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Casson fluids containing carbon nanotubes of various lengths and radii on a moving permeable plate reduce friction and improve equipment efficiency. They improve plate flow dynamics to improve heat transfer, particularly in electronic cooling and heat exchangers. The core objective of this study is to investigate the heat transmission mechanism and identify the prerequisites for achieving high cooling speeds within a two-dimensional, stable, axisymmetric boundary layer. This study considers a sodium alginate-based nanofluid containing single/multi-wall carbon nanotubes (SWCNTs/MWCNTs) and Casson nanofluid flow on a permeable moving plate with varying length, radius, and nonlinear thermal radiation effects. The plate has the capacity to move either parallel to or perpendicular to the free stream. The governing partial differential equations for the boundary layer, which are interconnected, are transformed into standard differential equations. These equations are then numerically solved using the Runge–Kutta fourth-order scheme incorporated in the shooting method. This research analyses and graphically displays the effects of factors including mass suction, nanoparticle volume fraction, Casson parameter, thermal radiation, and temperature ratio. Additionally, a comparison is made between the present result and the previous finding, which presented in a tabular format. The coefficient of skin friction decreases in correlation with an increase in Casson fluid parameters and Prandtl number. Heat transfer rate decreases with a variation in viscosity parameter, while it is increasing with an increase in Prandtl number. In addition, this study demonstrates that heat transfer rate for MWCNT is significantly higher than that of SWCNT nanoparticles. Thermal radiation and temperature ratio reduce the heat transfer rate, whereas nanoparticle volume fraction and Casson parameter enhance it over a shrinking surface.

Due to their widespread use in engineering, hybrid nanofluids have been the primary focus of mathematical and physical research. Only the improvement of hybrid nanofluids’ variable heat conductivity and viscosity has been considered so far. Hybrid nanofluid flow across an inclined cylinder has many potential uses, including heat transfer and cooling in electrical devices, energy storage, refrigerants, and the automobile industry. Examining the effects of buoyant force, variable viscosity, variable thermal conductivity, mass suction, convective thermal conditions, and a magnetic field on the stagnation point flow of a Al2O3–Cu/H2O hybrid nanofluid in an inclined cylinder is our objective in this work. In order to find solutions to boundary-condition flow-describing partial differential equations, we turn them into ordinary differential equations using similarity transformations. We achieve this by employing a numerical strategy known as the fourth-order Runge–Kutta technique, which incorporates shooting techniques. A graphical representation of the findings emphasizes the influence of many physical parameters on flow dynamics. In addition, we address the influence of drag force and rate of heat transfer on various elements, such as the Biot parameter, magnetic variable, viscosity variable, and thermal conductivity variable. The mixed convection and magnetic parameters cause the velocity profile to rise while the temperature profile falls. The research’s results elucidate the cause behind the rise in thermal contour of hybrid nanofluids, which is seen when there is an increment in thermal conductivity, radiation parameter, and Biot number. The heat transfer rate exhibits a significant increase of 36.87% in the aiding flow scenario when a 2.0 mass suction is applied in conjunction with a 0.01 hybrid nanofluid, as compared to the conventional fluid. In the scenario of opposing flow, the heat transfer rate exhibits a significant increase of 36.96% when compared to that of ordinary fluid. Heat transfer increases 43.00% when Rd increases from 0.1 to 0.5 for both assisting and opposing flow. [ABSTRACT FROM AUTHOR]

This paper focuses on developing and analyzing a new AR-iterative scheme designed for estimating fixed points of generalized non-expansive mappings of the Suzuki kind. The scheme’s stability and convergence properties are rigorously proven, highlighting its superior convergence rate for non-expansive mappings when compared to existing schemes in the literature. Additionally, an application of the AR-iterative scheme to differential equations is presented. These findings underscore the effectiveness and versatility of the proposed scheme in numerical analysis and computational mathematics. [ABSTRACT FROM AUTHOR]

The aim of this paper is to introduce a novel approach for estimating the fixed points of multi-valued non-expansive mappings using the AR-iteration scheme in the context of uniformly convex Banach spaces. We establish strong and weak convergence results, providing rigorous analytical proofs and illustrating the results with a detailed example. Our approach showcases the potential of the AR-iteration scheme in solving real-world problems, particularly in addressing two-point boundary value problems. We demonstrate the applicability and effectiveness of the AR-iteration scheme in numerical analysis and computational mathematics. Our results contribute significantly to the advancement of numerical methods in solving boundary value problems, offering new insights and directions for future research in this area. Furthermore, we provide a detailed explanation of Green’s function approach and its implications for various scientific and engineering applications, paving the way for future research in this area. [ABSTRACT FROM AUTHOR]

In this study, the Yamada-Ota model is used to look for an analysis of irreversibility when there is nonsymmetric magnetohydrodynamic flow inside a nanoliquid made of carbon nanotubes (CNTs) across an unsteady three-dimensional stretching surface. In this investigation, both single- and multi-walled carbon nanotubes (SWCNTs and MWCNTs, respectively) are considered, as they are both suspended in a water solution. Anisotropic slip conditions, nonlinear thermal radiation, and an induced magnetic field are all accounted for in the model. The PDEs are changed into a group of nonlinear Equations using the non-similarity transformations and then solved by using the BVP4c program in MATLAB. The effects of important parameters like magnetic field strength, unsteadiness, nanoparticle volume fraction, slip conditions and nonlinear thermal radiation are also looked at. Increasing the nanoparticle volume percentage results in a greater velocity field for SWCNTs than for MWCNTs. The profile of entropy production exhibits an upward trend in relation to the parameters Φ, M, Br, Rd and θw, however, it has a downward trend in relation to the parameter α. The Bejan number profile shows an upward trend in the concentration of α, while showing a decline in the cases of Φ, M, Br, Rd and θw. [ABSTRACT FROM AUTHOR]

Industrial applications in domains such as warm rolling, crystal development, thermal extrusion and optical fiber illustration are seeing a significant increase. These applications specifically focus on addressing the challenge of a cylinder in motion inside a fluid environment. Elevated temperatures may affect the viscosity and thermal conductivity of fluids. Understanding the relationship between temperature and the properties of fluids is crucial. In light of these presumptions, the primary goal of this study is to examine, under transverse magnetic field, shape factor, velocity, thermal slip conditions and viscous dissipation, how temperature-dependent fluid properties could enhance the heat transfer efficiency and performance evolution of ternary hybrid nanofluid. In order to study flow fluctuations, the impact of nanoparticle addition and improvements in heat transfer, a variable Prandtl number is also included. The use of similarity variables converts the controlling flow model from partial differential equations (PDEs) to ordinary differential equations (ODEs). Mathematica’s shooting strategy solves ODEs using the fourth-order Runge–Kutta (RK-IV) method. Numerical calculations were done after setting parameters to acquire the desired results. Analytical data are provided in tables and graphs for convenient usage. The results showed that the velocity profile increases as the values of ϕ3, Pr, M, Re and S grow, and decreases when the values of θr decrease. Re, Pr and S lower the temperature profile, whereas ϕ3, θr and Ec raise it. The skin friction profile steepens as ϕ3, S, Re and M increase relative to the stretched cylinder, and flattens as θr and ω decrease. The Nusselt number profile rises as θr, Pr, S and Re decrease with ϕ3, Ec and δ. When the Prandtl number goes from 3.0 to 6.2 in a ternary hybrid nanofluid with brick-shaped nanoparticles, the Nusselt number goes up by around 55.7%. [ABSTRACT FROM AUTHOR]

This work aims to examine the entropy production, heat transport, and dynamics of the unsteady thin film magnetohydrodynamic (MHD) flow of a nanofluid composed of alumina (Al2O3) and water. The fluid flow is seen to pass over an inclined sheet, taking into account the effects of buoyancy force, viscous dissipation, and joule heating. The system of partial differential equations (PDEs) is optimized under the boundary layer assumptions. Appropriate transformations are used to convert the governing partial differential equations (PDEs) and boundary conditions into dimensionless forms. Using MATLAB’s bvp4c code and a local non-similarity technique with up to second-degree truncation, we can obtain the findings of the enhanced model. The effect of multi-shape Al2O3 nanoparticles on flow, heat, and entropy-generating features is also investigated after the calculated results have been successfully aligned with published data. Mixed convection, nanoparticle volume percent, inclination angle, magnetic field intensity, mass suction, Eckert number, and Biot number are only a few of the governing parameters whose effects are graphically shown for selected values. As a result, the local Nusselt number and skin friction coefficient may be calculated. The skin friction and Nusselt number profiles exhibit a decreasing trend as the values of nanoparticle volume fraction (ϕ) magnetic (M) and unsteadiness (A) increase toward mixed convection (δ). On the other hand, Nusselt number profile increases with increasing values of mass suction parameter (S) The profiles of entropy generation and Bejan number show an upsurge as the values of the magnetic parameter (M) and Brinkman number (Br) increase. Conversely, the entropy generation reduces with an increase in the temperature difference parameter (Ω) and Bejan number increases. [ABSTRACT FROM AUTHOR]

The industrial sector has shown a growing interest in hybrid nanofluids affected by magnetohydrodynamics (MHD) owing to their wide range of applications, including photovoltaic water heaters and scraped surface heat exchangers. The main purpose of this study is to look at how entropy is created in a hybrid nanofluid of |${\rm{A{{l}_2}{{O}_3}{-}Cu}}$| mixed with |${\rm{{{H}_2}O}}$| at a non-axisymmetric stagnation point flow with Joule heating and viscous dissipation. By using appropriate non-similarity transformations, the partial differential equations (PDEs) governing the boundary layer region of this issue are transformed into a set of non-linear PDEs. The BVP4c MATLAB program, which uses local non-similarity and additional truncation, may fix the problem. The velocity profiles in both directions grow when the values of |${{\phi }_2},\ M,\lambda $|⁠ , and A parameters increase. The temperature profile rises as the values of A and |$Ec$| grow and lowers as |${{\phi }_2}$| and M increase. The obtained numerical findings demonstrate significant impacts on both the heat transfer rate and fluid flow parameters of the hybrid nanofluid. When the concentration of nanoparticles and the magnetic parameter are heightened, there is an enhancement seen in the skin friction coefficient and decline in heat transfer rate. In addition, the entropy production profile shows an increasing tendency as a function of the parameters |${{\phi }_2},\ M,$| and |$Br,$| while demonstrating a decreasing tendency of function of the parameter |$\alpha $|⁠. The Bejan number profile has a positive correlation with the parameter |$\alpha $| but shows a negative correlation with the variables |${{\phi }_2},\ M,$| and |$Br$|⁠. [ABSTRACT FROM AUTHOR]

AbstractThe unsteady nanofluid flow that rotates in both directions over a stretched surface could assist many technological and industrial processes. When the effects of slip conditions, aggregation, and changing viscosity are considered, the flow of nanofluid over a stretched surface can be used in surface coatings and deposition, energy harvesting devices, drug delivery systems, and cooling systems with better heat transfer. The major purpose of this study is to evaluate the influence that variable viscosity, slip conditions, and aggregation have on the flow behavior of nanofluids in three dimensions. This research looks specifically at non-axisymmetric stagnation point flows on stretched sheet. The governing equations are going to be modeled based on the assumptions that have been stated. Through a technique known as a similarity transformation, a complex system of nonlinear partial differential equations can be reduced to ordinary differential equations. This makes the system significantly easier to work with. The algorithm will be employed afterward to numerically solve the simplified set of equations. The results are obtained using the Runge–Kutta (RK-IV) and the shooting method. Graphical displays provide an easy way to examine how different parameters interact with one another and their impacts. With an increase in nanoparticle concentration, heat transfer rate shows an increasing trend. Due to the decrease in the instability parameter, rate of heat transfer decreases. Velocity profiles increases in both directions with increasing strain rate. A comparison of influences of nanoparticle aggregation with and without radiation is shown in the tables, highlighting the differences in Nusselt numbers. The results of the present study closely correspond to those reported in a prior publication for the same scenario, offering robust additional support for the findings. [ABSTRACT FROM AUTHOR]