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The purpose of this study is to examine the melting heat transfer of magnetohydrodynamics Casson nanofluid flow with viscous dissipation, radiation, and complete slip effects on a porous stretching sheet. Since, the study of melting heat transfer has mesmerized the attention of scientists and engineers in the sense of its enormous uses in industrial processes, solidification, casting, and technology.

Bejan number and entropy are analyzed. Exploration of irreversibility is modeled using the thermodynamics second law. There is a discussion on thermophoresis and Brownian diffusion along with first-order chemical reactions. Adequate transformations are introduced to convert the controlling partial differential equations to ordinary differential equations. The three-phase Lobatto solvers (bvp5c) are used to obtain numerical solutions of the transmitted equations.

The effects of various factors on temperature, velocity, concentration, Bejan number and entropy rate are shown graphically. The velocity field is enhanced by increasing the melting heat parameter, and it declines for growing magnetic parameters. Temperature is decreased for increasing parametric values of melting heat, porous and Casson parameters. A 7% decrease in the Sherwood distribution is seen when we increase the Brownian motion parameter from 0.1 to 0.2. Similarly, an 11% decrement is found in the Nusselt distribution for increasing the Brinkman number from 0.5 to 1.

Entropy and Bejan number experience dual tendencies whenever the melting heat parameter increases. Nusselt number and skin friction experience the opposite behavior for the increasing values of melting parameter. Sherwood number decreases for the increasing values of melting parameter. The velocity profile is directly related to the melting parameter and inversely related to porous and magnetic parameters. Thermophoresis and Brinkman parameters boost the temperature profile and it is controlled by melting and porous parameters. Some notable fields where the present study is used inevitably are silicon wafering, geothermal energy recovery and semiconductor manufacturing.

This study aims to investigate the effect of externally applied magnetic force and heat transfer with a heat source/sink on the Couette flow with viscous dissipation in a horizontal rotating channel. The magnetic force is added to the governing equations. The effects of fluid flow parameters are observed under the applied magnetic force. In this system, the magnetic force is applied perpendicular to the plane of the fluid flow. In recent years, the magnetic field has renewed interest in aerospace technology. The physical and theoretical approach in the multidisciplinary field of magneto fluid dynamics (MFD) is applied in the field of aerospace vehicle design.

Authors use the perturbation method to solve and find the approximate solutions of differential equations. First, convert the partial differential equation to ordinary differential equation and calculate the approximate solutions in two cases. The first solution got by assuming heat generating in the fluid and the second one got when heat absorbing. After applying the external magnetic force, the effects of various fluid parameters velocity, temperature, skin friction coefficient and Nusselt number are found and discussed using tables and graphs.

It is found that the velocity of the fluid has decreased tendency when the rotation of the fluid and magnetic force on the fluid increases. The temperature of the fluid, Prandtl value and Eckert number increased when the heat source generated heat. When heat absorbs the heat, sink parameter increases and the temperature of the fluid decreases. Also, while heat absorbs, the temperature increases when the Prandtl value and Eckert number increase.

The skin friction coefficient on the surface increases, when the rotation parameter and the magnetic force parameter of the fluid increase. In the case of heat generating, the Nusselt number increased, while the Eckert number and Prandtl numbers increased. Also, the Nusselt number has larger values when the heat source parameter has near the constant temperature, and it has smaller values when the temperature varies. In the case of heat-absorbing, the Nusselt number decreased when the Eckert and Prandtl numbers increased. Also, the Nusselt number varies up and down while the heat absorbing parameter increases.

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.

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.

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.

This study aims to enhance heat transfer efficiency while minimizing friction factor and entropy generation in the flow of Nickel zinc ferrite (NiZnFe₂O₄) nanoparticles suspended in multigrade 20W-40 motor oil (as specified by the Society of Automotive Engineers). The investigation focuses on the effects of the melting process, nonspherical particle shapes, thermal dispersion and viscous dissipation on the nanofluid flow.

The fundamental governing equations are transformed into a set of similarity equations using Lie group transformations. The resulting set of equations is numerically solved using the spectral local linearization method. Additionally, sensitivity analysis using response surface methodology (RSM) is conducted to evaluate the influence of key parameters on response function.

Higher dispersion reduces entropy production. Needle-shaped particles significantly enhance heat transfer by 27.65% with melting and reduce entropy generation by 45.32%. Increasing the Darcy number results in a reduction of friction by 16.06%, lower entropy by 31.72% and an increase in heat transfer by 17.26%. The Nusselt number is highly sensitive to thermal dispersion across melting and varying volume fraction parameters.

This study addresses a significant research gap by exploring the combined effects of melting, particle shapes and thermal dispersion on nanofluid flow, which has not been thoroughly investigated before. The focus on practical applications such as fuel cells, material processing, biomedicine and various cooling systems underscores its relevance to sectors such as nuclear reactors, tumor treatments and manufacturing. The incorporation of RSM for friction factor analysis introduces a unique dimension to the research, offering novel insights into optimizing nanofluid performance under diverse conditions.

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.

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.

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.