This study aims to explore the natural convection, magnetohydrodynamics and Ternary nanofluids containing Fe3O4, Cu and TiO2 in water-ethylene glycol within a hexagonal cavity containing a square obstacle. The Finite element method is utilized through the COMSOL Multiphysics 6. 1 software. By utilizing visual representations, the influence of key variables on flow patterns, temperature distribution, and local Nusselt number is effectively illustrated. Simulations were carried out with Rayleigh number ranging from 103 to 105, heat source and absorption coefficients ranging from-5 to 15, and Hartmann numbers of 0, 70 and 90. The Prandtl number for ethylene glycol is 29. 86. The findings of this research confirm that the proper incorporation of nanoparticles significantly enhances the heat transfer properties of base fluids.

Thermal conductivity of MWCNT(40%)-CuO(30%)-TiO2(30%) /Water nanofluid in different volume fractions and temperatures is modeled and analyzed by artificial neural network method. The type of artificial neural network is MLP. 48 experimental data series are used, 70%, 15%, and 15% are used for training, validation, and testing, respectively. The optimal neural structure has two hidden layers, in which there are 4 neurons in the first layer and 5 neurons in the second layer, with the transfer functions of logsig and tansig, respectively. Neural network training is done with Levenberg-Marquardt (ML) algorithm. The values of regression coefficient, R, and mean squared error, MSE, for the optimal structure are obtained as 0.9995753 and 2.8734E-06, respectively. The correlation equation is also presented to predict the thermal conductivity of nanofluid. The comparison between the correlation equation and the artificial neural network shows the superiority of the artificial neural network. MOD values for artificial neural network are also in the range of -3% to +7%.

The current paper examines the impact of radiation and Marangoni convective boundary conditions on the flow of Ternary hybrid nanofluids in a porous medium with mass transpiration effect on it. Estimated PDEs are converted to ODEs with consideration of the corresponding similarity transformations. The obtained non-dimensional reduced equations are solved by analytical process. A unique access based on the Laplace transform (LT) is used to find analytical solutions to the resulting equations. With the use of graphs, the exact solution may be investigated in the presence of many physical parameters such as solid volume fraction parameter, mass transpiration, porosity, radiation. The fluid flow contains three types of nanoparticles: spherical Silver (Ag), cylindrical SWCNT, and platelet graphene. Because of the shape composition of Ternary hybrid nanoparticles, variation in concentrations is a primary factor of thermal performance. The shape of nanoparticles in Ternary hybrid nanofluids has a major impact, and its application has the advantage of improving the cooling system's thermo-hydraulic performance.

This innovative study investigates the flow of Ternary hybrid nanofluid containing gyrotactic microorganisms in microchannel. The magnetic field, thermophoresis, and Brownian motion effects are analyzed. The transformation of the PDEs system into ODEs is carried out by using the group transformation method. The innovative findings examine the Newtonian and non-Newtonian models derived from the system of ODEs. Several graphs illustrate how different parameters affect the velocity profile, temperature, concentration, and microorganisms. The power-law index value increases the fluid flow velocity by about 9% at n = 3, 36% at n = 4 relative to the case of n = 2.5 at the center of the boundary layer. Moreover, the Ternary hybrid nanofluid exhibits a greater temperature compared to the nanofluid. The current results are compared to the researchers' findings to confirm the validity of the obtained results. When the Prandtl number is between 6 and 10, the Nusselt number reaches 45.49%.

Ternary nanofluids offer superior thermal properties, enhancing efficiency in thermal systems such as power generation, storage, and manufacturing. This study investigates the heat transfer and flow behavior of TiO2-Al2O3-Cu/water-based Ternary hybrid nanofluid at the stagnation point on a phase change surface, considering surface stretching/shrinking, magnetic field, and thermal radiation effects. Using similarity transformation, the governing equations are simplified and solved via the Keller Box method. The study compares key parameters, including the Nusselt number and skin friction, for Ternary, TiO2/water nanofluid, and Al2O3-TiO2/water hybrid nanofluids. Results show that Ternary nanofluid outperform hybrid and regular nanofluids, with the melting parameter reducing heat transfer by 15% and skin friction by 3%. Findings underscore the importance of phase change in optimizing Ternary nanofluids for heat transfer applications.

In this contribution, a laboratory comparison of the cooling capability of two-hybrid and three-hybrid nanofluids in a photovoltaic/thermal system equipped with a spiral plate-tube collector is devoted. Stable suspensions of water-graphene oxide/titanium oxide, water-graphene oxide/iron oxide and water-titanium oxide/iron oxide as binary hybrid nanofluid and watergraphene oxide/titanium oxide/iron oxide nanofluid as Ternary hybrid nanofluid have been used. Several experiments have been conducted to investigate the effect of nanofluid mass flow rate (20-80 kg/h) on system performance using a solar simulator. It was revealed that among the examined systems, the best thermal, electrical and overall performance always belongs to the photovoltaic/thermal system containing Ternary hybrid nanofluid, while the worst performance always belongs to the system containing water-titanium oxide/iron oxide nanofluid. belongs to. The results showed that the thermal efficiency, electrical efficiency and overall efficiency of the system containing Ternary hybrid nanofluid were in the ranges of 53. 14-80. 14, 13. 01-13. 02 and 89. 78-95. 29, respectively. is a percentage Also, it was found that the thermal, electrical and overall performance of the investigated systems improves with the growth of mass flow rate of nanofluids

Let A be a Banach Ternary algebra over a scalar  eld R or C and X be a Ternary Banach A{module. Let  ;  and  be linear mappings on A, a linear mapping D: (A; [ ]A)! (X; [ ]X) is called a Lie Ternary ( ;  ;  ){derivation, if...