The present study develops a hybrid analytical-computational approach to the thermal transport study of Reiner–Rivlin nanofluid flow with Arrhenius activation energy effects, aligning with UN Sustainable Development Goals 9 (Industry, Innovation, and Infrastructure) and 12 (Responsible Consumption and Production). The governing nonlinear partial differential equations are reduced to a coupled system of ordinary differential equations via Lie group transformations and solved numerically. An artificial neural network (ANN), trained using the Levenberg–Marquardt algorithm, is integrated with a modified Garson sensitivity analysis to quantify the effect of important parameters on the heat transfer. The ANN model exhibits excellent prediction accuracy with an overall correlation coefficient R=0.99977 . Results show that the thermal Biot number yields the highest positive impact, increasing the heat transfer rate by 54.61

Cardiovascular diseases and cancer remain critical threats to human health. The present study elucidates the biomedical application of Carreau bionanomaterial flow over a stretching cylinder, considering gold nanoparticles and external electro-magnetic fields that align with sustainable development goal (SDG) "Good Health and Well-Being". The shear-thinning nature of the Carreau bionanomaterial has been considered for its similarity with human blood. The governing equations, derived from conservation principles and a modified Buongiorno framework, accounting for radiation, higher-order chemical reaction, convective heating, nonuniform heat source, and second-order slip, are transmuted through similarity transformations to a coupled nonlinear set of ordinary differential equations. These equations are solved numerically using MATLAB's bvp5c solver and validated against limiting cases. Results indicate that stronger magnetic fields and weaker electric fields retard flow, facilitating improved blood-flow regulation, and targeted drug delivery. Neural network-driven sensitivity analysis and a multiple linear regression model, based on the modified Garson algorithm, highlight the relative significance of pertinent factors on the heat transfer rate. The results reveal that the Biot number and volume fraction of gold nanoparticles exhibit the strongest positive and negative associations, respectively.

The current research aims to endeavour the dynamics of Casson hybrid nanoliquid flow past a horizontal moving plate incorporating an irregular heat source and the thermal convective constraint at the wall. The nonlinear PDEs governing the flow are formulated using the Tiwari-Das model and further resolved in MATLAB with the aid of the built-in finite difference algorithm-based bvp5c scheme and apposite transformations. Moreover, the behaviour of the Cu-Al2O3 hybrid Casson nanoliquid (HCNL) has been compared to that of the Cu-Casson nanoliquid and Casson fluid. Per unit change in the volume fraction of alumina nanoparticles ascends the drag coefficient by 77.50 λ =0.5 and descends the friction factor by 107.92 λ =1.5 . The response surface methodology (RSM) has been employed to assess the consequence of the space-dependent heat source (SHS) parameter (0.02≤α_1≤ 0.04) , volume fraction of copper nanoparticles (0.01≤ϕ_1≤ 0.09) , and volume fraction of alumina nanoparticles (0.01≤ϕ_2≤ 0.09) on the heat transfer properties. It can be noted that the addition of copper nanoparticles tends to decline the Nusselt number. Further, sensitivity analysis is also carried out to determine which input parameters profoundly influence the model outputs. It is observed that the SHS parameter showcases negative sensitivity with the Nusselt number.

For its applications in aerodynamics, nuclear waste disposal, heat transfer enhancement, plasma studies, drug delivery, cooling systems, and power generators, the authors have investigated the dynamics of Reiner–Rivlin nanofluid flow past an inclined flat plate. Nonlinear chemical reaction, zero mass flux and Soret-Dufour effects are considered. Non-similar approach has been used to transform the mathematically modeled set of equations which are then solved using the finite-difference based bvp5c scheme in MATLAB. The validation of numerical results has been carried out through a restrictive comparison with the previously published studies and an excellent similarity is noted. A comparative analysis between the Newtonian (K=0) and non-Newtonian (K=24) cases is also carried out. It is observed that the heat transfer characteristics and velocity profiles are improved for the non-Newtonian nanofluid. Increase in the angle of inclination affects the velocity profile negatively. Increment in the similarity variable and angle of inclination brings an augmentation in the nanofluid temperature. Per unit change in the Soret parameter causes the heat transfer rate to ascend by 22

The present study numerically investigates hydromagnetic swirling blood flow with nanomaterial over a rotating cylinder. The impact of nonlinear radiation and Stefan blowing effect is explored. Moreover, Joule heating and viscous dissipation effects are considered to control the temperature profile. The problem is modelled using modified Buongiorno model. Suitable similarity variables are utilized to convert governing PDE’s to ODE’s and then numerically computed using bvp5c scheme. A five-level four-factor response surface methodology (RSM) is employed to optimise the impact of Hartmann’s number (0.2 ≤ M≤ 0.6 ), curvature parameter ( 0.1≤ K≤ 0.3 ), radiation parameter ( 0.1≤ Rd≤ 0.5) , and volume fraction of nanoparticles ( 0.01≤ϕ≤ 0.03) on the heat transfer rate. Streamlines have been employed to illustrate the direction and speed of flow profiles. It is observed that axial, swirl, and temperature profiles are at peak stage in the blowing case than suction. Heat transfer rate enhances with low magnetic field and cylindrical curvature. A similar trend is observed in the case of low volume fraction of single-wall carbon nanotubes and high radiation parameter respectively. Per unit change in the Hartman number reduces the shear stress due to swirl motion by 65.5829

For its applications in nuclear reactors, food processing, chemical engineering, water emulsions and thermal power generating systems, the significance of irregular heat source and Arrhenius energy on electro-magnetohydrodynamic hybrid nanofluid flow over a rotating stretchable disk with nonlinear radiation have been investigated. The flow problem has been modeled utilizing the modified Buongiorno model and the thermophysical characteristics of water-based Cu-Fe3O4 hybrid nanoliquid. Effects like passive control of nanoparticles, hydrodynamic slip and convective boundary conditions are also heeded to boost the realistic nature of this work. Further, engineering quantities like moment coefficient and pumping efficiency of the disk are also elucidated which boosts the novelty of this research work. The modeled governing equations are transmuted into a system of first-order ODEs, with the help of apposite similarity transformations, which are then numerically resolved using the finite-difference based bvp5c algorithm. It is noticed that per unit increase in the electric parameter decreases the skin friction coefficient by 41.75% and increases the heat transfer rate by 15.31%. It is also observed that the entrainment velocity is directly proportional to the changes in electric field parameter and is inversely proportional to the changes in volume fraction of copper and magnetite nanoparticles.

The present research examines the behavior of a Jeffrey nanofluid flow across a stretching sheet under the effect of electric and magnetic fields. It comprises the Buongiorno model as well as an exponential heat source. The impact of chemical reaction has also been taken into consideration. While assuming no mass flux, the study considers boundary conditions for thermal convection and velocity slip. Lie group transformations are employed to transform the set of governing equations into a dimensionless system and later simulated using the finite difference scheme. It is found that the velocity profile rises as the Deborah number is enhanced whereas the ratio of relaxation to retardation time parameter has an inverse effect on the velocity profile. It is noted that per unit change in the Deborah number descends the drag coefficient by 31.29%. In this study, the response surface methodology and sensitivity analysis have been conducted by choosing heat transport as the dependent variable and the electric-field parameter (0.01 <= E <= 0.03), exponential heat source parameter (0.02 <= Qe <= 0.06), and Biot number (0.15 <= Bi <= 0.25) as the independent variables. The Nusselt number escalates when the Bi number is increased and drops as the E values are raised. In the instance of the Biot number, the Nusselt number exhibits the maximum sensitivity.

For its application in cancer therapy, targeted drug delivery, radiofrequency ablation, and magnetic resonance imaging, the dynamics of electro-magnetohydrodynamic flow of blood-gold nanomaterial over a nonlinearly stretching surface utilizing the Casson model has been elucidated numerically. The impact of second-order hydrodynamic-slip, nanoparticle radius, first-order thermal-slip, inter-particle spacing and non-uniform heat source are also accounted. The modeled flow equations are transmuted into a nonlinear system of first-order ODEs (with the aid of apposite similarity variables) which are then resolved numerically utilizing the bvp5c scheme. The thermal field augments with an increase and a decrease in the inter-particle spacing and radius of gold-nanoparticles, respectively. However, a reverse trend is noted for the velocity profile when the radius and inter-particle spacing of gold-nanoparticles are altered. The trend and magnitude of the change in the drag rate and heat transfer rate under the influence of effectual parameters have been demonstrated statistically using slope of linear regression. It is noticed that per unit increase in the volume fraction of gold nanoparticles augments the heat transfer rate by 81.71% and reduces the surface drag by 163.51%. Further, per unit increase in the inter-particle spacing of gold nanoparticles augments the drag coefficient by 85.92% whereas per unit increase in the radius of gold nanoparticles reduces the skin friction coefficient by 49.71%.

The hydromagnetic flow of magnetite–water nanofluid due to a rotating stretchable disk has been numerically assessed. The nanofluid flow has been modeled utilizing the adapted Buongiorno model that considers the volume fraction-dependent effective nanofluid properties and the major slip mechanisms. In addition, experimentally gleaned functions of effective dynamic viscosity and effective thermal conductivity are deployed. The modeled equations are transformed into a first-order ODEs scheme employing Von Kármán’s similarity conversions and then resolved via the Runge–Kutta algorithm through the shooting technique. The impact of pertinent terms over the physical quantities, nanoliquid temperature and nanoliquid concentration is explained with the support of graphs. Results show that rising volume fraction of magnetite nanoparticles (NPs) and magnetic field term enhance the drag force. Mass transport rate is demoted with augmenting values of magnetic field parameter whereas is promoted with increase in Schmidt number. Further, it is detected that the changes in stretching strength parameter are directly proportional to Nusselt number and inversely proportional to the thermal field. The findings of this numerical analysis have applications in spin coating, rotating disk reactors, storage devices for computers, food processing, and rotating heat exchangers.

The significance of this investigation is to optimize the heat transfer rate of magnetohydrodynamic bioconvective hybrid nanofluid flow in the presence of heat source and thermal convection. The main focus is to examine the two-dimensional incompressible MHD (Cu-Ag)/H2O and (TiO2-Ag)/H2O hybrid nanofluid flow across the stretching cylinder with the Cattaneo-Christov heat flux model. The response surface methodological approach and sensitivity analysis have been employed to statistically scrutinize the influences of concentration, bioconvection, and thermo-diffusion on heat transfer rate. By applying suitable similarity vectors in controlling the partial differential equations, a system of equations (ODEs) is formed. A well-known method Runge Kutta with shooting has used for numerical simulations. The role of various involving factors on heat and mass transfer rate and skin friction factor is illustrated using tables, figures, and surface plots. The three-dimensional graphs displayed the synchronized effect of involving factors on physical quantities. The heat transfer rate is least responsive to variations in the magnetic parameter and most sensitive to the fluctuations of the Biot number. It is perceived that the nanoparticle concentration and motile concentration profiles declined with the increasing effect of chemical reaction parameters. The legitimacy of the current conclusions is established by the excellent agreement concerning present and previous consequences.

The present study aims to investigate the influence of magnetohydrodynamic (MHD) Carreau nanofluid flow past a stretching cylinder with quadratic Rosseland heat radiation. This paper examines the consequences of the Soret-Dufour effects when considering the influence of thermophoresis and Brownian effects. The convective and diffusive boundary conditions have been implemented. The modeled mathematical system of non-linear partial differential equations (PDEs) is transformed into a dimensionless representation using a non-similar approach. The ensuing set of dimensionless equations are solved numerically with local non-similarity method (LNM) aided by the finite difference algorithm. The findings of the study unveil that the presence of the Dufour and Soret effect declines the heat transfer and mass transfer rates, respectively. It is also noted that flow profiles are more profound in the case of stretching cylinder configuration. Per unit increase in the hydrodynamic slip parameter augments the drag coefficient by 35.87% and 33.40% for cylinder and sheet configurations, respectively. The present study has potential applications in biomedicine, such as targeted drug delivery, hyperthermia, theranostics and cardiovascular treatments.

The present study investigates the dynamics of Reiner-Rivlin nanofluid flow past an inclined flat plate considering quadratic radiation, external magnetic field and nonlinear buoyancy. Appropriate similarity transformations are employed to transform the mathematically modeled equations and are then resolved using the finite-difference based bvp5c scheme, which implements the four-stage Lobatto IIIa formula, in MATLAB. A comparative study between the transport phenomena of non-Newtonian and Newtonian case is also performed. It is observed that the Newtonian case exhibit higher solutal and thermal fields when compared to the non-Newtonian case. However, the results are reversed in the case of velocity profile. The Reiner-Rivlin nanofluid has improved heat transfer rate and drag coefficient characteristics than the Newtonian fluid. Augmentations in the inclination angle descend the velocity profile and ascend the thermal and solutal fields. The increment in the radiation parameter and Hartmann number causes an increment in the nanoliquid temperature. It is also observed that the velocity profile is directly proportional to the changes in the buoyancy ratio. Moreover, the present study has applications in the field of plasma studies, aerodynamics, and cooling systems.

The current study focuses on investigating the significance of magnetic field and multiple slip constraints on the water-based graphene Darcy-Forchheimer nanofluid flow over a rotating disk. For a realistic approach, the modified Buongiorno nanofluid model that incorporates the combination of effective thermophysical properties, thermophoretic diffusion, and Brownian diffusion has been utilized. Engineering quantities like moment coefficient and pumping efficiency of the disk are also elucidated. The transmutation of the mathematically modeled nonlinear equations into a system of first-order ODEs are achieved through Von Kármán’s similarity transformations and are then resolved using the shooting technique along with the Runge–Kutta-Fehlberg algorithm. The highest heat transfer rate is experienced for smaller values of magnetic field parameter, Forchheimer number, porosity parameter, and thermal slip constraint. An increment rate of 88.14355% in the azimuthal drag coefficient and a decrement rate of 39.849732% in the radial drag coefficient are noted when the values of hydrodynamic slip constraint are augmented. Further, per unit increase in the volume fraction of graphene nanoparticles descends the moment coefficient and the entrainment velocity by 456.25501% and 12.48875%, respectively. The tidings of this numerical simulation have applications in spin coating, centrifugal filtration, medical equipment, gas turbine rotors, and thermal power generating systems.

The hydromagnetic stagnation‐point flow of magnetite‐water nanofluid due to a rotating stretchable disk has been numerically accessed. The nanofluid flow has been modeled by employing the two‐phase modified Buongiorno model that incorporates the volume fraction dependent effective nanofluid properties, Brownian motion, and thermophoresis effects. Von Kármán's similarity transformations are utilized in transmuting the mathematically modeled equations into a system of first‐order ODEs which are then resolved numerically using the bvp4c numerical scheme. The consequence of influential parameters on the flow profiles and the physical quantities has been presented through graphs and tables. Engineering quantities like moment coefficient and pumping efficiency of the disk are also elucidated in this research work. Results show that an augmentation in the Hartmann number descends the velocity profiles and ascends the nanofluid temperature profile. Further, a drop in the drag coefficient and a rise in the heat transfer rate are noted with an increment in the velocity ratio parameter. The tidings of this numerical simulation have applications in spin coating, rotating heat exchangers, and rotating disk reactors.

Abstract The proposed study demonstrates the flow phenomenon and thermo-variation of a magnetized stretching sheet induced-radiative nanofluid flow. By incorporating the response surface methodology, the heat transfer rate of the thermally convective flow of nanofluid is optimized. The graphene nanomaterial is used in the water-based nanofluid. A dynamic magnetic field, thermal radiation, and the Cattaneo–Christov heat flux model have used to represent the thermal behavior of the nanofluid. The simulation utilizes experimentally estimated values for the nanomaterial’s thermal conductivity and viscosity. To further reveal the thermal enhancement of the flow, the impact of nanoparticle diameter and the solid-liquid interfacial layer is proposed at the molecular level. The response surface methodology and the sensitivity analysis has used to examine the effects of the nanoparticle volume fraction, Biot number, and magnetic parameter on the rate of heat transfer statistically. A set of equations is formed from the governing partial differential equations by implementing suitable similarity transformations. The bvp4c approach is used to solve the problem numerically. The effect of various parameters has displayed through tables, graphs, and surface plots on heat transfer, mass transfer, and the local Nusselt number. It is discovered that as the Biot number increases, so does the concentration and temperature profile. An excellent accord between the present and previously existing solutions is establishing the validity of the achieved results.

For its biomedical applicability, the electro-magnetohydrodynamic flow of blood-gold nanomaterial over a nonlinearly stretching surface utilizing the Casson model has been numerically elucidated. The impact of second-order hydrodynamic-slip, gold nanoparticles of different inter-particle spacing and radius, and non-uniform heat source are also accounted. The incorporation of nanofluid characteristics in the traditional Casson model improves the applicability, practicality and realistic nature of the modeled flow problem. The present study finds its application in radiofrequency ablation, magnetic resonance imaging, cancer therapy, and targeted drug delivery. Apposite similarity variables are employed to transmute the modeled flow equations into a nonlinear system of first-order ODEs which are then resolved using the bvp5c scheme. It is observed that the intensification in space-dependent heat source, temperature-dependent heat source and heat of reaction ascend the thermal field. It is noted that per unit increase in the inter-particle spacing ascends the drag coefficient by 70.2431176 ( 0.1 ≤α≤ 0.9) , reaction rate ( 0.1 ≤β≤ 0.9) , nanoparticle radius ( 0.5 ≤ R_np≤ 2.5) , and inter-particle spacing ( 0.5 ≤ h ≤ 2.5) on the mass transfer rate ( Sh_xRe_x^ - 1/2) has been scrutinized statistically using the five-level four-factor response surface optimized model. The mass transfer rate is maximum for larger values of inter-particle spacing and smaller values of reaction rate, heat of reaction and the radius of gold nanoparticles.

The flow past a stretching sheet has been explored by many scientists for its application in metal spinning, drawing of plastic films, glass blowing, crystal growing, and cooling of filaments. In addition, the presence of microorganisms enhances the stability of the fluid that plays a significant role in biotechnology, bio-microsystems, and bio-nano coolant systems. Therefore, the dynamics of bioconvective MHD hybrid nanofluid (TiO2 and Ag in water) flow over an exponentially stretching permeable surface considering thermal radiation, heat generation, chemical reaction, porosity, and dissipative effects has been investigated. Apposite similarity variables are applied in transforming the modeled PDEs into a system of nonlinear ODEs and are then solved utilizing the finite-difference based bvp5c algorithm. It is observed that an increase in the porosity parameter ascends the temperature and descends the velocity. It is also noted that the temperature profile is proportional to augmentations in radiation parameter, magnetic field parameter, Eckert number, and volume fraction of TiO2 and Ag nanoparticles. The mass transfer rate and the motile density number increase with mounting values of chemical reaction parameter. Further, multiple linear regression has been utilized to statistically scrutinize the effect of pertinent parameters on drag coefficient and heat transfer rate.

The size and intensity of the system of delocalized electrons are reflected in the form of the induced magnetic field. Even though this also affects nearby molecules, nothing is known on the significance of stagnant water conveying silver A(g), aluminum oxide Al2O3, and aluminum Al nanoparticles of different shapes on a horizontal surface experiencing convectively heating as applicable in the industry. Relevant similarity transformations were adopted to non-dimenzionalized the governing equations and solved numerically using the 3-stage Lobatto IIIa integration formula for a finite difference (MATLAB package bvp4c). Based on the analysis of the new results, it is worth concluding that either in the case of heat source or heat sink, an increment in the convective heating of the wall is a factor capable to boost the temperature distribution. Increasing effects of an inclined magnetic field are capable to cause the distance between the turning points of shear stress and that of the gradient of magnetic flux density to be located at the middle of the domain.

Convective heat transport gives the remarkable behaviour in the many industrial procedure owing it mechanical behaviours of the system. A study has been obtained to analyse thermal radiative flow on unsteady MHD tangent hyperbolic nanoliquid near a stagnation point under viscous dissipation and chemical reaction. Also, thermal-diffusion and thermo-diffusion have been considered. The nonlinear PDE’s are altered into a set of ODE’s through suitable transformation and which are then numerically utilized. Further, numerical outputs for friction factor, Nusselt number and Sherwood are produced in table. Moreover, velocity distribution is increasing for a larger value of We and reduces for n. Moreover, similar behaviour is noted for temperature profile. A comparison with accessible outcomes for limited case is obtained with tremendous achievement.

The study focuses on the aggregation kinematics in the quadratic convective magneto-hydrodynamics of ethylene glycol-titania ([Formula: see text]) nanofluid flowing through an inclined flat plate. The modified Krieger-Dougherty and Maxwell-Bruggeman models are used for the effective viscosity and thermal conductivity to account for the aggregation aspect. The effects of an exponential space-dependent heat source and thermal radiation are incorporated. The impact of pertinent parameters on the heat transfer coefficient is explored by using the Response Surface Methodology and Sensitivity Analysis. The effects of several parameters on the skin friction and heat transfer coefficient at the plate are displayed via surface graphs. The velocity and thermal profiles are compared for two physical scenarios: flow over a vertical plate and flow over an inclined plate. The nonlinear problem is solved using the Runge–Kutta-based shooting technique. It was found that the velocity profile significantly decreased as the inclination of the plate increased on the other hand the temperature profile improved. The heat transfer coefficient decreased due to the increase in the Hartmann number. The exponential heat source has a decreasing effect on the heat flux and the angle of inclination is more sensitive to the heat transfer coefficient than other variables. Further, when radiation is incremented, the sensitivity of the heat flux toward the inclination angle augments at the rate 0.5094% and the sensitivity toward the exponential heat source augments at the rate 0.0925%. In addition, 41.1388% decrement in wall shear stress is observed when the plate inclination is incremented from [Formula: see text] to [Formula: see text].