Fluid Flow Model Research Articles

Effect of flow modifiers on the fluid flow characteristics in a slab caster tundish

ABSTRACT In a slab caster tundish, controlling liquid steel flow is of paramount importance for clean steel production. A conventional tundish design consists of a pouring box, a weir and a dam. To improve the overall performance of a 40 ton slab caster tundish, three different arrangements by incorporating additional flow modifiers have been examined. A three-dimensional steady state fluid flow model has been developed using a RANS (Reynolds-Averaged Navier-Stokes) approach. Subsequently, transient scalar-transport equations were solved to obtain the C-curve of the tundish. A different approach has been followed to evaluate the inlet boundary condition to mimic the process conditions more accurately. The CFD predictions were validated with the results of the water model. Mean residence time, dead volume fraction and flow structures have been considered for evaluating tundish performance. All the proposed configurations have shown improvements in comparison to the base case. The mean residence time of the fluid was found to be the highest for the case having two pairs of weir and dam. However, the insights derived from the flow structures specifically plug flow in zone 2 and near the tundish outlet region suggest that that having a single weir and two dams is the optimal choice.

Crustal stress buildup/relaxation and pore pressure in preparation and sequential brittle-shear fault rupture — Implications for a general theory of earthquake nucleation

Compelling geoscience evidence has heightened the appreciation of abnormal (suprahydrostatic, sub/quasi/supralithostatic) pore pressure and multimode (brittle-shear) fault rupture leading to seismicity. However, preparation and rupture nucleation are yet to be adequately constrained and quantitatively modeled. This challenges crucial schemes, notably physics-based earthquake forecasting/prediction. In this multidisciplinary study, the transitions and associated critical points linking the preexisting fluid overpressure in the fault patches, temporal crustal stress, and sequential brittle-shear fault failure were considered. In preparation, tectonic loading was accompanied by processes such as off-fault yielding, permeability enhancement, and foreshocks that facilitate local/regional stress relaxation. Subsequent equalization of stress and the preexisting local overpressure triggers hydraulic fracturing that destabilizes major asperities. Almost instant shear failure follows with the spatially varying rupture velocity/intensity of the frictional slip because of localized asperity stress and syn-slip fluid-/melt-driven fracturing/dilation and lubrication. Based on the aforementioned critical points, quantitative modeling associated stress drop with the evolution of the stress and pore pressure. Equations for the time to onset of stress relaxation and time to rupture were derived using fluid flow and viscoelastic models. The seismic moment was estimated with classical seismological relations after modifications accounting for the smaller surface area during frictional slip. For retrospective testing, two cases of induced seismicity (2016 Fairview, Oklahoma, USA, and 2017 Pohang, South Korea) and multiple cases of natural seismicity (including the 2024 Noto Peninsula earthquake, Japan) were considered. The replication of triggering mechanisms, source properties, and time to rupture suggested that stress temporal relaxation and triggered anomalies (STRATA) encompass fundamental hydromechanical processes in seismogenesis. The setting and scale invariance of STRATA suggest it might be a general theory of earthquake nucleation. Based on the identified preparatory processes/retrospective validations, a physics-based earthquake forecasting/prediction scheme was developed. The nurseries/hypocenters of impending earthquakes are identified through the simultaneous consideration of locally preexisting fluid overpressure and spatiotemporal analysis of stress relaxation. Event size and rupture timing are estimated with the derived relations herein.

Regional controls on fluid flow in geothermal systems of the Taupo Volcanic Zone, New Zealand

ABSTRACT The Taupo Volcanic Zone (TVZ) provides almost 20% of New Zealand’s electricity production through seven of its 23 high-temperature geothermal systems. Fluid circulation in geothermal systems is influenced by permeable pathways, heat sources, and topography. To explore influences on systems in the TVZ, we have created regional-scale heat and fluid flow models using TOUGH2. We modelled several potential influences individually and in combination: TVZ rift boundaries, the densely faulted Taupo Fault Belt, varying thickness of volcanic cover, topographic loading, and localised heat sources inferred from magnetotelluric data. The locations of seven of the nine geothermal systems in our study area can be explained by TVZ-scale convection influenced by localised deep heat sources and hydraulic gradients due to topography. Regional-scale geology appears to be an additional influence at Rotorua and Ngatamariki, where cold recharge within the Taupo Fault Belt pushes modelled upflow towards the rift margins. At Ohaaki, modelled upflow is northwest of the system unless a dipping contact between basement and more permeable cover rocks is included. Modelled upflow zones do not correspond to geothermal systems at Te Kopia and Haroharo Volcanic Complex, which we hypothesise is related to uplift along the Paeroa Fault and shallow impermeable lava domes respectively.

Stochastic neuro-swarming intelligence paradigm for the analysis of magneto-hydrodynamic Prandtl–Eyring fluid flow with diffusive magnetic layers effect over an elongated surface

In recent years, the integration of stochastic techniques, especially those based on artificial neural networks, has emerged as a pivotal advancement in the field of computational fluid dynamics. These techniques offer a powerful framework for the analysis of complex fluid flow phenomena and address the uncertainties inherent in fluid dynamics systems. Following this trend, the current investigation portrays the design and construction of an important technique named swarming optimized neuro-heuristic intelligence with the competency of artificial neural networks to analyze nonlinear viscoelastic magneto-hydrodynamic Prandtl–Eyring fluid flow model, with diffusive magnetic layers effect along an extended sheet. The currently designed computational technique is established using inverse multiquadric radial basis activation function through the hybridization of a well-known global searching technique of particle swarm optimization and sequential quadratic programming, a technique capable of rapid convergence locally. The most appropriate scaling group involved transformations that are implemented on governing equations of the suggested fluidic model to convert it from a system of nonlinear partial differential equations into a dimensionless form of a third-order nonlinear ordinary differential equation. The transformed/reduced fluid flow model is solved for sundry variations of physical quantities using the designed scheme and outcomes are matched consistently with Adam's numerical technique with negligible magnitude of absolute errors and mean square errors. Moreover, it is revealed that the velocity of the fluid depreciates in the presence of a strong magnetic field effect. The efficacy of the designed solver is depicted evidently through rigorous statistical observations via exhaustive numerical experimentation of the fluidic problem.

A fully coupled thermo-poroelastic model for energy extraction in naturally fractured geothermal reservoirs: sensitivity analysis and flow simulation

The development of a novel method for modelling fluid flow and heat transfer in naturally fractured geothermal reservoirs represents a significant advancement in geothermal energy research. This Study presents a hybrid approach, which combines discrete fracture and single continuum techniques, to effectively capture the complex interactions between fluid flow and heat transfer in geothermal fractured reservoirs. In addition, the incorporation of the local thermal nonequilibrium method for simulating heat transmission accounts for the disparities in temperature between the rock matrix and the fluid, providing a more realistic representation of heat transfer processes. The study also presents a fully coupled thermo-poro-elastic framework that integrates fluid flow and heat transfer to comprehensively evaluate reservoir responses to injection/production scenarios. This coupled approach allows for the prediction of changes in reservoir properties, such as permeability and porosity, under varying fluid pressure and temperature conditions. The application of the proposed model to evaluate a geothermal reservoir’s long-term response to injection/production scenarios provides valuable insights into the reservoir’s behaviour and potential energy production capacity. The sensitivity analysis further enhances the model’s utility by identifying the key reservoir parameters that significantly influence the thermal depletion of the reservoir. Overall, this novel modelling approach holds promise for improving the understanding and management of naturally fractured geothermal reservoirs, contributing to the optimization of geothermal energy extraction strategies.

Irreversible and reversible chemical reaction impacts on convective Maxwell fluid flow over a porous media with activation energy

The Maxwell model of fluid flow in a rotating frame over a porous media is investigated in this paper. Binary chemical reactions and fluid movement under activation energy are both covered in this study. The impact of mass and heat transmission along the boundary layer is investigated in an equilibrium process. Using the method of similarity transformation, the controlling partial differential equations are changed into ordinary differential equations. The results are confirmed using the bvp4c Matlab built-in programme, and the altered equations are resolved utilizing a 4th order Runge Kutta based shooting method. Reversible and irreversible processes, activation energy, chemical reactions, Deborah numbers, and rotation parameters are some of the parameters for which the results are offered in tables and graphs. The prior objective of this study is to examine the impact of activation energy and chemical reactions on Maxwell fluid flow in an equilibrium setting. The concentration boundary layer for reversible flows is significantly finer than that of irreversible flows with the influence of activation energy, chemical reaction, and rotation factors. A reduced boundary layer thickness can improve the rates of heat and mass transmission in tremendous applications, such as exchangers of heat and chemical reactors. In this chemical process, sulphuric acid is utilized as a catalyst along with Maxwell fluid which affects the boundary layer reaction rate and selectivity. This is crucial for efficient catalytic process design. Controlling reaction rates using fluid elasticity and reaction kinetics is useful in operations that need accurate product production.

Fractional derivative modeling of heat transfer and fluid flow around a contracting permeable infinite cylinder: Computational study

Understanding the complex interplay between the contracting behavior of the cylinder and the fluid flow dynamics has implications for the design of porous structures for heat exchange and filtration systems. In this study, we investigate the dynamics and thermal behavior of fluid flow past a contracting permeable infinite cylinder. First, we developed a mathematical model based on the Navier–Stokes equations to describe the fluid dynamics around the contracting permeable infinite cylinder. A new simple well-behaved definition of fractional derivative called conformal fractional derivative introduced by authors Khalil et al., (2014) is employed to generalize the PDE’s of momentum and energy. The similarity transformation technique is utilized to transform the proposed mathematical problem into a non-linear ODE’s. Then, we utilized IPS technique to numerically solve the governing equations and obtain detailed insights into the flow patterns and thermal characteristics. We observed significant changes in the flow velocity and temperature distribution as the cylinder contracted, highlighting the intricate thermal behavior of the system. Additionally, the changes in the fraction order was found to have a notable impact on the overall flow patterns and heat transfer processes.

Flow field prediction in bed configurations: A parametric spatio-temporal convolutional autoencoder approach

The use of deep learning methods for modeling fluid flow has drawn a lot of attention in the past few years. Here we present a data-driven reduced-order model (ROM) for predicting flow fields in a bed configuration of hot particles. The ROM consists of a parametric spatio-temporal convolutional autoencoder. The neural network architecture comprises two main components. The first part resolves the spatial and temporal dependencies present in the input sequence, while the second part of the architecture is responsible for predicting the solution at the subsequent timestep based on the information gathered from the preceding part. We also propose the utilization of a post-processing non-trainable output layer following the decoding path to incorporate the physical knowledge, e.g. no-slip condition, into the prediction. The ROM is evaluated by comparing its predicted solution with the high-fidelity counterpart. In addition, proper orthogonal decomposition (POD) is employed to systematically analyze and compare the dominant structures present in both sets of solutions. The assessment of the ROM for a bed configuration with variable particle temperature showed accurate results at a fraction of the computational cost required by traditional numerical simulation methods.

Influence of activation energy and multidiffusive quadratic convective nanoliquid flow past a cone and wedge

The present problem aims to examine the impact of quadratic buoyancy-driven flow nanofluid flow on two specific geometries such as cone and wedge in the presence of binary chemical reactions with activation energy, using liquid hydrogen species. This analysis is relevant for various industrial applications and are widely used in thermal energy storage devices for cooling or heating processes. The fluid flow model's governing equations are numerically solved using a fifth-order boundary value approach in matrix laboratory (MATLAB). In order to obtain the numerical solution, we initially transformed the coupled equations of the flow model and the partial differential equations into ordinary differential equations using similarity variables. The graphs and tables illustrate the importance of different physical factors that impact fluid flow and heat transfer. The quadratic combined convection parameter leads to an augmentation in fluid velocity while also inducing an elevation in frictional forces between the object's surface and the fluid. The increased in values of Schmidt number cause a decrease in mass diffusivity, which in turn leads to lower concentration profiles and improved mass transport efficiency. The activation energy is directly proportional to the decreased amplitude of the concentration profiles of liquid hydrogen species.

An Improved Porosity Calculation Algorithm for Particle Flow Code

The widely used discrete-element particle flow software PFC’s (PFC 7.0 and previous versions) algorithm for calculating porosity is not sufficiently accurate. Because of this, when the particles are densely packed, the solution to the equation produces an algorithm exception for odd calculations of porosity, which results in the inability to calculate the results. This paper, based on a Darcy seepage model of fluid flow through a granular bed, analyzed the shortcomings of the two porosity calculation methods of PFC and the function analysis method. Combining this analysis with the theory of computer graphics, a new and efficient porosity calculation algorithm was proposed. The result showed that the new proposed porosity calculation algorithm calculated a more accurate and reasonable porosity field and made the iterative solution of the CFD equation more stable. This method makes porosity-related models of PFC more accurate. The algorithm can be not only used to calculate porosity, but also applied to other fields.

The Properties of the Physical Parameters in the Triple Diffusive Fluid Flow Model

The existence of more than one diffusive component in fluid mixtures is observed in these situations: underground water flow, the mechanism of acid rain, the existence of contaminant in some certain mixture, etc. These diffusive components are occurred with the single temperature gradient (since all of the elements are dissolved into the same mixture) and 2 types of concentration gradients (since the dual diffusive components are dissolved in the same mixture). Besides, many industrial and engineering processes are utilizing the concept of convective fluid flow especially over a shrinking sheet. Therefore, a mathematical model for triple-diffusive flow over a nonlinear compressing sheet has been developed in this paper, and subjected to the Soret-Dufour effects. The model comprises of five initial equations namely continuity, momentum, energy, concentration of component 1 and concentration of component 2 equations, together with boundary conditions. These initial equations are expressed as partial differential equations. However, the finalized equations are in the form of ordinary differential equations. Later, the bvp4c programme provided by the Matlab Software is used to solve the ordinary differential equations and the boundary conditions. Three distinct values of each governing parameter are fixed into the bvp4c function, to observe the behaviour of the physical parameters, namely as local Nusselt number and local Sherwood number. The main finding of the dual numerical solutions varies for increasing governing parameters until they intersect at the critical points. In conclusion, the governing parameters affects the heat and mass transfer of the fluid flow model model.

Shear-induced permeability evolution of natural fractures in granite: Implications for stimulation of EGS reservoirs

Permeability evolution of natural fractures during shearing is one of the critical issues in enhanced geothermal system (EGS). In this study, we conducted a series of numerical simulations of shear-flow tests under different normal stresses to investigate the permeability evolution and shear behavior of natural fractures during shearing. All numerical simulations in this study are executed based on a coupled hydro-mechanical pore network model (PNM) for fluid flow within the discrete element method (DEM). The numerical model uses a 33 mm × 25 mm fracture surface profile extracted from X-ray computed tomography scanning data of joints in a rock core retrieved from a 4.2-km-deep well at the Pohang EGS site. The results demonstrate a positive correlation between fracture permeability and shear displacement when the normal stress is relatively high. The central aspect of permeability evolution lies in the variation of local aperture distribution along the pathway: an increase in the variance of fracture aperture distribution leads to an increase in fracture permeability. Permeability evolution of fractures is significantly affected by normal stress, fracture roughness, and relative flow direction. Larger fracture roughness facilitates the formation of high-permeability pathways. Higher local normal stress often corresponds to lower local permeability. Moreover, high normal stress amplifies the effect of fracture roughness on permeability evolution. These findings enhance our comprehensive understanding of hydraulic-mechanical coupling effects during EGS stimulation.

Viscoelastic Fluid Flow Model for Hydrodynamic Behaviour of Magnetorheological Fluid in Valve and Shear Modes for a Damper System

In this present study, the flow behaviour of magnetorheological fluid in valve and shear modes for damping system is modelled and analysed. The fluid is modelled as viscoelastic fluid flowing between two parallel plates in pressure driven flow mode, and also as direct shear mode. In the work, the post-yield shear thinning or thickening behaviour of magnetorheological fluids are accounted for. The velocity and pressure distributions in the unsteady magnetorheological fluid flow between the electrodes of the damper are obtained by solving the momentum equation of the magnetorheological fluid flow using the Laplace transform method. There is an excellent agreement between the results of the present model and the results of the experimental studies. The adopted viscoelastic flow model describes that the rheological behaviour of the fluid is separated into distinct pre-yield and post-yield regimes. The fluid flow velocity, velocity gradient, and shear stresses have all been shown to be enhanced by an increase in the pressure drop. The viscosity of the fluid increases with an increase in the volume fraction of particles in the fluid, which causes the resistance of the fluid to flow to increase and thereby, reduces the fluid flow velocity. Fluid flow velocity is decreased as a result of increasing magnetic field strength. The design of clutches, rotary brakes, dampers, shock absorbers, prosthetic devices, polishing and grinding tools, etc. will all benefit greatly from the adoption of the current model.

Reduced-order modeling of unsteady fluid flow using neural network ensembles

The use of deep learning has become increasingly popular in reduced-order models (ROMs) to obtain low-dimensional representations of full-order models. Convolutional autoencoders (CAEs) are often used to this end as they are adept at handling data that are spatially distributed, including solutions to partial differential equations. When applied to unsteady physics problems, ROMs also require a model for time-series prediction of the low-dimensional latent variables. Long short-term memory (LSTM) networks, a type of recurrent neural network useful for modeling sequential data, are frequently employed in data-driven ROMs for autoregressive time-series prediction. When making predictions at unseen design points over long time horizons, error propagation is a frequently encountered issue, where errors made early on can compound over time and lead to large inaccuracies. In this work, we propose using bagging, a commonly used ensemble learning technique, to develop a fully data-driven ROM framework referred to as the CAE-eLSTM ROM that uses CAEs for spatial reconstruction of the full-order model and LSTM ensembles for time-series prediction. When applied to two unsteady fluid dynamics problems, our results show that the presented framework effectively reduces error propagation and leads to more accurate time-series prediction of latent variables at unseen points.

Determination of conditions for combustion front development near injection well following air injection into oil reservoir using fluid flow modeling

Determination of conditions for combustion front development near injection well following air injection into oil reservoir using fluid flow modeling

Optimizing Water-Cut and Boosting Oil Recovery: Geological Insights from Mishrif Reservoir, Buzurgan Oil Field

This study utilizes streamline simulation to model fluid flow in the complex subsurface environment of the Mishrif reservoir in Iraq's Buzurgan oil field. The reservoir faces challenges from high-pressure depletion and a substantial increase in water cut during production, prompting the need for innovative reservoir management. The primary focus is on optimizing water injection procedures to reduce water cuts and enhance overall reservoir performance. Three waterflooding tactics were examined: normal conditions without injectors or producers, normal conditions with 30 injectors and 80 producers and streamline simulation using the frontsim simulator. Three main strategies were employed to streamline water injection in targeted areas. Over a 22-year forecasting period and employing seven Strategies, streamline simulation were optimized both oil and water outputs. The hybrid Strategy-7 as mixed between all three outperformed Strategy-1 that was gave highest optimization result for only one strategy, yielding the highest cumulative oil production of 1281 million stock tank barrels, the highest oil recovery factor of 24.1%, and a minimal of 2.5% water cut. This study underscores the importance of streamline simulation in managing reservoirs under challenging subsurface conditions, highlighting that a thoughtful integration of streamlining tactics can significantly improve reservoir performance even enhancing oil recovery and addressing water-related issues. The findings contribute valuable insights for optimizing waterflooding strategies in similar globally geological contexts.

A defect correction weak Galerkin finite element method for the Kelvin–Voigt viscoelastic fluid flow model

In this paper, we present a defect correction weak Galerkin finite element method for solving the Kelvin–Voigt viscoelastic fluid flow model, which can guarantee that the discrete velocity is globally divergence-free. The second-order Crank–Nicolson difference scheme is considered for temporal discretization. In particular, combined with the defect correction method, the numerical oscillation effect is reduced at high Reynolds number. Our algorithm not only gives the stability and convergence of the numerical solutions of velocity and pressure but also is uniformly valid at the retardation time κ→0. Several numerical experiments are performed to verify the method has good behaviors.

Stratified numerical heat and mass transport mechanism in MHD Maxwell fluid flow with nonuniform heat source/sink

The present boundary layer flow of Maxwell fluid over a stretching sheet has good number of practical applications in metallurgy, drawing of plastics, polymer sheet extrusion including hot rolling extrusion, glass blowing, spinning of fibers, rubber and plastic sheets, crystal growing and many more. Due to these extensive applications of Maxwell fluid in engineering, medicine and manufacturing industries including the above-mentioned applications, authors have motived, inspired and investigated the present problem. However, in this research paper, the influences of Soret and Dufour effects on the steady-state Maxwell fluid flow past a stretching sheet with nonuniform heat source/sink are considered numerically. The thermal and concentration stratifications impacts are also incorporated. The viscous dissipation and magnetic field effects are also included in the respective governing equations. The main novelty and uniqueness of this numerical research is to generalize the earlier studies and describe the salient features of magneto-thermo visco-elastic dissipative Maxwell fluid motion about a stretching sheet with cross-diffusion effects under the influence of double stratification phenomena. To differentiate the non-Newtonian fluids from those of Newtonian fluids, a well-known Maxwell fluid flow model is used in the present study. The investigated physical problem results the highly nonlinear coupled partial differential equations (PDEs) and which are not amenable to any of the direct methods. Suitable similarity transformations are deployed to reduce the highly complex PDEs into the system of ordinary differential equations (ODEs). A robust BVP4C Matlab function is employed to solve the rendered dimensionless system of ODEs. The numerically generated computed data is plotted in terms of velocity, temperature and concentration profiles including engineering quantities of interest such as skin-friction, Nusselt and Sherwood numbers in the flow region. It is evident from the current analysis that, the amplified magnetic field decreases the velocity field and increases the thermal and concentration distribution fields. Accelerating Maxwell’s number diminished the flow velocity and increased the temperature field. Increasing Soret and Dufour numbers enhances the concentration and temperature fields, respectively. Amplifying Maxwell’s number raises the skin-friction coefficient and enlarging the thermal stratification parameter magnifies the thermal transport rate. The mass transport rate amplified with a raise in concentration stratification number in the flow region. Finally, it is provided that, the current results are excellently matching with earlier published results in the literature and it confirms the accuracy of the used numerical method and the produced similarity solutions.

Free convection in a square wavy porous cavity with partly magnetic field: a numerical investigation

Natural convection in a square porous cavity with a partial magnetic field is investigated in this work. The magnetic field enters a part of the left wall horizontally. The horizontal walls of the cavity are thermally insulated. The wave vertical wall on the right side is at a low temperature, while the left wall is at a high temperature. The Brinkman-Forchheimer-extended Darcy equation of motion is utilized in the construction of the fluid flow model for the porous media. The Finite Element Method (FEM) was used to solve the problem’s governing equations, and the current study was validated by comparing it to earlier research. On streamlines, isotherms, and Nusselt numbers, changes in the partial magnetic field length, Hartmann number, Rayleigh number, Darcy number, and number of wall waves have been examined. This paper will show that the magnetic field negatively impacts heat transmission. This suggests that the magnetic field can control heat transfer and fluid movement. Additionally, it was shown that heat transfer improved when the number of wall waves increased.

Analysis of MHD third-grade hybrid nanofluid model in Darcy-Forchheimer porous medium: Evaluation of the thermal performance of [formula omitted]-[formula omitted] cylindrical nanoparticles dispersed in ethylene glycol fluid

Researchers and scientists became interested in the newly developed idea of hybrid nanofluids because of their exceptional thermal conductivities, which resulted in enhanced thermal performance. These fluids have a wide range of uses in the industrial and technical fields. This novel class of fluids is playing a vital role in solar energy, automotive industry, cooling of the machine and manufacturing, heating and ventilation systems, electronic cooling, nuclear systems cooling, biomedical fields, space, ships, and defense systems. In light of the physical significance of the above-mentioned class of fluids, the current investigations are carried to examine the thermal performance of the mixture of cylindrical shaped aluminum oxide Al2O3 and copper Cu nanoparticles suspended in ethylene glycol using third-grade non-Newtonian fluid flow model. The fluid flow is induced by the stretching of the permeable sheet in exponential manner that is embedded in a Dacry-Forchheimer porous medium. The effects of Lorentz force applied normal to the flow and suction impacts have been incorporated in the current proposed model. The solutions of the flow model transformed to ordinary differential equations are computed using MATLAB built-in solver bvp4c. The solutions are presented in graphical representations. Graphical solutions reflect that fluid velocity slows down by growing the volume fractions of the nanoparticles. Increasing values of viscoelastic parameters reflect that there is a reduction in velocity and intensification in profiles of temperature and concentration have been noted. Rising values of cross-diffusion parameter is leading to the reduction in magnitude of velocity, and augmenting behavior of temperature and concentration has been seen. Observations indicate rising third-grade fluid parameter and porosity parameter lead to reduction in velocity. Increasing Schmidt number gives reduced Sherwood number, and magnetic field parameter improves the rate of hear transfer (Nusselt number) and skin friction coefficient for both Al2O3/ethylene glycol nanofluid and Al3O3-Cu/ethylene glycol-based hybrid nanofluid. The suggested model's validity is confirmed through comparison with previously released findings. Additionally, a grid independence test (sensitivity analysis) has been performed to verify the accuracy and verification of the numerical model.