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This study is to illustrate the thermometric exchange of Casson fluid’s double diffusive nonlinear radiative heat flux over vertical plate associated with convective boundary conditions, incorporating artificial intelligence (AI)-based neural network computation technique. The AI analysis provides enhanced and optimized results with predictive modeling. The analysis utilizes a dataset generated through Mathematica environment and then embedded the filtered matrix dataset in MATLAB employs AI analysis using the Neural Auto Regressive Exogenous (NARX) method for optimized solutions. Levenberg–Marquard algorithm is used to train neural network. The model’s importance and applications span nuclear reactors, aerodynamics, hydrodynamics, transportation and radiating processes of energy transfer. The physical problem is governed by PDEs that is transformed into a set of ODEs by using similarity transformation. The flow is analyzed against the variation in significant influencing parameter like Prandtl number (Pr), velocity ratio (λ), convective coefficient (γ), Rayleigh number (Ra), buoyancy ratio parameter (N), radiation parameter (R) and Casson fluid parameter (β). Findings of this paper are significant for various industrial, engineering and research-based activities. [ABSTRACT FROM AUTHOR]

Ternary nanofluids have been an interesting field for academics and researchers in the modern technological era because of their advanced thermophysical properties and the desire to increase heat transfer rates. Furthermore, the innovative, sophisticated artificial neural network strategy with the Levenberg–Marquardt backpropagation technique (LMBPT) is proposed for research on heat and mass transport over non-Newtonian ternary Casson fluid on a radially extending surface with magnetic field and convective boundary conditions. The main objective of the current research is to conduct a comparative study of numerical solutions of the ternary nanofluid model of heat/mass transport utilizing the artificial neural network (ANN) together with the (LMBPT). To accurately represent complex patterns, neural networks modify their parameters flexibly, resulting in more accurate predictions and greater generalization with numerical outcomes. The model equations were reduced from partial to ODEs through applying appropriate similarity variables. The shooting technique and the byp-4c algorithm were then used to analyze the numerical data. The current study reveals that a rise in the Casson parameter diminishes the fluid velocity but an opposite nature is seen in thermal distribution for rising behavior of heat source/sink and Biot number, and the concentration profile tends to deteriorate when the mass transfer is elevated. Furthermore, the resulting values of the significant engineering coefficients are numerically analyzed and tabulated. [ABSTRACT FROM AUTHOR]

In this paper, the self-propelled movement on gyrotactic swimming microorganisms into this generalized slip flow by nanoliquid over the stretching cylinder with strong magnetic field is discussed. Constant wall temperature was pretended as well as the Nield conditions of boundary. The intuitive non-Newtonian particulate suspension was included into applying Casson fluid by the base liquid and nanoparticles. This formation on the bio-mathematical model gives the boundary value problem by the nonlinear partial differential equations. Primly, modeled numerical system was converted to nondimensional against this help on acceptable scaling variables and the bvp4c technique was used to acquire the mathematical outcomes on the governing system. This graphical description by significant parameters and their physical performance was widely studied. The Prandtl number has the maximum contribution (112.595%) along the selected physical parameters, whereas the Brownian motion has the least (0.00165%) heat transfer rate. Anyhow, Casson fluid was established for much helpful suspension of this method on fabrication and coatings, etc. Therefore, this magnetic field performs like the resistive force of that fluid motion, and higher energy was enlarged into the structure exhibiting strong thermal radiation. [ABSTRACT FROM AUTHOR]

This paper investigates the effects of radiation, internal heat source and magnetohydrodynamics (MHD) on the mixed convective boundary layer flow of a Casson nanofluid within a porous medium that is saturated and subject to an exponentially stretching sheet. The nanofluid model incorporates Brownian motion and thermophoresis, and the Darcy model is employed for the porous medium. By applying an appropriate similarity transformation, the nonlinear governing boundary layer equations are converted into a set of nonlinear coupled ordinary differential equations. These equations are then solved numerically using the Hermite wavelet method, with simulations conducted through the MATHEMATICA programming language. The analysis covers various aspects including temperature distribution, velocity, solute concentration and several engineering parameters such as skin friction coefficients, the Nusselt number (rate of heat transfer) and the Sherwood number (rate of mass transfer), all evaluated based on dimensionless physical parameters. The results indicate that elevated radiation intensifies temperatures and leads to thicker thermal boundary layers. As the Casson parameter increases, both the velocity and the momentum boundary layer become narrower. Additionally, a more pronounced chemical reaction rate reduces the thickness of the solutal boundary layer. The accuracy and reliability of the numerical Hermite wavelet method are validated through a comparative analysis with previous studies, demonstrating excellent concordance and confirming the robustness of the computational approach. [ABSTRACT FROM AUTHOR]

The current paper deals with viscous dissipation effects in a permeable (or porous) channel filled with non‐Newtonian Casson fluid by considering the local thermal non‐equilibrium (LTNE) model. The dependency of the effective thermal conductivities of the solid and fluid phases on the respective temperatures has been studied along with the spatially varying Biot number. The Brinkman number Br, Casson fluid parameter γ, thermal conductivity variation parameter δ, porosity ϵ, Darcy number Da, and the ratio of fluid and solid phase thermal conductivities kr=kfks are the main governing parameters. The Darcy–Brinkman model is employed to govern the fluid flow in permeable media and the velocity profile has been obtained analytically. Moreover, the energy equations for both phases along with suitable boundary conditions are derived and solved with the fourth order boundary value solver. The findings of the current study depict that the Nusselt number increases with the increment in Casson fluid parameter and decreases with the increment in Brinkman number and thermal conductivity variation parameter. Overall, the heat transmission between the solid and fluid phases increases with the decrement in Brinkman number and thermal conductivity variation parameter. On the other hand, the heat transmission between both the phases magnifies by increasing the value of Casson fluid parameter. [ABSTRACT FROM AUTHOR]

Magnetohydrodynamics (MHD) have numerous engineering and biomedical applications such as sensors, MHD pumps, magnetic medications, MRI, cancer therapy, astronomy, cosmology, earthquakes, and cardiovascular devices. In view of these applications and current developments, we investigate the magnetohydrodynamic MHD electro-osmotic flow of Casson nanofluid during peristaltic movement in a non-uniform porous asymmetric channel. The effect of thermal radiation, heat source, and Hall current on the Casson fluid peristaltic pumping in a porous medium is taken into consideration. The effect of chemical reactions is also considered. The mass, momentum, energy, and concentration equations were constructed using the proper transformations and dimensionless variables to make them easier for non-Newtonian fluids. A lubricating strategy is used to make the system less complicated. The Boltzmann distribution of electric potential over an electric double layer is studied using the Debye–Huckel approximation. The temperature and concentration equations are addressed using the homotopy perturbation method (HPM), while the exact solution is determined for the velocity field. The study examines the performance of velocity, pressure rise, temperature, concentration, streamlines, Nusselt, and Sherwood numbers for the involved parameters using graphical illustrations and tables. Asymmetric channels exhibit varying behavior, with velocity declining near the left wall and accelerating towards the right wall while enhancing the Casson fluid parameter. The pumping rate boosts in the retrograde region due to the evolution of the permeability parameter value, while it declines in the augment region. The temperature profile optimizes as the value of the heat source parameter gets higher. The concentration profile significantly falls as the chemical reaction parameter rises. The size of the trapped bolus strengthens with a spike in the parameter for the Casson fluid. [ABSTRACT FROM AUTHOR]

This article presents the theoretical analysis of the nonlinear behavior of the blood flow through an angled arterial segment with overlapping stenosis. A mathematically created time-variant stenosis emerges from the formation of arterial narrowing brought on by atheroma. An elastic cylindrical tube with a moving wall is used to represent the artery, and the Casson liquid is used to simulate blood that flows through it. The nonlinear elements that arise in the equations, govern blood flow are taken into account. The impact of the pulsatile pressure gradient that caused by the regular heartbeat on the flow process in the stenosed artery is demonstrated mathematically. By employing the boundary conditions, the present analytical technique can easily compute the velocity profiles, wall shear stress, and flow resistivity. To carry out a systematic quantitative study, the desired quantities are numerically computed. The results are graphically presented in the discussion section. They provide an overview of how the degree of stenosis and the malleability of the artery wall influence blood flow abnormalities. The application of the current model is adequately justified by many significant conclusions. [ABSTRACT FROM AUTHOR]

The study investigates the heat and mass transfer of mixed peristaltic Casson fluid flow through a porous medium in the presence of electroosmosis. It uses the lubrication LWL-LRN analytical technique to transform flow-control equations into ordinary differential equations. The equation is simplified using a numerical solver, bvp4c, in MATLAB software. The study analyses the behaviour of momentum, thermal, solutal, and nanoparticle concentration using parameters such as the magnetic field parameter, porous, electroosmotic, Prandtl, thermal Grashof number, and solutal concentration. Comparing this work with the existing investigation reveals a high level of concordance regarding the impact of thermophoresis and Brownian variables on momentum fields. The study's novelty is the double-diffusive effects of Casson fluid, which provides a more accurate characterisation of its flow behaviour with convective boundary conditions over an inclined surface. Such observations are useful in real-life applications to capture the shear and stress-thinning properties and flow of synovial fluid in joints, as well as to understand blood flow in several physiological conditions. [ABSTRACT FROM AUTHOR]

In the present investigation, the radiative MHD flow of an incompressible viscous electrically conducting non-Newtonian Casson hybrid nanofluidover an exponentially accelerated vertical porous surface has been considered. Under the influence of slip velocity in a rotating frame, it takes Hall and ion slip impacts into account. Water and ethylene glycol mixture is considered a base Casson fluid. A steady uniform magnetic field is applied under the postulation of a low magnetic Reynolds number. The ramped temperature and time-altering concentration at the surface are considered. First-order consistent chemical reaction and heat absorption are also regarded. Silver and Titania nanoparticles are disseminated in base fluid water and ethylene glycol combination should be formed by a hybrid nanofluid. The Laplace transformation technique is employed on the non-dimensional governing equations to ensure closed-form analytical solutions. The graphical representations scrutinize the effects of physical parameters on the significant flow characteristics. The expression for non-dimensional shear stress, heat transfer rate and mass transfer are also evaluated. They are tabulated with different variations in implanted parameters. For uniform and ramped wall temperatures, the resultant velocity grows by an increase in Hall and ion slip parameters. The resultant velocity increases by an increase in volume fractions of nanoparticles with uniform wall temperature, and a reverse effect is observed with ramped wall temperature. The temperature of Casson hybrid Ag-TiO2/WEG nanofluid is relatively superior to that of Casson Ag-WEG nanofluid. Species concentration of Casson hybrid Ag-TiO2/WEG nanofluid decreases with an increase in Schmidt number and chemical reaction parameters. The heat absorption increases the Nusselt number near the surface, while Ag and TiO2 nanoparticle volume fractions tend to lessen it. [ABSTRACT FROM AUTHOR]

The main objective of this work is to investigate the convective flow of three hybrid nanoparticles with different base fluids on a spinning down pointed vertical cone in the presence of magnetic field along with prescribed surface heat flux and also analyzed the behavior on non-Newtonian profiles by using Casson model. The governing equations are transformed into nonlinear ordinary differential equations and then solved numerically using the fourth-order Runge–Kutta method with shooting technique. The effects of various physical parameters are examined graphically. Numerical values of Skin friction coefficient and Nusselt number are given in tabular form. From the results, one can conclude that tangential and swirl velocity profile gets detracted when its magnetic parameter hikes in the three hybrid nanofluids. [ABSTRACT FROM AUTHOR]

The energy storage features on natural convection in Casson fluids are investigated in this work using the finite element method. By measuring cylinders and wavy surfaces, we may examine flow patterns and the effectiveness of heat transmission systems. We study the variation of the mass and heat transfer rates as a function of the cylinder geometry. To approximately determine velocities and temperatures, the Ladyzhenskaya-Babuška—Brezzi (LBB)-stable element is employed. Following this discretization, the resulting discrete nonlinear system is linearized using Newton's method and subsequently solved using PARDISO. Fractional applications in Casson fluid analysis reveal insights into energy storage effects, employing finite element methods to explore flow patterns, heat transmission efficiency, and geometric variations while observing the impact of parameters such as Rayleigh, Hartmann, and Lewis numbers on fluid behavior and thermal properties. The preceding research has verified the accuracy of the numerical results. According to the results, concentration gradients and other modifications to liquids become more noticeable as the Rayleigh number grows. Convective heat transmission is reduced as the Ha is raised. When the Le grows, the deformation Nu avg and S h avg also increase. Reducing the beta makes the isotherms more stable and less affected by the motion of the fluid. [ABSTRACT FROM AUTHOR]

The magnetothermoconvective instability of blood in the presence of gold and iron oxide nanoparticles has an important role in the medical field for efficient and targeted drug delivery. In the present work, the Casson fluid model is incorporated to study the starting of convection current in the blood due to the presence of Au–Fe3O4 nanoparticles. The fluid layer is assumed to be internally heated, due to the plausibility of chemical reaction in blood and heat production ability of gold nanoparticles. Normal mode analysis is done and the resulting eigenvalue problem has been solved using Chebyshev spectral method. The effect of Lorentz force, nanoparticle volume fraction, spherical size of nanoparticles, and heat source parameter on the instability of fluidic system has been depicted graphically. The strengthening of Lorentz forces has a stabilizing impact on convection current whereas the heat source parameter, the diameter of the nanoparticle, and the Casson parameter have destabilizing effects. [ABSTRACT FROM AUTHOR]

We are examining a mathematical model of second-grade Casson fluid flow over a Riga surface. This analysis takes into account the effects of heat generation on a second-grade Casson fluid. Additionally, we have discussed the impacts of Soret and Dufour in the presence of thermal radiation. The study also includes an analysis of the influences of thermal and concentration slip. By considering these factors in the fluid flow, we have constructed a set of partial differential equations. Furthermore, these differential equations have been transformed into dimensionless ordinary differential equations. We have presented the influences of relevant parameters through tables and graphs. Velocity curve reveals declining behavior due to larger values of magnetic field factor. A high magnetic field coefficient means a strong magnetic field. As a result, the force acting on the charged particle increases, causing it to slow down or change direction. This change in force can cause the particle's velocity to decrease. [ABSTRACT FROM AUTHOR]

The designation of this research is to scrutinize the influence of convective nanofluids over a three-dimensional exponential surface with chemical reactive species in a free stream fluid flow by following Buongiorno's model. The continuity, momentum, energy, concentration and motile microorganism density partial differential equations that make up the physical governing equation problems are simultaneously transformed into ordinary differential equations system. By using MATLAB programming, the RKF approach has been followed in order to implement the shooting technique to solve this system that explores how changing fluid parameters affect the profile of physical quantities of interest. A parametric analysis has been done in the current study. The effects of fluid parameters such as chemical reaction, Brownian motion, free stream velocity, Lewis number, thermophoresis, and Prandtl number on concentration, temperature, and velocity profiles are graphically represented. Moreover, Contour plots are also drawn against computational fluid parameters to get desired results. Furthermore, calculated results are correlated with already existing outcomes along with residual error. It is inferred that; thermal and concentration fields increase for higher thermal and concentration Biot numbers serially. Additionally, it is found that skin friction coefficient declines with inclination in thermophoresis Nt (1.0 ≤ Nt ≤ 3.0) and Prandtl number Pr (1.0 ≤ Pr ≤ 4.0). The present investigation aims to support production businesses in achieving the desired level of quality of their products by effectively managing the transport phenomena. [ABSTRACT FROM AUTHOR]

The present study focuses on the MHD Radiative Casson fluid flow with the effect of triple diffusivity over a vertical porous wall along with convective boundary conditions. The governing equations for detecting the nature of the fluid under the influence of solutal diffusivity and thermal conductivity in triple diffusive boundary layer flow are derived. Non-linear partial differential equations are reduced to ordinary differential equations via similarity transformation. The BVP4C method in MATLAB software is then used to solve them. The outcomes of several physical dimensionless parameters like permeability, convective parameter, buoyancy ratio parameter, Casson parameter and chemical reaction parameter with source/sink impacts established by graphics. Also, the impression of the local skin friction coefficient, Nusselt number, and local Sherwood number are presented through the tables. [ABSTRACT FROM AUTHOR]

This study considers in depth the flow of the boundary layer of an incompressible, viscous, and steady Casson fluid through an expanding surface when thermal radiation, heat source, Soret, and Dufour effects are present. Using suitable similarity transformations, the governing non-linear partial differential equations are converted into coupled ordinary differential equations and then estimated using the MATLAB software bvp4c using a shooting process. Variable values of the parameters employed in the current inquiry are offered, together with solutions for the parameters of momentum, temperature, concentration, coefficient of local skin friction, and local Nusselt number. It is observed that the Casson fluid parameter improves fluid velocity and decreases the temperature. Also, it is found that thermal radiation and the presence of a heat source/sink increase the temperature of the fluid. We compared the present investigation with previously published papers and found them harmonious. [ABSTRACT FROM AUTHOR]

Flows involving two disks have significant applications in heat exchangers, rotating machinery parts, data storage devices, oceanography and viscometers. In this investigation, heat and mass transfer characteristics are examined in Casson flow between two orthogonally moving disks, with nonlinear thermal radiation under the slip and convective conditions, using the powerful tool of similarity transformation. A MATLAB code, based on quasi-linearization, has been developed for the numerical study. It is observed that, when the disks are receding, the disk expansion ratio raises the velocity profile near the center of the region between the two disks. The trend is, however, reversed when the disks are approaching each other. Moreover, all the governing parameters remarkably elevate the fluid temperature at a central region between the disks, for both cases. A remarkable lowering in concentration distribution is also noted with the Schmidt number and the chemical reaction parameter. Finally, compared to thermal and concentration profiles, it is the velocity distribution which is least affected. [ABSTRACT FROM AUTHOR]

This study examines the effect of heat production and radiation absorption on the magnetohydrodynamic Casson fluid flow at the stagnation point in a porous medium. We convert the group of fluid flow equations, which are non-linear partial differential equations with suitable boundary constraints, into a set of non-linear ordinary differential equations using similarity transformations. The homotopy analysis method (HAM) solves the converted system of ordinary differential equations. We draw graphs for numerous values of non-dimensional parameters and tables of surface drag force, rates of heat transfer, and mass transfer to analyze the relationship between velocity field, temperature field, concentration field, and other essential parameters involved in the study. We have proven that the Dufour number, radiation parameter, and heat generation parameter elevate the fluid temperature, whereas the magnetic parameter lowers it. The Casson fluid parameter, buoyancy force parameter, and mixed convection parameter all promote fluid movement throughout the flow field. The presented tabular data allows us to see the trend of heat and mass transfer rates, as well as drag force rates, against important parameters, enhancing our understanding of these rates. [ABSTRACT FROM AUTHOR]

This study employs numerical and statistical approaches to investigate the entropy optimization of steady Casson nanofluid flow over three different geometries subject to boundary conditions induced by convective flow. Multiple linear regression is employed to statistically examine. The present model incorporates several novel elements, such as Arrhenius activation energy, Brownian motion, the Cattaneo-Christov dual flux, thermophoresis, thermal radiation, and so on. Moreover, a comparison is presented between Newtonian and non-Newtonian fluids. By applying the proper similarity transformations, ordinary differential equations (ODEs) are ob- tained by converting foundational partial differential equations (PDEs). The Runge-Kutta fourth- order method is utilised to solve the obtained ODEs along with the shooting technique. The out- comes are visually depicted via tables and graphs. The velocity drops with increasing Grashof number, and the magnetic field becomes progressively more forceful as the suction parameter in- creases. The temperature gets reduced with the increase of the suction parameter, solute Grashof number increases with the magnetic field, thermophoresis, and radiation parameters. The entropy is observed to rise with the increase of the effective parameters (magnetic field, Brinkmann num- ber and radiation). The MAD (mean absolute deviation), MSE (mean squared error), and RMSE (root mean square error) values are approaching zero, indicating that the derived outcomes are highly accurate. A lower MAPE (mean absolute percentage error) suggests that the model has a higher level of precision. Therefore, the outcomes of the present model are more precise and eliable. This study has various potential applications such as power plant heat exchangers, ma- terial processing industries, and solar thermal energy systems. [ABSTRACT FROM AUTHOR]

The energy storage features on natural convection in Casson fluids are investigated in this work using the finite element method. By measuring cylinders and wavy surfaces, we may examine flow patterns and the effectiveness of heat transmission systems. We study the variation of the mass and heat transfer rates as a function of the cylinder geometry. To approximately determine velocities and temperatures, the Ladyzhenskaya-Babuška—Brezzi (LBB)-stable element is employed. Following this discretization, the resulting discrete nonlinear system is linearized using Newton's method and subsequently solved using PARDISO. Fractional applications in Casson fluid analysis reveal insights into energy storage effects, employing finite element methods to explore flow patterns, heat transmission efficiency, and geometric variations while observing the impact of parameters such as Rayleigh, Hartmann, and Lewis numbers on fluid behavior and thermal properties. The preceding research has verified the accuracy of the numerical results. According to the results, concentration gradients and other modifications to liquids become more noticeable as the Rayleigh number grows. Convective heat transmission is reduced as the Ha is raised. When the Le grows, the deformation Nuavg and Shavgalso increase. Reducing the beta makes the isotherms more stable and less affected by the motion of the fluid.

This study employs numerical and statistical approaches to investigate the entropy optimization of steady Casson nanofluid flow over three different geometries subject to boundary conditions induced by convective flow. Multiple linear regression is employed to statistically examine. The present model incorporates several novel elements, such as Arrhenius activation energy, Brownian motion, the Cattaneo-Christov dual flux, thermophoresis, thermal radiation, and so on. Moreover, a comparison is presented between Newtonian and non-Newtonian fluids. By applying the proper similarity transformations, ordinary differential equations (ODEs) are obtained by converting foundational partial differential equations (PDEs). The Runge-Kutta fourth-order method is utilised to solve the obtained ODEs along with the shooting technique. The outcomes are visually depicted via tables and graphs. The velocity drops with increasing Grashof number, and the magnetic field becomes progressively more forceful as the suction parameter increases. The temperature gets reduced with the increase of the suction parameter, solute Grashof number increases with the magnetic field, thermophoresis, and radiation parameters. The entropy is observed to rise with the increase of the effective parameters (magnetic field, Brinkmann number and radiation). The MAD (mean absolute deviation), MSE (mean squared error), and RMSE (root mean square error) values are approaching zero, indicating that the derived outcomes are highly accurate. A lower MAPE (mean absolute percentage error) suggests that the model has a higher level of precision. Therefore, the outcomes of the present model are more precise and reliable. This study has various potential applications such as power plant heat exchangers, material processing industries, and solar thermal energy systems.

This study examines the effect of heat production and radiation absorption on the magnetohydrodynamic Casson fluid flow at the stagnation point in a porous medium. We convert the group of fluid flow equations, which are non-linear partial differential equations with suitable boundary constraints, into a set of non-linear ordinary differential equations using similarity transformations. The homotopy analysis method (HAM) solves the converted system of ordinary differential equations. We draw graphs for numerous values of non-dimensional parameters and tables of surface drag force, rates of heat transfer, and mass transfer to analyze the relationship between velocity field, temperature field, concentration field, and other essential parameters involved in the study. We have proven that the Dufour number, radiation parameter, and heat generation parameter elevate the fluid temperature, whereas the magnetic parameter lowers it. The Casson fluid parameter, buoyancy force parameter, and mixed convection parameter all promote fluid movement throughout the flow field. The presented tabular data allows us to see the trend of heat and mass transfer rates, as well as drag force rates, against important parameters, enhancing our understanding of these rates.

The current investigation aims at to examine the effect of radiation absorption, heat generation and Dufour number on MHD Casson fluid flow past an exponentially accelerated vertical plate in a porous medium with chemical reaction. The governing equations for momentum, energy and concentration are solved by implementing the Laplace transformation method. Skin friction, rate of heat transfer and rate of mass transfer expressions are also extracted and depicted in tabular form. Investigation simulates that Casson parameter diminished the fluid velocity, whereas energy flux due to a mass concentration gradient improves the temperature field of the flow problem. In addition to this, temperature field is observed to be developed under the influence of radiation absorption and heat generation. Furthermore, the effects of different non-dimensional parameters on velocity field, temperature fluid and species concentration are exhibited graphically.

The aim of this article is to gain a better knowledge of the non-Newtonian features of Casson fluid flow under torsional motion through two concentric cylinders in a porous medium. This study is crucial because it has the ability to control the flow characteristics of Casson fluids in porous media using rotating cylinders for the optimization of industrial processes. The flow-narrating differential equations are converted into a set of nonlinear differential equations. To obtain numerical results to flow problem, a computational model is developed. Numerical solutions are acquired employing the fourth-order exactness programme (Bvp4c), and findings are validated by comparing them to the Runge-Kutta fourth-order approach. Consequences of various distinct parameters for fluid flow and heat transfer are interpreted in graphical and tabular form. It is found that both fluid velocity and temperature increase with growing inputs of outer angular velocity (0.3≤Ω2≤0.9). Skin friction coefficient (CfsTa) is observed to decline in the case when both cylinders are rotating in same direction (Ω1=0.7andΩ2=0.7) with enhanced inputs of Hartmann number (0.5≤Ha≤2.0), while Nusselt number (Nus) profiles are enhanced with rising inputs of the Forchheimer parameter (0.2≤Fr≤0.8) when both cylinders are rotating in opposite direction (Ω1=0.7andΩ2≤−0.7).

The analysis of non-Newtonian fluid flow over an oscillating surface often involves numerical simulations and experimental investigations. Computational fluid dynamics method including finite difference or finite element techniques can be used to crack the governing equations of the fluid flow. In this work, we used the Crank–Nicolson numerical technique to analyze the numerical behavior of unsteady boundary layer flow of Casson fluid with natural convection past an oscillating vertical plate. The temperature-dependent viscosity is assumed for the flow analysis. The impact of chemical reaction and heat generation coefficient is used to examine the mass and heat transferal rates. The investigation of non-Newtonian fluid flow over an oscillating surface is crucial for a wide range of industrial, biomedical, and scientific applications. The governing model of equations occurs in the form of nondimensional PDEs and then we use the dimensionless variables in order to achieve the dimensional PDEs. These equations are numerically solved by using the Crank–Nicolson technique. The Crank–Nicolson scheme is used because it has the ability to provide accurate and stable solutions and make it a valuable numerical technique in various scientific and engineering disciplines. The findings indicate the significance of numerous parameters on the mass, velocity and energy regions. The numerical outcomes of skin friction are observed due to fluid parameter, viscosity parameter, Grashof numbers of heat and solutal rates. [ABSTRACT FROM AUTHOR]

The use of nanoparticles in heat transmission is an interesting research subject and many scholars have shown an interest in this topic. In accordance with the motivating relevance of nanomaterials, the current research advocates for an evaluation of Casson nanofluid using porous medium thermal analysis in conjunction with vibrant implementations of mixed convection through a chemical reaction. Additionally, a nonlinear suction/injection phenomenon is taken into consideration. A consistent flow pattern is created by the stretched porous structure. The extended Casson nanofluid model is used to identify the heat production of non-Newtonian fluids. The essential incentives for choosing the Casson nanofluid model are validated as it simultaneously achieves Casson fluid, nanofluid and porous medium outcomes. The convective transport of nanofluid has been addressed using convective temperature boundary conditions and convective flow. A dimensionless form with similarity variables is used to simplify the fundamental equations for the provided flow model. The fourth-order Runge–Kutta (RK) strategy is deployed to arrive at a numerical solution for simulated flow. The physical conveyance of flow variables is accessed visually. It is calculated from engineering quantities (i.e., skin friction, Nusselt number and Sherwood number) to generate the numerical values. The velocity declines with increasing porosity and material factors while opposite outcomes are witnessed for buoyancy factors (mixed convection and buoyancy ratio) and injection factor. [ABSTRACT FROM AUTHOR]

This thermal research communicates the thermal aspect of hybrid Casson nanofluid in the presence of entropy generation and double stratification. The contributions of Buoyancy force are studied through mixed convection. Darcy Forchheimer condition is also applied in momentum equation along with the effects of thermal radiation, viscous dissipation and convective condition. The flow is generated by stretching a thin needle. Double stratification effect is implemented in boundary conditions of the thermal and concentration equation. Transformations are implemented to form ordinary differential equations from partial differential equations. The shooting numerical method is used to find the solution of local similar expressions. The motion of the fluid slows down for higher Casson fluid parameter and Forchheimer number. The temperature shows the contrast behavior for Brinkman number and thermal relaxation parameter. Solutal relaxation parameter and thermophoresis parameter have opposite behavior for concentration parameter. The entropy generation enhances for Forchheimer number and Casson fluid. [ABSTRACT FROM AUTHOR]

The blood flow over a stenotic artery is important investigation in mathematical fluid mechanics due to its significance in biomedical sciences. The present investigation aims to examine how nanoparticles affect circulation in a stenotic artery. We examine the significance of magnetized Casson nanofluid flow over a stenotic artery under consideration of the mathematical flow problem. By using the suitable self-similarity variables, the partial differential equation is transformed into ordinary differential equations. Then, the non-dimensional equations are solved using the MATLAB software in the Bvp5c scheme. By increasing the magnetic properties of the circulatory system's cells, which is a scheme that was previously utilized by raising the magnetic field parameter, there was a predictable decrease in the blood flow. Covering the stenosed artery with a greater amount of copper nanoparticles improves its heat transmission efficiency. The present technique may help distribute medications throughout the circulatory system.

The present investigation focused on the influence of magnetohydrodynamic Gold-Fe3O4 hybrid nanofluid flow over a stretching surface in the presence of a porous medium and linear thermal radiation. This article demonstrates a novel method for implementing an intelligent computational solution by using a multilayer perception (MLP) feed-forward back-propagation artificial neural network (ANN) controlled by the Levenberg-Marquard algorithm. We trained, tested, and validated the ANN model using the obtained data. In this model, we used blood as the base fluid along with Gold-Fe3O4 nanoparticles. By using the suitable self-similarity variables, the partial differential equations (PDEs) are transformed into ordinary differential equations (ODEs). After that, the dimensionless equations were solved by using the MATLAB solver in the Fehlberg method, such as those involving velocity, energy, skin friction coefficient, heat transfer rates and other variables. The goals of the ANN model included data selection, network construction, network training, and performance assessment using the mean square error indicator. The influence of key factors on fluid transport properties is presented via tables and graphs. The velocity profile decreased for higher values of the magnetic field parameter and we noticed an increasing tendency in the temperature profile. This type of theoretical investigation is a necessary aspect of the biomedical field and many engineering sectors.

The current study presents the results of a numerical investigation of thermal radiation's consequences, ohmic heating, and electromagnetic hydrodynamic drag on the Casson fluid flow across a flat surface. By incorporating suitable similarity parameters, the equations that regulate the system are converted into non-linear ordinary differential equations. The MATLAB Bvp4c algorithm is used for computing nonlinear ODEs numerically. To optimize the industrial and ecological processing, it is crucial to study the flow of Casson fluids (including drilling muds, fossilised coatings, different sedimentation, and specific lubricating petroleum products, polyethylene dissolves, and a range of colloids) in the presence of heat transmission. Graphics and tables have been employed to present computational findings for various spans of the tangible variables that dictate the velocity and temperature distributions. The fluid rate decreases when the magnetic and Casson parameters rise, whereas fluid velocity increases as the local electric parameters grow. This exemplifies the intricate relationship between electromagnetic radiation and fluid mechanics. Growing Eckert number, thermal radiation, specific heat, and Biot number boost temperature profiles, whereas growing Casson parameter and local electric parameters diminish them, showing diverse impacts on heat transmission phenomena. Additionally, this inquiry pertains to the coefficient of skin friction and Nusselt values were covered. New experimental studies will benefit from this theoretical work, nevertheless.

This work analyzed numerically the impacts of viscous dissipation, Joule heating and inclined magnetic field on reactive-diffusion magneto-hydrodynamic radiative mixed convection oscillatory non-Newtonian Casson fluid (CF) fluxing across a slanted semi-infinite vertical plate inserted in a porous medium. The framed dimensional flow controlling partial differential equations were modified to dimensionless partial differential equations by bringing in applicable scaling variables and then numerically solved by imposing the finite difference scheme. The outcomes are established with graphical representations to inspect the flow fields’ performance for diverse flow parameters. At the same time, numerical data of skin friction and heat and mass transferal rates near the surface area are presented in a tabular format. This research study discovered that the viscous dissipation and radiation effects intensify the temperature and velocity fields while heat ingestion has a contrary effect. Both velocity and concentration distributions are diminished by the chemical reaction and Schmidt number while the converse trend was noted with thermo-diffusion effect. The velocity distribution was narrowed by the angled magnetic field, Casson parameter, and magnetic field but the porosity parameter exposed the opposite impact. The influence of the magnetic field and Casson parameters incited to decline the friction. Heat absorption in the flow makes the Nusselt number rise but improving viscous dissipation and radiation effects have pointed to an opposite trend. The chemical reaction parameter increases the Sherwood number but thermo-diffusion decreases it. Further, validation with already published results is accomplished and an excellent agreement is realized. [ABSTRACT FROM AUTHOR]

This study investigates the impact of an inclined magnetic field (MHD) on entropy generation in double diffusive natural convective flow in a wavy enclosure filled with a non-Newtonian Casson fluid. The Galerkin Finite Element Method (GFEM) is employed to numerically solve the standard formulation, utilizing quadratic polynomials for momentum interpolation and a linear interpolating function for model approximation. The discretized system is resolved using Newton's approach and PARDISO's matrix factorization. Through simulations of varying ranges of Rayleigh numbers (1 e 3 ≤ Ra ≤ 1 e 5 ) , Casson parameter (0.1 ≤ β ≤ 10) , Hartmann numbers (0 ≤ Ha ≤ 40) , Lewis numbers (0.1 ≤ Le ≤ 5) , and inclined angle gamma (0 ≤ γ ≤ 60 o ) , the study provides valuable insights into the behavior of double diffusive natural convection in the wavy enclosure. Isotherms, iso-concentration contours, and streamlines are analyzed to assess different input distributions, and the study presents graphical representations and tabular data on heat transfer, mass transfer rate, and entropy production. [ABSTRACT FROM AUTHOR]

AbstractThe free convective, unsteady, two-dimensional (2D) magnetohydrodynamic (MHD) Darcy–Forchheimer Casson fluid flow via a vertical stretching sheet containing gyrotactic microorganisms was the novel aspect of this investigation. We rewrote the collection of partial differential equations (PDEs) as nonlinear ordinary differential equations (ODEs) by considering an appropriate similarity variable. We solved the overhaul of nonlinear ODEs using MATLAB’s bvp4c approach. This study rigorously investigates the significance of gyrotactic microorganisms for Casson fluid motility. Additionally, this work investigates the impact of various parameters, including magnetic parameters, thermophoresis, Brownian motion, and radiation parameters, on temperature, motile microorganisms, velocity, and concentration profiles. We use graphs to illustrate the outcomes of various fluid flow parameters. Numerical tables display the effects of different parameters on skin friction, Sherwood number, Nusselt number, and the quantity of motile microorganisms. The unsteady parameter causes a drop in the velocity, temperature, concentration, and the density profile of microorganisms. Additionally, the Casson parameter leads to a decrease in the flow profile, while simultaneously increasing the heat, concentration, and microorganism density profiles. The microorganism density profile decreases as the bioconvection Schmidt number, Peclet number, and motile microbe parameter increase. We deem the new results extremely satisfactory when compared to earlier research. The fields of environmental remediation, biomedical sciences, and engineering may find this examination useful. [ABSTRACT FROM AUTHOR]

This paper presents exact, analytical, and numerical solutions to the two‐dimensional Casson fluid boundary layer flow over a moving wedge with varying wall temperature. The boundary layer flow of the Casson fluid with varying wall temperature is governed by a system of partial differential equations called Prandtl boundary layer equations modified by Casson fluid. By applying similarity transformations the governing system of partial differential equations is reduced to a system of nonlinear ordinary differential equations called as the Falkner–Skan equation modified by Casson fluid flow with heat transfer (C‐FSEHT). In the beginning, an exact solution of the C‐FSEHT is obtained for the particular values of physical parameters (i.e., β=−1$\beta = -1$, Pr=cc+1$\text{Pr} = \frac{c}{c+1}$, N=0$N = 0$, see nomenclature) in terms of two standard functions, namely error function and exponential function. Thus, obtained exact solution is then modified to obtain the analytical solution of C‐FSEHT for general values of physical parameters, in terms of power series. The analysis of the asymptotic behavior of the problem, when the wedge velocity is very large (λ→∞$\lambda \rightarrow \infty$), is performed using the Dirichlet series. A comparative analysis is performed using the Chebyshev collocation technique (CCT) to validate the obtained results in all the scenarios. The effect of governing parameters, which are the Casson parameter c$c$, Hartree pressure gradient parameter β$\beta$, moving wedge parameter λ$\lambda$, Prandtl number Pr$Pr$, and wedge temperature parameter N$N$ on the skin friction coefficient, temperature coefficient, velocity profiles, and temperature profiles is discussed in detail. Multiple solutions are found analytically for fixed values of governing parameters. The fact that an increase in the value of the Casson parameter (c$c$) reduces the thickness of both velocity and temperature boundary layers, is also validated during the study. [ABSTRACT FROM AUTHOR]

This study examines the effects of Newtonian heating along with heat generation, and thermal radiation on magnetohydrodynamic Casson fluid over a vertical plate. At the boundary, the Newtonian heating phenomena has been employed. The problem is split into two sections for this reason: momentum equation and energy equations. To transform the equations of the given model into dimensionless equations, some particular dimensionless parameters are defined. In this article, generalized Fourier’s law and the recently proposed Caputo Fabrizio fractional operator are applied. The corresponding results of non-dimensional velocity and heat equations can be identified through the application of Laplace transform. Moreover, Tzou’s algorithm as well as Stehfest’s algorithm is implemented to recognize the inverted Laplace transform of heat and momentum equations. Finally, a graphical sketch is created using Mathcad 15 software to demonstrate the results of numerous physical characteristics. It has been reported that the heat and velocity drop with rising Prandtl number values, whereas the fluid’s velocity has been seen to rise with increasing Grashof number values. Additionally, current research has shown that flow velocity and temperature increase with rising values of a fractional parameter. [ABSTRACT FROM AUTHOR]

In arteries blood flow is the usual example for a Casson fluid flow among the other vital utilizations of this fluid model. Thus, it would be helpful to study the Brownian motion diffusion and thermophoresis diffusion in Casson fluid for biomedical applications. In this analysis, the electrically conducting Casson nanofluid, with suction and convective boundary condition, has been addressed in a shrinking surface. The mechanism of convective heat transfer has been elaborated with Ohmic heating and viscous dissipation effects. The numerical solutions to the governing equations have been obtained by applying the similarity transformation to the nonlinear partial differential equations. The present model is employed to examine the viscoplastic characteristics in the porous regime. This dimensionless ruling problem, along with physical boundary conditions, is handled numerically by using a Runge–Kutta Fehlberg scheme. The outcomes of the present study show that the rate of heat and mass transfer at the surface of the shrinking sheet enhances with the growth in Casson fluid parameter and magnetic parameter. Furthermore, it is observed that the shear stress at the wall rises with the increment in magnetic parameter. Moreover, unsteadiness parameter is the decreasing function of heat and mass transfer rates. [ABSTRACT FROM AUTHOR]

The present work examines the convective Casson fluid flow over a stretching sheet with viscous dissipation and porous medium. The impact of thermal and mass transport is examined in terms of Soret and Dufour effects. The flow behaviour and heat transfer are investigated by subjecting the fluid to an induced magnetic field and suction/injection. The governing equations describing the flow problem are formulated using partial differential equations (PDEs). Similarity transformations are utilized to transform the governing equations into a system of ordinary differential equations (ODEs). Following that, the MATLAB solver bvp5c is utilized to grasp the results. Graphs serve as a function to display the consequences of flow on attributed parameters. Furthermore, the engineering properties such as skin friction, Nusselt number, and Sherwood number are represented through tables and graphs. Besides, the results of the present study are validated with the existing results, whereas a fine correspondence has been noticed. The findings show that the velocity of the fluid decreases by 8%, when the parameter of the induced magnetic field rises from 0.1 to 0.2. Similarly, a 3% decrement in the velocity profile is observed, while increasing the suction/injection parameter from 1.2 to 1.4. The temperature of the fluid is escalated for the increasing values of the Eckert number. Our analysis indicates a positive correlation between the Nusselt number and increasing Dufour number values. Similarly, the Sherwood number exhibits enhancement with a rise in the chemical reaction parameter. This combination has some applications in designing cooling systems for microfluidic devices, optimizing drag reduction in magnetohydrodynamics (MHD) devices, and developing novel separation processes. [ABSTRACT FROM AUTHOR]

This research stands out due to its utilization of a Casson ternary hybrid nanofluid (THNF) consisting of SiC, SWCNTs and MWCNTs , and H 2 O as the base fluid. Additionally, the introduction of slip flow, convective heat transfer boundary, and applied magnetic field are the objectives to elucidate the heat transfer behavior on fluid flow and energy profile. The article emphasizes the analysis of heat transfer properties in a 2D flow of magnetohydrodynamic Casson ternary nanofluid past a stretching sheet. The effect of non-uniform heat absorption/generation is considered in the study to better understand the heat transfer phenomena. By operating suitable similarity variables, the governing equations are transmuted into a dimensionless form. The numerical outcomes are obtained through the Runge–Kutta-based shooting scheme. The uniqueness of this paper stems from employing a Casson THNF with partial velocity jump and convective boundary. The highlight of the study is that an increment in the Casson parameter enhances fluid yield stress, reducing momentum and thermal boundary layer thickness. Elevated suction reduces boundary layer thickness, while magnetic fields influence fluid thermal conductivity, leading to higher Nusselt numbers and enhanced convective heat transfer. The findings derived from this study offer valuable insights applicable to a range of engineering and industrial processes. [ABSTRACT FROM AUTHOR]

The current study presented here demonstrates the magnetohydrodynamics (MHD) Casson fluid flow within an infinite vertical plate with consequences of Brownian, thermophoresis, and chemically responsive systems. The governing equations are numerically computed by employing a sixth-order Runge–Kutta (R–K) algorithm, whereas Nachtsheim–Swigert (N–S) shooting iteration technique has been used as the main tool for calculating the current statement. The novelty of this study is dealing with the impression of Brownian and thermophoresis effect using shooting technique. The nonlinear governing problems have been transformed into coupled nonlinear ordinary differential equations using a suitable transformation. Numerical simulation is presented for the various interesting profiles. The velocity, temperature, and concentration profiles along with skin fraction, Nusselt, and Sherwood number take into account with the varying contributions of the parameters and deployed through graphs and tables. However, one of the current study's key findings is that skin friction improves with expanding values of the thermal convective parameter while diminishing with increasing values of the Casson term, magnetic factor, and Eckert number. The current research has an enormous demand for Brownian and thermophoresis effects within the fields involving cosmology, power systems, ionized studies, and nanotechnology. [ABSTRACT FROM AUTHOR]

This study focuses on the mathematical modeling of dual convection energy transfer in a wavy cavity. The non-Newtonian Casson fluid model is envisioned as being capable of describing characteristics of viscoelastic liquids. An inclined magnetic field that is governed by Lorentz force is also taken into consideration. The Galerikin discretization is used to solve the leading formulation numerically. Quadratic polynomials interpolate momentum, concentration, and temperature equations, while linear functions imitate pressure distribution. The discretized version of the domain is analyzed with regard to the rectangular and triangular elements. The Newton's technique and PARDISO, factorization-based nonlinear solver, are utilized to resolve the nonlinearly discretized system. Patterns of streamlines, isoconcentration, and isothermal contours are depicted in order to examine the variation in the inflow distributions. [ABSTRACT FROM AUTHOR]

This analysis emphasizes the significance of radiation and chemical reaction effects on the boundary layer flow (BLF) of Casson liquid over a linearly elongating surface, as well as the properties of momentum, entropy production, species, and thermal dispersion. The mass diffusion coefficient and temperature-dependent models of thermal conductivity and species are used to provide thermal transportation. Nonlinear partial differential equations (NPDEs) that go against the conservation laws of mass, momentum, heat, and species transportation are the form arising problems take on. A set of coupled dimensionless partial differential equations (PDEs) are obtained from a set of convective differential equations by applying the proper non-similar transformations. Local non-similarity approaches provide an analytical approximation of the dimensionless non-similar system up to two degrees of truncations. The built-in Matlab (Version: 7.10.0.499 (R2010a)) solver bvp4c is used to perform numerical simulations of the local non-similar (LNS) truncations. [ABSTRACT FROM AUTHOR]

The blood flow over a stenotic artery is important investigation in mathematical fluid mechanics due to its significance in biomedical sciences. The present investigation aims to examine how nanoparticles affect circulation in a stenotic artery. We examine the significance of magnetized Casson nanofluid flow over a stenotic artery under consideration of the mathematical flow problem. By using the suitable self-similarity variables, the partial differential equation is transformed into ordinary differential equations. Then, the non-dimensional equations are solved using the MATLAB software in the Bvp5c scheme. By increasing the magnetic properties of the circulatory system's cells, which is a scheme that was previously utilized by raising the magnetic field parameter, there was a predictable decrease in the blood flow. Covering the stenosed artery with a greater amount of copper nanoparticles improves its heat transmission efficiency. The present technique may help distribute medications throughout the circulatory system. [ABSTRACT FROM AUTHOR]

Fractional calculus expands the idea of differentiation to fractional/non‐integer orders of the derivatives. It includes the memory‐dependent and non‐local system's behaviors while fractal–fractional derivatives is the generalization of fractional‐order derivatives which refers to a combination of fractional calculus and fractal geometry. In this article, we have considered the magnetohydrodynamic (MHD) flow of Casson hybrid nanofluid through a vertical open channel with the effect of viscous dissipation and Newtonian heating. The problem is modeled in terms of non‐linear and coupled integer‐order PDEs which is further generalized through fractal–fractional derivative of power law kernel. Due to non‐linearity and complexities, we have adopted the numerical procedure as it is used when the analytical solutions of PDEs are frequently difficult or impossible for complicated situations. We have established the numerical algorithms for both the classical and fractal–fractional‐order model and compared the results. The existence and uniqueness of the model's solution has been shown theoretically. The effect of various embedded parameters on the heat transfer and fluid flow has been simulated and presented through various figures while skin friction and Nusselt number are tabulated. The effect of fractional and fractal parameter is also shown. As the present model is taken for the hybrid nanofluid flow and for the heat transfer applications, we have considered mineral transformer oil as a base fluid while titania and cadmium telluride nanoparticles are dispersed in it. From the results, it is observed that hybrid nanofluid have a better heat transfer enhancement up to 19.71% while the unitary nanofluids are only capable to enhance the heat transfer up to 9%. [ABSTRACT FROM AUTHOR]

This research examines the flow of incompressible Casson fluid with gyrotactic microorganisms and thermophoretic particle deposition across a sheet, incorporating a nonlinear heat source and the convective boundary conditions. Our motivation stems from the need to optimize heat transfer in renewable energy systems and improve thermal regulation in aerospace engineering, which could inform advancements in heat shield design. The impact of this study extends to renewable energy, aiding heat transfer optimization, and in aerospace engineering, it may inform heat shield design. Medical imaging, chemical engineering and environmental remediation benefit from insights into the fluid behavior and particle transport. Based on heat source and thermophoretic particle deposition, this work investigates the concentration, temperature flow and microorganism distributions. Using suitable similarity variables, all equations for the proposed flow are converted into ODEs. The reduced equations are evaluated using the RKF45 method. The impacts of significant parameters on temperature, concentration, microbiological and flow profiles are determined with the support of graphs. The thermal and concentration distributions are improved with an increase in the thermal radiation, heat generation and magnetic parameter. This study enhances knowledge across disciplines including healthcare diagnostics, chemical engineering and ecological restoration by offering fresh perspectives on the dynamics of fluid movement and the transportation of particles. [ABSTRACT FROM AUTHOR]

This work investigates the Casson ternary hybrid nanofluid flow on a dual-directional elongating surface with variable porosity. The flow is affected by chemical reactivity, exponential heat source and thermally radiative effects. To control the thermal feature of flow, the impacts of Brownian motion and thermophoresis are also incorporated in the flow model along with Cattaneo–Christov mass/heat flux phenomena. Appropriate variables have been employed to convert the leading equations to dimension-free form and then solved by using the bvp4c approach. It has been noticed as an outcome of this work that, with the upsurge in magnetic and variable porous factors, both the primary and secondary velocities have been diminished. Augmentation in thermal profiles is caused by the escalation in radiation, thermophoresis, Brownian motion factors and thermal Biot number while it has reduced with the upsurge in thermal relaxation factor. Concentration distribution has increased by the growth in thermophoresis, activation energy factors and concentration Biot number, whereas it has diminished with escalation in Brownian motion, chemical reactivity and mass relaxation factors. Moreover, concentration distribution also declined with a higher Schmidt number. To ensure the validation of the current model, its results have been compared with previously established datasets available in the literature. A closed agreement between our results and the dataset published previously has been noticed, which ensures the authenticity of the current work. [ABSTRACT FROM AUTHOR]

The current problem is concerned with the investigation of Casson ternary hybrid nanofluid flow through microchannel. Nanofluids containing three distinct kinds of nanoparticles have a lot of industrial and engineering applications as a result of their amazing thermal properties. The nanoparticles (alumina $A{l_2}{O_3}$Al2O3, titanium oxide $Ti{O_2}$TiO2, and copper oxide $CuO$CuO) are immersed in base fluid (ethylene glycol ${C_2}{H_6}{O_2}$C2H6O2) resulting in ternary hybrid nanofluid ($A{l_2}{O_3} + Ti{O_2} + CuO/{C_2}{H_6}{O_2}$Al2O3+TiO2+CuO/C2H6O2). For the problem under consideration, the momentum distribution, temperature distribution, entropy generation, and Bejan number have been examined. With the aid of tables and graphs, comparisons of ternary hybrid, binary hybrid, and mono nanofluids have also been investigated. With nondimensional variables, the governing equations are transformed into a dimensionless form and solved using the Chebyshev Collocation Method (CCM). Analysis shows that the increment in Reynolds number, Brinkmann number, and exponential heat source parameter results in an enhancement in the dimensionless temperature and the variational improvement of the thermal radiation parameter reduces the thermal distribution. Hence, the findings show that ternary hybrid nanofluids perform better in terms of thermal conductivity performance than either binary hybrid or mono nanofluids. [ABSTRACT FROM AUTHOR]

The main motivation of this study is to examine the effects and behavior of Casson nanofluid mainly in reference to oblique stagnation points across a stretching surface. Oblique stagnation point (OSP) motions have so many applications, like artificial fibers, sticky materials, drying paper, and freezing electrical equipment, and numerous applications for endothermic and exothermic processes exist, including in heat exchangers, cooking, and drying damp clothes. Because of these applications on various domains, the Casson nanofluid OSP motion via a stretching sheet is studied with endothermic/exothermic chemical processes and convective boundary conditions (CBC). Similarity transformations are employed to convert partial differential equations (PDEs) into a collection of ordinary differential equations (ODEs). Furthermore, some significant engineering coefficients are discussed and also evaluated the behaviors of several nondimensional factors using the Runge–Kutta–Fehlberg-45 numeric method with a shooting scheme and graphical representations. The outcomes signify that temperature and concentration both rise with a rise in the Casson parameter and activation energy (AE) respectively. A higher Biot value leads to a higher temperature profile. A temperature profile increases with an enhance in the Casson parameter. The addition of a solid fraction will enrich the mass transmission rate in combination with AE. [ABSTRACT FROM AUTHOR]