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The magnetohydrodynamic (MHD), forced convective, rotating flow of nanofluid is investigated induced by eccentric rotations of a unsteady stretching porous disk and that of the fluid at infinity. The fluid is assumed to be incompressible, viscous, and electrically conductible. The disk and fluid away from the disk rotate about non-coincident axes at the same angular velocity. The forced convection is due to the temperature gradient between the uniform temperatures of the disk and that of the fluid far away from the disk. Consideration of the Joule heating as well as viscous dissipation have been taken into account. Nanofluids based on copper, alumina, and titania have also been assumed. Exact solution has been carried out for the velocity field. Numerical solution, on the other hand, is obtained using Crank–Nicolson algorithm for the temperature profiles. Several physical aspects of the investigation are discussed and explained by means of dimensionless parameters, Prandtl number Pr, Eckert number Ec, porosity parameter S, magnetic parameter M 2 and unsteady stretching parameter. With increasing nanoparticle volume fraction, the velocity profile is reduced, while the thickness of the boundary layer upsurges. As the unsteady parameter C gets higher values, the velocity profile enhanced whereas the temperature profile gets weaker. Fluid temperature decreases as suction parameter S raises. [ABSTRACT FROM AUTHOR]

The hybrid nanofluid (HNF) flow consists of polymer/CNT matrix nanocomposite material (MNC) across coaxial cylinders is numerically described in this study. The HNF flow is inspected under the consequences of thermal radiation, exponential heat source/sink and viscous dissipation. The HNF is prepared by adding polymer/CNT MNC in water. MNCs are highly productive elements with unique designs and properties. The MNCs are widely used in biomedicine and electrical applications due to their exceptional thermophysical properties. Based on their exceptionally high electrical conductivity, CNT/polymer nanoparticles (NPs) are also utilized as shielding for electrostatic discharge and electromagnetic interference (EMI). The HNF flow is modeled with the help of energy, continuity, and momentum equations. MATLAB package bvp4c is used to numerically handle the modeled equations. It has been perceived that the intensifying numbers of polymer/CNT MNC will lessen the fluid velocity and temperature profile in cases of both nanofluid and HNF. [ABSTRACT FROM AUTHOR]

This paper focuses on flow structures and thermal fields of the Carreau–Yasuda (CY) nanofluid model through a two-dimensional, wavy, complicated vertical asymmetrical conduit filled with porous elements. Formulations of the viscous dissipation in the case of CY nanofluids are derived and nonlinear radiation flux as well as joule heating are examined. Buongiorno's nanofluid approach, which involves Brownian motion and thermophoresis aspects is considered. The electrical conductivity of the suspension is considered as a variable where it depends upon the ambient temperature and concentration distributions and the Joule heating impacts are not neglected. The approach of solving the problem is contingent upon converting the system to dimensionless form then the lubrication approach with low magnetic Reynold numbers is applied. Numerical solutions are found for the resultant system, and wide ranges are considered for Weissenberg number We, non-Newtonian parameter n and Darcy number D a , namely, 0 ≤ We ≤ 2 , − 0. 5 ≤ n ≤ 1. 5 and 0 ≤ D a ≤ 1. 6 , respectively. The major results indicated that gradients of the pressure are higher in case of shear thickening (n > 1) comparing to in the instance of shear thinning (n < 1). Also, the velocity is enhanced, close to the channel's lowest portion, as the Weissenberg number is growing. The variable electrical conductivity gives a higher mass transfer rate compared to the constant property. [ABSTRACT FROM AUTHOR]

Our focus here is on examining the behavior of a boundary layer that regulates the movement of a non-Newtonian fluid undergoing a chemical reaction on a radiative paraboloid surface. This includes studying the fluid’s movement, temperature, and mass transfer. The fluid being studied pertains to the Williamson fluid model, which is described as a type of extended Newtonian fluid. We have considered the effects of Joule heating and dissipation through viscous phenomena based on the rules of heat and mass movement. The equations in the mathematical structure of partial differential equations (PDEs) governing the fluid continue to flow model in the problem. A subsequent evolution of these equations into ODEs by incorporating similarity variables. The velocity field’s schematic behavior is attributable to the magnetic parameter, thickness parameter, and the Weissenberg number, which exhibit velocity profile decline. In this research, both thermal radiation and Eckert number are highlighted, and it is concluded that both of these variables substantially raise the temperature field. We continue to track the concentration-reducing chemical reaction characteristic that remains tracked along with concentration transfer. Furthermore, the study includes a comprehensive presentation of comparative analyses with previously published scholarly works. [ABSTRACT FROM AUTHOR]

This paper aims at developing non-similar solutions for heat transfer augmentation in ternary hybrid nanofluids. Nanofluid is composed of three distinct (Silver, Copper, Aluminum oxide) nanosize particles while water is considered as a base fluid. Darcy–Forchheimer expression with variable porosity and permeability is adopted. Joule heating and viscous dissipations are also considered. Non-similar approach is utilized. Numerical solutions are computed by bvp4c solver of MATLAB. Graphical illustrations for flow and thermal fields behavior are provided. Comparative results are obtained for ternary hybrid nanofluid and nanoliquid. Physical quantities such as skin drag coefficient and Nusselt number are computed and interpreted. Our results reveal that rate of heat transfer augments substantially for Ag/water nanofluid in comparison to other classes of nanofluid. [ABSTRACT FROM AUTHOR]

Significance: The thermal energy transfer in nanofluid flow over an exponentially stretching surface has crucial practical configurations in various industrial processes, and it has potential applications in heat exchangers, chemical engineering, energy harvesting, and material processing. Purpose: This study is devoted to exploring the features of free convection in the thermally stratified, unsteady flow of Casson fluid over an inclined, exponentially stretching surface. Moreover, the implications of nonlinear thermal radiation, activation energy, and thermal/salute stratification effects are examined over the thermal energy transport distributions. Diffusion-thermo and thermo diffusion impressions are also taken into consideration. Methodology: By introducing reasonable transformations, partial differential equations are altered into ordinary differential equations. A nonlinear system of differential equations is solved numerically by employing the Midrich numerical technique. Findings: The impacts of diverse fluid parameters like the Soret/Dufour number, temperature difference parameter, radiation parameter, thermal/salute stratification parameter, magnetic parameter, and Prandtal number are assessed and depicted in plots by explaining the physical justifications of each parameter. Also, numerical values of sink friction and local Nusselt and Sherwood numbers are computed and examined for different values of pertinent variables involved in the problems. It is found that the rate of thermal energy transport is significantly enhanced by the larger estimation of the radiation parameter. Furthermore, it is perceived that the escalation in the temperature ratio constant leads to increased thermal convection in the fluid, while the larger thermal stratification constant decays the rate of heat transport in the fluid. Additionally, the rate of thermal transport is de-escalated due to the escalation in the intensity of thermal stratification parameter. [ABSTRACT FROM AUTHOR]

The objective of this paper is to investigate the heat transfer mechanism while considering the attributes of viscous dissipation, Joule heating, and nonlinear thermal radiations in the three-dimensional steady incompressible flow of Carreau liquid on an extendable rotating disk. By using the similarity transformation, the governed equations were converted into the nonlinear coupled ordinary differential equations. The essential characteristics of various variables like Prandtl number, Lewis number, Carreau liquid parameter, Brownian motion, thermophoresis parameter, radiation parameter, Eckert number and Hartmann number on velocity, thermal, and concentration are discussed through graphs and tables. The presented investigation divulges that the thermal and mass transfer rates enhance when Brownian motion and thermophoresis processes extended and manifest as opposing features on the concentration field. [ABSTRACT FROM AUTHOR]

The present study investigates the entropy generation of chemically reactive micropolar hybrid nanoparticle motion with mass transfer. Magnetic oxide (Fe3O4) and copper oxide (CuO) nanoparticles were mixed in water to form a hybrid nanofluid. The governing equations for velocity, concentration, and temperature are transformed into ordinary differential equations along with the boundary conditions. In the fluid region, the heat balance is kept conservative with a source/sink that relies on the temperature. In the case of radiation, there is a differential equation along with several characteristic coefficients that transform hypergeometric and Kummer's differential equations by a new variable. Furthermore, the results of the current problem can be discussed by implementing a graphical representation with different factors, namely the Brinkman number, porosity parameter, magnetic field, micropolar parameter, thermal radiation, Schmidt number, heat source/sink parameter, and mass transpiration. The results of this study are presented through graphical representations that depict various factors influencing the flow profiles and physical characteristics. The results reveal that an increase in the magnetic field leads to a reduction in velocity and entropy production. Furthermore, temperature and entropy generation rise with a stronger radiation parameter, whereas the Nusselt number experiences a decline. This study has several industrial applications in technology and manufacturing processes, including paper production, polymer extrusion, and the development of specialized materials. [ABSTRACT FROM AUTHOR]

Understanding and optimizing heat transfer processes in complex fluid systems is the driving force behind studying the magnetohydrodynamic (MHD) flow of Al2O3–Cu∕H2O nanofluid across a radiative moving wedge, taking into account the impacts of viscous dissipation and Joule heating. Nanofluids, such as Al2O3–Cu∕H2O, increase heat transmission and thermal efficiency. However, the complicated challenges caused by fluid characteristics and radiative heating need a thorough investigation. This study examines MHD hybrid nanofluid heat transfer via a permeable wedge using joule heating, mass suction, viscous dissipation, variable viscosity, thermal radiation, variable thermal conductivity, and variable Prandtl number. We use similarity transformation to solve the ordinary differential equations that follow from the governing partial differential equations. We then check the results for correctness and dependability. To ensure the reliability and validity of the outcomes, source parameters are crucial to the validation process. The consequence of changing these parameters on the heat transmission properties of the MHD hybrid nanofluid is studied for both the scenario without and with thermal radiation by methodically analyzing the percentage increase or reduction. The validation process also includes a comparison of the computed values, such as the heat transfer rate and skin friction factor, with established theoretical predictions. This examination guarantees that the numerical solution, executed using the bvp4c technique in MATLAB, corresponds to the anticipated physical behavior of the system being studied. In addition, the findings exist using both graphical and tabular forms, which allows for a clear and succinct illustration of how different physical limitations affect flow characteristics. [ABSTRACT FROM AUTHOR]

Bioconvection in nanofluids refers to the sensation where biological microorganisms, such as bacteria or algae, interact with nanoparticles suspended in a fluid, resulting in convective motion. This phenomenon has garnered interest due to its vital applications in diverse fields such as biotechnology, nanotechnology, and environmental engineering. This paper deals with the magneto-hydrodynamic (MHD) Reiner-Rivlin nanofluid flow by a stretchable porous sheet in the manifestation of the gyrotactic type of microorganisms. The Reiner-Rivlin nanofluid is considered to be incompressible and electrically conducting. Energy relation is developed by accounting the effects of dissipative forces, Joule heating, and radiative heat flux. Brownian dispersion and thermophoretic characteristics of solid tiny particles are accounted. Furthermore, chemical responses with modified Arrhenius kinetics are reflected in mass concentration relation. The acquired system of highly nonlinear partial differential equations (PDEs) is reduced into ordinary differential equations (ODEs) through appropriate transformations and then elucidated numerically via the shooting method (Runge–Kutta–Fehlberg). The study investigates the impact of various factors on fluid velocity, thermal field, heat and mass transfer rates, mass concentration, and microorganism motile density through graphs and tables. It is observed that Reiner-Rivlin fluid velocity decays versus Hartmann number and porosity constant, whereas the reverse scenario is observed for fluid material constant. Thermal field upsurges due to Hartmann and Eckert numbers. Moreover, the intensity of heat transfer escalates for higher Prandtl number and thermal radiation parameters. [ABSTRACT FROM AUTHOR]

The present study investigates the entropy generation of chemically reactive micropolar hybrid nanoparticle motion with mass transfer. Magnetic oxide (Fe3O4) and copper oxide (CuO) nanoparticles were mixed in water to form a hybrid nanofluid. The governing equations for velocity, concentration, and temperature are transformed into ordinary differential equations along with the boundary conditions. In the fluid region, the heat balance is kept conservative with a source/sink that relies on the temperature. In the case of radiation, there is a differential equation along with several characteristic coefficients that transform hypergeometric and Kummer’s differential equations by a new variable. Furthermore, the results of the current problem can be discussed by implementing a graphical representation with different factors, namely the Brinkman number, porosity parameter, magnetic field, micropolar parameter, thermal radiation, Schmidt number, heat source/sink parameter, and mass transpiration. The results of this study are presented through graphical representations that depict various factors influencing the flow profiles and physical characteristics. The results reveal that an increase in the magnetic field leads to a reduction in velocity and entropy production. Furthermore, temperature and entropy generation rise with a stronger radiation parameter, whereas the Nusselt number experiences a decline. This study has several industrial applications in technology and manufacturing processes, including paper production, polymer extrusion, and the development of specialized materials.

The investigation of the flow of pair stress fluid over an inclined flat plate has garnered considerable interest in recent times owing to its extensive applicability in diverse domains such as engineering, fluid mechanics, and heat transfer. This work theoretically investigates the steady and dissipative flow of a ternary hybrid nanofluid (composed of Ethylene Glycol, Copper (II) oxide, Titanium dioxide, and Silica) over a tilted flat plate. The analysis takes into account quadratic thermal radiation, Ohmic heating, and irreversibility. We transformed the problem's equations into a set of ordinary differential equations and solved them using the bvp4c solver. The results are shown for two instances of shape factors, namely cylindrical and brick. The results pertaining to the engineering factors of interest are elucidated through the utilisation of multiple linear regression. An increase in the couple stress parameter ( Cs ) is shown to result in an elevation in fluid velocity and entropy formation. Observations indicate that for values of 0.5 ≤ C s ≤ 3 , the friction factor increases at a rate of 0.04584044 (for the cylindrical shape) and 0.04583592 (for the brick shape). It has been observed that when the Eckert number (Eck ) increases, the temperature of the fluid becomes more intense. Additionally, for values of 0 ≤ Eck ≤ 0.5 , the rate of heat transmission decreases by 0.291088899 for the cylindrical shape and 0.284062962 for the Brick shape. Furthermore, it has been observed that the Bejan number decreases when the couple stress parameter and Brinkman number increase. [ABSTRACT FROM AUTHOR]

Entropy measures the disorderness and randomness in the thermal systems. It has significant influence over efficiency and performances of the thermal systems. The motive of the research paper is to present a comparative analysis of entropy generation of a heat dissipative Darcy–Forchheimer flow of copper (Cu/H2O)-based mono and (CuAl2O3/H2O)-based hybrid nanofluid under the influence of thermal dispersion. The mathematical model of the conceptualized flow problem is formulated using single phase nanofluid model along with Darcy–Forchheimer equation for non-Darcy porous medium flow. The system of dimensional Partial Differential Equation (PDE) depicting the flow problem is converted in the system of dimensionless Ordinary Differential Equation (ODE) using the suitable similarity variables and has been solved by MATLAB’s bvp4c package. The flow variables, engineering parameters like skin friction and Nusselt number along with entropy generation, have been analyzed for the active parameters inherited in the problem. The findings suggest that heat transfer rate on the surface enhances with the increment in thermal dispersion parameter. Further, it is reported that the hybrid nanofluid generates lesser entropy as compared to the mono-nanofluid. This research has potential to serve the real-life applications based on electronics and geothermal systems. [ABSTRACT FROM AUTHOR]

The basic objective of this article is to highlight the impact of Joule heating, thermal radiation, and viscous dissipation on heat transfer rate and friction drag in the flow of viscous nanofluid subject to the curved stretching sheet. Moreover, the effects of magnetic field and two-heating process termed as prescribed surface temperature and prescribed heat flux is considered on the surface. The nanofluid is addressed as a mixture of alumina ( $ Al_2O_3 $ A l 2 O 3 ) nanoparticle and ethylene glycol ( $ C_2H_6O_2 $ C 2 H 6 O 2 ) base fluid. Initially, certain dimensionless variables have been addressed to modify the governing partial differential equation (PDEs) and the associated boundary condition into non-dimensional ordinary differential equations (ODEs) coupled with boundary conditions. Subsequently, the resulting equations are solved numerically by implementing bvp4c package in MATLAB. Multiple graphical results for heat transfer rate, friction drag, velocity, and temperature are obtained under the influence of several flow parameters like radiation parameter, Eckert number, curvature parameter, stretching parameter, Hartmann number, and volume fraction of nanoparticles. Moreover, several interesting results for the flat surface ( $ K \to \infty $ K → ∞), with prescribed heat flux and surface temperature have been determined. The current radiative and dissipative flow coupled with the Joule heating process have countless applications in various industrial and engineering techniques. [ABSTRACT FROM AUTHOR]

Regression analysis helps predict and understand the complex phenomena exhibited by fluids by examining the impact of independent variables on dependent variables. This article introduces a study that utilizes statistical analysis to explore the flow and heat transport behavior dynamics of a two-dimensional electrically conducting hybrid nanomaterial near the stagnation point. The innovation of this research lies in the novel synthesis method, which involves integrating molybdenum dioxide and aluminum oxide into a water-based fluid. The impacts of viscous dissipation, Joule heating (without an electric field), and convective boundary conditions are considered. This approach shows promise for practical applications across various industries. By comprehending and optimizing the behavior of hybrid nanofluids, potential benefits in the efficiency and performance of the system can be realized in areas such as electronics cooling and industrial heat exchangers. A significant aspect of this research involves the intelligent utilization of an external magnetic field oriented perpendicular to the flow direction. While this enhances energy flow, it also moderates the velocity profile of hybrid nanofluids. During regression analysis, it is observed that the effect of the Eckert number on the Nusselt number is greater than that of the Biot number. [ABSTRACT FROM AUTHOR]

This study investigates mixed convection heat transfer in the vertical channel of magneto-hydro-dynamic (MHD) generators, considering the effects of magnetic fields, Joule heating, and viscous dissipation. The key objectives are to derive an accurate analytical solution for the complex non-linear heat transfer equations and provide insights into optimizing MHD generator design. An innovative mathematical approach involving differential transforms and power series expansions is utilized to solve the coupled partial differential equations. Validation is conducted by comparing results to existing numerical and analytical research. Parametric analysis of dimensionless quantities reveals that increasing the Hartmann number enhances fluid velocity in the channel core but suppresses temperature near the walls due to the magnetic damping effect. Higher Λ (ratio of buoyancy forces to viscous forces) values decrease both velocity and temperature profiles. The magnetic field effectively regulates flow and thermal behavior. Joule heating power rises with a higher Hartmann number but declines as Λ increases due to heightened viscous dissipation. These outcomes elucidate the impacts of critical parameters on heat transfer characteristics and performance. The robust analytical approach and findings pave the pathway for the optimized design of efficient MHD generators. Further work can examine additional configurations and parametric effects to deepen understanding of magneto-hydrodynamic mixed convection phenomena. [ABSTRACT FROM AUTHOR]

Maxwell-fluid represents the flow of polymers used in the food processing industry and the cooling of copper plates. Much research has focused on maxwell-fluid flows across stretched surfaces. This article takes a different approach by examining the impacts of the magnetic and electric force on such surfaces. We aim to understand the behaviour of non-Newtonian Maxwell hydromagnetic boundary layer flow when exposed to magnetic and electric fields. The novelty of this investigation is to construct a two-equation non-similar model. It aims to examine the momentum, thermal and mass transport of Maxwell fluid with suspended conducting nanoparticles, which incorporates viscous dissipation, chemical reaction, an external magnetic and electric field, Brownian motion and thermophoresis. Moreover, the rheological behaviours of the nanofluids are significant in defining them for convective heat transfer. The partial differential equations describe the problem, and after applying suitable transformations, it is finally transformed into a set of non-similar, nonlinear and coupled non-dimensional ordinary differential equations. To get results, the bvp4c method built within MATLAB is utilized. An analysis of pertinent parameters affecting non-Newtonian fluids and the nanophase of fluids is shown in this study. Findings show that as the strength of the inclination angle decreases, the velocity profile becomes more pronounced. The temperature field improves as the heat generation parameter rises. The dimensionless concentration tends to decrease with Brownian motion. Its potential applications include medical sciences, microelectronics, biomedicine and various industrial processes.

Ternary nanomaterials are now recognized as useful not only for thermal efficiency importance but also to enhance physical characteristics of liquids. Insertion of three nanoparticles in base liquid is characterized as ternary hybrid nanomaterial. Such materials have better magnet properties, electrical conducting and mechanical resistance. Here we discuss three-dimensional magnetized stretched flow of ternary nanofluid through porous space is addressed. Porous space is scrutinized by Darcy-Forchheimer relation. Convective condition is imposed. Nanoparticles here include copper, polyphenol coated and aluminum oxide and water as conventional liquid. Energy equation consists of radiation, magnetohydrodynamics, dissipation and heat generation. Resulting dimensionless system is computed by Newton built in-shooting technique. Outcomes of velocity, temperature, skin friction and Nusselt number for emerging parameters of interest are organized. Comparison of results for ternary nanofluid (CoFe2O3+Cu+Al2O3/H2O), hybrid (CoFe2O3+Cu/H2O) and nanofluid (CoFe2O3/H2O) is examined. It is found that temperature and velocity against Hartman number have reverse trends. Temperature and Nusselt number for radiation have increasing features. Similar characteristics for temperature through heat generation and Eckert number is noticed. Larger thermal Biot number corresponds to rise the Nusselt number and temperature. An increase in temperature through Forchheimer number is witnessed while reverse trend holds for velocity.

This investigation incorporating the fluctuation in heat and mass transfer associated to the mixed convection magnetized flow of viscous fluid due to inclined surface with porous media. The contribution of Soret effects and viscous dissipation appliances is addressed. Furthermore, the heat transfer improvement is also assessed by thermal radiation, heat source and joule heating effects. The chemical reaction enrollment is also studied for concentration phenomenon. The convection of problem into non-dimensional framework is based on implication of new variables. The perturbation technique is followed to tracking the analytical outcomes. Physical visualization and interpretation of results under the influence of perturbed parameters have been studied. It is observed that heat and mass transfer enhances due to Soret number. Presence of chemical reaction leads to decrement of concentration profile. Claimed results presents applications in heat and mass transfer processes, chemical reaction, manufacturing systems, chemical engineering, extrusion processes etc.

The hybrid nanofluids can enhance cooling systems in microelectronics by enhancing heat dissipation from processes which makes them vital for maintaining optimal performance. They are also beneficial in solar systems where efficient heat transfer is essential for exploiting the energy detention. Thus, this study has studied the three-dimensional flow of a water-based hybrid nanofluid comprising of Fe3O4 and CuO nanoparticles on a bi-directional extending sheet. The bi-directional extending sheet is subjected to thermal convective and velocity slip conditions. In addition, the effects of heat source, magnetic field, thermal radiation, viscous dissipation, and Joule heating are employed. The partial differential equations (PDEs) that represent the mathematical model are subsequently converted to ordinary differential equations (ODEs) by applying the appropriate similarity variables. The shooting technique is incorporated to determine the computational solution of the converted ODEs. The effectiveness of the current study is confirmed by published results, which also validate the current outcomes. Based on the results, it is concluded that CuO and Fe3O4 solid nanoparticle volume fractions improved the thermal distribution while decreasing the velocity distributions along x and y-axes. The thermal distribution is improved by the thermal heat source, thermal radiation, thermal Biot number, and thermal Eckert numbers. CuO-water nanofluid has a higher velocity panel than CuO-Fe3O4/water hybrid nanofluid. Conversely, the CuO-Fe3O4/water hybrid nanofluid has a higher thermal profile than the CuO-water nanofluid. CuO-water nanofluid flow has higher surface drags than CuO-Fe3O4/water hybrid nanofluid flow. CuO-water nanofluid has a lower heat transfer rate than CuO-Fe3O4/water hybrid nanofluid.

Many scholars performed the analysis by using the non-Newtonian fluids based on the nano and hybrid nano particles in blood arteries to investigate the heat transport for cure in several diseases. These performances are presented to investigate the blood flow behaviour with extended form of the novel tetra hybrid Das and Tiwari nanofluid system attached by the Carreau fluid. The assessment of energy transport has been achieved based on the thermal radiation, heat source/sink, Joule heating, and viscous dissipation. The obtained partial differential equation from physical problem is transformed into ordinary differential equations (ODEs) by using the similarity variables. Furthermore, system of nonlinear ODEs attached with boundary conditions are transported into the system of first-order ODEs with initial conditions. For the numerical solution of obtained ODEs, the numerical solutions have been performed based on the RK method. The numerical results are plotted through figures, tables, and statistical graphs. Magnetic forces and inclined magnetic effects are caused to reduce velocity of blood. Temperature of blood within the arteries is increased by increasing the parameter of thermal radiation.

This study aims to investigate the Joule effect, thermal radiation, and Coriolis effects in unsteady magnetohydrodynamics (MHD) micropolar flow over a 3-D unstable sheet. A magnetic field is typically applied to the surface; additionally, it is assumed that the fluid is conducting electricity. Other micro-rotations are also considered. The physical issue is resolved with the help of the fundamental equations, and the issue's complexity is reduced with the use of similarity variables. In the present approach, the homotopy analysis method (HAM) is employed. The heat, skin's friction factor, temperature, micro movements, and velocity associated with the emerging parameters and transfer rates are considered. The boundary layer thickness is increased as the parameter of vorticity increases. When the magnitude of the magnetic field increases, the skin friction coefficient decreases. The state variables are approximated up to six decimal places numerically. The numerical values of −f″(0) and −θ′(0) are computed to higher decimal places and compared with the available literature to validate the results. The outcomes obtained are compared with the available literature; the results here are corroborated, and the performance of the HAM is demonstrated.

This study examines the molecules motion influences and thermal attributes in power-law non-Newtonian dissipative fluids' magnetohydrodynamic behavior, Joule heating, electromigration, and Cattaneo-Christov effects. Effects of Hall on both flow velocity and temperature, as well as the heat transport are considered. The investigation looks at heat transference that occurs when there is a slippage consequence, how the temperature influences the viscosity of the fluid, and how the potential parameters influence the exponential non-Newtonian flow of fluid via an extensible sheet. Runge-Kutta-Fehlberg's approach, which is based on the shooting procedure, was used to develop computational solutions for nonlinear ordinary differential equations. When exposed to a deformation that is generated by expansion, pressure, or agitation, a dilatant fluid is characterized by a phenomenon in which its viscosity rises and may harden. This phenomenon is referred to as the dilatation phenomenon. High shearing rates provide the impression that it is stable. When expanded, subjected to pressure, or agitated, dilatant fluids become more viscous and transform into solids. Both the non-equilibrium that occurs within the fluid and the reduction of the irreversibility processes that occur within it are caused by the acquired charges that are a result of Hall effect of fluid molecules.

Tetra hybrid nanofluids are significant due to their unique properties like thermal and electrical conductivity enhancement, increased heat transfer, and improved fluid flow characteristics. This attempt proposes a tetra hybrid cross nanofluid model with the implementation of cubic autocatalysis in the context of blood flow passing through a stenosis artery. The model includes the effects of nanofluid, magnetic field, thermal radiation, and the cubic autocatalysis mechanism. This research investigates the innovative application of cubic autocatalysis within the context of blood flow through a tetra hybrid cross nanofluid model, specifically designed to simulate conditions within a stenosis horizontal artery. The equations governing the fluid flow are solved using the bvp5c method, and the numerical solutions are obtained for various parameter values. Specifically, the cubic autocatalysis mechanism profoundly impacts the velocity and concentration profiles of the blood flow. The proposed model and the obtained results provide new insights into the physics of blood flow passing through stenosis arteries. They may have important implications for the diagnosis and treatment of cardiovascular diseases. This article has a unique combination of tetra hybrid cross nanofluid model, cubic autocatalysis, and blood flow passing through the stenosis artery. These facts are not typically studied together in the context of blood flow.

Entropy generation optimization has significant applications in biomedical engineering, including angioplasty therapy, more rapid focused medication delivery and streamlining of medical instruments functionality. This study seeks to explore entropy generation optimization in stagnant blood flow region with tetra-hybrid nanofluid through a curved stretching surface embedded by blood tissues. Aiming to enhance heat transfer rate, SiO2+TiO2+Fe2O3+Au nanoparticles are considered with a combination of radiation effects, viscous dissipation and joule heating. Numerical solutions are obtained by Runge-Kutta-Fehlberg 5th order method with shooting strategy. Validation of code is done by comparing the current result of distinct curvature parameter values for drag force to existing studies and attaining high concordance. Numerical results in surface drag force and thermal transmission rate for unsteadiness parameter and curvature parameter are investigated. Improvement of curvature parameter enriches the blood flow's velocity and reduces the pressure distribution. Tetra-hybrid nanofluid volume fraction and platelet shape factor for nanoparticles have efficient heat transfer rate. Curvature parameter enhances the heat transfer rate by 141.4 % and minimizes the resistance of blood flow as 42.49 %. Entropy generation optimization worked well for tetra-hybrid nanofluid compared to pure blood flow, enhanced by 47.7 %. Overall results have major utilization in biomedical engineering field and medical devices optimization.

This investigation focuses on the nanoparticle shape effect on the flow of conducting non-Newtonian Maxwell nanoliquid through an absorptive expanding surface. Insertion of inertial drag due to the Darcy–Forchheimer model and the dissipative heat in the flow phenomena supplements the work. The thermal properties of the fluid show its important role because of the use of various thermophysical models such as the Gharesim model of viscosity and the Mintsa model of thermal conductivity. The proposed mathematical model is designed by the implementation of suitable similarity transformations and then a numerical scheme is adopted to solve the transformed phenomena. In particular, shooting-based traditional Runge–Kutta (RK) fourth order is implemented for the solution. The behavior of the parameters that are participating in the flow phenomena is deployed via graphs and the computation of the engineering coefficients is displayed in tables. The impression of innumerable governing flow constraints is interpreted with the validation of these investigations with the earlier investigation. However, the major outcomes are; the particle concentration contributes its significant characteristics in enhancing the fluid velocity as well as temperature for the increasing shape. The dissipative heat formulated by the Eckert number also augments the fluid temperature in association with the thermal radiation whereas the unsteadiness parameter retards it significantly. [ABSTRACT FROM AUTHOR]

In this article, the impact of Joule heating on the thermal performance of Williamson nanofluid is analyzed under the influence of viscous dissipation along with the Joule heating. Also, the flow is subjected to Thompson and Troian slip conditions that directly influence the velocity of the flow at the boundary. Meanwhile, to achieve the even distribution of nanoparticles in the nanofluid, gyrotactic microorganisms are dispersed whose motion is due to the virtue of density gradient. The heat conduction at the surface is governed by the convective condition which allows the interpretation of the Biot number. The mathematical model is constructed employing these presumptions using partial differential equations, which are then subsequently reduced using similarity transformations to get the ordinary differential equations (ODEs). The RKF-45 numerical approach is used to solve the nonlinear ODE system thus acquired, and the findings are validated by comparing them to the previously published works. The results of this study showed that the higher values of thermophoresis and Brownian motion parameters cause more heat conduction. Also, the rise in the Eckert number that relates to the internal friction enhances the temperature conducted by the nanofluid. Meanwhile, the Lorentz force helps in controlling the flow velocity. [ABSTRACT FROM AUTHOR]

This study examines the molecules motion influences and thermal attributes in power-law non-Newtonian dissipative fluids' magnetohydrodynamic behavior, Joule heating, electromigration, and Cattaneo-Christov effects. Effects of Hall on both flow velocity and temperature, as well as the heat transport are considered. The investigation looks at heat transference that occurs when there is a slippage consequence, how the temperature influences the viscosity of the fluid, and how the potential parameters influence the exponential non-Newtonian flow of fluid via an extensible sheet. Runge-Kutta-Fehlberg's approach, which is based on the shooting procedure, was used to develop computational solutions for nonlinear ordinary differential equations. When exposed to a deformation that is generated by expansion, pressure, or agitation, a dilatant fluid is characterized by a phenomenon in which its viscosity rises and may harden. This phenomenon is referred to as the dilatation phenomenon. High shearing rates provide the impression that it is stable. When expanded, subjected to pressure, or agitated, dilatant fluids become more viscous and transform into solids. Both the non-equilibrium that occurs within the fluid and the reduction of the irreversibility processes that occur within it are caused by the acquired charges that are a result of Hall effect of fluid molecules. [ABSTRACT FROM AUTHOR]

The purpose of the current study is to evaluate the mass and energy transmission of a blood-based Casson Ferrofluid flow across a stretching cylinder. The consequences of the Casson parameter, cylinder curvature, thermal radiation, chemical reaction, and non-Newtonian viscous dissipation are also considered. The nanofluid flow phenomena are mathematically designed in the form of a system of nonlinear PDEs which are degraded and non-dimensionalized to the set of ODEs by using suitable similarity transformations. The homotopy analysis method has been applied to find out a semi-analytical solution for the nonlinear set of ODEs. The significance and physical behavior of flow parameters are graphically characterized versus the velocity, energy, and mass profiles. The numerical outcomes for Sherwood number, drag force and Nusselt number are also presented through Tables. A comparative evaluation has been done for validation purposes to authorize and justify the present results. From the tabular and graphical results, it has been noticed that the velocity profile lowers while the energy profile develops versus the variation of magnetic factor. The impact of curvature factor boosts the velocity and mass transfer rate of the Casson nanofluid while reducing the temperature curve. Furthermore, the consequences of the thermophoresis effect raise the temperature profile of the Casson Ferrofluid flow. [ABSTRACT FROM AUTHOR]

This study aims to investigate the Joule effect, thermal radiation, and Coriolis effects in unsteady magnetohydrodynamics (MHD) micropolar flow over a 3-D unstable sheet. A magnetic field is typically applied to the surface; additionally, it is assumed that the fluid is conducting electricity. Other micro-rotations are also considered. The physical issue is resolved with the help of the fundamental equations, and the issue's complexity is reduced with the use of similarity variables. In the present approach, the homotopy analysis method (HAM) is employed. The heat, skin's friction factor, temperature, micro movements, and velocity associated with the emerging parameters and transfer rates are considered. The boundary layer thickness is increased as the parameter of vorticity increases. When the magnitude of the magnetic field increases, the skin friction coefficient decreases. The state variables are approximated up to six decimal places numerically. The numerical values of − f ″ (0) and − θ ′ (0) are computed to higher decimal places and compared with the available literature to validate the results. The outcomes obtained are compared with the available literature; the results here are corroborated, and the performance of the HAM is demonstrated. [ABSTRACT FROM AUTHOR]

This paper examines how nanoparticle aggregation and a consistent magnetic field influence the peristaltic movement of a dissipative nanofluid, which is caused by the sinusoidal deformation of the boundary. The viscosity of TiO2/H2O nanofluids is accurately determined by the Krieger-Dougherty model with nanoparticle aggregation, while thermal conductivity (TC) is estimated through the Bruggeman model. The set of governing equations are modeled in a fixed frame by utilizing the conservation laws of energy, mass and momentum. Galilean transformation is utilized to transform the system of equations into a wave frame, which is then converted into a dimensionless form. The assumption of a small Reynolds number and long wavelength serve to further simplify the set of equations, which are subsequently addressed through the implementation of the differential quadrature method (DQM), a highly effective numerical technique. Quantities of interest, namely velocity, pressure gradient, temperature, trapping phenomena, heat transfer, and volumetric entropy generation are analyzed across a range of physical parameters, including the solid volume fraction (Φ=0.01−0.04), Eckert number (Ec=0.0−0.1), Hartman number (Mh=0.2−2.2), Grashof number (Gr=1.0−3.0) and temperature ratio parameter (θd=0.5−2.5). A comparative analysis is conducted between the scenario involving aggregation and the one without aggregation. It is observed that nanoparticle aggregation significantly alters these quantities.

This work inspects 3D magnetohydrodynamic hybrid nanofluid flow on a permeable elongating surface. The emphasis of this paper is on the study of hybrid nanofluid flow within a rotating frame, taking into account the simultaneous impact of both thermal and velocity slip boundary conditions. The chosen base fluid is water, and the hybrid nanofluid comprises two nanoparticles Cu\text{Cu} and Al2O3{\text{Al}}_{2}{\text{O}}_{3}. The effect of the magnetic and porosity parameters is taken into account in the momentum equation. The thermal radiation, Joule heating, and heat source are considered in the energy equation. Using a similarity system, we transform the PDEs of the proposed model into ODEs, which are then solved numerically by the bvp4c technique. The magnetic field shows a dual nature on primary and secondary velocities. Enrich magnetic field decreases the primary velocity and enhances the secondary velocity. The rotation parameter has an inverse relation with both velocities. The temperature profile amplified with the escalation in heat source, magnetic field, rotation factor, and Eckert numbers. The skin friction is boosted with magnetic parameters while the Nusselt number drops.

Aim: This paper presents a numerical simulation of the mixed convective boundary layer (BL) motion of a bio-rheological liquid over an inclined plate under viscous dissipation and Joule heating effects. This is significant because of the various applications of electro-osmotic force, inclined plates, and viscoelastic fluids in the biochemical engineering and industrial domains. Furthermore, the BL flow is controlled by electromagnetic force (EMF). In this study, a non-Newtonian liquid model, called the Jeffrey fluid model, was employed. Method: The rheological equations of the current study are nonlinear partial differential equations (PDEs). By applying a set of similarity transformations, these PDEs become coupled ordinary differential equations (ODEs), which are then solved numerically using the NDSolve method under realistic boundary constraints. Outcomes: Numerical solutions for the velocity profile (f′(ξ)), temperature distribution (Θ(ξ)), skin friction (shearing stress), and Nusselt number (heat transfer rate) were obtained subject to convective boundary constraints. These numerical outcomes are dependent on 12 embedded parameters: Hartmann number (Ha), viscoelastic time relaxation parameter (γ), inclination of the inclined plate with a horizontal line (ω), mixed convection parameter (Ω), electro-osmotic parameter (k), electro-osmotic velocity parameter (Uhs), Prandtl number Pr, Brinkman number (Br), suction/blowing parameter (s), velocity slip parameter (ϱ), Joule heating parameter (Γ), and thermal slip parameter (δ). The authors discussed how these embedded variables affect rheological features through graphs and tables. The numerical solutions of viscous liquids are also discussed, and these outcomes are compared with the numerical solutions of a viscoelastic liquid. The enhancements of the Θ(ξ) and f′(ξ) are largely dependent on the Joule heating parameter, Brinkman number, and Hartmann number. As the Prandtl number increases, diminishing behavior is observed in the Θ(ξ) and f′(ξ). Increasing the magnetic and viscoelastic parameters increases the magnitudes of the skin friction coefficient and local Nusselt number. The validation of the numerical procedure is discussed by recovering the outcomes of research works from the available literature. Significances and applications: This mathematical study has diverse applications in the electromagnetic multiphase processes, magnetic power generators, chemical engineering phenomena, polymer industry systems, and the thermal enhancement of mechanical and industrial processes.

As a result of the tremendous development in all aspects of life, the increase in population day after day, and the scarcity of freshwater resources sufficient to meet the needs of living organisms on the surface of the earth, all these reasons called for an attempt to treat wastewater supported by solar energy to raise the temperature and facilitate the operation of wastewater treatment systems. Health in areas rich in solar resources. This approach reduces reliance on traditional energy sources in the wastewater treatment process. This theoretical study aims to create a mathematical model for the problem of water turbidity due to impurities (wastewater). Non-Newtonian fluid flow equations are established in the case of using renewable energy in various forms of nano-photocatalysts, as well as magnetic force which has a clear effect on the process of removing impurities from the aqueous fluid. Chebyshev's method was used to obtain numerical solutions to the problem, which were represented by a set of drawings and tables, that highlighted the effective role of both the magnetic field and sunlight in eliminating impurities. Increasing the Lorentz force and thermal radiation increases the strength of hydrogen bonding of the aqueous liquid mixed with particles of tri-hybrid nanomaterials larger than the aqueous liquid, which in turn works to raise the thickness of the thermal layer in the blade shape higher than the rest of the shapes. This study gives future insights for further research endeavors.

The study of heat transfer in fluid flows across permeable media is critical in many engineering applications, including energy systems, cooling technologies, and chemical processes. This study aims to explore the impact of joule heating and heat transfer flow of an MHD dissipative ternary fluid through a channel embedded in a Darcy-Forchheimer permeable medium. Additionally, the utilization of ternary hybrid nanofluids, composed of a base fluid and three nanoparticles Al2O3, MoS2, and Cu has emerged as a promising avenue for augmenting thermal conductivity and heat transfer rates. The governing equations are transformed into a set of coupled ordinary differential equations by employing similarity variables and simplified by bvp4c and artificial neural network (ANN) model approaches. Results reveal that significant enhancement in the velocity field at the lower channel wall and reductions at the upper wall, while fluid temperature decreases with increasing Prandtl number. Further, the heat transfer rate increases with an increase in the Prandtl number and magnetic field whereas the skin friction decays with an increase in the magnetic field. Meanwhile, the comparison was carried out for the temperature field by using bvp4c & ANN and the results are strongly correlated.

A metallic alloy is a combination of two or more elements, often called a compound or a solution. Steel is largely composed of carbon, a nonmetal, but alloys are often made up of metals. In this article, the authors have explored the electrically conducting water-based viscous nanofluids flow past a rotating disk surface. The nanofluids flow is composed of titanium and aluminum alloys where water is used as a base fluid. Two important cases, namely the stretching case and the shrinking case, were investigated to analyze the flow behaviors due to the different embedding factors. The impacts of viscous Joule heating, thermophoresis, Brownian motion, activation energy, nonlinear thermal radiation, and chemical reaction are investigated here. By employing an appropriate set of variables for shifting the leading equations to dimension-free form. The mathematical model is solved numerically by incorporating the bvp4c MATLAB scheme. Current work is validated with previous studies. The outcomes showed that the radial velocity increases when the disk surface stretches and reduces when the disk surface shrinks. On the other hand, the Azimuthal velocity increases when the disk surface shrinks and reduces when disk surface stretches. Both the radial and Azimuthal velocities are the diminishing functions of the magnetic factor, whereas temperature is the growing function of magnetic factor. In addition, the temperature is more influenced by the magnetic factor in the case of nonlinear radiation. The higher magnetic factor increases skin friction. In addition, the stretching case experiences more surface drag than the shrinking case. It is found that nanofluid flow containing titanium alloy has perceived the greater impacts of the embedded factors compared to the nanofluid flow containing aluminum alloy.

The axisymmetric stagnation point flow of brick and blade-shaped Silver and Copper nanoparticles immersed in an ethylene glycol base fluid under the influence of an induced magnetic field over an unsteady radial stretching surface is investigated in this study. The unsteady phenomenon is considered because most flow issues in practice are unsteady. The fundamental laws of mass, momentum, and energy conservation are used to present the physical model. Heat transmission is also examined under the effects of magnetohydrodynamics, Joule heating, viscous dissipation, and convective boundary conditions to give a realistic physical investigation. Scaling analysis transforms the flow-governing issue into a collection of higher-order nonlinear ODEs. These are, then, solved numerically using the fourth-order Runge–Kutta and shooting techniques. Moreover, the numerical technique is validated by calculating residual error. It is concluded that, compared to the Ag–EG nanofluid, the Cu–EG nanofluid had the highest IMF, lowest temperature, minimum surface drag, and maximum heat flux, making it the ideal choice for creating a radial module. [ABSTRACT FROM AUTHOR]

AbstractNumerically the hybrid nanofluid (HNF) flow comprised of aluminum alloys (AA7072 and AA7075) across to coaxial cylinders is reported in the current analysis. The fluid flow has been examined under the significances of viscous dissipation, thermal radiation, and exponential heat source/sink. The HNF is produced by the addition of AA7072 and AA7075 nanoparticles (NPs) in water. Aluminum alloys are mostly used for the electric module wrapping, electronic machinery, automotive body, solar and wind energy controlling, and energy generation. The flow has been modeled in the form of momentum, continuity, and energy equations. Numerical approach parametric continuation method (PCM) is used to solve the modeled equations. The consequences of flow and energy parameters on the temperature, velocity, skin friction, and Nusselt number have been revealed through figures. It has been noticed that the fluid velocity drops, whereas the energy curve develops with the escalating influence of magnetic field. Furthermore, the rising numbers of AA7072 and AA7075 NPs in the water diminish the fluid velocity and temperature profile. Energy curve accelerates with the growing values of Brinkman number. It can be observed that the energy transmission rate upsurges up to 13.17% by the addition of AA7072 and AA7075 NPs in the water. [ABSTRACT FROM AUTHOR]

This investigation explores the convective MHD stagnation point flow of Casson nanofluid over a stretching sheet in a porous medium with higher-order chemical reactions and multiple slips. The examination of heat transmission is carried out in the presence of radiation, Joule heating, viscous dissipation, and heat source. The system of governing equations was simplified by using appropriate transformations. The transformed equations are tackled numerically by a Runge-Kutta-based shooting technique with the bvp5c MATLAB package. The graphical and numerical results for different parametric values are discussed and presented through figures and tables. It is observed that an increase in the magnetic field, porosity, and Casson fluid parameter reduces the velocity whereas the opposite trend is seen in the case of the thermal Grashof number and the solutal Grashof number. Increasing values of radiation and Joule heating parameters, and the Eckert number, lead to an increase in the temperature. The chemical reaction, suction, and solutal slip were found to reduce the concentration. The friction factor was reduced due to the higher values of the thermal Grashof number, solutal Grashof number, and the velocity ratio parameter. Also, an increase in the Brownian motion and thermal slip parameters decreases the heat transfer rate. The computational results of the Nusselt number have been validated with published results in the literature and found good agreement. The results obtained in this investigation have applications to biomedical, engineering, and industrial sectors such as food processing, polymer manufacturing, glass, and fiber production, improving oil recovery, and material processing. [ABSTRACT FROM AUTHOR]

The present study offers a thorough evaluation of the influence of partial slip conditions and viscoelastic behavior on axial fluid flow driven by a cylinder or plate experiencing axial deformation with linear velocity. The momentum transport features a partial velocity slip which generates a nonlinear Robin-type boundary condition, while the energy transport employs a linear thermal slip boundary condition, as opposed to the previous studies that were limited to the no-slip conditions. The adoption of a quadratic surface temperature led to a novel and precise similarity solution. Furthermore, the study investigates the impact of an electrically conducting fluid assumption on momentum transport and viscous heating mechanism on thermal transport. The study utilizes a powerful routine that produces numerical results for a full range of parameters. Numerically evaluated coefficient of skin friction for the viscoelastic fluid flow is analyzed over a range of second-grade fluid parameters. In addition, heat transfer rates are determined for a variety of controlling parameters. A comparison of the present numerical approach with the homotopy scheme used by a previous study is presented and deliberated. [ABSTRACT FROM AUTHOR]

In this piece of communication, a theoretical investigation of two dimensional boundary layer flow of Magnetohydrodynamics (MHD) Carreau nanofluid axisymmetric flow past unsteady radially stretching porous disk is made. The investigation includes the effects of viscous dissipation, Joule heating, thermal radiation, suction/injection, Darcy–Forchheimer porosity model and binary chemical reaction with activation energy, etc. To examine the impacts of the aforementioned effects, the conservation laws are formulated with strongly nonlinear partial differential equations (PDEs), which are then transformed into a system of initial value problems (IVPs) using appropriate similarity transformations and techniques. The 5th order Runge–Kutta with the shooting technique is used to find numerical solutions aided by Python programming with built in program “fsolve”. The method is validated with other published articles under common assumptions and it agrees nicely. The impacts of the pertinent parameters on velocity, temperature, concentration, skin friction coefficient and the rates of mass and heat transfers with in the flow regime are displayed using graphs and tables. The main outcomes include the motivation of local Nusselt and Sherwood numbers for shear thickening (n=1.5) than shear thinning (n=0.5) cases of the Carreau nanofluid. The momentum boundary layer of the Carreau nanofluid gets thinner with an increase in Forchheimer number, unsteady and suction parameters. A dual nature is observed for concentration of the Carreau nanofluid with a rise in Eckert number, i.e increasing in concentration around the wall and decreasing far away from the wall. The rise in destructive and constructive chemical reaction parameters disperse and accumulate the concentration of the system, respectively.

For treating and diagnosing cardiovascular diseases, the field of biomedical engineering is significant because it develops new ways and techniques. Stenosis is the narrowing of an artery, and it leads reduction in the flow rate of blood. This study investigates the blood flow mechanism in an artery using a mathematical model of Carreau nanofluid with four distinct nanoparticles. Tetra nanofluid model produces significant advancement in the simulation of blood flow through the stenosed arteries. The model is capable of predicting the pressure drop and velocity distribution for diagnosing and treating stenosis. The spectral relaxation approach is used to present the model's efficiency and effectiveness, which makes it a suitable method for solving the governing equations of this study. The findings of this study have important implications for the development of new treatments and diagnostic techniques for stenosis and other cardiovascular diseases.

The aim of present study is to examine the augmentation of thermal energy transfer in hybrid nanofluid flow caused by a rotating Riga disk in the presence of thermal radiation and chemical reaction. The silver and aluminium oxide nanoparticles are used to examine the thermal effect of water base fluid. The Darcy-Forchheimer model is considered to endorse the inertial and porous media effects and makes the model more realistic from the physical scenario. Levenberg-Marquardt backpropagation algorithm is considered to analyze the hybrid nanofluid’s properties. Using scaling group transformations, the governing partial differential equations are transformed into a system of ordinary differential equations. Resulting ordinary differential equations are solved numerically by applying a suitable shooting technique by MATLAB. The results obtained for the governing differential equations have been incorporated into a dataset on which the neural network has been trained. The effects of physical parameters have been analyzed for velocity, temperature, and concentration profiles. The determination, designing, convergence, verification, and stability of the Levenberg-Marquardt backpropagation neural network algorithm are validated on the assessment of achieved accuracy through performance, fit, regression, and error histogram plots for the discussed hybrid nanofluid. It is observed that fluid velocity reduces for enhanced Darcy-Forchheimer number, magnetic parameters and boosted for enhanced modified Hartmann number. Temperature profile increases by increasing the Brownian motion and thermophoresis parameters.