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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.

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 investigates the behavior of viscous hybrid ferromagnetic fluids flowing through plain elastic sheets with the magnetic polarization effect. It examines flow in a porous medium using Stefan blowing and utilizes a versatile hybrid ferrofluid containing MnZnFe₂O₄ and Fe₃O₄ nanoparticles in the C2H2F4 base fluid, offering potential real-world applications. The study focuses on steady, laminar and viscous incompressible flow, analyzing heat and mass transfer aspects, including thermal radiation, Brownian motion, thermophoresis and viscous dissipation with convective boundary condition.

The governing expression of the flow model is addressed with pertinent non-dimensional transformations, and the finite element method solves the obtained system of ordinary differential equations.

The variations in fluid velocity, temperature and concentration profiles against all the physical parameters are analyzed through their graphical view. The association of these parameters with local surface friction coefficient, Nusselt number and Sherwood number is examined with the numerical data in a table.

This work extends previous research on ferrofluid flow, investigating unexplored parameters and offering valuable insights with potential engineering, industrial and medical implications. It introduces a novel approach that uses mathematical simplification techniques and the finite element method for the solution.

The main focus is to provide a non-similar solution for the magnetohydrodynamic (MHD) flow of Casson fluid over a curved stretching surface through the novel technique of the artificial intelligence (AI)-based Lavenberg–Marquardt scheme of an artificial neural network (ANN). The effects of joule heating, viscous dissipation and non-linear thermal radiation are discussed in relation to the thermal behavior of Casson fluid.

The non-linear coupled boundary layer equations are transformed into a non-linear dimensionless Partial Differential Equation (PDE) by using a non-similar transformation. The local non-similar technique is utilized to truncate the non-similar dimensionless system up to 2nd order, which is treated as coupled ordinary differential equations (ODEs). The coupled system of ODEs is solved numerically via bvp4c. The data sets are constructed numerically and then implemented by the ANN.

The results indicate that the non-linear radiation parameter increases the fluid temperature. The Casson parameter reduces the fluid velocity as well as the temperature. The mean squared error (MSE), regression plot, error histogram, error analysis of skin friction, and local Nusselt number are presented. Furthermore, the regression values of skin friction and local Nusselt number are obtained as 0.99993 and 0.99997, respectively. The ANN predicted values of skin friction and the local Nusselt number show stability and convergence with high accuracy.

AI-based ANNs have not been applied to non-similar solutions of curved stretching surfaces with Casson fluid model, with viscous dissipation. Moreover, the authors of this study employed Levenberg–Marquardt supervised learning to investigate the non-similar solution of the MHD Casson fluid model over a curved stretching surface with non-linear thermal radiation and joule heating. The governing boundary layer equations are transformed into a non-linear, dimensionless PDE by using a non-similar transformation. The local non-similar technique is utilized to truncate the non-similar dimensionless system up to 2nd order, which is treated as coupled ODEs. The coupled system of ODEs is solved numerically via bvp4c. The data sets are constructed numerically and then implemented by the ANN.

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.

To improve the thermal performance of base fluid, nanoparticles of three types are dispersed in the base fluid. A novel theory of non-Fourier heat transfer is used for design and development of models. The thermal performance of sample fluids is compared to determine which types of combination of nanoparticles are the best for an optimized enhancement in thermal performance of fluids. This article aims to: (i) investigate the impact of nanoparticles on thermal performance; and (ii) implement the Galerkin finite element method (GFEM) to thermal problems.

The mathematical models are developed using novel non-Fourier heat flux theory, conservation laws of computational fluid dynamics (CFD) and no-slip thermal boundary conditions. The models are approximated using thermal boundary layer approximations, and transformed models are solved numerically using GFEM. A grid-sensitivity test is performed. The accuracy, correction and stability of solutions is ensured. The numerical method adopted for the calculations is validated with published data. Quantities of engineering interest, i.e. wall shear stress, wall mass flow rate and wall heat flux, are calculated and examined versus emerging rheological parameters and thermal relaxation time.

The thermal relaxation time measures the ability of a fluid to restore its original thermal state, called thermal equilibrium and therefore, simulations have shown that the thermal relaxation time associated with a mono nanofluid has the most substantial effect on the temperature of fluid, whereas a ternary nanofluid has the smallest thermal relaxation time. A ternary nanofluid has a wider thermal boundary thickness in comparison with base and di- and mono nanofluids. The wall heat flux (in the case of the ternary nanofluids) has the most significant value compared with the wall shear stresses for the mono and hybrid nanofluids. The wall heat and mass fluxes have the highest values for the case of non-Fourier heat and mass diffusion compared to the case of Fourier heat and mass transfer.

An extensive literature review reveals that no study has considered thermal and concentration memory effects on transport mechanisms in fluids of cross-rheological liquid using novel theory of heat and mass [presented by Cattaneo (Cattaneo, 1958) and Christov (Christov, 2009)] so far. Moreover, the finite element method for coupled and nonlinear CFD problems has not been implemented so far. To the best of the authors’ knowledge for the first time, the dynamics of wall heat flow rate and mass flow rate under simultaneous effects of thermal and solute relaxation times, Ohmic dissipation and first-order chemical reactions are studied.

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.

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 present findings aim to investigate the thermal behavior of water-based nanofluid flow over a rotating surface, focusing on understanding the effects of different types of nanoparticles on thermal efficiency, considering thermal radiation and variable viscosity effects. By considering four distinct nanoparticles – silicon dioxide titanium dioxide, aluminum oxide and molybdenum disulfide – the study aims to provide insights into how nanoparticle addition influences heat production, thermal boundary layer thickness and overall thermal performance.

The study employs computational methods, utilizing the BVP mid-rich algorithm for the solution procedure. The computational approach allows for a detailed investigation of the thermal behavior of nanofluid flows across a rotating surface under varying conditions.

The study concludes that adding nanoparticles in the base liquid increases heat production in the system, resulting in enhanced thermal boundary layer thickness. The comparative analysis shows that different nanoparticle types exhibit varying effects on thermal efficiency, suggesting that careful selection of nanoparticles can optimize heat transport and thermal management processes. Moreover, there's a noteworthy uptrend in the radial velocity profile concerning the stretching parameter, whereas a converse trend is observed in the thermal profile.

This study contributes original insights by comprehensively investigating the thermal behavior of water-based hybrid nanofluid flow over a rotating surface.

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.