Numerical Study of Natural Convection of Biological Nanofluid Flow Prepared from Tea Leaves under the Effect of Magnetic Field

The heat transfer of a biological nanofluid (N/F) in a rectangular cavity with two hot triangular blades is examined in this work. The properties used for nanoparticles (N/Ps) are derived from a N/P prepared naturally from tea leaves. Silver N/Ps are distributed in a 50–50 water/ethylene glycol solution. The cavity’s bottom wall is extremely hot, while the upper wall is extremely cold. The side walls are insulated, and the enclosure is surrounded by a horizontal magnetic field (M/F). The equations are solved using the control volume technique and the SIMPLE algorithm. Finally, the Nu is determined by changing the dimensions of the blade, the Rayleigh number (Ra), and the Hartmann number (Ha). Finally, a correlation is expressed for the Nu in the range of parameter changes. The results demonstrate that an increment in the Ra from 103 to 105 enhances the Nu more than 2.5 times in the absence of an M/F. An enhancement in the strength of the M/F, especially at the Ra of 105, leads to a dramatic reduction in the Nu. An increase in the height of the triangular blade intensifies the amount of Nu in weak and strong convection. The enlargement of the base of the triangular blade first enhances and then decreases as the Nu. The addition of 5% silver biological N/Ps to the fluid enhances the Nu by 13.7% in the absence of an M/F for high Ras.


Introduction
Free convection and forced convection are two different types of convective heat transfer (H/T) which are used in many fields such as cooling [1][2][3][4][5][6][7], solar systems [8][9][10][11], and nanofluid-based systems [12][13][14]. In forced convection, an external machine such as a pump, fan, or compressor is employed to flow the fluid, but in free convection, one does not need an external force to move the fluid, and the fluid moves due to the density gradient. Since no external force is required to flow the fluid, this type of H/T is widely used in low-energy devices [15][16][17][18][19]. Some industrial appliances that do not use electricity employ this type of H/T to transfer heat, for cooling or heating. Cooking ovens, industrial ovens, cooling in industrial refrigerators, etc., are some applications of H/T in the industry and in the daily life of human beings. Many researchers have used closed cavities to investigate this type of H/T [20][21][22]. Therefore, different researchers have studied cavities with different shapes [23][24][25]. The cavities with more complex shapes such as triangles, etc., have attracted less attention. Pordanjani and Aghakhani [26] showed that an enhancement in the Rayleigh number (Ra) enhances the free convection and increases the rate of H/T in a complex closed cavity. In another study, Das et al. [1] evaluated the impact of the Rayleigh number on the flow field. In addition, Sheremet et al. [4] determined the amount of Nusselt number in an enclosure by changing the Rayleigh number. The influence of changes in fluid flow and the amount of stream function with the Rayleigh number has been studied by Aghakhani et al. [3]. The results of the article [4] demonstrated that an increment in the Rayleigh number improves free convective heat transfer.
The study of nanofluids (N/Fs) is one of the areas that has gotten a lot of scientific interest in the recent two decades [27][28][29][30]. Water is mainly used for cooling various devices in small and large industries. Water is available and cheap. Its THCO, on the other hand, is poor, limiting its H/T. Enhancing the THCO of H/T by dispersing various nanoparticles (N/Ps) in it is one approach to boost it. [31][32][33]. Ethylene glycol (EG) is also used as antifreeze in many industries but also has low THCO. Hence, different N/Ps are added to this fluid to intensify its THCO. So far, many researchers have used N/Fs in their research [34][35][36][37][38][39]. There are many articles on nanofluids. The effect of nanofluid on Nusselt number was investigated by Rahimi et al. [2]. In addition, in another article by Revnic et al. [6], the influence of the presence of nanofluid on heat transfer was investigated. Rahimi et al. [1] studied the average Nusselt number by changing the volume percentage of nanoparticles and revealed that adding nanoparticles to the base fluid can increase the amount of heat transfer. Among these, the type of N/Ps is also important. In recent years, the use of biological N/Ps has received more attention from researchers [40,41]. These N/Ps are eco-friendly and can be prepared from environmental materials. Therefore, some researchers have used this type of N/Fs in their research [42,43]. In one of these studies conducted by Bahiraie and Heshmatian [44], the effect of using eco-friendly silver/water N/F on the efficiency of a heat exchanger was investigated. The results of this study showed that the use of this biological N/F is effective in the improvement of H/T.
One of the most important factors influencing H/T is the magnetic field (M/F) [45][46][47]. The M/F is generally present in various industries due to the presence of electricity. Therefore, it is necessary to study the effect of this external source on H/T. In some research, it enhances [48] or reduces [49] the H/T based on the geometry of the cavity. Therefore, various researchers have studied the effect of the M/F in different geometries of cavities [50][51][52]. The effect of the magnetic field on fluid flow was numerically studied by Afrand [15]. In another study, the impact of the magnetic field on the heat transfer rate was investigated by Selimefendigil and Öztop [20]. It was found that the heat transfer rate is reduced by applying the magnetic field. Selimefendigil and Öztop [21] also studied the influence of the Hartmann number on heat transfer and the Nusselt number. In one of these studies, Aminossadati [49] studied the H/T of copper/water N/F in a triangular cavity under an M/F using the SIMPLE algorithm numerically. In the middle of the cavity, there was a cavity-shaped heat source that heats the fluid inside the cavity. The results demonstrated that an increment in the Ra, a reduction in the Hartmann number (Ha), and a decrease in the distance between the heat source and the cold wall improve the thermal efficiency.
Today, the use of N/Fs is much higher than before. Therefore, the environmental consideration of using N/Ps is one of the challenges in this field that can be considered. The use of biological N/Ps can prevent damage to the environment. On the other hand, due to the importance of natural convection in industry, this paper investigates the effect of using biological N/F of silver in 50-50 EG/water on natural convection under the effect of an M/F in a cavity with two triangular blades. In addition, to find the best case for maximum H/T, the effect of Ra, Ha, blade height, and width on Nu is studied. The innovation of the present work is to find the highest rate of H/T by changing the geometry of the blade in a cavity with a new geometry under the impact of the M/F in the presence of the biological N/F. Finally, a correlation is given for the Nu.

Problem Description
As shown in Figure 1, the cavity is a rectangle with a length-to-width ratio of 3. On the cavity bottom wall, two triangular blades with a W-height and an H-base are placed. There is an Ag/water-EG (50-50) N/F inside the enclosure. Silver N/Ps are biologically prepared from tea leaves. The preparation process of N/Ps is shown in Figure 2. The upper wall is at and the lower one and the blades are at . The side walls are also insulated. There is also a horizontal M/F next to the enclosure.

Governing Equations and Boundary Conditions
To non-dimensionalize the equations, use the following dimensionless parameters: The two-dimensional equations that govern the fluid flow are as follows. These equations are constructed using a laminar and steady flow and a Newtonian incompressible fluid as assumptions. It is worth noting that the buoyancy force is approximated using the Boussinesq approximation. The effect of viscosity loss and radiation H/T is neglected [53,54]: The dimensionless boundary conditions are shown in Figure 3.
The definition of a local Nu on top wall for a N/F is: The following equation is used to estimate the average Nu on a cold wall:

N/F Properties Equations
The relationships used to obtain N/F properties other than THCO are given as follows [55,56]: = ( ) (15) = 1 + 2.5 (16) Biological silver N/Ps obtained from tea leaves are used to prepare the N/F. The THCO of the biological N/F is [57]: = 0.981 + 0.00114 × + 30.661 × (17) The rest of the properties of EG and silver N/Ps are given in Table 1.

Numerical Procedure
To solve the equations, they are non-dimensionalized and then solved using dimensionless boundary conditions. The equations are discretized using the volume control approach first, and then solved in FORTRAN using the SIMPLE algorithm. The convergence criterion for all equations is assumed to be 10 −8 .
It is important to do a good grid analysis in order to answer the equations. A structured square mesh is utilized for this purpose. Various simulations are carried out in order to assess the solution's independence from the grid. For example, the average Nu is presented in Table 2 for different grids when Ra = 105, Ha = 0, and W = H = 0.2. Due to the changes in the Nu, the grid resolution of 150 × 450 is selected for the simulations.

Validation
To confirm the correctness of the simulations, it is important to compare the results to those of other previously reported research. When the findings of this study are compared to those of other studies, valid conclusions are reached. For example, the results of Oztop and Abu-Nada [61], who examined free convection H/T, are compared. Figure 4 shows the average Nu findings for various volume fractions and Ras. The results are in good agreement and there is just a little difference between them, as can be seen in Figure  4.                 Table 3 presents the Nu and its changes for different volume percentages of biological N/Ps when Ra = 10 5 , Ha = 0, and W = H = 0.2. As the silver biological N/Ps are added to the water-EG mixture, the Nu is enhanced from 4.52 to 5.14. In other words, by adding 5% silver N/Ps, the Nu can be enhanced by 13.7%. The addition of biological N/Ps to water and EG mixture enhances the THCO, resulting in an enhancement in the Nu. Eventually, a correlation is presented for the Nu in terms of the blade height and base values, as well as the Rayleigh and Has numbers. In this correlation, the value of the Nu can be obtained by changing each of these parameters. The parameters affecting the Nusselt number, including the Rayleigh number, Hartmann number, the height of obstacles, and the base of triangles were determined after analyzing the results. Then, these parameters were exported to one of the software for estimating the correlations, and points were provided to the user to perform recalculations. After performing 101 runs with FORTRAN software, the data were presented in the form of three-dimensional diagrams and correlations for the Nusselt number. This correlation was the best one with a minimum error than other correlations, which is discussed below:

Conclusions
In this paper, a biological N/Fs flow in a rectangular cavity with two triangular blades was simulated when a M/F was applied in the x-direction. By changing the Ra and Ha, the height, and the base values of the triangular blade, the value of the Nu was calculated. Finally, a correlation was presented for the Nu. The following are the most important findings: 1. An enhancement in the Rayleigh number from 10 3 to 10 5 intensifies the value of the Nusselt number more than 2.5 times in the absence of a magnetic field. Enhancing the Rayleigh number at all heights and bases of the triangular fin enhances the value of the Nusselt number.

Conflicts of Interest:
The authors declare no conflicts of interest.