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In contemporary times, there has been a significant focus among researchers on hybrid nanofluids derived from oils, owing to their remarkable and substantial utility in the domains of engineering, mechanics, and industrial applications. The aim of this research is to determine the impact of incorporating tantalum and nickel nanoparticles in mineral oil on thermal characteristics and flow patterns, with the objective of predicting possible improvements. The dependence of the role of both nanoparticles on their shapes is evaluated for column, platelet, lamina, cylinder, and tetrahedron-type shapes. This work analyzes the thermal performance of two different nanofluids individually made of tantalum and nickel nanoparticles while also examining the synergistic effects produced due to the simultaneous suspension of these particles. A profound understanding of the intricate flow dynamics and thermal energy transfer phenomena along a vertical surface holds paramount importance in the pursuit of optimizing heat exchange procedures, formulating effective cooling systems, and designing thermally efficient devices. Furthermore, it contributes to the advancement of climate modeling, the precision of weather forecasting, and the refinement of the operational effectiveness of solar thermal systems. The basic mathematical model is formulated subject to free convection, time-dependent flow and heat conditions, and thermal radiation. This governing system is made non-dimensional to lessen the intricacy and provide the basis for the utilization of fractional operators. In order to assess the effectiveness of fractional modeling techniques, constant proportional Caputo (CPC) and Atangana–Baleanu (ABC) derivatives are operated for the model generalization. Most of the time, solving fractional models via an analytic method are not a feasible technique because it produces extremely complex and implicit mathematical expressions. However, in this study, the Laplace transform is served as a solution procuring technique, and series and integral form exact solutions are extracted for CPC and ABC derivative-based models, respectively. To interpret modifications in thermal and velocity patterns arising from diverse physical phenomena, numerous graphical depictions of exact solutions are communicated. Moreover, the implications of varying a number of critical factors, including the fractional parameter, nanoparticles' shapes and proportions, and radiation term, on shear stress and thermal productivity of the hybrid nanofluid are discussed using the tabulated findings. On comparing shape effects and individual suspensions of considered nanoparticles, it is observed that lamina shape and nickel nanoparticles are relatively more effective regarding the improvement of thermal performance. The model based on the CPC derivative yields lower profiles of temperature and flow functions as compared to the ABC derivative-based model. The results indicate that introducing homogeneous proportions of tantalum and nickel nanoparticles into mineral oil raises its heat-transferring capacity by up to 47.60%. These findings suggest that the examined hybrid nanofluid performs extremely well as a lubricant and a cooling agent. [ABSTRACT FROM AUTHOR]

The advancement of cutting tool components and design is presently promoting innovative developments in numerous different machining-related industries. The characteristics of nanofluid are important for machining activities such as the drilling process, grinding, rotating, milling, and cutting. Various machining procedures require distinct lubricating oils and nanofluids for cutting-edge innovations. The significant contribution of the current mechanism is to explore the fluctuating heat and mass flux of Darcy–Forchheimer chemically reactive nanofluid along a buoyancy-driven porous plate under solar radiation region. Flow through a Darcy medium has a wide range of applications such as the use of oil in various hydrothermal transfer control, radioactive nuclear disposal systems, water improvement, and filtration of water. The dimensional model is transformed into non-dimension for scaling factors. The primitive-based transformation is applied on steady and oscillatory parts for smooth algorithm in FORTRAN language machine by using an implicit finite difference method. The numerical and graphical results of velocity, temperature, and concentration are executed by the Gaussian elimination method. To enhance the frequency and wavelength, the impact of solar radiations is applied on periodic nanoparticles with Darcy–Forchheimer relation. The novelty of this proposal is to explore the wave oscillations, amplitude, and phase angle of thermal and concentration boundary layer of Darcy–Forchheimer nanofluid flow under chemical reaction and solar radiation region. It is noticed that the prominent wavelength and frequency in thermal and concentration boundary layers is generated under porous and solar radiation region. The significance of temperature variation increases as solar radiation, chemical reaction, Brownian motion, and thermophoresis increase. It is found that minimum oscillation in heat transport is observed as Pr decreases but maximum oscillation in heat transfer is sketched as Pr enhances. [ABSTRACT FROM AUTHOR]

The novelty of this study is to develop the oscillation, amplitude and periodical behavior of thermal and concentration boundary layers of transient Darcian nanofluid flow over stationary circular cylinder. For the improvement of cutting forces, lubrication and cooling in machining operations, workpiece cutting temperature and tool durability, the nanofluids have significant role with the effects of thermophoretic nanoparticles and rate of reactions. The aim of current work is to deduce the oscillations, amplitude, and frequency analysis of mass and heat transmission of Darcian nanoparticles motion around porous stretchable cylinder with thermal radiation and heat generation effects. For physical and thermo parameters, the governing mathematical equations are transformed into convenient equations. The smooth and similar programing algorithm is developed in FORTRAN language (Lahey‐95) by using primitive and oscillatory stokes transformations. The primitive steady and oscillating model is solved numerically by using Gaussian elimination and implicit finite difference techniques. The steady outcomes of velocity, temperature, and concentration distributions are plotted for various physical parameters within defined boundary values. The range of parameters such as 0.01≤ξ1≤2.0$0.01 \le {\xi }_1 \le 2.0$, 0.01≤ξ1≤3.0$0.01 \le {\xi }_1 \le 3.0$, 1.0≤Rd≤25.0$1.0 \le {R}_d \le 25.0$, 0.1≤Fr≤2.0$0.1 \le {F}_r \le 2.0$, 0.1≤NT≤1.0$0.1 \le {N}_T \le 1.0$, and 0.1≤γ≤1.5$0.1 \le \gamma \le 1.5$ is used. The steady results are again used to display the oscillatory skin friction, oscillating heating rate, and oscillating mass transport around α=π/3$\alpha = \pi /3$ and α=π$\alpha = \pi $ positions of stretching porous cylinder. The increasing amplitude of velocity and temperature slip distribution grows well as diffusion‐convection parameter and thermal radiation increases at both angles. The slip temperature and slip concentration grows significantly as convective parameter increases. The impact of thermophoresis and rate of reactions enhances the oscillations and amplitudes of mass and heat transmission around stretchable cylinder as porous effect decreases. It is very important in nanofluid lubrications, drilling, rotating, milling, and cutting tools machines. [ABSTRACT FROM AUTHOR]