Artificial neural networks play a vital role in predicting and analyzing magnetohydrodynamic natural convection of Boger nanofluids around a semi-circular obstacle inside a triangular cavity, providing key insights for enhancing thermal performance. This study conducts a detailed numerical investigation of Boger nanofluid flow within a triangular cavity, governed by the Cattaneo–Christov heat flux model and influenced by non-uniform internal heat sources/sinks, thermal radiation, and Lorentz forces. A semi-circular obstacle with distinct thermal boundary conditions is placed inside the cavity, which features adiabatic bottom-left and bottom-right inclined walls, while the central segments of the top, left, and right walls are maintained at a high temperature. Heat transfer arises due to the movement of these heated regions and temperature gradients within the cavity, leading to complex convection behavior. The dimensionless nonlinear partial differential equations are solved using the finite element method, accompanied by a comprehensive parametric analysis. The effects of critical parameters such as solvent fraction ( 200 ≤β _1 ≤ 300 ), time relaxation ratio ( 7 ≤β _2 ≤ 11 ), Darcy number ( 10^-2≤ Da ≤ 10 ), Rayleigh number ( 10^1.5≤ Ra ≤ 10^2.5 ), time ( 0.05 ≤ Ra ≤ 0.5 ), and thermal relaxation parameter ( 10 ≤γ≤ 50 ) are evaluated through changes in isotherms and streamlines. Results indicate that increasing the solvent fraction enhances vertical velocity and temperature distribution but reduces the Nusselt number along the heated surfaces and semi-circular region. Moreover, higher values of thermal relaxation and radiation parameters tend to suppress the temperature field. The analysis concludes that heat transfer, as reflected by the Nusselt number, is more efficient on the cold semi-circular boundary compared to the heated semi-circular. The ANN predictions exhibit excellent consistency with FEM simulations, lending credibility to the ANN framework as a surrogate modeling strategy for estimating local Nusselt numbers in complex thermal systems.

The thermal analysis and Lorentz force influence on Micropolar fluid in the presence of Brownian motion of solid particles across the extending surface subject to two-phase fluid is investigated. Recent years have seen a growing interest among researchers in two-phase fluids due to highly extensive modern technological applications. The comprehensive scrutiny is conducted on an electrically conducting Micropolar dusty nanofluid with a magnetic field. The mathematical model is developed in the form of nonlinear in nature partial differential equations (PDEs) for a two-phase Micropolar nanofluid and dusty phase. The flow governed equations are reduced to ordinary ones by applying similarity transformations. The reduced system of ordinary differential equations (ODEs) has been integrated with the aid of the built-in function MATLAB solver bvp4c with the shooting technique. The results for different values of prominent parameters for both the Micropolar nanofluid phase and dusty phase are estimated and elaborated through graphical results. From the results, it is concluded that the dust particle fraction causes a reduction in fluid velocity, while the thermal field for both phases is boosted. The thermal and concentration species are boosted with the thermophoresis parameter.

This study presents a numerical analysis of nonlinear buoyancy-driven convection nanofluid flow with heat and mass transfer inside a semi-circular cavity containing a centrally heated T-shaped obstacle. The investigation focuses on buoyancy-driven flow influenced by the Soret and Dufour effects, emphasizing the roles of thermodiffusion and diffusion-thermo coefficients along with the Schmidt number. The mathematical model incorporates the Dufour effect in the energy equation and the Soret effect in the concentration equation to accurately capture their contributions to the transport processes. The governing PDEs are solved using an integrated physics-informed FEM-ANN-GNN framework where the finite element method (FEM) provides high-fidelity numerical solutions, a dense artificial neural network (ANN) approximates the nonlinear input-output mapping of flow and transport fields, and a graph neural network (GNN) encodes spatial connectivity for structurally informed surrogate predictions. The study is significant in its development of a highly efficient physics-informed framework that enables near-FEM accuracy while reducing computational cost and enabling rapid parametric exploration of complex buoyancy-driven systems. The nonlinear boundary value problem is examined across controlling variables such as the impact of various semi-circular obstacle conditions (cold, adiabatic, and heated), magnetic field (1.0 <= M <= 5.0), Rayleigh number (10 & sup2; <= Ra <= 10(5)), thermal buoyancy force (0.0 <= N-* <= 2.0), Darcy number (10(-)& sup3; <= Da <= 10(-)& sup1;), nonlinear thermal convection due to temperature (0.2 <= lambda <= 0.6), Brownian diffusion (1.0 <= N-b <= 5.0), thermophoresis (1.0 <= N-t <= 5.0), Eckert number (1.0 <= Ec <= 3.0), and Schmidt number (2.0 <= Sc <= 6.0). The results indicate that the behavior of temperature, concentration, and velocity magnitude improves with an increase in Rayleigh number, thermal buoyancy force, nonlinear thermal convection due to temperature, and Brownian diffusion, while the local Nusselt number decreases due to dissipation. Additionally, the semi-circular cavity with a heated central T-shaped obstacle exhibits superior velocity, temperature, and concentration distributions compared to cold and adiabatic configurations. Model performance evaluated through MAE, RMSE, and R & sup2; shows that the GNN achieves R & sup2; > 0.995 with significantly lower MAE/RMSE than the ANN while maintaining excellent agreement with FEM, proving the efficacy of the GNN approach in enhancing computational efficiency for real-time thermofluidic predictions.

This paper investigates heat and mass transfer phenomena by assessing advanced thermal conductivity models (TCMs) that significantly influence the flow of metallic (Au) nanoparticles under suitable boundary conditions. By integrating high TCMs with innovative interfacial fractal theory, we demonstrate a marked enhancement in thermal and concentration transfer. The analysis further investigates the physical model of a hybrid porous channel under the influence of nanofluid flow, magnetohydrodynamics (MHD), and chemical reactions. A detailed numerical investigation of nonlinear partial differential equations, converted into higher-order nonlinear ordinary differential equations (ODEs) using similarity transformations, reveals results by employing single-phase models of nanofluids. The ODEs are solved numerically via the shooting approach combined with the fourth-order Runge-Kutta method, using Mathematica to produce both graphical and numerical results. A comparative graph for expanding/contracting cases deliberated under the impact of MHD and chemical reaction. For expanding and suction cases, volume fractions of nanoparticles increase the function of the Nusselt number. Similarly, MHD is also an increasing function of shear stress near the porous surfaces. As the radius of the nanoparticle (d(p)) and the inter-particle spacing (h) increase, the radial velocity and temperature profiles also rise in both porous walls. It shows that chemical reactions alter thermal and mass transfer characteristics, with optimal parameters identified for maximizing efficiency. The research uncovers nonlinear interactions between flow dynamics and nanoparticle characteristics, explores the impact of external magnetic fields, and examines how boundary conditions influence transfer processes. Overall, this work enhances our understanding of using fractal theory to improve heat and mass transfer in engineering applications involving metallic nanoparticles.

Significance: This study explores the vital aspects of applied side of heat transfer in different areas like in heat exchangers, electronic device cooling, and energy storage units. This article is significant because it investigates the flow around circular obstacles and makes vital contribution for modern industrial systems. Cause of the article: This article implements the Physics Informed Neural Networks (PINNs) on established study related to heat transfer enhancement in diamond based nanofluid inside a square cavity having a fixed circular obstacle. The inclusion of circular obstacle induces localized temperature gradient sand recirculating vortices. Basically, this article tells how geometric barriers influence convective heat transfer. Furthermore, computes the involved mathematical model using data-efficient PINNs optimization Scheme: The mathematical model based on square cavities configuration around circular obstacle is formulated and system of Partial Differential Equations (PDEs). After making them dimensionless, the PINNs framework has been utilized to get the predicted results. Preconditioned Davidon-Fletcher-Powell (PDFP) optimizer is employed to enhance convergence rate, prediction accuracy and training stability of the PINN framework. Key outcomes: Conclusion of this attempt shows that the configuration and data used to train the PINN model found well and discretization of this model separates boundary points from interior points. The velocity components maintain near-zero values at all walls, and this confirms the precise accurate suppression artificial penetration velocities. Thermal surfaces exhibit well-defined gradients that compress toward the hot wall as Pr increases.

Stratified immiscible fluid flows are central to functional gradient material fabrication, where thermal and hydrodynamic interactions strongly influence the final material performance; however, the combined roles of non-Newtonian rheology, nanoparticle dispersion, and magnetic field effects remain insufficiently explored. This study focuses on mixed convection heat transfer with double impermeable layers inside a vertical channel, consisting of a Jeffrey fluid in region I and a Casson nanofluid in region II, and a transverse magnetic field in steady uniform flow. A transformation-based computational approach is employed to resolve the coupled momentum and energy transport. The main focus shows that increasing the nanoparticle loading has similar effects in both regions, significantly increasing the heat transfer efficiency and reducing the velocity by increasing the flow resistance. Furthermore, the Jeffrey and Casson parameters provide improved flow rates and thermal uniformity in fluid layers, which inhibit convective motion but provide good stability and control of the flow. These observations provide good physical information and useful suggestions for improving the thermal and hydrodynamic properties in complex functional gradient material processing systems.

This paper analyses the nation's advancements in renewable energy in Iraq from 2013 to 2023, emphasizing the potential of solar, wind, and biomass technologies. Iraq possesses substantial renewable energy resources, with an estimated technical potential of 500 MW from solar energy, as it receives an average daily solar irradiance of 5–6 kWh/m 2 , in addition to more than 200 MW of existing wind power capacity. Nonetheless, a number of obstacles still existed such as insufficient legislative frameworks, grid interconnection concerns, and substantial initial investment costs impede large-scale implementation. The transition into renewable energy necessitates significant expenditures, projected in the billions of dollars, to develop infrastructure, facilitate research, and promote adoption. The research finds that solar and wind energy might diminish Iraq's carbon footprint by 30–40% during the next twenty years. The analysis examines governmental measures and methods to accelerate the transition, encompassing financial incentives, regulatory reforms, and public awareness campaigns. By confronting these problems and utilizing its extensive renewable resources, Iraq may attain a sustainable energy future, alleviating economic and environmental pressures while guaranteeing long-term energy security.

Nanofluids have emerged as advanced heat transfer media due to their incorporation of nanoscale materials such as nanopolymers, nanofilms, nanotubes, nanowires, nanoshells, metals, non-metals, and carbon-based nano-structures dispersed in conventional base fluids. Their superior thermal and physical properties have enabled applications in diverse engineering domains. The present study investigates the bioconvective flow of a Prandtl nanofluid containing motile microorganisms over a stretching surface, accounting for the effects of the activation energy, thermal radiation, and Biot number. The governing equations are transformed via similarity mappings and solved numerically using MATLAB BVP4C shooting method. Furthermore, Response Surface Methodology (RSM) and sensitivity analysis are applied to quantify the effects of key physical parameters. Results show that motile microorganisms enhance bioconvective transport, thereby improving heat and mass transfer efficiency. This work demonstrates strong potential for engineering and biomedical applications such as the design of efficient bioreactors, development of microbial fuel cells, precision drug delivery, advanced biomedical cooling devices, and sustainable wastewater treatment using bio-nanofluids. Moreover, the study offers theoretical foundations that can be extended to bio-inspired nanotechnology, optimized microfluidic thermal systems, and energy-efficient biomedical transport processes.

Researchers and manufacturers’ primary focus is on the dissipation of energy throughout the heat transfer process. The use of traditional fluids, which have poor heat transfer qualities, was the primary cause of the inefficiency of heat exchange devices during transportation. Conversely, when we replaced the fluids with nanofluids that possessed favorable thermal conductivity qualities, thermal devices performed better. We utilized a variety of nanoparticles due to their high heat conductivity. This study examines the importance of using nanofluid in flow of heat transfer. The model of flow consisted of partial differential equations (PDEs) representing equations for concentration, momentum, energy transmission, and continuity. We transformed the generated model into ordinary differential equations (ODEs) using feasible analogies. The MATLAB environment was used to perform numerical simulations that established the profiles of concentration, velocity, and thermal transfer. We also evaluated the effects of a wide range of factors, including Deborah, Hartman, buoyancy, the size of an external heat source, and other chemical reactions. Nanoparticles increase thermal conductivity. We also juxtapose the results with those from previously published studies. Furthermore, as the Nusselt number and skin friction increase, they exhibit a positive correlation with the variables linked to the Hartman number and buoyancy parameter. The heat transfer rates are 29.26%. 37.12 In the order mentioned, as a result, heat transmission rates increased by 14.23%. There is no text provided. At higher levels of the MHD fluid parameter, the temperature profiles dropped and the velocity profiles rose. The temperature profile rises as the external heat source gets stronger. On the contrary, the buoyancy parameters rise as it goes down. This topic is relevant in various domains, including heat exchangers, electronic device cooling, and automotive cooling systems.

This study investigates the effect of the single-walled carbon nanotube (SWCNT) nanoparticle radius on the mixed convection and nanolayer thermal conductivity flow of a Boger nanofluid over a stretching disk. Due to their elastic and non-Newtonian properties, Boger fluids are applicable in fields like polymer processing, rheological studies, enhanced oil recovery, and industries such as biomedical, food, and cosmetics, where simulating complex fluid flow behaviors is crucial. The research further explores the heat and mass transfer of the Boger fluid, considering factors such as viscous dissipation, Joule heating, magnetic field influence, porous medium permeability, and activation energy, while focusing on the flow behavior of motile microorganisms. The partial differential equations (PDEs) governing the system are reformulated in dimensionless form using appropriate non-dimensional variables. The finite element method (FEM) is used to solve these nonlinear and complex flow equations through an iterative approach, generating both numerical solutions and graphical representations of the nonlinear system via MATLAB programming. To ensure the reliability and accuracy of the numerical solution, convergence criteria are assessed, and results are compared with established reference solutions. The impact of various dimensionless variables on different flow profiles is analyzed through 2D and 3D graphical representations, as well as numerical analysis of key physical quantities. The study finds that expanding the nanoparticle radius increases skin friction, while the Nusselt number decreases in the porous disk, with optimal results occurring at a & lowast; = 0.1. The velocity profile improves with a higher solvent fraction, but diminishes as the relaxation time ratio increases at 7 & lowast; = 0.7 and a & lowast; = 1.96. Increasing nanolayer thickness enhances temperature distribution, whereas a larger particle diameter reduces the heat transfer rate in nanofluid flow. Higher values of dimensional activation energy enhance the concentration profile, while an increase in temperature difference and dimensional reaction rate parameters reduces the mass transfer rate with variations in a & lowast; and 7 & lowast;. Additionally, higher values of the bioconvection Lewis and Peclet number parameters have opposite effects on microorganism distribution for different values of a & lowast; and 7 & lowast;, with the Sherwood number decreasing with larger dimensional activation energy values, and larger values of the motile Schmidt number enhancing the flow of motile microorganisms.

The Processes Editorial Office retracts the article “Finite Element Study of Magnetohydrodynamics (MHD) and Activation Energy in Darcy–Forchheimer Rotating Flow of Casson Carreau Nanofluid” [...]

Nanoparticles play a crucial role in enhancing thermal management, biomedical applications, and advanced industrial processes. This study presents a detailed numerical analysis of heat and mass transfer in a reactive nanofluid containing tetrahedral nanoparticles (aluminum oxide, copper, iron oxide, and titanium oxide), flowing between two orthogonally arranged porous disks. The investigation incorporates the effects of heat generation/absorption, the Cattaneo–Christov heat flux model, activation energy, chemical reactions, and three nanoparticle shapes: spherical, brick, and platelet. Furthermore, the roles of nanolayer thermal conductivity, viscous dissipation, and Joule heating in the heat transfer process are thoroughly examined. The governing nonlinear partial differential equations are transformed into ordinary differential equations using similarity transformations and are solved numerically using the shooting method combined with the fourth-order Runge–Kutta technique. The graphical results are generated using Mathematica software. The findings reveal that the platelet-shaped nanoparticles exhibit significantly superior heat transfer performance, particularly in the suction case, as indicated by higher Nusselt number values compared to other shapes. Increasing the nanolayer thickness enhances the heat transfer rate in both injection and suction scenarios. However, a larger nanoparticle radius leads to opposite fluid behavior in suction and injection cases, as reflected in the Nusselt number values for the lower disk. Moreover, increasing the expansion ratio and magnetic field parameters reduces the radial velocity profile in the central region between the disks but enhances it within the momentum boundary layers near both porous surfaces. Higher values of heat generation or absorption lead to a reduction in the temperature profile, while an increase in activation energy improves mass transfer, as evident from the concentration profile.

The study of nanofluid flows over stretchable wedge geometries has long held significance in fluid mechanics due to its wide‐ranging thermal engineering applications. This work investigates the heat transfer characteristics and flow behavior of a ternary hybrid nanofluid over a stretchable wedge under forced convection, considering both low and high nanoparticle volume fractions. Here, we use water as a base fluid and copper oxide, titanium dioxide, and silicon dioxide as nanoparticles. Ternary hybrid nanofluids exhibit superior thermal conductivity and heat transfer capabilities compared to conventional base fluids, offering potential benefits in applications such as solar thermal systems, heat exchangers, heat pumps, naval propulsion, air purification systems, automotive cooling, electric chillers, nuclear reactors, turbines, and biomedical devices. The unsteady, incompressible, and two‐dimensional governing equations comprising the continuity, momentum, energy, and species concentration equations are transformed into non‐dimensional form. These equations are solved numerically using the BVP4C shooting method implemented in MATLAB to analyze the influence of key parameters on velocity, temperature, and concentration profiles. Results reveal that increasing the nanoparticle volume fraction decreases the velocity while enhancing the thermal profile. Both heat and mass transfer rates rise with higher nanoparticle loading, but decrease near the free stream. At early stages of flow, heat transfer rates are minimal, yet temperature profiles are significantly elevated due to nanoparticle dispersion. This study provides valuable insights into optimizing thermal performance over stretchable wedge geometries. The findings hold particular relevance for thermal energy storage, moisture control systems, and temperature‐regulated storage applications such as cooling warehouses, garment preservation, and food storage, where enhanced heat transfer efficiency is crucial.

The flow of fluids containing nanoparticles is essential in industrial applications, particularly in nuclear cooling systems and reactors, where it enhances energy efficiency. This study investigates the transport phenomena of ternary hybrid nanofluids (THNFs), created by mixing a host fluid with three distinct nanoparticles. In this article, nano-sized particles , , and are mixed in a base fluid, water (). The growing interest in tri-hybrid nanofluids is due to their remarkable ability to improve thermal performance, making them ideal for heat exchanger applications. The primary objective of this study is to explore the magnetohydrodynamics (MHD), thermal radiation, and laminar mixed convection flow of a tri-hybrid Casson nanofluid between orthogonally permeable porous disks, incorporating binary chemical reactions with Arrhenius activation energy. Additionally, the study examines the impact of motile microorganisms on flow stability and entropy generation, serving as a measure of thermodynamic irreversibility. The study evaluates the effects of three viscosity models (simple, dynamic, and effective diameter) on skin friction and assesses spherical, non-spherical, and nanolayer thermal conductivity (TC) models based on Nusselt number variations. The governing nonlinear partial differential equations (PDEs) are transformed into a dimensionless form using similarity variables and solved numerically via the finite difference method (FDM) in MATLAB. Computational results reveal that higher activation energy enhances heat and mass transfer rates, while an increased nanoparticle volume fraction significantly improves skin friction. The nanolayer TC model exhibits superior heat transfer performance compared to spherical and non-spherical models. Moreover, the interplay of bioconvection and ternary nanoparticles enhances flow stability and thermal transport efficiency. Elevating the magnetic field strength and Casson parameter results in a decline in velocity and entropy generation. As the values of the Schmidt number and Peclet number increase, mass transfer improves, while bioconvection flow decreases. In the variations of different parameters, our analysis indicates that the tri-hybrid nanofluid exhibits significantly improved flow behavior compared to mono- and hybrid nanofluids.

The paper examines the two-dimensional incompressible flow of dusty water-based nanofluid across a stretched surface, incorporating the effects of buoyancy, Brownian motion, motile microorganisms, suction, thermophoretic diffusion, and magnetohydrodynamics. Bioconvection in dusty nanofluids plays a crucial role in optimizing heat storage. Gyrotactic microorganisms combined with dust and nanoparticles enhance heat transmission and system stability. Similarity transformations reduce governing nonlinear partial differential equations (PDEs) to ordinary differential equations (ODEs), which are then solved numerically using MATLAB's built-in bvp4c method. The accuracy and efficacy of the numerical approach are confirmed by its close agreement with prior studies. A graphical representation illustrates the influence of physical parameters on skin friction, temperature, Nusselt number, and velocity profiles. The findings indicate that increasing thermophoretic diffusion and Brownian motion significantly increase temperature profiles for both phases. Stronger suction boosts heat dissipation by lowering the temperature and increasing the Nusselt number. Thermal buoyancy increases velocity while reducing temperature in both phases, owing to improved convective flow. The skin friction grows by 2.72% as the magnetic parameter M increases from 0.5 to 1, then follows an additional elevation of 2.40% as M climbs from 1 to 1.5, suggesting that the magnetic influence on shear stress is gradually diminishing. For Prandtl numbers 0.7, 2, 7, and 20, the heat transmission is 6.87%, 13.73%, 28.60%, and 50.79%, respectively, indicating that heat transfer improves with increasing Prandtl numbers. This study offers valuable insights into the behavior of dusty nanofluids, with particular emphasis on their role in heat transfer mechanisms.

This study focuses on the two-dimensional magnetohydrodynamic Darcy-Forchheimer flow of a Boger nanofluid over a stretching sheet, incorporating multiple enhancements in the diameter-based viscosity and thermal conductivity models. The heat transfer analysis considers the effects of thermal radiation, viscous dissipation, and Joule heating. To account for nanoparticle geometry, non-spherical thermal conductivity and diameter-based viscosity models are applied based on various shapes and size factor of copper nanoparticles. The influence of metallic nanoparticle morphology on heat transfer performance is analyzed through nanofluid flow simulations. The governing nonlinear partial differential equations are converted into dimensionless form using appropriate similarity variables, with the pressure term eliminated via the penalty method. The resulting dimensionless equations are solved using the finite element method (FEM), and all simulations are performed in MATLAB. The impact of various parameters on the velocity and temperature profiles reveals distinct behaviors across the three viscosity and thermal conductivity models. An increase in the solvent fraction parameter enhances the velocity profile, with the third diameter-based viscosity model demonstrating optimal flow behavior at smaller nanoparticle diameters. Conversely, higher Forchheimer numbers suppress the velocity profile, with the second diameter-based viscosity model showing the most significant reduction at larger diameter values. Larger copper nanoparticle diameters and higher shape factors enhance heat transfer in the temperature profile for the non-spherical thermal conductivity model, with platelet-shaped nanoparticles exhibiting the best thermal performance.

Heart failure and stroke continue to be the most common cause of global death, with atherosclerosis artery stenosis becoming a significant contributor. Although prior research has progressed in comprehending blood circulation behaviour, however, the incorporation of artificial intelligence (AI) and machine learning (ML) in the examination of ternary nanofluids for stenosed arterial diseases signifies a notable breakthrough in this domain. We proposes an integration of ML technique with computational fluid dynamics (CFD) to analyse the non-linear dynamics of thermal characterization in blood-based tri-hybrid nano-fluid flow, influenced by thermal radiation, variable heat sources and sinks, and aligned magnetic field effects within a blood artery exhibiting cosine stenosis. The investigation is based on AI approach, the Levenberg-Marquardt algorithm (LMA), with back propagation Artificial Neural Network (ANN-BP). The mathematical model is developed in the form of partial differentia equations and transformed into ordinary differential equation by similarity scaling, and then numerically evaluated by a modified finite difference approach, the Keller-Box method. The suggested ANN-LMA accuracy is compared to the ML solution for boundary layer flow. Regression values indicate an excellent fit between the predictions and the real data. It is observed that the inclined magnetic angle affects the drag force and heat transfer rate. There is a 27.9% increase in the heat transfer rate for ternary nano-fluid. Conclusively, the non-linear interaction between the magnetic field and nanofluid flow may significantly enhance heat transfer rates, which could have potential applications in biomedical sciences.

Tri-hybrid nanofluids, which consist of three different nanoparticles dispersed in a base fluid, have shown excessive potential as a new generation of thermal materials because of their exceptional heat transfer properties. These fluids are particularly useful for next-generation thermal systems, such as microfluidic cooling devices, solar collectors, aerospace heat exchangers, and nuclear reactor cooling systems. In this article, the heat transfer characteristics of a Williamson-type tri-hybrid nanofluid over a bidirectional stretching sheet under the influence of thermal radiation, magnetic field, and porosity are explored. The main objective is to build and test an effective hybrid framework that combines conventional numerical methods with artificial intelligence to reliably forecast the flow and thermal properties of complicated nanofluid systems. The primary objective is to develop and validate a hybrid numerical-machine learning algorithm that integrates MATLAB's BVP4C solver and an Artificial Neural Network with Bayesian Regularization (ANN-BRA) for estimating velocity and temperature distributions under varying physical parameters. The partial differential equations governing (PDEs) are transformed to ordinary differential equations (ODEs) via similarity variables and numerically resolved to train the ANN. This is the first use of ANN-BRA trained on BVP4C-generated data to simulate tri-hybrid nanofluids inside a Williamson fluid framework. The ANN-BRA model obtains exact regression (R = 1) and a mean squared error (MSE) less than 10-11, which reflects high precision and generalization. Outcomes indicate that an increased magnetic field (M) and porosity (phi) decrease the flow velocity, while an elevated volume fraction of nanoparticles (phi n) strengthens thermal boundary layers. The Eckert number (Ec), Biot number (Bi), and thermal radiation (Rd) are indicated to have strong influences on heat transfer rates. This work presents both numerical and physical understanding of tri-hybrid nanofluid behavior and a useful modeling methodology to optimize practical thermal engineering applications.