#### Abstract

The heat transfer ratio has some important applications in industries and the engineering sector. In this model, the authors used the hybrid nanofluid because the heat transfer ratio of hybrid nanofluid is more as compared to the base fluid; the key objective of this research work is to boost up the heat transfer ratio, for example, to regulate the energy is possible only by adding the heat transmission mechanism in the flow model. The current research paper investigates the steady 3D MHD mixed convection couple stress flow of hybrid nanofluid with hall and ion slip effect. The objective of the current research work is to increase the heat consignment ratio, which is the demand of the manufacturing and engineering sector, this type of flow has some important applications in the industries sector and engineering sector for the purpose of cooling and hotness effect, also hotness and cooling play some important role in daily life. To transform the nonlinear partial differential equation to a nonlinear ordinary differential equation we used the defined similarity transformation. The transform nonlinear ordinary differential equations are solved by an approximate analytical method. The important obtained results are presented in the graphs. The influence of different parameters such as couple stress parameter, mixed convection parameter, nanoparticle volume friction, Hall parameter, magnetic field parameter, thermophores parameter, Eckert number, and prandtl number are taken over graphs. The (skin friction coefficient), (nusselt number), convergence control parameter, and comparison of the present work with the published work are described in the form of tables.

#### 2. Mathematical Formulation

Consider 3D time independent incompressible mixed convection flow of and over an exponentially spreading surface in two lateral directions. The sheet is set at and the flow is restricted at . Due to the applied magnetic field the fluid is electrical conducted, which is applied in z direction and perpendicular to the -plane. Under the supposition of small magnetic Reynolds number the induced magnetic field is ignored. is the velocity of the sheet in the direction and is the velocity of the sheet in the direction where and are constant and the temperature of the sheet is given as as shown is Figure 1.

The universal Ohm’s law along with Hall and ion slip values is as follows:

In equation (1), represents current density vector, the intensity of the electric filed is denoted by , the velocity vector is denoted by , the magnetic field is denoted by , the cyclotron frequency is denoted by , and the electrical collision time is denoted by . All the assumption for mathematical model is describes in Thammanna, et al. [50]. The standard boundary layer supposition the equation governing the continuity, momentum, and energy is as follows:

shows the velocity components, shows density of the hybrid nanofluid, shows kinematic viscosity of the hybrid nanofluid, shows thermal conductivity, represent gravitational acceleration, shows distance along the surface, and shows the distance perpendicular to the surface. The boundary conditions for the defined flow problem are as follows:

The Radiative heat flux is as follow:

In equation (8), shows Stefan–Boltzmann constant and shows the mean absorption coefficient, the similarity transformations are defined as follows:

Using equation (9) in equations (2)–(6), equation (9), satisfied (2), identically transformed equations (3)–(6) to the following nonlinear ordinary differential equations.

Along with boundary conditions,

shows the magnetic field parameter, shows prandtl number, shows the nonlinear thermal radiation parameter, shows Eckert number, shows the thermophores parameter, shows couple stress parameter, shows heat source parameter, shows mixed convection parameter, shows stretching ratio parameter, shows independent variable, shows hall parameter, shows ion slip parameter. The skin friction coefficients and and local Nusselt number are defined as follows:

The nondimensionless of Skin frication and Nusselt number are as follows:where .

#### 3. Method of Solution

Equation (13) is solve analytically by optimal homotopy asymptotic method given below.

represents the linear operator, x represent the independent variable, represents the unknown function, represents the nonlinear operator, and represents the boundary operator with the help of this method, and we have

The initial solution one for velocity equation and one for temperature equation is obtained from the following equation:

Liao [25, 26] presented this method to find the residual error so of equations (10)–(13) can be written as follows:

#### 4. Results

The following tables and figures show be convergence flow problem.

#### 5. Discussion

The objective of this research paper is to enhance the heat transfer ratio by using hybrid nanofluids. The hard elements dissolve in the base liquid and after its constant diffusion the hybrid nanofluid is produced. The converted nonlinear ordinary differential equation, two for velocity equations and one for temperature equation are solved by optimal homotopy analysis method. The total results of the given flow problem are presented through Figures 213, Figure 1 shows geometry of the flow problem, the influence of different parameters on velocity profile both x and y direction are shown in Figures 210, the influence of different parameters on temperature profile are shown in Figures 1113, Table 1 shows the thermo-physical properties of water, and nanoparticles, Tables 2 and 3 show the convergence control parameter for both velocity x and y direction, Table 4 shows convergence control parameter for temperature equation of the defined flow problem, Tables 5 and 6 show the influence of different parameter on Skin friction and Nusselt number, respectively, while Tables 7 and 8 show the compression of the present research work and the already publish research work. Table 2 shows the convergence of the defined velocity equation in x direction, from Table 2 we noted that by increasing the number of iteration residual error is decreasing, which show the convergence of the given flow problem, similarly Table 3 show the convergence of the velocity equation in y direction, and Table 4 shows the convergence of the temperature equation. Table 5 shows the impact of (magnetic field parameter, couple stress parameter, mixed convection parameter, hall parameter, and velocity ratio parameter) on (Skin frication), physically by increasing these parameters the surface frication forces are also increasing, and as a result the (Skin frication) is also increasing as shown in Table 5. From Table 6, we noted that is the increasing function of (heat source parameter, Reynold, thermophoresis parameter, and magnetic field parameter). Physically increasing these parameters, thermal energy is stored in the system due to the frictional force and as a result is increasing. Tables 7 and 8 show the compression of the present work and already publish work. The variation in couple stress parameter on velocity along x direction is shown in Figures 2 and 6 along with y direction for both and , from both Figures 2 and 6, we observed that velocity is the decreasing function of couple stress parameter . This effect occurred due to the production of resistive type forces known as viscous forces, these force increases with the growing size of couple stress parameter , which face the fluid particles motion. Due to this the motion of fluid drop as a result the velocity profile is decreased and converged to zero. This type of flow has some important application in industries and engineering sector, because such type of flow increases the heat transfer ratio. Figures 3 and 7, shows variation of (magnetic field parameter) on velocity distribution on both x and y direction for both and . Figure 3 shows the impact of on x direction, while Figure 7 shows the impact of on velocity profile on y direction, from both Figures 3 and 7 we see that velocity is decreasing function of that is increasing magnitude of magnetic field parameter decreases in velocity filed. This impact occurred by the production of resistive types of forces called Lorentz force. These forces improves with the growing strength of , which decreases the motion of fluid and converge to zero. This type of flow has some important application in industries and engineering sector, because such type of flow increases the heat transfer ratio. Figures 4 and 8 shows the influence of over velocity profile in both x and y direction for both and , Figure 4 show the influence of on x direction, while Figure 8 show the influence of on y direction. From both Figures 4 and 8, we observer that velocity filed is a growing function of , that is, the large value of increase the velocity profile, this effect is due to the buoyancy impact for both base fluid and hybrid nanofluid. Figures 5 and 9 show variation in on velocity profile for both and . Figure 5 shows the effect of on velocity filed in x direction and Figure 9 shows the influence of on velocity filed in y direction. From both Figures 5 and 9, we observe that velocity profile is the growing function of the Hall , that is, the growing value of rise the velocity filed. This impact is due to the inverse relation of and , that is, by decreeing the , due to this Lorentz forces is decreasing so as result velocity of both base fluid and hybrid Nano fluid is increasing as shows in Figures 5 and 9, and converge to zero, this type of flow is used in industries sector for Colling effectdecreeing. Figure 10, shows the variation in nanoparticle volume frication on velocity profile for both and , we see that velocity filed is the decreasing function of , that is, the increasing magnitude of nanoparticle volume frication , decrees the velocity distribution and converges to zero. This effect is produced due to the viscous forces, which increases with the increasing of nanoparticle volume friction and as a result the moment of the fluid particle decreasing, such type of flow Is used in industries sector as a hotness agent, which plays an important role. Figure 11 shows the relation between thermophoresis parameter and temperature profile for both and , we see that temperature filed is the growing function thermophoresis parameter. Therefore, enhancing the thermophoresis parameter heat energy is stored in the system because of the frictional force, which appear in the form of heat and as a result temperature filed is increasing, the uses of this type of flow in industries for the increasing of heat energy so with the help of this flow we can reduced the consumption of energy, which is the required demand of engineering and industries sector. Figure 12 shows the relation between Eckert number and temperature profile for both and . From Figure 12, we see that temperature profile is the growing function of Eckert number. Therefore enhancing the Ecker number heat energy is stored in hybrid nanofluid because of the drug or frictional force which appear in the form of heat and as a result temperature filed is increasing, we can use Ecker number as hotness agent in productions sector to decrees the consumption of energy The uses of this type of flow in industries for the increasing of heat energy so with the help of this flow we can reduced the consumption of energy, which is the required demand of engineering and industries sector. Figure 13 is schemed for on both hybrid nanofluid and base fluid. It is obvious from Figure 13 that temperature is the decreasing function prandtl number, essentially the viscous diffusion is more than thermal diffusion and consequently, the greater quantity of the decreases temperature filed and converges to zero, prandtl number can be used as a Colling agent in manufacturing sector.

#### 6. Conclusion

The heat transfer ratio of hybrid nanofluid is more as compare to the common nanofluid, due to this consequence the researchers take more interest in hybrid nanofluid nowadays. This paper investigates 3D MHD mixed convection couple stress flow of hybrid nanofluid with hall and ion slip effect analytically. The purpose of this study is to increase the heat transfer ratio with the help of hybrid nanofluid. The present work is found to be very good for the future standpoints because the purpose of this work is the enhancement of heat transfer ratio, in future we will face the shortages of energy sources so with the help of this analysis we gain command on energy feeding, this type of flow problem has some important application in manufacturing field, medical field, auto mobile field for example, the getting of energy is not sufficient, but also to regulate the feastings of energy and this is possible only to support the growth heat transmission liquids . The heat transmission is important in science and technology. In future we will face the problem to adjust the consumptions of energy, in our research article we used hybrid nanofluid which helped in the enhancement of heat transfer ratio which have some important applications, for example, the achievement of energy is not enough, but also to adjust the consumptions of energy and this is possible only to approve the development heat transmission liquids. The heat transmission which is the demand of the industry, for application of nanotechnology and engineers have challenged such huge numbers of application, identifying with heat transmission fluids. Still, with the development of nanometer sized particles and its uses in the heat transfer fluids have overall improved thermal conductivity. The development of heat transport via nanofluid have involved a number of scientist due to a lot of uses in various sectors such as distillation and separation of bio-molecules, biosensors, atomic system cooling, manufacture of glass fiber, thermal storing, in solar water boiler, in field of defense, MRI, thermal absorption process, drag delivery, and transportation (thermal management od vehicle and cooling of engine). The key finding of the present research article are as follows:(1)The velocity profile along and direction is increasing by increasing the Hall parameter(2)The velocity profile along and direction is decreasing by increasing magnetic field parameter (3)The velocity profile along direction is increasing by increasing mixed convection parameter (4)The velocity profile along direction is decreasing by increasing the couple stress parameter(5)The temperature profile is decreasing by increasing prandtl number (6)The temperature profile is increasing by increasing the thermophoresis parameter (7)The temperature profile is increasing by increasing Eckert number.

#### Nomenclature unit

 : Cartesian coordinates : Velocity components : Velocities of the stretching sheet () : Thermal radiation parameter : Heat source : Local temperature () : Magnetic field : Nusselt number : prandtl number : Surface temperature () : Constant magnetic field : Ambient temperature () : Brownian motion parameter : Thermophoresis parameter : Skin friction coefficient in x-direction : Skin friction coefficient in y-direction : velocity ratio parameter : Hall parameter : Ion slip parameter : Mixed convection parameter : Dimensionless concentration θ: Dimensionless temperature.

#### Data Availability

The data used to support the findings of this study are available from the corresponding author upon request.

#### Conflicts of Interest

The authors declare no conflicts of interest.