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The consequences of viscous, ohmic, thermal radiation, and chemical reaction on an incompressible, steady, magnetized nanofluid moving through a stretched surface are investigated for choosing two distinct Nanoliquids (Cuo/water and Silver/water). Through the similarity transformations, the controlling dimensional equations of momentum, energy, and concentration were simplified to nondimensional forms. The solution to the resulting problem is obtained by Bvp4c. The velocity, temperature and concentration are significantly shown for various emerging factors. On both kinds of nanofluids, thermal is grown consistently with an increasing Eckart number. It does, however, lessen as the radiation term values increase. Moreover, if the Schmidt number ranges on the concentration fluid flow indicate that the H(η) profile is going to fall. The tendency for H(η) to boost as the Soret number raises is becoming increasingly noticeable. Ag/water has a higher heat flow rate than Cuo/water when the amounts of Eckart and Radiation numbers are changed. Tables and plots displayed an engineering physical parameter such as coefficient of skin friction, rate of heat transmission and mass transfer.
magneticfield, eckart number, thermal radiation, schmidt number, soret number
Nanofluids covers a comprehensive variety of technology improvements, such as industry cooling systems, nanofluid cooler, geothermal power extraction, nuclear reactors, electronic circuit cooling, combustion, and so on [1]. Nanofluid is a dispersion of Nanoparticles in standard fluids(kerosine, ethylene glycol, water). It is dramatically improve their performance at industrial processes and scientific circles. Metals, oxides, and carbon nanotubes are commonly used to produce NP’s. The word Nanofluid was introduced by Choi [2] in the year 1995. The research of smooth flow of thermal convection over a stretching/shrinking sheet is a significant concern due to its growing engineering settings and relevance in a wide range of technical operation. Many engineering fields deals with boundary layer flow along a stretching surface. Aleem et al. [3] illustrated the effects of heat generating, chemical reacting, and radiation of five nano particles with a normal fluid water flow across a vertical plate. The laplace transformation is used to resolve this fluid problem. Anjali Devi and Prakash [4] used Runge kutta integration technique to resolve the laminar stream through a stretched space with thickness and power law velocity in the occurence of megnetic field. Kandasamy and Devi [5] studied the impact of heat and mass transmission on the occurrence of chemical changes along with the humid object. Furthermore, numerous researchers have used computational and analytical tools to examine the impact of radiation, and thermal expansion over a stretching sheet. Because of their essential physical attributes. Hazarika et al. [6] expressed the Magneto hydrodynamic movement of heat production, chemically reacting nanomaterials/H_{2}O over an elongating penetrable medium and finding the solution of non linear ODE problem by RKShooting techniques. Afridi and Qasim [7] presented the entropy production of CuH_{2}O and AgH_{2}O two nanofluids moved along a slendring stretching space. Esmawan et al. [8] explored the CuoH_{2}O nanofluid can be utilized as a cooling medium due to its high thermal conductivity. Yirga and Tesfay [9] studied the behavior of viscous and chemical reaction on heatflux of magnetic nanoliquid stream over a porose space. Ghasemia and Hatamib [10] explored the sun ray effects on twodimensional stagnation point flow of magnetic nanofluid along a stretching surfce. Ganga et al. [11], Khidir and Sibanda [12] and Hamad and Ferdows [13] studied the consequences of thermophoresis, thermal absorption/generation, brownian motion of nanofluid as a fuction of surface.
The function of an oblique magnetic field on Casson nanofluid over a stretched sheet contained in a wet pore spaces with the condition of radiation and a uneven heat sink/source is analyzed by Panigrahi et al. [14]. Thiagarajan and Dinesh [15] examined the chemically reacting heat flux and hydromagnetic nanofluid stream through a exponentially stretching surface with viscous, radiation and ohmic effects. Babu et al. [16] investigated a pssive heat exchanger and radiating Mhd non newtonian nanoliquid due to extending surface. Haq et al. [17] analyzed the effects of aligned magnetic field of CNTs in two distinict standard fluids along a moved slip plane. Satya Narayana et al. [18] studied the numerical result of non linear radiating on the three dimensional casson nanofluid of a double stress surface. Sithole et al. [19] addressed the Mhd, viscous, non linear radiation and genertation of entropy in second grade nanofluid moves through a stretching surface. Khan et al. [20] incorporated the impacts of radiation, Mhd, multiple slip on viscoelastic nanofluid’s unsteady stream over a penetrable medium. Ridha and AlAbboodi [21] inspected the two phase liquidsolid hydordynamics of inclined fluidized beds. Piancastelli [22] revealed the impact of outside warm air recycling to provide continuous, high efficiency defrosting of airtoair heat pumps.
The idea of this paper were srcuntized by Shankar and Gorfie [23] to implenting the comparative analysis are done between two naoliquids such as copper oxide/water and silver/water with the impacts of magnetic,electrical,thermal radiation,chemical reaction. The physical quantaties Skin friction, Nusselt and sherwood numbers are have been explored through Graphs and Tabels(II  V). The thermophysical attributes of copper oxide, water and silver are given in Table 1 is refered from [7, 24].
Table 1. Thermophysical characteristics
Fluid and Nanoparticles 
Water 
Cuo 
Ag 
Density ρ (kg/m^{3}) 
997.1 
6500 
10500 
Thermal condunctivity K(w/mk) 
0.613 
18 
429 
Thermal capacity C_{p} 
4179 
540 
235 
Assumed that in a stretching surface, the steady boundary layer flow of electrical and magnetic nanofluid moves on it. Suppose a system of cartesian coordinate under which the surface relates to the x and y axis and the liquid occupies the designated space y≥0. Taken u=U_{w}(x) characterizes surface velocity in the region of x. The axis y is subjected to a homogeneous vertical magnetic field of strength B_{0}(x). The generated magnetic field, external electric field and electric field related to polarized changes are supposed to be insignificant compared to the used magnetic field (Figure 1). The flow is created by the constant extending of the surface, which is achieved by the operation of two equivalent and opposing forces on the axisx to hold the starting point is stationary. Let $T_w$ and $C_w$ are surface temperature and concentration respectively. The liquid has a systematic ambient temperature, concentration as $T_{\infty}, \ C_{\infty}$ where $T_w>T_{\infty}, C_w>C_{\infty}$. The following are the equations for continuity, momentum, energy and nanomaterials fraction [23, 25, 26].
Figure 1. Physical depiction of flow model
$u \frac{\partial u}{\partial x}+v \frac{\partial v}{\partial y}=0$ (1)
$u \frac{\partial u}{\partial x}+v \frac{\partial u}{\partial y}=\frac{\mu_{n f}}{\rho_{n f}} \frac{\partial^2 u}{\partial y^2}\frac{\sigma B_0^2(x) u}{\rho_{n f}}$ (2)
$\begin{aligned} u \frac{\partial T}{\partial x}+v \frac{\partial T}{\partial y} & =\alpha_{n f} \frac{\partial^2 T}{\partial y^2}+\frac{\mu_{n f}}{\left(\rho C_p\right)_{n f}}\left(\frac{\partial u}{\partial y}\right)^2 \\ & \frac{1}{\left(\rho C_p\right)_{n f}} \frac{\partial q_r}{\partial y}+\frac{\sigma B^2(x) u^2}{\left(\rho C_p\right)_{n f}}\end{aligned}$ (3)
$u \frac{\partial C}{\partial x}+v \frac{\partial C}{\partial y}=D\left(\frac{\partial^2 C}{\partial y^2}\right)+D_1\left(\frac{\partial^2 T}{\partial y^2}\right)K_0\left(CC_{\infty}\right)$ (4)
$v=0, \quad u=b_1 x, \quad T=T_W, C=C_W a t \ y=0$ (5)
$u \rightarrow 0, T \rightarrow T_{\infty,\quad} C \rightarrow C_{\infty}$ at $y \rightarrow \infty$ (6)
where, $\left(\rho C_p\right)_{n f}, \ \mu_{n f}, \rho_{n f}, \ \alpha_{n f}$ are represented as heat capacitance, dynamic viscosity, effective density and thermal diffusivity of nanoliquid are given below:
$\mu_{n f}=\frac{\mu_f}{(1\varphi)^{5 / 2}}$
$\rho_{n f}=(1\varphi) \rho_f+\varphi \rho_f$
$\alpha_{n f}=\frac{k_{n f}}{\left(\rho C_p\right)_{n f}}$
$\left(\rho C_p\right)_{n f}=\varphi\left(\rho C_p\right)_s+(1\varphi)\left(\rho C_p\right)_f$ (7)
MaxwellGranett model approximate the thermal conductivity of nanofluids confined to spherical nano particle.
$\frac{k_{n f}}{k f}=\frac{k_f2 \varphi\left(k_fk_s\right)+2 k_f}{k_s+\varphi\left(k_fk_s\right)+2 k_f}$
Let us introduce a similarity transformations:
$\left.\begin{array}{c}u=b_1 x, v=\left(b_1 v_f\right)^{0.5} \\ T=G(\eta)\left(T_wT_{\infty}\right)+T_{\infty} \\ C=H(\eta)\left(C_wC_{\infty}\right)+C_{\infty} \\ \eta=y\left(b_1 / v_f\right)^{0.5} \\ \psi=\left(b_1 v_f\right)^{0.5} x F(\eta)\end{array}\right\}$ (8)
Incorporating the above mentioned transformation into the governing Eqns. (1) to (4) reduces to:
$\mathrm{F}^{\prime \prime \prime}+\mathrm{S}_1 F F^{\prime \prime}\mathrm{F}^{\prime}\left(\mathrm{S}_1 \mathrm{~F}^{\prime}+\mathrm{S}_1 \mathrm{~S}_2^{1} \mathrm{M}\right)=0$ (9)
$\left(\frac{\mathrm{k}_{\mathrm{nf}}}{\mathrm{k}_{\mathrm{f}}}+\mathrm{NR}\right) \mathrm{G}^{\prime}+\mathrm{PrS}_3\left(\mathrm{FG}^{\prime}2 \mathrm{~F}^{\prime} \mathrm{G}\right)+\operatorname{EcPr}\left(\mathrm{S}_3 \mathrm{~S}_4^{1} \mathrm{~F}^{\prime \prime 2}+\mathrm{MF}^2\right)=0$ (10)
$\mathrm{H}^{\prime \prime}\mathrm{Sc}\left(2 \mathrm{HF}^{\prime}\mathrm{F} H^{\prime}+\mathrm{G} \gamma\right)=0$ (11)
and the corresponding boundary conditions are:
$\mathrm{F}(0)=0, F^{\prime}(0)=1, \mathrm{G}(0)=1, \mathrm{H}(0)=1$ at $\eta=0$ (12)
$F^{\prime}(\eta) \rightarrow 0, \mathrm{G}(\eta) \rightarrow 0, \quad \mathrm{H}(\eta) \rightarrow 0$ at $\eta \rightarrow \infty$ (13)
where, the dimesional less parameters are:
$\operatorname{Pr}=\frac{v}{\alpha}, M=\frac{\sigma B_0{ }^2}{b_1 \rho_f}, E c=\frac{U_w{ }^2}{\left(C_p\right)_f\left(T_wT_{\infty}\right)}$
$N R=\frac{16 \sigma^* T_{\infty}^2}{3 k_1 k_f}, \gamma=K_0 / b_1, S c=\frac{v}{D}, S r=\frac{D_1\left(T_wT_{\infty}\right)}{D\left(C_wC_{\infty}\right)}$
$S_1=(1\varphi)^{5 / 2}\left[1\varphi+\varphi\left(\frac{\rho_s}{\rho_f}\right)\right]$
$S_2=\left[1\varphi+\varphi\left(\frac{\rho_s}{\rho_f}\right)\right], S_3=1\varphi+\varphi \frac{\left(\rho C_p\right)_s}{\left(\rho C_p\right)_f}$
$S_4=(1\varphi)^{5 / 2}\left[1\varphi+\varphi \frac{\left(\rho C_p\right)_s}{\left(\rho C_p\right)_f}\right]$
Wall friction $C_f$, Local Nusselt number $N u_x$, Sherwood number $S h_x:$
In the heat transfer issue, the physical quantaties are very important
$C_f(1\varphi)^{2.5} \sqrt{R e_x}=2 F^{\prime \prime}(0)$ (14)
$\left(N u_x / \sqrt{R e_x}\right)\left(k_f / k_{n f}\right)=\left(\frac{k_{n f}}{k_f}+N R\right) G^{\prime}(0)$ (15)
$\left(\begin{array}{l}S h_x / \sqrt{R e_x}\end{array}\right)=H^{\prime}(0)$ (16)
where, the local Reynolds number is $R e_x=x u_w / v_f$.
Figure 2. Behavior of φ=0.1,0.2,0.3,0.4 on F'(η)
Figure 3. Behavior of φ=0.1,0.2,0.3,0.4 on G(η)
Figure 4. Behavior of φ=0.1,0.2,0.3,0.4 on H(η)
Figure 5. Behavior of M on F'(η)
Figure 6. Behavior of M on G(η)
Figure 7. Behavior of Ec on G(η)
Figure 8. Behavior of Nr = 0.3,0.5,0.7,0.9 on G(η)
Figure 9. Behavior of γ on H(η)
Figure 10. Behavior of Sc on H(η)
Figure 11. Behavior of Sr on H(η)
Figure 12. Behavior of F''(0)
Figure 13. Behavior of heat flux
Figure 14. Behavior of mass transfer
Employing Bvp4c, the issue of steady incompressible magnetic nanofluid exposed to the interaction of radiation and chemical reaction are resolved.
Table 2. Comparison of the value of wall temperature gradient G’(0) for different values of prandtl numbers Pr
Pr 
0.72 
1 
3 
10 
100 
Kameswaran^{27} 
1.08852 
1.33333 
2.50973 
4.79687 
15.71163 
Bandari & Eshetu^{23} 
1.08862 
1.333332 
2.509727 
4.797002 
15.719830 
Present study 
1.088072 
1.336515 
2.510414 
4.790748 
15.706363 
Table 3. Skin friction
Silver/water 

φ 
M=1 
M=2 
M=3 
M=4 
0 0.1 0.2 0.3 
1.414237 1.506424 1.495368 1.411504 
1.732051 1.742890 1.675841 1.549874 
2.000000 1.950921 1.838710 1.676909 
2.236067 2.138814 1.988287 1.794985 
Copper oxide/water 

φ 
M=1 
M=2 
M=3 
M=4 
0 0.1 0.2 0.3 
1.414237 1.400385 1.333021 1.224412 
1.732051 1.652090 1.532702 1.381582 
2.000000 1.870247 1.709263 1.522710 
2.236067 2.065492 1.869226 1.651844 
Figures 2, 3 and 4 are exhibits an interaction of volume fraction on momentum, thermal and concentration distributions. In these plots, varying the values of φ accelerates the momentum and heat boundary layers. But we have the opposite result on the concentration boundary layer. The magnetic variable M on energy and velocity distributions are depicted on Figures 5 and 6. It can be seen that as the magnetic interaction parameter M increases, so does the temperature. Electrically conducting nanofluids have the lowest resistance due to the Lorentz force, so the thickness of the thermal layer is increased. It reveals that Ag/water nanofluid is faster than Cuo/water. But the same parameters of M decelerates the velocity profile. Figure 7 shows the Ec (viscous dissipation) influenced on the temperature field. By increasing Ec, greatest force is used to dispel the viscosity. From this we can observe that the temperature trend are rising as the Eckart number rises. Therefore the silver/water nanofluid increased faster than Cuo/water nanofluid in G(η) trend.
The behaviour of thermal radiation in the temperature field is predicted on Figure 8, it is depicted that the temperature field is diminished as the distinct values of NR number rises. In that sense, copper oxide nanofluid is decreased faster than silver nanofluid. Figure 9 illustrates that the chemical reaction influences H(η) in the stretched sheet. An Increment of the $\gamma$ on Ag/water concentration stream flows are reduced slower than Cuo/water in H(η). The effect of Sc number over concentration demonstrated on Figure 10. The higher value of Sc on concentration fluid flow, shows that decreasing trend for H(η). Here also, Ag/water flows are diminished slower than Cuo/water. Figure 11 illustrates the increasing trend of H(η) when rising value of Sr number. In this profile Cuo/water flows are greater than Ag/water liquid on H(η).
Table 4. Heat transfer
φ 
M 
Ec 
NR 
Cuo/H_{2}O 
Ag/H_{2}O 
0 
3.5 
0.4 
0.5 
0.572471 
0.571118 
0.1 



0.354474 
0.253104 
0.2 



0.094855 
0.111102 
0.3 



0.222061 
0.543737 
0.4 



0.617706 
1.075997 
0 
3.5 
0.5 
1 
0.326598 
0.285563 
0.1 



0.786823 
0.942975 
0.2 



1.323770 
1.702583 
0.3 



1.959464 
2.600567 
0.4 



2.722927 
3.687149 
0 
3.5 
0.6 
1.5 
1.854260 
1.788512 
0.1 



2.582843 
2.830585 
0.2 



3.423554 
4.033851 
0.3 



4.404306 
5.448278 
0.4 



5.560916 
7.142247 
Table 5. Mass transfer
φ 
M 
Ec 
NR 
γ 
Sc 
Sr 
Cuo/H_{2}O 
Ag/H_{2}O 
0 
3.5 
0.4 
0.5 
0.5 
1 
0.1 
1.344603 
1.343643 
0.1 






1.386628 
1.382557 
0.2 






1.437663 
1.434346 
0.3 






1.498642 
1.499700 
0.4 






1.570620 
1.580097 
0 
3.5 
0.4 
0.5 
1 
2 
0.2 
2.339931 
2.336706 
0.1 






2.396334 
2.397088 
0.2 






2.462938 
2.472098 
0.3 






2.540798 
2.562742 
0.4 






2.631175 
2.670813 
0 
3.5 
0.4 
0.5 
1.5 
3 
0.3 
3.485571 
3.228511 
0.1 






3.548078 
3.305495 
0.2 






3.620515 
3.397781 
0.3 






3.704035 
3.506679 
0.4 






3.799989 
3.634224 
Figures 12, 13 and 14 examine the skin friction, heat and mass transfers of velocity, thermal and concentration profiles against volume fraction. The skin friction rate of both nanofluids are decremented against φ = 0,0.1,0.2,0.3,0.4 and M = 1,2,3,4. Here, the Nanofluid Cuo/water have a lower friction rate comparing to Ag/water. The rate of heat is transferred for both nanofluids, when raising the parameters of M = 3.5, Ec = 0.4, 0.5,0.6 and NR = 0.5,1.0,1.5 Ag/water nanofluid have a greater heat transfer values than Cuo/water. In Figure 14, the first set of data demonstrates the monotonic behaviour of two different nanoliquids with respect to the M = 3.5, Ec = 0.4, Nr = 0.5, Sc = 1,2,3, Sr = 0.1,0.2,0.3 and $\gamma$= 0.5,1.0,1.5 parameters when plotted against the volume fraction.The second group of data, which exhibits the separate parameters Sc, Sr, and γ versus the volume fraction, shows that the ratio of Ag/water flows greater than the ratio of Cuo/water. But in the third category values are illutstrated that cuo/water flows faster than Ag/water. Overall, while rasisng respective parameters against the volume percent its shows that increment on mass transfer profile.
We made comparisons with earlier published article by Kameswaran [27] and Shankar and Gorfie [23] in the absence of thermal radiation, magnetic field, Ohmic heating to validate the accuracy of the numerical results. The results are in good agreement, as shown in Table 2. Table 3 shows the solution of skin friction for various volume fraction and magnetic field. Table 4 represents the values of heat flux of different volume fraction, Eckart and radiation parameters in the occurrence of M. Table 5 represents the values of mass transmision of different volume fraction, Soret number, Schmidt number and $\gamma$ in the occurrence of M, Ec, NR.
The issue of boundary layer flow of electrically, magnetized and chemically reacted nanoliquids(Ag/water and Cuo/water) along a stretched surface, with influence of radiation, viscous and ohmic are discussed. The nonlinear ODE solved by Bvp4c(matlab).
The result of the problem is:
(i) Thermal profile is constantly increased with increasing Eckart number on both kind of nanofluids. However, it is decreased with increasing radiation term values.
(ii) The higher values of Sc number on concentration fluid flow, shows that decreasing trend of H(η) profile. The increasing trend of H(η) occurs when raising value of Sr number.
(iii) By rising the levels of Eckart and radiation numbers, Ag/water having a greatest heat flux rate than Cuo/water.
Symbol 
Quantity 
ρ_{s} 
Density of nanoparticle 
ϕ 
Volume fraction 
ρ_{f} 
Density of base fluid 
(ρC_{p})_{s} 
Heat capacity of nanoparicle 
(ρC_{p})_{f} 
Heat capcity of base fluid 
k_{nf} 
Thermal conductivity of nanofluid 
k_{s} 
Thermal conductivity of nanoparticle 
k_{f} 
Thermal conductivity of base fluid 
Pr 
Prandtl number 
M 
Magnetic parameter 
Sc 
Schmidt number 
Ec 
Eckart number 
Sr 
Soret number 
NR 
Radiation parameter 
γ 
Chemical reaction parameter 
σ 
Electrical conductivity 
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