absorbs/supplies through a permeable cone. As a new carbon precursor, Indigofera tinctoria leaf extract was employed by Jothi et al. [17] for the synthesis of nitrogen-functionalized carbon nanodots by a low-cost hydrothermal method. A simple hydrothermal synthetic approach for producing luminous carbon dots was described by Vinoth Kumar et al. [18] utilizing an abiogenous precursor of rice bran without the use of any surface passivating agents. Among many methods to remove organic and inorganic pollutants from industrial efuents, photocatalysis is an extremely well known one. As described by Zhang et al. [19], dyeing has mainly been used in the textiles, paints, and leather industries. Methylene blue (MB) is a colourant that is widely utilised in a variety of sectors. It causes allergic dermatitis, eye burns, mutations, cancer, and skin irritation in animals as well as humans as examined by researchers [20,21]. Since the medicinal, dyestufs, and printing industries have expanded fast, raw sewage is being dumped into rivers and lakes on a daily basis, endangering both humans and marine life. Tus, using contemporary technology to treat natural plant dye-containing industrial efuent has become critical, as discussed by Asuntha et al. [22]. As explained by Carneiro et al. [23], there are a number of ways to remove noxious contaminants emitted by waste efuents. Te adsorbent capacity of microplastics in sewage sludge may difer for diferent metal irons and plastic types based on the study conducted by Li et al. [24]. Hao et al. [25] investigated the on-chip catalytic degradation capability of organic dyes using rod-like zero-valent iron (rZVI) formed with a novel polydisc nanoassembly structure. A simple and eco-friendly method for preparing ZnFe 2 O 4 nanoparticles and reduced graphene oxide (rGO) nanoporous composites was constructed by Baynosa et al. [26] who developed a fast and environmentally sustainable process that uses pure water as the solvent and does not require any further heat processing. Te numerical solution technique was used by Ragulkumar et al. [27,28] to investigate the efects of viscidity dissipative, MHD, between diferent fows of nanofuid within an upright cone with surface temperature and velocity.
A magnetohydrodynamic (MHD) nanofuid fow towards a vertical sinusoidal wavy surface was reported by Zeeshan et al. [29]. A squeezing fow between rotating circular plates using nanofuid bioconvection was developed by Zeeshan et al. [30]. Te time-dependent electrically conductive fow with heat and mass transport that contains gyrotactic microorganisms was theoretically investigated by Majeed et al. [31]. Te buildup of Cu and TiO 2 NPs in the engine oil organizes a nanofuid. Te authors [32][33][34][35][36] investigated hybrid nanofuid MHD mixed convection in Wand M-shaped porous systems using an artifcial neural network, as well as non-Darcian porosity complex wavy enclosing.
Tis research collectively highlights the single component photocatalytic systems as using an immersed heated vertical cone for removing MB from industrial wastewater. Diferent photocatalytic systems were also examined for their efects on the degradation of MB. In this study, guidelines will be provided to develop efcient photocatalytic devices for the removal of MB from wastewater by an upright immersed heated cone. Te point of using a heated cone is that by absorbing excess heat from sunlight radiation and concentrating it into the liquid, it enables rapid degradation of MB dye from wastewater due to continuous heat transfer.

Formulation of the
Problem. An investigation of magnetohydrodynamic MB dye with nanofuid fow across a vertical cone was conducted using a nonuniform radiative. A cone's radius and half-angle are determined by r and ω, respectively. Figure 1 shows the fow confguration diagram with the x-axis equidistant to the cone surface and the y-axis ordinary to it. Under the assumption that cone surface thermal reading and species are always lower than T ∞ and C ∞ , Tw > T ∞ and Cw > C ∞ are calculated. In addition, T ∞ and C ∞ are the numerical values that represent the ambient temperature and concentration at a distance from the surface, respectively. Te third term on the right side of momentum equation (2) consists of a combination of thermal reading and species buoyancy terms, and the fnal term is the MHD term. A second term on the right side of temperature equation (3) relates to thermal radiation. A frst-order chemical reaction is indicated by the end term in difusion equation (4). Te equations for continuity, momentum, energy, and spices, as proposed by researchers [1,4,8], may be represented as follows: Equation of continuity: (1)

Equation of concentration:
Initial and peripheral conditions are where q w (x) � ax n , q * w (x) � bx n . Te expressions for density ρ nf , heat capacitance (ρc p ) nf , and thermal expansion coefcient (ρβ) nf for nanofuids are provided by Te following nondimensional quantities are discussed: As a result of the Rosseland approximation [11], the radiative fux qr is given by the following expression: If the term T ′ -T ′ ∞ inside the fow is sufciently small, the linear version of equation (11) can be derived by ascending T ′4 by utilizing the Taylor series expansion around T ′ ∞ while removing upper-order terms.
Te Scientifc World Journal Te governing equations [27] are given as follows in nondimensional form.
Equation of continuity: Equation of momentum: Equation of energy: Equation of concentration: where Initial and boundary conditions [28] in nondimensional form are T � 0 for all X and Y,

Engineering Curiosity.
Mathematically, the nondimensional coefcient of local skin friction (τ X ), the local Nusselt number (Nu X ), and the local Sherwood number Sh X [1] are defned as

Method of Numeric Solution
Crank-Nicolson form FDEs are used with initial and boundary conditions (18) to solve the unstable, nonlinear PDEs (13)- (16). A dimensionless equation was converted into a fnite diference equation by using the appropriate fnite diference operator with grid discretization. Te fnite diference equations for velocity, temperature, and concentration are produced by utilizing specifcally chosen constant values. To convert fnite diference equations into algebraic equations, we need to obtain them. Tese algebraic equations are presented as a tridiagonal system, and their solutions are found using the Tomas technique. Te size of each step in both directions ∆X and ∆Y is 0.05, with a time step of t � 0.01, and X max � 1 and Y max � 20 demonstrate the boundary conditions associated with y ⟶ ∞. First, the spatial mesh sizes are reduced by 50% in one direction and then by 50% in both directions to execute the calculations. Comparing and contrasting the results is done. It is crucial for one to understand that in every case, the results only difer at the ffth decimal place. As a result, the decision of mesh size appears to be appropriate. Te U k i,j and V k i,j coefcients that appear in the fnite-diference equations are treated as constants at each time step. Te grid points i, j, and k are all situated along the X, Y, and time axes, respectively. Te values of U, V, and T are known at any grid point when t � 0 from the initial conditions with grid discretization, which is given by Te Scientifc World Journal

Results and Discussion
In this work, four distinct kinds of nanoparticles, Cu, Ag, Al 2 O 3 , and TiO 2 , are tested as shown in Table 1, employing water as the base nanofuid. As shown in Figures 2-7, transmission electron microscopy of nanofuids, MB-dye degradation, as well as spatial velocity and temperature inside the boundary layer are afected by the magnetic parameter (M), radiation parameter (Rd), chemical reaction (λ), and nanoparticles type. Figure 2 shows the spherical nature of the diferent nanofuids, and it is confrmed by HR-TEM analysis. In addition, all the nanoparticles are below 20 nm. Figure 3 shows the catalytic degradation of MB dyes by the formed nanofuids to determine their photocatalytic activity. Te UV spectrum confrms the presence of an absorption peak at 664 nm for MB dye. Te degradation of MB dye was achieved by photocatalytic intensities induced by diferent levels of sunlight irradiation without a catalyst (carbon nanodots) and the use of a vertical cone. Furthermore, the MB dye degrades in around 180 minutes in the absence of a catalyst (carbon nanodots) but only to a 52 percent extent. As shown in Figure 4, MB dye-containing nanofuids with a catalyst (carbon nanodots) were immersed in the prepared heated vertical cone, resulting in a signifcant degradation of the dye intensity. Te heated upright cone is immersed in the liquid containing the nanoparticle-mixed MB dye, and heat transmission to the fuid occurs through the heated cone by irradiating it with sunlight at various time periods. As a result, the heat emitted by the heated cone is absorbed by the nanoparticle, raising the temperature of the liquid and further degrading the MB dye. Finally, the degradation of MB dye happens at 81.40 percent as portrayed in Table 2, after which it becomes stable and takes around 120 minutes at high photocatalytic activity. A comparison of various water-based nanofuid velocities is presented in Figure 5(a). It has been confrmed that a reduction in velocity occurred by using diferent nanofuids. In contrast to Al 2 O 3 -water, the velocity of the Ag-water nanofuid was higher. Additionally, it can be observed that the magnitude of the buoyancy force is overrun considerably by the mainstream velocity. Similarly, as shown in Figures 6(a) and 7(a), utilizing diferent nanofuids resulted in a reduction of temperature and concentration. As compared to Cu-water, Al 2 O 3 -water nanofuids exhibited a higher temperature and concentration. Tis implies that because copper has a high thermal conductivity, heat can move through it fast and the aluminum-water interaction boosts the reaction rate and amount of hydrogen generated. Te reaction is slowed down by a larger λ, reducing the probability of a successful collision between the reactants.
In Table 3, the coefcient of skin friction and local Nusselt number values for the Prandtl number are compared. Rising (Pr) values signify a decline in the local friction coefcient with growing local Nusselt numbers.
As shown in Figures 5(b), 6(b), and 7(b), M and Rd have a signifcant efect on the fow, velocity, temperature, and concentration profles for nine diferent values. M � 0 for lack of magnetic feld occurs for no applied magnetic feld. All velocities accelerated as M increased ( Figure 5(b)). In a boundary layer region, it has been demonstrated that the magnetic force allows for a decreasing boundary layer as the velocity terms remain positive in the momentum equation. Te Lorentz force, which is associated with the boundary layer of a magnetic feld, gets thinner with an increase in M and Rd. As the radiation and magnetic lines move past the vertical cone, the free stream velocity is regarded as determining how the lines move. As a result of the magnetic feld, the fuid that had been decelerated by viscous force is accelerated, which also counteracts the efects of viscous force. Tus, as M and Rd increase, the fuid's velocity decreases as well. Similarly, as demonstrated in Figures 6(b) and 7(b), increasing M and Rd causes a rise in temperature and concentration. Furthermore, for permeable cones, the thermal and species boundary layer thickness rises as M and Rd increase, while temperature and concentration remained the same. Te magnetic force is perpendicular to the momentum force, resulting in a uniform circular motion, which causes momentum to decline and the MHD efect to rise. In the case of the increasing wall temperature rate, the MHD and thermal radiation efects can be incorporated. As a result, a voltage is induced if a conductor is moved relative to a magnetic feld, resulting in a current fowing between the terminals, which emits high-frequency electromagnetic radiation in comparison to low-frequency radiation. Chemical reactions that result in an increase due to the average kinetic energy of molecules increase the thickness of the thermal boundary layer. Figures 5(c), 6(c), and 7(c) demonstrate that when comparing the three factors, velocity, temperature, and concentration all start rising when the value of lambda (λ) begins to fall because more molecules or ions interact to form new compounds and the rate of reaction increases. A decrease in species boundary peak thickness is evident as M and Rd values increase. Te reason behind this is that the involvement of a feld of magnetism in a liquid that conducts electricity provides a force known as the Lorentz force, which opposes the fow of direction as well as causes   Te Scientifc World Journal depreciation in concentration profles. Hence, chemical reactions have a tendency to lower mass transfer rates at the surface cone. Tis happens because more molecules or ions interact when the concentration of all reactants increases, resulting in a faster reaction rate.

. Conclusion
In this work, we used numerical simulations to examine the process of radiative chemical reaction for the degradation of methylene blue using free convective nanofuid fow past an upright cone. Te illustrations indicate that there are fuctuations in velocity, temperature, and concentration based on the absorbance of the nanoparticles, which occurs most commonly during heat and mass transfer. As a result, Al 2 O 3 in Figures 6(a) and 7(a), whereas Ag in Figure 5(a), has a signifcantly larger temperature, concentration, and velocity. Te given Figures (5(b), 6(b), 7(b), 5(c), 6(c), and 7(c)) show that the magnetic feld, radiation, and chemical reaction dominate the liquids and their values rise. Te nanoparticles present may produce overheat, thus increasing their velocity, temperature, as well as concentration, and their efect can be a precursor to the decay of the MB dye. Te efectiveness of nanomaterials as catalysts from an environmental perspective analyzed for the degradation of MB by using a catalyst and heated upright cone for water degradation was attained within 120 min. Overall reports suggest that nanofuids containing MB dye can be converted to 81.40% water degradation and used for environmental remediation applications. In addition, our future research direction is towards free convection nanofuid fow past a vertical wavy cone mediator for methylene blue degradation with MHD radiative chemical reaction and mass transfer.    Gr L : Termal Grash of number (− ) g: Acceleration due to gravity (m·s − 1 ) k:

Data Availability
Te data used to support the fndings of this study are included within the article.

Conflicts of Interest
Te authors declare that they have no conficts of interest.