Series Solutions of Three-Dimensional Magnetohydrodynamic Hybrid Nanofluid Flow and Heat Transfer.

Hybrid nanofluids have many real-world applications. Research has shown that mixed nanofluids facilitate heat transfer better than nanofluids with one type of nanoparticle. New applications for this type of material include microfluidics, dynamic sealing, and heat dissipation. In this study, we began by placing copper into H2O to prepare a Cu-H2O nanofluid. Next, Cu-H2O was combined with Al2O3 to create a Cu-Al2O3-H2O hybrid nanofluid. In this article, we present an analytical study of the estimated flows and heat transfer of incompressible three-dimensional magnetohydrodynamic hybrid nanofluids in the boundary layer. The application of similarity transformations converts the interconnected governing partial differential equations of the problem into a set of ordinary differential equations. Utilizing the homotopy analysis method (HAM), a uniformly effective series solution was obtained for the entire spatial region of 0 < η < ∞. The errors in the HAM calculation are smaller than 1 × 10-9 when compared to the results from the references. The volume fractions of the hybrid nanofluid and magnetic fields have significant impacts on the velocity and temperature profiles. The appearance of magnetic fields can alter the properties of hybrid nanofluids, thereby altering the local reduced friction coefficient and Nusselt numbers. As the volume fractions of nanoparticles increase, the effective viscosity of the hybrid nanofluid typically increases, resulting in an increase in the local skin friction coefficient. The increased interaction between the nanoparticles in the hybrid nanofluid leads to a decrease in the Nusselt number distribution.

Shape-Factor Impact on a Mass-Based Hybrid Nanofluid Model for Homann Stagnation-Point Flow in Porous Media.

This paper studies the impact of shape factor on a mass-based hybrid nanofluid model for Homann stagnation-point flow in porous media. The HAM-based Mathematica package BVPh 2.0 is suitable for determining approximate solutions of coupled nonlinear ordinary differential equations with boundary conditions. This analysis involves discussions of the impact of the many physical parameters generated in the proposed model. The results show that skin friction coefficients of Cfx and Cfy increase with the mass of the first and second nanoparticles of the hybrid nanofluids w1 and w2 and with the coefficient of permeability in porous media. For the axisymmetric case of γ = 0, when w1 = w2 = 10 gr, wf = 100 gr and Cfx = Cfy = 2.03443, 2.27994, 2.50681, and 3.10222 for σ = 0, 1, 2, and 5. Compared with w1 = w2 = 10 gr, wf = 100 gr, and σ = 0, it can be found that the wall shear stress values increase by 12.06%, 23.21%, and 52.48%, respectively. As the mass of the first and second nanoparticles of the mass-based hybrid nanofluid model increases, the local Nusselt number Nux increases. Values of Nux obviously decrease and change with an increase in the coefficient of permeability in the range of γ < 0; otherwise, Nux is less affected in the range of γ > 0. According to the calculation results, the platelet-shaped nanoparticles in the mass-based hybrid nanofluid model can achieve maximum heat transfer rates and minimum surface friction.

Spherical Hybrid Nanoparticles for Homann Stagnation-Point Flow in Porous Media via Homotopy Analysis Method.

Non-axisymmetric stagnant-point flows for flat plates in porous media containing spherical Cu-Al2O3-H2O nanoparticles are studied using the homotopy analysis method (HAM). The governing equations are transformed into three coupled non-linear ordinary differential equations through similarity transformations. A large degree of freedom is provided by HAM when selecting auxiliary linear operators. By transforming nonlinear coupled ordinary differential equations with variable coefficients into linear ordinary differential equations with constant coefficients, nonlinear coupled ordinary differential equations can be solved. Over the entire domain, these equations can be solved approximately analytically. The analysis involves a discussion of the impact of many physical parameters generated in the proposed model. The results have shown that skin friction coefficients of Cfx and Cfy increase with volume fraction of hybrid nanofluid and the coefficient of permeability increasing. For the axisymmetric case of γ = 0, when volume fraction, φ, φ1, φ2 = 0, 5%, 10%, 20%, Cfx = Cfy = 1.33634, 1.51918, 1.73905, 2.33449, it can be found that the wall shear stress values increase by 13.68%, 30.14%, and 74.69%, respectively. In response to an increase in hybrid nanofluid volume fractions, local Nusselt numbers Nux increase. Nux decrease and change clearly with the coefficient of permeability increasing in the range of γ < 0; the values of Nux are less affected in the range of γ > 0.

Nanoparticle Sphericity Investigation of Cu-Al2O3-H2O Hybrid Nanofluid Flows between Inclined Channels Filled with a Porous Medium.

With the porous medium-filling inclined channels, we investigate the nanoparticle sphericity of Cu-Al2O3-H2O hybrid nanofluid flows. We consider the constant flow rate through the channels as well as the uniform heat flux on wall channels. We provide analytical solutions for both the velocity and temperature fields. Several parameters are considered in the analytical solutions, including the mixed convection variable, the Peclet number, the channel tilt angle, and nanoparticle sphericity and volume fractions. The significant findings of this study are that the effective thermal conductivity increases when increasing the temperature in the same nanoparticle volume fractions. Nanoparticles with a smaller average sphericity size have a greater specific surface area and contain a greater concentration of small particles, which enhances the internal heat transfer of nanofluids. The other noteworthy observation of this study is that when the nanoparticle volume fraction increases from 0.1 to 0.2, although the heat transfer enhancement rate has slowed down, it has also increased by about 25%. The hybrid nanofluids have suitable stability, and the enhanced heat transfer effect is better with the increase in nanoparticle compositions.

Fully Developed Opposing Mixed Convection Flow in the Inclined Channel Filled with a Hybrid Nanofluid.

This paper studies the convective heat transfer of a hybrid nanofluid in the inclined channel, whose walls are both heated by the uniform heat flux. The governing ordinary differential equations are made nondimensional and solved analytically, in which explicit distributions of velocity, temperature and pressure are obtained. The effects of flow reversal, wall skin friction and Nusselt number with the hybrid nanofluid depend on the nanoparticle volume fractions and pressure parameters. The obtained results indicate that the nanoparticle volume fractions play a key role in delaying the occurrence of the flow reversal. The hybrid nanofluids hold more delayed range than conventional nanofluids, which is about 2.5 times that of nanofluids. The calculations have been compared with the base fluid, nanofluid and two kinds of hybrid models (type II and type III). The hybrid model of type III is useful and simplified in that it omits the nonlinear terms due to the interaction of different nanoparticle volumetric fractions, with the relative error less than 3%. More results are discussed in the results section below.