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A theoretical framework to investigate three-dimensional Williamson fluid flow over a bidirectional extended flat horizontal surface is proposed in this dissertation. Artificial intelligence and machine learning fields have seen tremendous growth in prominence along with the rapid advancement of related technology. This work trains a machine learning model based on artificial neural networks to handle the mathematical formulation incorporating heat source and Hall effects using the Levenberg–Marquardt approach. Additionally, the impact of activation energy on fluid concentration is incorporated into the analysis. Cattaneo-Christov double diffusion models are used to model heat transfer combined with the effects of thermal radiation. The solutions, serving as reference datasets for various scenarios, have been generated numerically using the BVP4C approach. Artificial neural networks are utilized for training, testing, and validating these numerical computations using a 70:15:15 ratio. The predictive model accuracy is evaluated using various statistical metrics, including linear regression, histograms, fitting analysis, and mean squared error evaluations, with the least error ranging between 10−3 and 10−4, based on individual error analysis of four parameters. The findings show that temperature rises with the M parameter, whereas velocity declines by increasing the M parameter. Concentration rises with increasing activation energy parameter and falls with decreasing Sc. The results show that artificial neural networks can provide a successful replacement for forecasts for the future, and the fluid flow structure simulated here may result in better industrial designs. [ABSTRACT FROM AUTHOR]

The investigation of velocity slip combined with the dissipative heat corresponds to the non-Newtonian Williamson hybrid nanofluids utilizing the "Cattaneo-Christov heat flux model" is crucial in advanced applications in several sectors. The proposed analysis focuses on the hybrid nanofluid comprised of magnesium oxide (MgO) and zirconium dioxide (ZrO2) in water which boosts the thermal conductivity along with the performance of the fluid. The magnetized Williamson fluid is a particular type of non-Newtonian fluid that exhibits essential applications to biomedical engineering. The insertion of magnetization along with porosity suggests considering the dissipative heat impact associated with Joule and Darcy which energies the heat transport phenomena. The limitation of classical Fourier laws is addressed by the consideration of the Cattaneo–Christov heat flux framework along with the thermal radiation. The designed flow model with dimensional terms is transformed into a corresponding non-dimensional form by implementing similarity functions. Further, these transmuted equations are solved numerically via the shooting-based Runge–Kutta technique. The parametric analysis of the flow phenomena is obtained and arranged graphically. The validation with earlier investigation displays a valid association in particular scenarios. The main outcomes reveal that the resistivity characteristics produced by the interplay between permeability and magnetization regulate fluid velocity, especially when combined with the non-Newtonian Williamson parameter. Furthermore, in both nanofluid and hybrid nanofluid scenarios, the fluid temperature is greatly raised by the effects of thermal radiation and the Eckert number. [ABSTRACT FROM AUTHOR]

This study investigates the dynamic properties of a Casson hybrid nanofluid flow over a rotating disk, emphasizing the influences of Electroviscous forces and Cattaneo-Christov heat flux. The nanofluid comprises Silver (Ag) nanoparticles and Multi-Walled Carbon Nanotubes (MWCNTs) dispersed in a water base fluid, chosen for their superior thermal properties and stability. A comprehensive mathematical model, comprised of Partial Differential Equations (PDEs) transformed into Ordinary Differential Equations (ODEs) through a similarity transformation method, is developed to explore this complex phenomenon. The analysis combines multiple variables including magnetic fields, viscous dissipation, Joule heating, and radiative as well as convective effects. The findings reveal significant impacts on skin friction, fluid flow characteristics, and heat transfer behavior due to the synergistic effects of the considered parameters. The study’s novelty lies in its detailed examination of Electroviscous effects within a rotating disk setup, extending beyond traditional analyses by integrating the specific thermal and viscous properties of Silver and MWCNT nanoparticles. This approach offers new insights into optimizing heat transfer applications in industrial processes, particularly in high-speed rotational systems. [ABSTRACT FROM AUTHOR]

Purpose: Recent advancements in technology have led to the exploration of solar-based thermal radiation and nanotechnology in the field of fluid dynamics. Solar energy is captured through sunlight absorption, acting as the primary source of heat. Various solar technologies, such as solar water heating and photovoltaic cells, rely on solar energy for heat generation. This study focuses on investigating heat transfer mechanisms by utilizing a hybrid nanofluid within a parabolic trough solar collector (PTSC) to advance research in solar ship technology. The model incorporates multiple effects that are detailed in the formulation. Design/methodology/approach: The mathematical model is transformed using suitable similarity transformations into a system of higher-order nonlinear differential equations. The model was solved by implementing a numerical procedure based on the Wavelets and Chebyshev wavelet method for simulating the outcome. Findings: The velocity profile is reduced by Deborah's number and velocity slip parameter. The Ag-EG nanoparticles mixture demonstrates less smooth fluid flow compared to the significantly smoother fluid flow of the Ag-Fe3O4/EG hybrid nanofluids (HNFs). Additionally, the Ag-Ethylene Glycol nanofluids (NFs) exhibit higher radiative performance compared to the Ag-Fe3O4/Ethylene Glycol hybrid nanofluids (HNFs). Practical implications: Additionally, the Oldroyd-B hybrid nanofluid demonstrates improved thermal conductivity compared to traditional fluids, making it suitable for use in cooling systems and energy applications in the maritime industry. Originality/value: The originality of the study lies in the exploration of the thermal transport enhancement in sun-powered energy ships through the incorporation of silver-magnetite hybrid nanoparticles within the heat transfer fluid circulating in parabolic trough solar collectors. This particular aspect has not been thoroughly researched previously. The findings have been validated and provide a highly positive comparison with the research papers. [ABSTRACT FROM AUTHOR]

Studying the impact of Ferrohydrodynamic interaction on the flow of Casson‑Williamson nanofluid present a significant insight into complex fluid behaviour in several fields including aerospace engineering, energy systems, drug delivery, chemical engineering, and various industries. Owing to its usage, current investigation deals with effect of magnetic dipole on the time‑based unsteady nanofluid flow of homogeneous and heterogeneous reaction driven by a curved stretching sheet with slip and melting heat boundary conditions. This research predicts the optimal ranges of parameters for achieving higher heat transport performance by studying the Cattaneo-Christov heat flux model and an exponential heat source. The governing equations are converted into dimensionless form by employing suitable similarity transformations. The Galerkin-weighted residual technique is used to numerically solve the resulting non-dimensional equations with the assistance of the MATHEMATICA 11.3 software. The outcome indicates that the thermal buoyancy parameter significantly enhances fluid motion, while the thermal radiation parameter reduces the fluid temperature. This outcome greatly influences the prospective uses of Ferrohydrodynamic interaction in enhancing heat and mass transport in nanofluid cooling systems.

This research communication explores the Darcy - Forchheimer flow of a chemically reacting non-Newtonian Maxwell fluid over a stretching sheet, incorporating the Cattaneo – Christov heat flux under a convective boundary condition. The fluid flow is described by a set of partial differential equations, which are subsequently transformed into a system of nonlinear ordinary differential equations. To solve these equations numerically, the BVP4C Method was employed after appropriately defining non dimensional variables and implementing similarity transformations. The impacts of diverse active parameters such as Deborah parameter, Darcy‑Forchheimer parameter, magnetic parameter, Biot number, and porous parameter are examined on the velocity, temperature, and concentration profiles. In addition, the value of the Skin friction, Nusselt number is calculated and presented through tabular forms.

AbstractThe aim of this study is to characterize the Cattaneo-Christov heat flux in magnetohydrodynamics (MHD) radiative flow of Williamson nanofluid through a stretched sheet when confronted with heat source, Arrhenius activation energy and motile microorganisms. Also, the Darcy-Forchheimer model is a widely used and precise technique for modeling fluid dynamics in porous medium. The controlling partial differential equations (PDE) are minimized to ordinary differential equations (ODE) using suitable similarities. The final outcomes were computed numerically using the BVP4C MATLAB interface. The graphical portrayal serves to comprehensively show and build upon the effect of several aspects. The results reveal the increased velocity distribution with the intensifying values of magnetic field, porosity, suction, and Forchheimer number. The thermal gradient is enhanced with the increase in heat source, and radiation, while it diminishes with the augmentation of the thermal relaxation parameter. Furthermore, the concentration maximizes when the activation energy is large. This research shows a favorable link between Peclet quantity and motile microbe density. Additionally, this work numerically analyses and tabulates important engineering metrics such as skin friction, Nusselt number, Sherwood number, and motile density number. The present study has huge interest due to its applications such as food processing, crystal formation in rocks, microelectronic semiconductors, crystal fiber, electronic power plants, and many more. [ABSTRACT FROM AUTHOR]

This study presents a comparative analysis of chemically reacted nanofluids, specifically single-walled carbon nanotubes (SWCNT) and multi-walled carbon nanotubes (MWCNT), incorporating the advanced modeling of Cattaneo-Christov heat fluxes. It centers on the numerical examination modelling of Cattaneo-Christov heat fluxes to reveal the involvement of carbon nanotubes with the influence of chemical reaction and mass diffusivity of an MHD surface stretching causes nanofluid to flow. A comprehensive assessment is conducted regarding the impact of pertinent limitations on focus. For this, we applied the BVP-4C MATLAB procedure. The investigation includes the development of mathematical models and their numerical solutions to explore the thermal and fluid dynamic behavior of SWCNT and MWCNT nanofluids under chemical reactions. ϕ, M, α, Da, NR, g, Rc, and Sc are varied to assess their impact on temperature, velocity, and concentration profiles are depicted through graphical representations. The Sherwood and Nusselt numbers and skin friction can also be recognised for practical reasons for numerous estimations of physical parameters. Comparative insights reveal distinct behaviors between SWCNT and MWCNT nanofluids, with SWCNT exhibiting superior thermal conductivity and enhanced heat transfer rates. This model's conclusions are relevant to biological fluids as well as industrial circumstances. These findings agree up to 99.9% with the previous studies and are represented by tabular values. [ABSTRACT FROM AUTHOR]

In the current work, inclined magnetic field, thermal radiation, and the Cattaneo-Christov heat flux are taken into account as we analyze the impact of chemical reaction on magneto-hydrodynamic Casson nanofluid flow on a stretching sheet. Modified Buongiorno's nanofluid model has been used to model the flow governing equations. The stretching surface is embedded in a porous medium. By using similarity transformations, the nonlinear partial differential equations are transformed into a set of dimensionless ordinary differential equations. The numerical solution of transformed dimensionless equations is achieved by applying the shooting procedure together with Rung-Kutta 4th-order method employing MATLAB. The impact of significant parameters on the velocity profile , temperature distribution , concentration profile , skin friction coefficient , Nusselt number and Sherwood number are analyzed and displayed in graphical and tabular formats. With an increase in Casson fluid , the motion of the Casson fluid decelerates whereas the temperature profile increases. As the thermal relation factor expands , the temperature reduces, and consequently thermal boundary layer shrinks. Additionally, by raising the level of thermal radiation the temperature profile significantly improves, and an abrupt expansion has also been observed in the associated thermal boundary with raise thermal radiation strength. It was observed that higher permeability hinders the acceleration of Casson fluid. Higher Brownian motion levels correspond to lower levels of the Casson fluid concentration profile. Moreover, it is observed that chemical reaction has an inverse relation with the concentration level of Casson fluid. The current model's significant uses include heat energy enhancement, petroleum recovery, energy devices, food manufacturing processes, and cooling device adjustment, among others. Furthermore, present outcomes have been found in great agreement with already published work. [ABSTRACT FROM AUTHOR]

This investigation has significant applications in the fields of mechanical, industrial, and biomedical engineering, biosciences, and technology, particularly in areas such as blood pumping, drug delivery, glass-fiber production, paper production, and nuclear reactors. This study explores the numerical analysis of a mathematical model of entropy generation in convective magnetohydrodynamic (MHD) flow of Williamson nanofluid model over a stretching sheet with Cattaneo–Christov heat flux and suction/injection. Furthermore, heat generation, viscous dissipation, Joule heating, radiation, and chemical reaction are considered. The appropriate transformations are used to transform the nonlinear partial differential equations (PDEs) into nonlinear ordinary differential equations (ODEs). The transformed equations are solved numerically using bvp5c MATLAB package. The effects of the involved physical parameters on the flow quantities and the entropy generation are presented and discussed in detail with figures and tables. It is observed that the thermal field is enhanced by increasing the Eckert number, the Joule heating, and the thermal relaxation parameters. Also, the concentration field is observed to be a decreasing function of the augmented chemical reaction parameter. Further, the increasing magnetic field and the Williamson parameter led to an increase in the skin friction coefficient. Moreover, the entropy generation increases due to an increase in the diffusion parameter and the Brinkman number. [ABSTRACT FROM AUTHOR]

Ternary hybrid nanofluids (Thnf) are used in several fields, including enhancements of heat transfer, solar power systems, medical devices, electronics cooling, aviation industry, and automotive sector. Furthermore, Thnf provide a versatile solution to boost energy transport for the industrial applications. In the current analysis, an incompressible magnetized Thnf flow with the natural convection through a curved surface using Darcy–Forchheimer medium is addressed. The heat transfer is simulated by using the Cattaneo–Christov (C–C) heat flux model. Aluminum alloys (Ti6Al4V, AA7072 and AA7075) are dispersed in water (H2O) and ethylene glycol (C2H6O2) to synthesize the modified hybrid nanofluid. The model equations are reform into ODEs (ordinary differential equations) by using the similarity substitution. The non-dimensional set of ODEs is further numerically estimated through PCM (Parametric continuation method). The physical behavior of velocity, energy outline, Nusselt number and skin friction for distinct values of emerging variables are computed and analyzed in detail. The finding reveals that an improvement in entropy generation has been observed versus the rising values of unsteadiness and variable porosity parameters. The rising effect of permeability parameter enhances the velocity curve; whereas, fluid velocity drops with the influence of inertia coefficient. [ABSTRACT FROM AUTHOR]

The current study investigates the three-dimensional radiative and convective Casson hybrid nanofluid flow and heat transfer with the Cattaneo–Christov heat flux model over an inclined spinning and extending disk subjected to an applied magnetic field. Additionally, the study considers the impacts of Joule’s heating and viscous dissipation. Mathematical modelling of the nanofluid flow problem containing Ag and multiwalled carbon nanotubes (MWCNT) nanoparticles with water as the base fluid in a Darcy medium is done using a cylindrical coordinate system. The simplified system of equations is subjected to the spectral quasilinearisation method (SQLM) approach for the graphical and tabular representations. Examining key parameters, such as magnetic field, Bejan number, angle of inclination, disk movement parameter and disk rotation reveals interesting results on velocity and temperature profiles. The research concludes that the Bejan number increases with higher values of temperature ratio, radiation and magnetic parameters, while it decreases with increasing Casson parameter and Brinkman number. Radial wall friction decreases with improved magnetic field, temperature ratio, stretching and porosity parameters, but tangential wall friction increases. The present results are compared with the one already existing in literature to validate the numerical scheme and the results are found to agree well with the previously published work. The application of hybrid nanofluid flow over rotating and stretching disks is widespread in various fields, including rotating machinery, electronic devices, patient treatment instruments, crystal growth method, etc. [ABSTRACT FROM AUTHOR]

A hybrid nanofluid is an amalgamation of two or more types of nanoparticles in a customary and possesses a variety of industrial applications. This exploration examines the blend of copper (Cu) and gold (Au), and engine oil as a hybrid nanofluid. The model considers the Hall current, Cattaneo–Christov (C-C) heat flux, thermal stratification, nonuniform heat source, and nonlinear thermal radiative effects for heat analysis. Ordinary differential equations (ODEs) are obtained through a similarity transformation scheme, and the model is visualized using a MATLAB function bvp4c. Graphs are presented to demonstrate the impact of various parameters on velocities and temperatures, and the wall drag coefficient and wall heat transfer rate are calculated and tabulated for both disks. The results show that a stronger Hall effect leads to a decrease in tangential velocity, while nonuniform heat sources increase fluid temperature. Thermal radiation and stratification have opposite effects on liquid temperature. It is interesting to note that for the radiation parameter at Rd = 0.5 , a higher heat transfer rate occurred at the lower disk, i.e., (N u 1 = − 3.63314) as compared to the upper disk (N u 2 = − 3.63324). Moreover, for the stratification parameter at S = 0.2 , it is observed that the heat transfer rate is lesser at the upper disk (N u 2 = − 3.64374) than at the lower disk (N u 1 = − 3.64274). Verification of the truthfulness of the proposed model is also included in the article. [ABSTRACT FROM AUTHOR]

Hybrid nanofluids generally exhibit better thermal efficiency than traditional nanofluids due to the synergistic effects of different types of nanoparticles. The combination of these nanoparticles can improve stability, thermal conductivity, and heat transfer performance. This study aims to investigate the effects of Hall current and ion slip on a three-dimensional, steady flow of hybrid nanofluid induced by a bidirectional extending surface while considering the presence of Zinc oxide (ZnO) and Gold (Au) nanoparticles dispersed in Kerosene oil and water to establish two different hybrid nanofluids. Additionally, a heat transfer analysis is conducted in the presence of Cattaneo-Christov (C-C) heat flux and variable heat source/sink. The characteristics of fluid flow are elaborated using the Tiwari and Das model, and a comparison between the two hybrid nanofluid models is presented in detail. The novelty of the envisioned model lies in the heat transfer comparison of two assumed hybrid nanofluid flows in the presence of Hall current and the ion slip over a bidirectional extended surface. The other assumed factors also boost the uniqueness of the model under consideration. To convert the flow model of partial differential equations into ordinary differential equations, relevant transformations are implemented, which are then numerically handled using the bvp4c scheme. The consequences of dimensionless quantities on flow and temperature distributions are highlighted using graphs, and the surface drag coefficients and surface heat transfer rates are also assessed and summarized. The study shows that ZnO-Au/water combination leads to higher heat transfer rates compared to ZnO-Au/Kerosene Oil. Additionally, the proposed model is validated in this research work. [ABSTRACT FROM AUTHOR]

The study of nanofluids using a stretchy disc has lately gained importance in fluid mechanics. This work investigates the impacts of the Cattaneo-Christov model, heat radiation, and melting events on TiO2–Al2O3/water and Ag–MoS2/water hybrid nanofluids over a disc. The results show that hybrid nanofluids greatly increase the thermal conductivity and heat transfer capabilities of base fluids. Water-based hybrid nanofluids are used in military applications such as solar thermal energy, heating pumps, heat exchanger devices, ships, air cleaners, the automotive industry, electric chillers, nuclear-powered systems, turbines, and equipment. To explain the flow of hybrid nanofluids, the two-dimensional nonlinear governing equations, which include the continuity, momentum, and heat transfer rate equations, are expressed in a non-dimensional form. The bvp4c solver firing technique in MATLAB is used to solve these non-dimensional equations and investigate the physical effects of various parameters on velocity and temperature profiles. Increasing the magnetic parameter and nanoparticle volume fraction substantially affects the velocity profile in opposing flow. Greater values of the thermal radiation and heat source-sink parameters result in a greater temperature profile. In addition, raising the thermal relaxation and melting parameters improves the temperature profile. The study's findings may be utilized in various sectors, including drainage, chemical engineering, solar panels, solar absorption and filtration, groundwater hydrology, solar cells, and other sheet flow applications. [ABSTRACT FROM AUTHOR]

This study aims to analyze the heat transfer behavior of the magnetohydrodynamic blood-based Casson hybrid nanofluid in the occurrence of a non-Fourier heat flux model and linear thermal radiation over a horizontal porous stretching cylinder with potential applications in biomedical engineering. The present investigation utilised titanium dioxide and silver nanoparticles, which exhibit considerable potential in the realm of cancer therapy. Thus, there is a growing interest among biomedical engineers and clinicians in the study of entropy production as a means of quantifying energy dissipation in biological systems. Suitable self-similarity variables are employed to transform the nonlinear mathematical equations such as velocity, temperature, skin friction coefficient, and heat transfer rate, which are computed via homotopy perturbation method (HPM). HPM computations have been executed to solve the influences of various parameters such as porosity parameter (K = 0.0 , 1.0 , 2.0) , Curvature parameter (α = 0.0 , 1.0 , 3.0 , 5.0) , Casson parameter (β = 0.0 , 0.5 , 1.5) , inertia coefficient (Fr = 0.5 , 1.5 , 2.5) , thermal relaxation parameter ( δ ∗ = 0.0 , 0.5 , 1.0) , radiation (Rd = 0.0 , 0.5 , 1.0) , Eckert number (Ec = 0.0 , 0.1 , 0.2) , Brinkman number (Br = 0.5 , 1.0 , 1.5) and temperature difference parameter ( α 1 = 0.0 , 0.5 , 1.0). The comparison using the homotopy perturbation technique produces a more accurate and reliable consequence than the numerical method (Runge-Kutta method). The higher values of the Casson and Curvature parameters decrease the velocity profile. The temperature profile of M = 1 and M = 0 increases with improving values of the thermal relaxation parameter. Entropy generation rises to enhance Brinkman number values, whereas Bejan number exhibits the reverse influence. Improving the value of the heat source parameter declines the Nusselt number. [ABSTRACT FROM AUTHOR]

This is a numerical study of gyrotactic microorganism, heat and mass transfer futures of hybrid Williamson nanofluid made up of $ \textrm{water} - \textrm{Ag}/\textrm{MWCNT} $ water − Ag / MWCNT nanoparticles over swirling cylinder with Cattaneo–Christov heat flux. Suitable similarity transformations are presented to convert the governing partial differential equations into ordinary differential equations. The set of ordinary differential equations along with boundary conditions are solved by using the finite element technique. The sketches of swirling velocity, axial velocity, temperature, concentration and density of microorganism with individual pertinent quantities, such as volume fraction parameter of $ \textrm{Ag} $ Ag nanoparticle $ (0.01 \lt \phi 1 \lt 0.04), $ (0.01 < ϕ 1 < 0.04) , volume fraction parameter of $ \textrm{MWCNT} $ MWCNT nanoparticle $ (0.01 \lt \phi 2 \lt 0.04) $ (0.01 < ϕ 2 < 0.04) , Magnetic field parameter $ (0.1 \lt M \lt 0.7), $ (0.1 < M < 0.7) , Weissenberg number $ ({0.5 \lt \textrm{We} \lt 0.8}) $ (0.5 < We < 0.8) , Prandtl number $ ({2.2 \lt \textrm{Pr} \lt 8.2}), $ (2.2 < Pr < 8.2) , Reynolds number $ ({0.5 \lt \textrm{Re} \lt 2.0}), $ (0.5 < Re < 2.0) , Chemical reaction parameter $ (0.1 \lt \textrm{Cr} \lt 0.7) $ (0.1 < Cr < 0.7) , Peclet number $ ({0.1 \lt \textrm{Pe} \lt 0.7}), $ (0.1 < Pe < 0.7) , Bio-convection Lewis number $ (1.0 \lt \textrm{Sb} \lt 1.6) $ (1.0 < Sb < 1.6) , Biot number $ (0.2 \lt \textrm{Bi} \lt 0.8) $ (0.2 < Bi < 0.8) , thermal relaxation parameter $ (0.5 \lt \gamma \lt 2.0) $ (0.5 < γ < 2.0) and Suction parameter $ ({0.1 \lt {V_0} \lt 0.7}) $ (0.1 < V 0 < 0.7) , are depicted through graphs. Moreover, the numerical estimates of local density number of microorganisms, heat and mass transfer rates for different parameters are specified in a tabular form. The calculations show that local skin friction coefficient, Sherwood number and local density of microorganism intensify with increasing values of both volume fraction parameters $ ({\phi 1})\textrm{ } $ (ϕ 1) and $ ({\phi 2}) $ (ϕ 2). Also, the density of microorganisms and profiles of concentration are elevated in the fluid region with rising values of Weissenberg number. Temperature of hybrid nanofluid deteriorates with increasing values of thermal relaxation parameter. [ABSTRACT FROM AUTHOR]

The effect of Cattaneo–Christov heat flux on hydromagnetic flow of non-Newtonian (Maxwell, Jeffrey and Oldroyd-B) fluids filled with Darcy–Forchheimer porous medium with thermal radiation, uneven heat source/sink and variable thermal conductivity is studied numerically. The mathematical problem is developed with the help of momentum, and energy equations using the suitable transformation variables. The numerical results for the transformed highly nonlinear ordinary differential equations are presented for Maxwell, Jeffrey and Oldroyd-B fluid cases. For numerical computations, an effective numerical solver namely bvp4c package is used. Effects of various controlling restrictions on the flow, and thermal fields are examined. Numerical computations for the friction factor and local Nusselt number are executed. [ABSTRACT FROM AUTHOR]

In the present exploration, entropy production on hydromagnetic pulsating flow of Au + SWCNT/blood and Au + MWCNT/blood-based Jeffrey hybrid nanofluid in a vertical porous channel with Cattaneo-Christov theory has been inspected. The impacts of Ohmic heating, viscous dissipation, and thermal radiation are considered. The transformation of the governing partial differential equations into a system of ordinary differential equations is made by applying the perturbation method and then numerically solved by the fourth-order Runge-Kutta method aided by bvp4c shooting technique built-in MATLAB software. The effects of various emerging parameters and variables on velocity, temperature, entropy generation, and the Bejan number are displayed through graphs. The consequences of physical parameters on heat transfer rate are prearranged in a table. This analysis demonstrates that the velocity of both hybrid nanofluids is intensified with an upsurge in the Grashof number, while it is decreasing by giving higher values in an applied magnetic field. The temperature of both hybrid nanofluids increases with an increment in the radiation parameter, and Eckert number. The entropy generation is an increasing function of Eckert number and radiation parameter. The heat transfer rate has a higher impact in the case of (Au + MWCNT/blood) hybrid nanofluid as compared to (Au + SWCNT/blood) hybrid nanofluid and mono nanofluid. [ABSTRACT FROM AUTHOR]

The thermal bioconvective investigation of magnetized Reiner-Rivlin nanofluid is the focus of research. The suspension of microorganisms is necessary to assess the stability of nanofluids and their consistent functioning. The heat transfer results are influenced by the radiated impact and the impacts of an external heating source. One might propose the use of the Cattaneo-Christov heat flux technique to simulate heat and mass transport difficulties. The convective boundary conditions are used for the analysis of the flow problem. The issue is modeled using a differential system. Incorporating dimensionless variables greatly simplifies the translation of the governing issue. The numerical simulation of the final system is performed using the shooting approach. The impact of settings on the thermal issue is evaluated and shown visually using graphs. Various uses of parameters in the thermal model have been presented. The heat transfer is found to increase because of the Reiner-Rivlin fluid parameter. The concentration profile decreases because of the concentration relaxation parameter. The profile of the microorganism decreases as the Peclet number increases, while the constant for Reiner-Rivlin fluid leads to increased observations. [ABSTRACT FROM AUTHOR]

This study investigates heat transfer rates in (AA7075-AA7072/Methanol) hybrid nanofluid flows, considering non-uniform heat sources and Cattaneo–Christov heat flux, with significant implications for aerospace engineering by enhancing thermal management in aircraft engines. The findings could revolutionize automotive cooling system efficiency, optimize heat dissipation in electronic devices, and advance the design of renewable energy systems such as concentrated solar power plants. The study aims to conduct a comparative analysis of (AA7075/Methanol) nanofluid and (AA7075-AA7072/Methanol) hybrid nanofluid flow, examining heat transfer rates, non-uniform heat sources, and Cattaneo–Christov heat flux theory around a stretching cylinder. Thermal radiation and the Biot number are also evaluated. Two different nanoparticles, AA7072 and AA7075, are used with methanol to create AA7075/Methanol nanofluid and AA7075-AA7072/Methanol hybrid nanofluid. The study compresses the resultant non-linear partial differential equation system and applies suitable similarity transformations to reduce the governing partial differential equations with boundary conditions to dimensionless form. The BVP4C shooting method in MATLAB is employed to numerically and graphically solve these dimensionless ordinary differential equations. The results indicate that higher curvature parameter values correlate with increased velocity and temperature distribution profiles. A rise in nanoparticle volume fraction reduces the radial velocity profile but increases the temperature profile. Temperature distribution profiles increase with higher thermal radiation parameter and Biot number values, while higher thermal relaxation parameter values decrease temperature. Additionally, thermal distribution profiles rise with increasing values of both the time-dependent heat source constant and space-dependent heat source parameter. [ABSTRACT FROM AUTHOR]

Artificial neural networks have revolutionized machine learning by providing exceptional capabilities for modeling complicated mechanisms and solving various challenges. Backpropagation is an important training technique in the field of artificial neural networks. However, this technique must be optimized when working with complicated fluid dynamics. This study analyzes the three-dimensional radiative flow of a tangent hyperbolic fluid driven by the Cattaneo-Christov flux system across a porous stretching sheet using ANN backpropagation enhanced by Bayesian Regularization approach. Heat and mass transfer analysis includes thermal radiation, chemical reactions and Cattaneo-Christov flux model. Porosity, radiation, chemical reaction rate, and ion slip effect are among the important physical characteristics that are modified to see how they affect fluid dynamics. Using MATLAB's BVP4C solver, the velocity, temperature, and concentration profiles that result from these model equations provide the training dataset for ANNs. The dataset is divided into 80 % for training, 10 % for testing, and 10 % for validation. Performance plots, regression graphs, and error histograms are used to analyze the performance of the LMT-based ANN and demonstrate its high accuracy and efficiency. With an R2 value of 1, the ANN produced a mean squared error of around 10⁻11. Fluid mobility drops as the magnetic parameter grows, while the thermal profile exhibits an increasing trend. Similarly, decreasing fluid velocity is the outcome of raising the porosity parameter. The study's conclusions have great potential for use in sectors that need sophisticated cooling and heating equipment.

Abstract In this article, the numerical solutions for the heat transfer flow of an upper-convected Maxwell fluid across an exponentially stretched sheet with a chemical reaction on the Cattaneo–Christov heat flux model have been investigated. Using similarity transformation, the controlling system of nonlinear partial differential equations was transformed into a system of ordinary differential equations. The resulting converted equations were solved numerically by a successive linearization method with the help of MATLAB software. A graphic representation was created to analyze the physical insights of the relevant flow characteristics. The findings were presented in the form of velocity, temperature, and concentration profiles. As the relaxation time parameter varied, the local Nusselt number increased. The thermal relaxation time was shown to have an inverse relationship with fluid temperature. Furthermore, the concentration boundary layer becomes thinner as the levels of the reaction rate parameter increase. The results of this model can be applicable in biological fluids and industrial situations. Excellent agreement exists between the analysis's findings and those of the previous studies.

The present study implements the incompressible smoothed particle hydrodynamics (ISPH) method with an artificial neural network (ANN) to simulate the impacts of Cattaneo-Christov heat flux on the double diffusion of a nanofluid inside a square cavity. The cavity contains a rotated wavy circular cylinder and four fins fixed on its borders. The rotational motion of an inner wavy cylinder interacting with a nanofluid flow is handled by the ISPH method. An adiabatic thermal/solutal condition is applied for the embedded wavy cylinder and the plane cavity's walls. The left wall is a source of the temperature and concentration, $ {T}_{h}\&{C}_{h} $, and the right wall with the four fins is maintained at a low temperature/concentration, $ {T}_{c}\&{C}_{c} $. The pertinent parameters are the Cattaneo-Christov heat flux parameter $ \left({0\le \delta }_{c}\le 0.001\right) $, the Dufour number $ \left(0\le Du\le 2\right) $, the nanoparticle parameter $ \left(0\le \phi \le 0.1\right) $, the Soret number $ \left(0\le Sr\le 2\right) $, the Hartmann number $ \left(0\le Ha\le 80\right) $, the Rayleigh number $ \left({10}^{3}\le Ra\le {10}^{5}\right) $, Fin's length $ \left({0.05\le L}_{Fin}\le 0.2\right) $, and the radius of a wavy circular cylinder $ \left(0.05\le {R}_{Cyld}\le 0.3\right) $. The results revealed that the maximum of a velocity field is reduced by $ 48.65\% $ as the $ {L}_{Fin} $ boosts from $ 0.05 $ to $ 0.2 $, and by $ 55.42\% $ according to an increase in the $ {R}_{Cyld} $ from $ 0.05 $ to $ 0.3 $. Adding a greater concentration of nanoparticles until 10% increases the viscosity of a nanofluid, which declines the velocity field by $ 36.52\%. $ The radius of a wavy circular cylinder and the length of four fins have significant roles in changing the strength of the temperature, the concentration, and the velocity field. Based on the available results of the ISPH method for $ \stackrel{-}{Nu} $ and $ \stackrel{-}{Sh} $, an ANN model is developed to predict these values. The ideal agreement between the prediction and target values of $ \stackrel{-}{Nu} $ and $ \stackrel{-}{Sh} $ indicates that the developed ANN model can forecast the $ \stackrel{-}{Nu} $ and $ \stackrel{-}{Sh} $ values with a remarkable accuracy.

In this article, the numerical solutions for the heat transfer flow of an upper-convected Maxwell fluid across an exponentially stretched sheet with a chemical reaction on the Cattaneo–Christov heat flux model have been investigated. Using similarity transformation, the controlling system of nonlinear partial differential equations was transformed into a system of ordinary differential equations. The resulting converted equations were solved numerically by a successive linearization method with the help of MATLAB software. A graphic representation was created to analyze the physical insights of the relevant flow characteristics. The findings were presented in the form of velocity, temperature, and concentration profiles. As the relaxation time parameter varied, the local Nusselt number increased. The thermal relaxation time was shown to have an inverse relationship with fluid temperature. Furthermore, the concentration boundary layer becomes thinner as the levels of the reaction rate parameter increase. The results of this model can be applicable in biological fluids and industrial situations. Excellent agreement exists between the analysis's findings and those of the previous studies. [ABSTRACT FROM AUTHOR]

This study examines the flow of the ternary nanofluid over a rotating stretchable cylinder with a torsional motion under the influence of a Cattaneo–Christov heat flux. In order to accomplish the goals of this simulation, a ternary hybrid nanofluid (THNF) that is based on water and incorporates nanoparticles with three distinct morphologies is considered. For assessing the colloidal mixture of spherical, cylindrical, and platelet shaped nanoparticles, the necessary models are used. By using appropriate similarity transformations, the modeled equations are reduced to a set of ordinary differential equations (ODEs). These ODEs are then solved using the finite element approach. The numerical integration's validity and reliability, as well as the newly obtained results, were thoroughly analyzed. Results reveal that the larger values of Reynolds number enhance the system's inertial force, which resists the liquid accelerating force and declines both velocities and heat transport. The rise in values of volume fractions and Reynolds number declines the skin friction coefficients along swirling and radial directions. The increase in values of both the thermal relaxation time parameter and Reynolds number improves the rate of heat transport. [ABSTRACT FROM AUTHOR]

This research communication explores the Darcy - Forchheimer flow of a chemically reacting non-Newtonian Maxwell fluid over a stretching sheet, incorporating the Cattaneo – Christov heat flux under a convective boundary condition. The fluid flow is described by a set of partial differential equations, which are subsequently transformed into a system of nonlinear ordinary differential equations. To solve these equations numerically, the BVP4C Method was employed after appropriately defining non dimensional variables and implementing similarity transformations. The impacts of diverse active parameters such as Deborah parameter, Darcy-Forchheimer parameter, magnetic parameter, Biot number, and porous parameter are examined on the velocity, temperature, and concentration profiles. In addition, the value of the Skin friction, Nusselt number is calculated and presented through tabular forms. [ABSTRACT FROM AUTHOR]

The present study implements the incompressible smoothed particle hydrodynamics (ISPH) method with an artificial neural network (ANN) to simulate the impacts of Cattaneo-Christov heat flux on the double diffusion of a nanofluid inside a square cavity. The cavity contains a rotated wavy circular cylinder and four fins fixed on its borders. The rotational motion of an inner wavy cylinder interacting with a nanofluid flow is handled by the ISPH method. An adiabatic thermal/solutal condition is applied for the embedded wavy cylinder and the plane cavity’s walls. The left wall is a source of the temperature and concentration, Th & Ch, and the right wall with the four fins is maintained at a low temperature/concentration, Tc & Cc. The pertinent parameters are the Cattaneo-Christov heat flux parameter (0 ≤ δc ≤ 0.001), the Dufour number (0 ≤ Du ≤ 2), the nanoparticle parameter (0 ≤ ∅ ≤ 0.1), the Soret number (0 ≤ Sr ≤ 2), the Hartmann number (0 ≤ Ha ≤ 80), the Rayleigh number (10³ ≤ Ra ≤ 105), Fin’s length (0.05 ≤ LFin ≤ 0.2), and the radius of a wavy circular cylinder (0.05 ≤ RCyld ≤ 0.3). The results revealed that the maximum of a velocity field is reduced by 48.65% as the LFin boosts from 0.05 to 0.2, and by 55.42% according to an increase in the RCyld from 0.05 to 0.3. Adding a greater concentration of nanoparticles until 10% increases the viscosity of a nanofluid, which declines the velocity field by 36.52%. The radius of a wavy circular cylinder and the length of four fins have significant roles in changing the strength of the temperature, the concentration, and the velocity field. Based on the available results of the ISPH method for Nu and Sh, an ANN model is developed to predict these values. The ideal agreement between the prediction and target values of Nu and Sh indicates that the developed ANN model can forecast the Nu and Sh values with a remarkable accuracy. [ABSTRACT FROM AUTHOR]

The heterogeneous fluid model is expressed for the nanofluid flow to study the significance of the Fourier’s and Fick’s laws. The magnetohydrodynamics couple-stress bioconvective nanofluid flow is considered across an extending surface with the effect of exponential heat source/sink and stratified boundary conditions. The solid nanoparticulates and concentrations of motile microorganisms are added to the nonlinear system of differential equations conveying the non-Newtonian nanoliquid flow model. Moreover, the combined effect of the heat flux and thermal radiation is also evaluated. The similarity transformations are employed to transfigure the system of partial differential equations into the lowest order of ordinary differential equations. The Artificial Neural Network Levenberg Marquardt Back-propagation optimization algorithm is employed to solve these equations. To authenticate the outcomes, the dataset is formed using the MATLAB package “bvp4c”. The dataset is created for diverse circumstances of flow factors, as well as validation and testing of the Artificial Neural Network. The accuracy of the model is estimated through numerous statistical tools (histogram, curve fitting, regression measures, and performance plots). The outcomes are presented through the table and figures. It has been noticed that the couple-stress nanofluid flow declines with the influence of magnetic field and mixed convection. The couple-stress nanofluid temperature augments with the enhancement of the thermophoresis effect, buoyancy ratio factor, Rayleigh number, and thermal radiation. Moreover, the concentration curve lessens under the impact of the Lewis number while enriched with the outcome of the concentration stratification parameter. The absolute error of reference and targeted date is attained within 10−3–10−6 that proves the exceptional precision of the results. [ABSTRACT FROM AUTHOR]

Activation energy is the fundamental unit of energy required to initiate chemical reactions. Some instances of initiation energy use include liquid dispersions bite dust fashioning, polymer ejection, food handling, and paper manufacturing. In view of this, the present study investigates the impact of steady, incompressible magnetized Casson–Maxwell non-Newtonian nanofluid between two stationary porous disks. The fluid movement is created by uniform injection in the direction of the axial of stationary disks. It is noticed that the thermal conductivity of the fluid varies with varying temperature. By using Buongiorno nanofluid concept the Cattaneo–Christov thermal expression is implemented. Along with this, activation energy is considered. By introducing the suitable similarity variables, the fluid model is reduced in terms of ordinary differential equations and numerical solutions are generated by using inbuild bvp4c function in MATLAB. The various dimensionless parameters impact on velocity, temperature, and concentration are presented graphically. A numerical table is presented to show the variation of local-Nusselt and -Sherwood numbers on various values of different parameters. The study reveals that improvement in Casson parameter will incline the fluid velocity, but an opposite trend is seen in the case of a magnetic field. A rise in the Brownian motion and thermophoresis parameter will enhance both temperature profiles. Improved values of activation energy will increase the concentration. The rate of heat transfer is observed more in the case of the upper disk than the lower disk. [ABSTRACT FROM AUTHOR]

This study offers the impacts of MHD Jeffery fluid research on a stretching cylinder. The Cattaneo–Christov heat model is acquired instead of the Fourier law of heat conduction to construct the energy equation. The order analysis of a fluid model is performed using the boundary layer theory. On differential equations, appropriate similarity transformations are used to attain the differential equations. The following nonlinear equations were then mathematically solved utilising the shooting method. The visual inspection of the conclusions of the velocity, thermal and concentration profiles is completed for several important thermophysical parameters. For numerous thermos physical variables, the numerical variation in the valuations of the mass transport rate, coefficient of skin friction and heat rate transfer has been assessed and provided in a table. The main conclusions of the study show that temperature, concentration distribution and flow speed all decrease as the curvature parameter increases. It has also been deduced in this investigation that the higher values of the Lewis number higher the mass transfer rate and lower the heat flux at the surface of the cylinder. These results exhibit a more favourable agreement across all findings when compared to previous findings. [ABSTRACT FROM AUTHOR]

AbstractThis research scrutinizes the impact of the Thompson and Troian slip effect on a two-dimensional flow of ternary nanoliquid induced by an extending sheet near a stagnation point. Nanoparticles Iron oxide (Fe2O3), Nickle Zinc ferrite (NiZnFe2O4), and Magnesium zinc iron oxide (MnZnFe2O4) are dispersed in Ethylene glycol (C2H6O2) to establish ternary nanofluid. The induced magnetic field influences the flow, and the analysis of heat and mass transfers takes into account the Cattaneo–Christov (C–C) heat flux with homogenous–heterogeneous (H–H) reactions, respectively. To expedite the reaction, a surface-catalyzed process is introduced to efficiently control both (H–H) reactions within a reduced time frame. Utilizing the Tiwari and Das framework, the fluid flow characteristics are elucidated. Appropriate transformations are applied to derive ordinary differential equations (ODEs), which are then numerically deciphered via the bvp4c scheme. Graphs are portrayed to highlight the consequence of non-dimension quantities on the flow and temperature profiles. The surface drag coefficient and heat flux rate are also assessed and summarized. Outcomes revealed that for large estimates of the velocity slip parameter, the surface drag coefficient is enhanced while the heat flux rate is reduced. It is also interesting to note that because of the high estimations of ferromagnetic nanoparticles, the rate of heat transfer is elevated significantly. The validation of the proposed model is also included. [ABSTRACT FROM AUTHOR]

Hybrid nanomaterials significantly enhance thermal systems through improved thermal conductivity, efficient energy storage, and customized thermomechanical properties. Due to their superior thermophysical characteristics, binary/ternary hybrid nanofluids are crucial in fields such as industry, biomedicine, transportation, and pharmaceuticals. This study examines the hydromagnetic flows and heat transfer properties of binary (CuO+Fe3O4/sodium alginate) and ternary (CuO+Fe3O4+MoS2/sodium alginate) hybrid Maxwell nanofluids over a radially stretching rotating disk. The governing flow equations incorporate Cattaneo–Christov heat flux, mixed convection, velocity and thermal slips, nonlinear radiation, viscous dissipation, and Joule heating in a Darcy–Forchheimer porous medium. These axisymmetric partial differential equations are transformed into ordinary differential equations using similarity variables, and the spectral quasilinearization method (SQLM) is applied for numerical solutions. Results reveal the effects of relevant parameters on velocity, temperature, skin friction, and heat transfer rates. Novelty lies in the comparative analysis of flow behaviors and entropy production rates between binary and ternary hybrid Maxwell nanofluids. When the heat source is included, the Nusselt number increases by 12.9% for ternary nanofluids and 16.07% for binary nanofluids as the thermal relaxation number increases from 0.5 to 1.5. Furthermore, the ternary hybrid nanofluid shows greater resistance to Lorentz and porous medium forces and exhibits a higher temperature distribution and better thermal management capabilities compared to the binary hybrid nanofluid.

Aim of the present study: It must study liquid flow over surfaces above the earth because its surface rotation stimulates liquids heated amid the sun. Consequently, the Coriolis impact force is investigated on Casson convective flow fluid with Cattaneo-Christov heat flux over the rotating paraboloid upper surface. Significance of the present study: The simultaneous effects of the Lorentz force and Coriolis force occurring due to MHD flow contribute significantly to solar wind, sunspots, and more physical natural phenomena. As a result, Navier-Stokes equations governing the flow are derived and incorporated with the appropriate body forces. Methodology: PDEs are converted to ODEs by identical variants/variables that make the governing equations non-dimensional. The results of this problem are represented graphically using BVP4C. Conclusion: In the present study, some of the significant results are: While both ANN and ANFIS-PSO could accurately forecast the truth values, we found that ANFIS-PSO is more accurate; as the temperature rises, β and Gr consider and resist heat transmission with K and Ec, While Ec and Nt increase the concentration, K, β, Gr, Nb, and Sc impede mass transfer. table 3 compares the current study's findings with those of the previous research; the results are nearly identical, demonstrating the precision and accuracy of the current model.

The primary heat source from the sunlight is solar energy (SE), which is used in photovoltaic (PV) panels, solar power plates, PV, streetlights, and solar-based hybrid nanocomposites. Currently, research is focused on analyzing and improving the efficiency of SE, particularly for powering aircraft, by combining solar power with nanotechnology advancements. As such, this study focuses on examining concentrated solar power and proposes a method to improve the performance of solar airplanes by employing nanotechnology. Furthermore, the work is based on the investigation of the flow rate, thermal distribution, and entropy generation of the magnetized tangent hyperbolic hybrid nanofluid (HNF) along the interior parabolic solar trough collector of an aircraft wing. This work utilizes similarity variables to simplify the partial derivative model into ordinary differential equations. These equations are then solved using the Galerkin weighted residual approach with the help of MATHEMATICA 11.3 software. From the obtained outcomes, it is reflected that the HNFs have high thermal conductivity than the NF. Intensification of Weissenberg number improves the performance of airplane wings subjected to heat transmission. Therefore, this research contributes to improved thermal management in advanced nanotechnology and solar aircraft.

The heat and mass transportation for nanofluid across a swirling cylinder under the actions of magnetic effects and Cattaneo–Christov heat flux is reported in the current analysis. The objective of this study is to examine the energy and mass transmissions through hybrid nanofluid under the influence of heat source/sink and reactive species. The hybrid nanoliquid has been prepared by the dispersion of silver (Ag) and gold (Au) nanoparticles (NPs) in the base fluid ethylene glycol (C2H6O2). The flow phenomena are expressed in the form of nonlinear partial differential equations and are converted to a nondimensional form, by employing the similarity substitution. For the computational estimation of the problem, the parametric continuation method is employed. The demonstration of velocity, mass, and energy outlines versus distinct physical factors is exposed in the form of figures. It has been perceived that the axial and swirling velocity outline drops with the influence of the Reynolds number, magnetic effect, and the insertion of Au and Ag NPs in C2H6O2. Furthermore, the hybrid nanofluid energy curve declines with the effect of the Reynolds number, thermal relaxation factor, and the volume friction of NPs.

This paper concentrates on the examination of mass and heat transfer on a time-dependent hydromagnetic flow of Carreau-nanofluid on a radially stretchable surface. The heat equation is modeled by the incorporation of modified heat flux recognized as the Cattaneo–Christov heat flux theory along with the Joule heating. Also, for nanofluid flow, the Buongiornos model is employed to investigate the impacts of thermophoresis parameter and Brownian motion. In addition, a first-order chemical reaction is also assumed in the nanoparticle concentration equation. Flow phenomena are developed mathematically by considering momentum, nanoparticle concentration, and energy equations by utilizing conveniently transformed variables. Numerical solutions of the obtained differential equation are computed by employing the shooting method for thermal relaxation and chemical reaction parameters as shear thinning and shear thickening fluids. The consequences of various physical parameters on the flow, energy, and nanoparticle concentration are investigated and discussed via graphs and tables. Also, the variation in wall heat flux and wall mass flux are computed numerically. The present analysis admits that the temperature and the associated thermal boundary layer thickness are the growing functions of thermal relaxation parameters for both shear thickening and shear-thinning fluids. The concentration of the nanoparticle is also decreasing the function of the chemical reaction parameter. [ABSTRACT FROM AUTHOR]

Energy utilization is a significant aspect of the manufacturing industrial processes, and inefficient transferring of heat is one of the disadvantages which can affect the quality measures of end product. Therefore, by controlling the heat transferring rate, the efficiency of manufacturing processes can be improved. Thus, the variable thermal relaxation time factor in the theory of Cattaneo-Christov is main concern of this analysis. The non-isothermal flow by means of a porous medium is modeled and analyzed for a viscous fluid. The fluid deformation is discussed under stretching mechanism. A study is also executed to interrogate the heat transfer features under the heat flux model of Cattaneo-Christov. Thermal relaxation time is also considered which is determined by temperature. The aspect of thermal stratification is also implemented to see the modifications in temperature. The flow and energy equations are reduced by appropriate variables. The reduced constitutive flow equations are then computed using an analytical convergent technique. The significant impacts of the numerous parameters on the flow field and heat transport features are evaluated in detail through various plots. Skin friction coefficient is evaluated mathematically. Results found that the temperature significantly decreases with increased stratification effects. For larger thermal relaxation time parameter, the temperature function shows increasing behavior. [ABSTRACT FROM AUTHOR]

AbstractThe study of flow of blood through the blood vessels carries nanoparticles which opens new ways in the research. This study explores one such flow of trihybrid nanoparticles suspended in blood over a curved stretching surface which undergoes the Darcy-Forchheimer porosity model. The analysis employs Cattaneo-Christov heat flux model along with chemical reaction, linear heat source allowing the surface to slip with heat and mass convection. The trihybrid nanofluids consist of a mixture of titanium dioxide, iron oxide, and silica nanoparticles mixed with base fluid (blood) to generate TiO2-Fe3O4-SiO2/blood hybrid nanofluids. Runge-Kutta-Fehlberg 4th–5th order technique, a robust numerical technique, was employed to obtain mathematical solutions. Throughout the numerical process, all parameters, except those under examination, were kept at their default values. Additionally, various plots were generated based on numerical results to illustrate the obtained data. The findings indicate that an increase in the Forchheimer number and porosity results in a reduction in the velocity profile. Furthermore, an increase in the radiation parameter and thermal Biot number leads to an increase in the temperature profile, while the temperature profile decreases with an increase in the thermal relaxation parameter. Additionally, an increase in the chemical reaction parameter and concentration Biot number results in an increase in the concentration profile. Moreover, higher Brinkman and Prandtl numbers enhance the Nusselt number. [ABSTRACT FROM AUTHOR]

This entire study aims to prove the impacts of non-linear thermal radiation and entropy generation on Casson and Williamson hybrid nanofluids through a comparative analysis of the magnetohydrodynamic flow in a porous, curved stretching sheet with the Cattaneo-Christov heat flux model. We used hybrid nanofluid blood based on gold (Au) and Aluminium oxide (Al2O3) nanoparticles. The governing non-linear coupled Partial Differential Equation (PDE) are transformed into non-linear coupled Ordinary Differential Equations (ODE) using the Maple software solver using the Homotopy Perturbation Method. The Homotopy Perturbation Method (HPM) results are compared with the Numerical Method (NM) results, and HPM gives reliable results. The results are provided through the table and graphical representations for several parameters such as velocity, temperature, entropy production, Bejan number, Nusselt number, and skin friction respectively. The velocity profile decreases for Williamson and Casson hybrid nanofluids over a curved stretching sheet while the magnetic field parameters increase. Due to magnetic force associated with Lorentz force, which is known as resistive force, velocity decreases. The Magnetic field on the entropy generation for Casson and Williamson hybrid nanofluids. As the Magnetic field increases, the entropy generation increases for Williamson and Casson hybrid nanofluids. This problem is used in various biomedical situations, including resistive impedance to flow, arteria wall shear stress, and heating impact owing to radiation throughout the surgical process by altering the strength of the applied magnetic field. [ABSTRACT FROM AUTHOR]

After applying a magnetic field, the behavior of the partly ionized liquids is completely different from that of the ordinary fluids. In this study, we concentrated on the Cattaneo–Christov heat flux model-based three-dimensional partly ionized bio-convective flow of a second-order fluid on a bidirectional permeable stretching surface. The development of the thermal and solutal flow models takes into account the impacts of non-uniform sources and sinks, Ohmic viscous dissipation, and chemical reactions. In addition, the surface boundary effects of electron and ion collisions with convective boundary conditions are seen. The mathematical flow model is transformed appropriately to create an ordinary differential equations, which is then numerically solved with MATLAB's BVP4C approach. To demonstrate the physical relevance of the flow field along various developing parameters, graphical and tabular results are created. It is noteworthy to note that while fluid temperature decreases with stronger values of the second-order fluid parameter, fluid velocity improves in both directions. In addition, it is shown that raising the thermal and concentration relaxation parameters, respectively, causes a drop in the fluid temperature and nanoparticle concentration. [ABSTRACT FROM AUTHOR]

ATSS model for magnetohydrodynamic Darcy-Forchheimer radiative ternary nanoliquid flow by curved stretched sheet is constructed. Ternary nanoliquid consists of three different nanoparticles (gold (Au), zinc oxide (ZnO) and multi-walled carbon nanotube (MWCNT)) in ordinary liquid (Carboxymethylcellulose water (CMC-H2O)). Cattaneo-Christov heat flux and convective condition are discussed. Thermal equation has Ohmic heating, heat generation/absorption and radiation. Entropy production along with cubic autocatalysis chemical reaction is discussed. The obtained differential nonlinear systems are numerically computed by using ND-solve method. Graphical discussion for liquid flow, entropy rate and temperature via influential parameters for nanomaterial (Au/CMC-H2O), hybrid nanomaterial (Au+ZnO/CMC-H2O) and ternary nanomaterial (Au+ZnO+MWCNT/CMC-H2O) is organized. Computational outcomes for coefficient of skin friction and Nusselt number are studied. Opposite trend of velocity and skin friction for curvature is noticed. Velocity reduces against higher magnetic field. Augmentation for temperature against Eckert and thermal Biot numbers is noticed. Entropy production enhancement for radiation and diffusion parameter is observed. Thermal transport rate for radiation and thermal relaxation time has an increasing effect.

The non-Newtonian liquid scheme is created to address the limitations of the classical (Newtonian) scheme in terms of accurately reflecting real-world fluid flow behavior in industrial applications and improving operational efficiency. The Reiner–Philippoff model, one of the many extant models, modeling non-Newtonian fluids, is of concern because it only captures a few features in some circumstances. Thus, this study aims to investigate the theoretical aspects of Cattaneo–Christov for heat diffusion fusion of Reiner–Philippoff liquid stream in the presence of Darcy–Forchheimer media. Furthermore, the procedure of heat transport is taken out in the occurrence of nonlinear heat radiative, viscous dissipation and Ohmic heating. The partial derivatives of nonlinear differential equations are changed into similarity equations of a certain form by using appropriate similarity transformations. Furthermore, the Runge–Kutta–Fehlberg method with shooting approach is utilized to solve the dimensionless model. The influence of pertinent fluid flow parameters is illustrated graphically. The further engineering curiosity of a local Nusselt number is illustrated and analyzed. It is found that velocity curve is boosted with the augmenting scales of Reiner–Philippoff liquid parameter and Forchheimer number. Further, it is analyzed that increasing the thermal relaxation parameter and Eckert number reduces the heat transport rate at the surface. [ABSTRACT FROM AUTHOR]