The purpose of this study is to investigate the simultaneous effects of normal wall transpiration, stretching strength parameter, velocity slip and nanoparticles on the flow of a ternary hybrid nanofluid through an elastic surface. The goal is to understand the behavior of the flow field, temperature distribution, skin friction and temperature gradient under these conditions, and to explore the existence and nature of solutions under varying parameter values.
The analysis involves expressing the flow field, power-law temperature field, skin friction and temperature gradient in closed-form formulas. The study examines both stretching and shrinking surfaces, distinguishing between unique and dual solutions. The methodology includes deriving exact solutions for exponential and algebraic temperature and temperature rate formulas analytically by deriving the system of governing equations into ordinary differential equations.
The study reveals that for a stretching sheet, the solution is unique, whereas dual solutions are observed for a shrinking surface. Special solutions are provided for various parametric values, showing the behavior of the exponential and algebraic temperature and temperature rate, with a focus on identifying turning points that demarcate the existence and non-existence of single or multiple solutions. The solutions are represented through graphs and tables to facilitate a comprehensive qualitative analysis. The research identifies turning points that determine the presence or absence of single or multiple solutions, uncovering multiple solutions for different parameter sets. These findings are displayed graphically and in tabular form, highlighting the complex interplay between the parameters and the resulting flow behavior.
This analysis contributes to the field by providing new insights into the multiple solution phenomena in ternary hybrid nanofluid flows, particularly under the combined effects of normal wall transpiration, stretching strength, velocity slip and nanoparticle presence. The identification of turning points and the exact solutions for various temperature profiles are of significant value, offering a deeper understanding of the factors influencing the flow and thermal characteristics in such systems. The study’s findings have potential applications in optimizing fluid flow in engineering systems where such conditions are prevalent.
This paper aims to explore dual solutions for the flow of a hybrid nanofluid over a permeable melting stretching/shrinking sheet with nanoparticle shape factor, second-order velocity slip conditions and viscous dissipation. The hybrid nanofluid is formulated by dispersing alumina (Al2O3) and copper (Cu) nanoparticles into water (H2O).
The governing partial differential equations (PDEs) are first reduced to a system of ordinary differential equations (ODEs) using a mathematical method of similarity transformation technique. These ODEs are then numerically solved through MATLAB’s bvp4c solver.
Key parameters such as slip parameter, melting parameter, suction parameter, shrinking parameter and Eckert number are examined. The results reveal the existence of two distinct solutions (upper and lower branches) for the transformed ODEs when considering the shrinking parameter. Increasing value of Cu-volume fraction and the second-order velocity slip enhances boundary layer thicknesses, whereas the heat transfer rate diminishes with rising melting and suction parameters. These numerical results are illustrated through various figures and tables. Additionally, a stability analysis is performed and confirms the upper branch is stable and practical, while the lower branch is unstable.
The analysis of hybrid nanofluid flow over a shrinking surface has practical significance with applications in processes such as solar thermal management systems, automotive cooling systems, sedimentation, microelectronic cooling or centrifugal separation of particles. Both steady and unsteady hybrid nanofluid flows are relevant in these contexts.
While the study of hybrid nanofluid flow is well-documented, research focusing on the shrinking flow case with specific parameters in our study is still relatively scarce. This paper contributes to obtaining dual solutions specifically for the shrinking case, which has been less frequently addressed.
This study aims to investigate the heat and mass transfer characteristics of a temperature-sensitive ternary nanofluid in a porous medium with magnetic field and the Soret–Dufour effect through a tapered asymmetric channel. The ternary nanofluid consists of Boron Nitride Nanotubes (BNNT), silver (Ag) and copper (Cu) nanoparticles, with a focus on understanding the thermal behaviour and performance across mono, hybrid and tri-hybrid nanofluids. This paper also examines the thermal behaviour of MHD oscillatory nanofluid flow and carries out an uncertainty analysis of the model using the Taguchi method.
The governing equations for this system are transformed into coupled linear partial differential equations using non-similarity transformations and solved numerically with the Crank–Nicolson scheme. The impact of temperature sensitivity at three distinct temperatures (5°C, 20°C and 60°C) is incorporated to analyse variations in viscosity and Prandtl number. The study also examines the combined effects of Soret–Dufour numbers and thermal radiation on heat and mass transfer within the nanofluid.
The results demonstrate that the inclusion of BNNT, Ag and Cu nanoparticles significantly enhances heat and mass transfer rate, with copper nanoparticles showing superior performance in terms of skin friction and heat transfer rates. The Soret and Dufour effects play critical roles in modulating heat and mass diffusion within tri-hybrid nanofluids. The study reveals that temperature sensitivity alters heat and mass transfer characteristics depending on the temperature range, with pronounced variations at elevated temperatures. The influence of thermal radiation and the Peclet number is found to significantly impact temperature distribution and overall heat transfer performance within the asymmetric channel.
To the best of the authors’ knowledge, this study is the first to analyse the heat and mass diffusion in a ternary nanofluid composed of BNNT, Ag and Cu nanoparticles, considering porous media, oscillatory flow and thermal radiation within a tapered asymmetric channel. The research extends to a novel examination of temperature sensitivity in mono, hybrid and tri-hybrid nanofluids at varying temperature gradients. Furthermore, a comparative analysis of skin friction and heat transfer rates between copper, alumina and ferro composites is presented for optimising the nanofluid performance.
This paper aims to study numerically the non-Newtonian solution of carboxymethyl cellulose in water along with copper oxide nanoparticles, which flow turbulently through twisted smooth and finned tubes.
The twisted-tape inserts of rectangular and triangular sections are investigated under constant wall heat flux and the nanoparticle concentration varies between 0% and 1.5%. Computational fluid dynamics simulation is first validated by experimental information from two test cases, showing that the numerical results are in good agreement with previous studies. Here, the impact of nanoparticle concentration, tube twist and fins shape on the heat transfer and pressure loss of the system is measured. It is accomplished using longitudinal rectangular and triangular fins in a wide range of prominent parameters.
The results show that first, both the Nusselt number and friction factor increase with the rise in the concentration of nanoparticles and twist of the tube. Second, the trend is repeated by adding fins, but it is more intense in the triangular cases. The tube twist increases the Nusselt number up to 9%, 20% and 46% corresponding to smooth tube, rectangular and triangular fins, respectively. The most twisted tube with triangular fins and the highest value of concentration acquires the largest performance evaluation criterion at 1.3, 30% more efficient than the plain tube with 0% nanoparticle concentration.
This study explores an innovative approach to enhancing heat transfer in a non-Newtonian nanofluid flowing through an oval tube. The use of twisted-tape inserts with rectangular and triangular sections in this specific configuration represents a novel method to improve fluid flow characteristics and heat transfer efficiency. This study stands out for its originality in combining non-Newtonian fluid dynamics, nanofluid properties and geometric considerations to optimize heat transfer performance. The results of this work can be dramatically considered in advanced heat exchange applications.
This research focuses on the controlling irreversibilities in a radiative, chemically reactive electromagnetohydrodynamics (EMHD) flow of a nanofluid toward a stagnation point. Key considerations include the presence of Ohmic dissipation, linear thermal radiation, second-order chemical reaction with the multiple slips. With these factors, this study aims to provide insights for practical applications where thermal management and energy efficiency are paramount.
Lie group transformation is used to revert the leading partial differential equations into nonlinear ODE form. Hence, the solutions are attained analytically through differential transformation method-Padé and numerically using the Runge–Kutta–Fehlberg method with shooting procedure, to ensure the precise and reliable determination of the solution. This dual approach highlights the robustness and versatility of the methods.
The system’s entropy generation is enhanced by incrementing the magnetic field parameter (M), while the electric field (E) and velocity slip parameters (ξ) control its growth. Mass transportation irreversibility and the Bejan number (Be) are significantly increased by the chemical reaction rate (Cr). In addition, there is a boost in the rate of heat transportation by 3.66% while 0.05⩽ξ⩽0.2; meanwhile for 0.2⩽ξ⩽1.1, the rate of mass transportation gets enhanced by 12.87%.
This paper presents a novel approach to analyzing the entropy optimization in a radiative, chemically reactive EMHD nanofluid flow near a stagnation point. Moreover, this research represents a significant advancement in the application of analytical techniques, complemented by numerical approaches to study boundary layer equations.
This paper aims to present a numerical investigation for two-dimensional fractional Helmholtz equation using the Aboodh integral homotopy perturbation transform scheme (AIHPTS).
The proposed scheme combines the Aboodh integral transform and the homotopy perturbation scheme (HPS). This strategy is based on an updated form of Taylor’s series that yields a convergent series solution. This study analyzes the fractional derivatives in the context of Caputo.
This study illustrates two numerical examples and calculates their approximate results using AIHPTS. The derived findings are also presented in tabular form and graphical representations.
In addition, He’s polynomials are calculated using HPS, so the minimal computational outcome is a defining feature of this method and gives a competitive advantage over other series solution techniques.
Numerical data and graphical illustrations for different fractional order levels confirm the proposed method’s successful performance. The results show that the proposed approach is speedy and straightforward to execute on fractional-ordered models.
Using passive techniques like twisted tapes and corrugated surface is an efficient method of heat transfer improvement, since the referred manners break the boundary layer and improve the heat exchange. This paper aims to present an improved dual-flow parabolic trough collector (PTC). For this purpose, the effect of an absorber roof, a type of turbulator and a grooved absorber tube in the presence of nanofluid is investigated separately and simultaneously.
The FLUENT was used for solution of governing equation using control volume scheme. The control volume scheme has been used for solving the governing equations using the finite volume method. The standard k–e turbulence model has been chosen.
Fluid flow and heat transfer features, as friction factor, performance evaluation criteria (PEC) and Nusselt number have been calculated and analyzed. It is showed that absorber roof intensifies the heat transfer ratio in PTCs. Also, the combination of inserting the turbulator, outer corrugated and inner grooved absorber tube surface can enhance the PEC of PTCs considerably.
Results of the current study show that the PTC with two heat transfer fluids, outer and inner surface corrugated absorber tube, inserting the twisted tape and absorber roof have the maximum Nusselt number ratio equal to 5, and PEC higher than 2.5 between all proposed arrangements for investigated Reynolds numbers (from 10,000 to 20,000) and nanoparticles [Boehmite alumina (“λ-AlOOH)”] volume fractions (from 0.005 to 0.03). Maximum Nusselt number and PEC correspond to nanoparticle volume fraction and Reynolds number equal to 0.03 and 20,000, respectively. Besides, it was found that the performance evaluation criteria index values continuously grow by an intensification of nanoparticle volume concentrations.
Double flow-focusing nozzles (DFFNs) form a coaxial flow of primary liquid with micro-crystalline samples, surrounded by secondary liquid and focusing gas. This paper aims to develop an experimentally validated numerical model and assess the performance of micro-jets from a DFFN as a function of various operating parameters for the water–ethanol–helium system, revealing the jet's stability, diameter, length and velocity.
The physical model is formulated in the mixture-continuum formulation, which includes coupled mass, momentum and species transport equations. The model is numerically formulated within the finite volume method–volume of fluid approach and implemented in OpenFOAM to allow for a non-linear variation of the fluid's material properties as a function of the mixture concentration. The numerical results are compared with the experimental data.
A sensitivity study of jets with Reynolds numbers between 12 and 60, Weber numbers between 4 and 120 and capillary numbers between 0.2 and 2.0 was performed. It was observed that jet diameters and lengths get larger with increased primary and secondary fluid flow rates. Increasing gas flow rates produces thinner, shorter and faster jets. Previously considered pre-mixed and linear mixing models substantially differ from the accurate representation of the water–ethanol mixing dynamics in DFFNs. The authors demonstrated that Jouyban–Acree mixing model fits the experimental data much better.
The mixing of primary and secondary liquids in the jet produced by DFFN is numerically modelled for the first time. This study provides novel insights into mixing dynamics in such micro-jets, which can be used to improve the design of DFFNs.
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