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In this research article, the viscous, steady, and incompressible two-dimensional hybrid nanofluid flow composed of Fe3O4 and Au nanoparticles on an extending sheet has been presented. An inclined magnetic field impact is used for evaluating the impacts of various factors in that case. Furthermore, the influences of porosity, Brownian motion, thermophoresis, thermal and space-dependent heat sources, and thermal radiation factors are also used in this work. The numerical analysis is done by using the bvp4c technique. Validation of the present results confirms that the present analysis is valid. The outcomes show that the higher magnetic factor reduces velocity distribution while increasing the frictional force at the surface due to Lorentz forces which oppose the fluid flow. The friction force at the sheet’s surface is higher when the sheet stretches as compared to the case when the sheet shrinks. Increase in the magnetic factor increases the skin friction of sheet’s surface which consequently increases the rate of thermal transmission at the surface along with thermal distribution. The higher values of thermal radiation and thermal-dependent heat source increase the thermal transportation rate of sheet’s surface. Insights from this investigation can improve electronics cooling systems, vital for devices prone to overheating. Optimizing heat transfer with magnetohydrodynamic water-based hybrid nanofluids containing Fe3O4 and Au nanoparticles ensures efficient heat dissipation, enhancing device performance and longevity.

The boundary-layer flow on a shrinking/contracting sheet has abundant industrial applications, which include continuous glass casting, metal or polymer extrusions, and wire drawing. In this regard, the present analysis focuses the hybrid nanofluid flow on an exponentially extending sheet. The water-based hybrid nanofluid flow contains CoFe2O4 and TiO2 nanoparticles. Heat transfer rate analysis involves the utilization of the Cattaneo–Christov heat flux model. Moreover, the Brownian motion and thermophoresis effects are used in this novel work. The mathematical model is presented in the form of system of partial differential equations, which is then transformed into system of ordinary differential equations (ODEs) using the similarity variables. The system of ODEs is evaluated by homotopy analysis method. The variation in the flow profiles has been investigated using figures and tables. The conclusions demonstrate that the effect of magnetic parameter is 52% better for hybrid nanofluid flow than for the pure water. Conversely, the increasing magnetic parameter diminishes the thermal transfer rates for water, TiO2–H2O, CoFe2O4–H2O, and TiO2–CoFe2O4/H2O. The increasing thermophoresis parameter upsurges the thermal flow rate of nanofluids and hybrid nanofluid, while the increasing Brownian motion parameter lessens the thermal transfer rates of nanofluids and hybrid nanofluid. The increasing effect of thermophoresis parameter is 39% better for hybrid nanofluid than for the base fluid. However, the declining impression of Brownian motion factor is 48% greater for hybrid nanofluid related to pure water.

Hybrid nanofluid problems are used for augmentation of thermal transportation in various industrial applications. Therefore, the present problem is studied for the heat and mass transportation features of hybrid nanofluid caused by extending surface along with porous media. In this investigation, the authors have emphasized to analyze hybrid nanofluid flow containing diamond and copper nanoparticles on an extending surface. Furthermore, the velocity, temperature, and concentration slip constraints are adopted to examine the flow of fluid. Heat source, chemical reactivity, thermal radiation, Brownian motion and effects are taken into consideration. Nonlinear modeled equations are converted into dimensionless through similarity variables. By adopting the homotopy analysis method, the resulting equations are simulated analytically. The impacts of various emerging factors on the flow profiles (i.e., velocities, temperature, concentration, skin frictions, local Nusselt number, and Sherwood number) are shown using Figures and Tables. The major key findings reveal that the hybrid nanofluid temperature is higher but the concentration is lower for a Brownian diffusivity parameter. Moreover, increment role of heat transport is achieved due to the increment in radiation factor, thermophoresis, Brownian motion factors, and Eckert number. It has also been observed that velocity in x-direction converges in the region −0.8≤ℏf≤0.5-0.8\le {\hslash }_{\text{f}}\le 0.5, in y-direction velocity is convergent in the zone −0.6≤ℏg≤0.35-0.6\le {\hslash }_{\text{g}}\le 0.35, while temperature converges in the region −0.6≤ℏθ≤0.4-0.6\le {\hslash }_{\text{θ}}\le 0.4 and concentration converges in the region −0.5≤ℏφ≤0.4-0.5\le {\hslash }_{\text{φ}}\le 0.4.

This research delves into dynamics of magnetohydrodynamic second-grade fluid flow influenced by the presence of gyrotactic microorganisms on a stretching sheet. The study takes into account various factors such as thermal radiation, chemical reactivity, and activation energy, all of which contribute to the complex behavior of fluid flow in this system. The interaction between the magnetic field and the fluid, combined with the biological aspect introduced by gyrotactic microorganisms, adds complexity to the overall analysis. The mathematical model is presented in the form of partial differential equations (PDE)s. Using the similarity variables, the modeled PDEs are transformed into ordinary differential equations. Homotopy analysis method is used for the solution of the modeled equations. After a detailed insight into this investigation, it is established that the velocity distribution declined for growth in magnetic factor and second-grade fluid parameter. The thermal characteristics are augmented for the greater values of radiation, thermophoretic and Brownian motion factors, while these profiles are weakened for upsurge in thermal relaxation time factor and Prandtl number. The concentration characteristics declined with the enhancement in Schmidt number, mass relaxation time, chemical reaction, and Brownian motion factors, while they amplified with enhancement in activation energy and thermophoresis factors. The microorganisms’ profiles are the declining functions of bioconvection Lewis and Peclet numbers. This study included a comparative analysis, which aligns closely with existing research, demonstrating a strong concordance with established findings.

A metallic alloy is a combination of two or more elements, often called a compound or a solution. Steel is largely composed of carbon, a nonmetal, but alloys are often made up of metals. In this article, the authors have explored the electrically conducting water-based viscous nanofluids flow past a rotating disk surface. The nanofluids flow is composed of titanium and aluminum alloys where water is used as a base fluid. Two important cases, namely the stretching case and the shrinking case, were investigated to analyze the flow behaviors due to the different embedding factors. The impacts of viscous Joule heating, thermophoresis, Brownian motion, activation energy, nonlinear thermal radiation, and chemical reaction are investigated here. By employing an appropriate set of variables for shifting the leading equations to dimension-free form. The mathematical model is solved numerically by incorporating the bvp4c MATLAB scheme. Current work is validated with previous studies. The outcomes showed that the radial velocity increases when the disk surface stretches and reduces when the disk surface shrinks. On the other hand, the Azimuthal velocity increases when the disk surface shrinks and reduces when disk surface stretches. Both the radial and Azimuthal velocities are the diminishing functions of the magnetic factor, whereas temperature is the growing function of magnetic factor. In addition, the temperature is more influenced by the magnetic factor in the case of nonlinear radiation. The higher magnetic factor increases skin friction. In addition, the stretching case experiences more surface drag than the shrinking case. It is found that nanofluid flow containing titanium alloy has perceived the greater impacts of the embedded factors compared to the nanofluid flow containing aluminum alloy.

In the present analysis, we have analyzed the three-dimensional flow of an electromagnetohydrodynamic copper–aluminum/water hybrid nanofluid flow on a Riga plate. The heat and mass flux model proposed by Cattaneo-Christov is deliberated here. Thermal radiation, thermophoretic diffusion, Brownian motion, and chemical reaction phenomena are considered in analyzing the flow problem. Thermal convective, mass convective, and velocity slip conditions are adapted in this analysis. Suitable resemblance variables are implemented for the conversion of the model equations to dimension-free form. The homotopy analysis method is adopted to solve the modeled equations. The obtained results show that the velocity profiles are reduced with an increasing estimation of the slip factors. Additionally, the nanoparticles’ concentration and the temperature of the hybrid nanofluid increase with higher values of thermal and solutal Biot numbers. The Nusselt number is increased with an increase in the radiation factor and thermal Biot number.

Due to its widespread applications in areas including heat exchangers, cancer therapy, heat storage devices, biomedicine, and biotechnology, nanofluid has become one of the most important fluids in thermal engineering. One difficulty with these applications of nanofluids is the improvement of heat conductivity via nanoparticles. This aims to illustrate the bioconvectional cross-flow of a nanofluid in the existence of swimming gyrotactic microorganisms over a vertical stretching cylinder. We consider the chemical reaction and thermal radiation in the energy and concentration equations. Through the use of appropriate dimensionless variables, a nonlinear system of partial differential equations has been transformed into ordinary differential equations (ODEs). The BVP4c method is applied to construct the resultant governing ODEs. The significance of physical variables is demonstrated through plots and tabular data. Our finding explains that the temperature intensifies due to larger curvature parameters and Weissenberg variables, while the opposite effect is examined in the velocity profile. With upsurge in thermophoresis parameter, the temperature upsurges accordingly. As the bioconvection Lewis number rises, microbial concentration falls. The results obtained in this investigation could be useful in practical applications like numerous areas of engineering, biotechnology, nanotechnology, and medical sciences etc.

In this study, the (Cu and Al2O3/water) hybrid nanofluid flow is carried out in a porous cavity. The thermophysical structures of solid materials are used from the available literature to improve the thermal performance of the base fluid. The mathematical model as a porous cavity is mainly used in the distillation process and is vital for the storage of thermal energy. The magnetic field is also employed perpendicular to the flow field and the impact of the magnetic parameter examined versus fluid motion. Similarity variables are used to transform governing equations as simplified partial differential equations. The model is solved using the control volume-based finite element method. Boussinesq–Darcy force is employed for the motion of the fluid flow, and the Koo–Kleinstreuer–Li model is used to assess the characteristics of the hybrid nanofluids. The roles of the Hartmann number, Rayleigh number, porosity factor in the porous medium, and drag fin improve traditional fluids’ thermal distribution presentation. Recent results predict that the two different kinds of nanoparticles speed up the heat transfer through the porous cavity. The percentage analysis shows that the hybrid nanofluids (Cu and Al2O3/water) are prominent in improving traditional fluids’ thermal distribution. Finally, the grid sensitivity test is also carried out for hybrid nanoparticles to demonstrate that the results are asymptotically coherent.

The aim of the present study is to simulate double diffusion in a circular cylinder over a rectangular cavity by utilizing incompressible smoothed particle hydrodynamics (ISPH) method. An originality of this study is adopting the ISPH method in simulating double diffusion in a novel domain of a circular cylinder over a rectangular shape occupied by Al2O3{{\rm{Al}}}_{2}{{\rm{O}}}_{3}–H2O{{\rm{H}}}_{2}{\rm{O}} and heterogeneous porous media. The variations of Darcy parameter (Da) between 10−31{0}^{-3} and 10−51{0}^{-5} with two levels of porous media, (0≤η1=η2≤1.5)(0\le {\eta }_{1}={\eta }_{2}\le 1.5), Rayleigh number (103≤Ra≤105)(1{0}^{3}\le {\rm{Ra}}\le 1{0}^{5}) with variable buoyancy ratio parameter (0≤N≤2)(0\le N\le 2), solid volume fraction ϕ\phi between 0 and 0.05, and Lewis number (10≤Le≤40)(10\le {\rm{Le}}\le 40) on the features of heat/mass transport as well as velocity field are discussed. It is found that the homogeneous porous medium reduces the temperature and concentration within a combined cavity. A decrease in Darcy parameter from 10−21{0}^{-2} and 10−51{0}^{-5} suppresses the maximum of a nanofluid velocity by 75% regardless the levels of porous media. An increase in parameters Ra and N enhances the heat and mass transmission, as well as the nanofluid velocity. Adding more concentration of nanoparticles until 5%5 \% reduces the nanofluid velocity. The variations of boundary conditions are acting effectively in changing the temperature and concentration circulations within a combined cavity. Besides, the variations of boundary conditions change the maximum of the velocity field by 86.9%.