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This study aims to explore entropy evaluation in the bi-directional flow of Casson hybrid nanofluids within a stagnated domain, a topic of significant importance for optimizing thermal systems. The aim is to investigate the behavior of unsteady, magnetized and laminar flow using a parametric model based on the thermo-physical properties of alumina and copper nanoparticles.

The research uses boundary layer approximations and the Keller-box method to solve the derived ordinary differential equations, ensuring numerical accuracy through convergence and stability analysis. A comparison benchmark has been used to authenticate the accuracy of the numerical outcomes.

Results indicate that increasing the Casson fluid parameter (ranging from 0.1 to 1.0) reduces velocity, the Bejan number decreases with higher bidirectional flow parameter (ranging from 0.1 to 0.9) and the Nusselt number increases with higher nanoparticle concentrations (ranging from 1% to 4%).

This study has limitations, including the assumption of laminar flow and the neglect of possible turbulent effects, which could be significant in practical applications.

The findings offer insights for optimizing thermal management systems, particularly in industries where precise control of heat transfer is crucial. The Keller-box simulation method proves to be effective in accurately predicting the behavior of such complex systems, and the entropy evaluation aids in assessing thermodynamic irreversibilities, which can enhance the efficiency of engineering designs.

These findings provide valuable insights into the thermal management of hybrid nanofluid systems, marking a novel contribution to the field.

This paper aims to describe a numerical simulation method of ice accretion on BO105 helicopter blades for predicting the effects of trailing edge flap deflection on ice accretion.

A numerical simulation method of ice accretion is established based on Myers model. Next, the shape and location of ice accretion of NACA0012 airfoil are calculated, and a comparison between calculated results and experimental data is made to validate the method. This method is used to investigate the effect of trailing edge flap deflection on ice accretion of a rotor blade.

The numerical method is feasible and effective to study the ice accretion on helicopter rotor blades. The downward deflection of the trailing edge flap affects the shape of the ice.

This method can be further used to predict the ice accretion in actual flights of the helicopters with multielement airfoils.

The numerical simulation method here can lay a foundation of the research about helicopter flight performance in icing condition through predicting the shape and location of ice accretion on rotor blades.

In this study, we investigate the effects of an extended ternary hybrid Tiwari and Das nanofluid model on ethylene glycol flow, with a focus on heat transfer. Using the Cross non-Newtonian fluid model, we explore the heat transfer characteristics of this unique fluid in various applications such as pharmaceutical solvents, vaccine preservatives, and medical imaging techniques.

Our investigation reveals that the flow of this ternary hybrid nanofluid follows a laminar Cross model flow pattern, influenced by heat radiation and occurring around a stretched cylinder in a porous medium. We apply a non-similarity transformation to the nonlinear partial differential equations, converting them into non-dimensional PDEs. These equations are subsequently solved as ordinary differential equations (ODEs) using MATLAB’s bvp4c tools. In addition, the magnetic number in this study spans from 0 to 5, volume fraction of nanoparticles varies from 5% to 10%, and Prandtl number for EG as 204. This approach allows us to examine the impact of temperature on heat transfer and distribution within the fluid.

Graphical depictions illustrate the effects of parameters such as the Weissenberg number, porous parameter, Schmidt number, thermal conductivity parameter, Soret number, magnetic parameter, Eckert number, Lewis number, and Peclet number on velocity, temperature, concentration, and microorganism profiles. Our results highlight the significant influence of thermal radiation and ohmic heating on heat transmission, particularly in relation to magnetic and Darcy parameters. A higher Lewis number corresponds to faster heat diffusion compared to mass diffusion, while increases in the Soret number are associated with higher concentration profiles. Additionally, rapid temperature dissipation inhibits microbial development, reducing the microbial profile.

The numerical analysis of skin friction coefficients and Nusselt numbers in tabular form further validates our approach. Overall, our findings demonstrate the effectiveness of our numerical technique in providing a comprehensive understanding of flow and heat transfer processes in ternary hybrid nanofluids, offering valuable insights for various practical applications.

Analyzing and reducing entropy generation is useful for enhancing the thermodynamic performance of engineering systems. This study aims to explore how polymers and nanoparticles in the presence of Lorentz forces influence the fluid behavior and heat transfer characteristics to lessen energy loss and entropy generation.

The dispersion model is initially used to examine the behavior of polymer additives over a magnetized surface. The governing system of partial differential equations (PDEs) is subsequently reduced through the utilization of similarity transformation techniques. Entropy analysis is primarily performed through the implementation of numerical computations on a non-Newtonian polymeric FENE-P model.

The numerical simulations conducted in the presence of Lorentz forces provide significant insights into the consequences of adding polymers to the base fluid. The findings suggest that such an approach minimizes entropy in the flow region. Through the utilization of polymer-MHD (magnetohydrodynamic) interactions, it is feasible to reduce energy loss and improve the efficiency of the system.

This study’s primary motivation and novelty lie in examining the significance of polymer additives as agents that reduce entropy generation on a magnetic surface. The author looks at how nanofluids affect the development of entropy and the loss of irreversibility. To do this, the author uses the Lorentz force, the Soret effect and the Dufour effect to minimize entropy. The findings contribute to fluid mechanics and thermodynamics by providing valuable insights for engineering systems to increase energy efficiency and conserve resources.

The purpose of the study is to analytically as well as numerically investigate the weight of throughflow on the onset of Casson nanofluid layer in a permeable matrix. This study examines both the marginal and over stable kind of convective movement in the system.

A double-phase model is used for Casson nanofluid, which integrates the impacts of thermophoresis and Brownian wave, whereas for flow in the porous matrix the altered Darcy model is occupied under the statement that nanoparticle flux is disappear on the boundaries. The resultant eigenvalue problem is resolved analytically as well as numerically with the help of Galerkin process with the Casson nanofluid Rayleigh–Darcy number as the eigenvalue.

The findings revealed that the throughflow factor postpones the arrival of convective flow and reduces the extent of convective cells, whereas the Casson factor, the Casson nanoparticle Rayleigh–Darcy number and the reformed diffusivity ratio promote convective motion and also decrease the extent of convective cells.

Controlling the convective movement in heat transfer systems that generate high heat flux is a real mechanical challenge. The proposed framework proved that the use of throughflow is one of the most important ways to control the convective movement in Casson nanofluid. To the best of the authors’ knowledge, no inspection has been established in the literature that studies the outcome of throughflow on the Casson nanofluid convective flow in a porous medium layer. However, the convective flow of Casson nanofluid finds many applications in improving heat transmission and energy efficiency in a range of thermal systems, such as the cooling of heat-generating elements in electronic devices, heat exchangers, pharmaceutical practices and hybrid-powered engines, where throughflow can play a significant role in controlling the convective motion.

Thermophoresis deposition of particles is a crucial stage in the spread of microparticles over temperature gradients and is significant for aerosol and electrical technologies. To track changes in mass deposition, the effect of particle thermophoresis is therefore seen in a mixed convective flow of Williamson hybrid nanofluids upon a stretching/shrinking sheet.

The PDEs are transformed into ordinary differential equations (ODEs) using the similarity technique and then the bvp4c solver is employed for the altered transformed equations. The main factors influencing the heat, mass and flow profiles are displayed graphically.

The findings imply that the larger effects of the thermophoretic parameter cause the mass transfer rate to drop for both solutions. In addition, the suggested hybrid nanoparticles significantly increase the heat transfer rate in both outcomes. Hybrid nanoparticles work well for producing the most energy possible. They are essential in causing the flow to accelerate at a high pace.

The consistent results of this analysis have the potential to boost the competence of thermal energy systems.

It has not yet been attempted to incorporate hybrid nanofluids and thermophoretic particle deposition impact across a vertical stretching/shrinking sheet subject to double-diffusive mixed convection flow in a Williamson model. The numerical method has been validated by comparing the generated numerical results with the published work.

The hybrid nanofluid flow due to a rotating disk has numerous applications, including centrifugal pumps, paper production, polymers dying, air filtration systems, automobile cooling and solar collectors. This study aims to investigate the convective heat transport and magnetohydrodynamics (MHD) hybrid nanofluid flow past a stretchable rotating surface using the Yamada-Ota and Xue models with the impacts of heat generation and thermal radiation.

The carbon nanotubes such as single-wall carbon nanotubes and multi-wall carbon nanotubes are suspended in a base fluid like water to make the hybrid nanofluid. The problem’s governing partial differential equations are transformed into a system of ordinary differential equations using similarity transformations. Then, the numerical solutions are found with a bvp4c function in MATLAB software. The impacts of pertinent parameters on the flow and temperature fields are depicted in tables and graphs.

Two solution branches are discovered in a certain range of unsteadiness parameters. The fluid temperature and the rate of heat transport are enhanced when the thermal radiation and heat generation effects are increased. The Yamada-Ota model has a higher temperature than the Xue model. Furthermore, it is observed that only the first solution remains stable when the stability analysis is implemented.

To the best of the authors’ knowledge, the results stated are original and new with the investigation of MHD hybrid nanofluid flow with convective heat transfer using the extended version of Yamada-Ota and Xue models. Moreover, the novelty of the present study is improved by taking the impacts of heat generation and thermal radiation.

This study aims to explore the thermal energy diffusion and flow features of a hybrid nanofluid in a thin film. In particular, the focus is to elicit the impact of shape factor in the backdrop of a magnetic field. The hybrid nanofluid is the amalgamation of various shaped nanoscale particles of copper and alumina in water.

The equations of motion and energy are modeled using the Tiwari–Das model. The differential equations governing the physics of the designed model have been obtained by the application of scaling analysis. To achieve quantitative outcomes, Runge–Kutta–Fehlberg numerical code along with shooting techniques is used. Validation of the derived outcomes with available data in literature reveals a greater accuracy of the numerical procedure used in this investigation.

The dynamics of the slender nano liquid film is explored eliciting the impact of various flow parameters. The rate of energy transport of the Cu-Al₂O₃/ water with blade-shaped nanoparticle, at a fixed Prandtl number (=2) is enhanced by 14.7% compared to that evaluated with spherical particles. The presence of hybrid nanoparticles has an affirmative impact in boosting the rate of heat transfer (RHT). The temperature and the rate of thermal diffusion of the hybrid nanofluid are more prominent than those of the Cu-H₂O case. The numerical outcomes of this investigation are collated with the already published works as a limiting case and are found to be in good agreement.

The adopted methodology helped to obtain the results of the present problem. To the best of authors’ knowledge, it can be shown that the originality of the work with the table of comparison. There is a good agreement between present outcomes with the existed results.

The purpose of this study is to consider the dynamics of Casson–Walters-B alongside gyrotactic microorganisms through the investigation of antibacterial and antiviral mechanisms using silver nanoparticles (AgNPs). The Casson fluid and Walters-B flow from the penetrable plate to the boundary layer (BL) in this analysis. The antiviral and antibacterial mechanisms of AgNPs were separately examined in this study.

The physical phenomenon of this problem was analyzed with partial differential equations (PDEs). These PDEs were changed into ordinary differential equations (ODEs) to further explain the significance of pertinent control parameters. The set of equations is solved numerically by implementing the spectral relaxation method (SRM). SRM is a numerical technique that uses the basic techniques of Gauss-Seidel. The SRM first decouples and linearizes the coupled nonlinear set of ODEs.

In this finding, it is found that the thermal radiation parameter produces higher temperatures within the BL to cause blockage in viral replications. It is found in this study that the magnetic parameter assisted in disinfection by lowering the antiviral and antibacterial mechanisms within the momentum BL. This is evident from the reduction in the velocity and momentum BL as the Casson and Walters-B parameters increase.

This paper is unique because it examined the antiviral and antibacterial mechanisms by using AgNPs. Prior to the authors’ understanding, no study of this type was conducted in the past. To the best of the authors’ knowledge, no other study in the past has examined the mechanisms of antiviral and antibacterial separately within the BL. Also, the simultaneous flow of Casson (honey) and Walters-B fluids were considered flowing through the vertical porous plate to the BL.

This investigation delves into the rationale behind the preferential applicability of the non-Newtonian nanofluid model over alternative frameworks, particularly those incorporating porous medium considerations. The study focuses on analyzing the mass and heat transfer characteristics inherent in the Williamson nanofluid’s non-Newtonian flow over a stretched sheet, accounting for influences such as chemical reactions, viscous dissipation, magnetic field and slip velocity. Emphasis is placed on scenarios where the properties of the Williamson nanofluid, including thermal conductivity and viscosity, exhibit temperature-dependent variations.

Following the use of the OHAM approach, an analytical resolution to the proposed issue is provided. The findings are elucidated through the construction of graphical representations, illustrating the impact of diverse physical parameters on temperature, velocity and concentration profiles.

Remarkably, it is discerned that the magnetic field, viscous dissipation phenomena and slip velocity assumption significantly influence the heat and mass transmission processes. Numerical and theoretical outcomes exhibit a noteworthy level of qualitative concurrence, underscoring the robustness and reliability of the non-Newtonian nanofluid model in capturing the intricacies of the studied phenomena.

Available studies show that no work on the Williamson model is conducted by considering viscous dissipation and the MHD effect past over an exponentially stretched porous sheet. This contribution fills this gap.