Darcy Forchheimer Flow Research Articles

Analytical simulation of Darcy-Forchheimer nanofluid flow over a curved expanding permeable surface

Abstract This research paper presents an analytical simulation of Darcy-Forchheimer flow over a porous curve stretching surface. In fluid dynamics, the Darcy-Forchheimer model combines Forchheimer adjustment and high-velocity effects with Darcy's formula for porous media flow: two nanofluid particles, molybdenum disulfide, and graphene oxide, form nanofluid with the base fluid blood. The governing partial differential equations for momentum and energy are converted into a nonlinear ordinary differential equations system by applying the appropriate similarity transformations. The homotopy analysis method (HAM) is used to solve the transform equations analytically. The impact of essential factors includes the Forchheimer parameter, porosity parameter, slip parameter, Eckert number, nanoparticle volume friction, magnetic field parameter, and curvature parameter. The results have applications in the design of sophisticated cooling systems, where effective thermal control is essential.

Darcy-Forchheimer Flow of Casson Nanofluids Towards a Spinning Disk with Non-Uniform Heat Source

Darcy-Forchheimer Flow of Casson Nanofluids Towards a Spinning Disk with Non-Uniform Heat Source

Electro-magnetohydrodynamic (EMHD) Darcy–Forchheimer flow of Sutterby nanofluid with variable thermal conductivity over a stretching sheet: Finite difference approach

This paper examines the enactment of a two-dimensional, steady, non-Newtonian nanofluid flow over a stretching sheet. The utilization of magnetic influences acting in the direction normal to the Darcy–Forchheimer boundary layer flow of the Sutterby nanofluid with variable thermal conductivity is taken into consideration. This study takes into account the effects of thermophoresis and Brownian motion. The study found that a 15% increase in magnetic field strength resulted in a 10% increase in heat transfer rate. Similarly, a 20% increase in nanoparticle volume percentage causes a 12% increase in the convective heat transfer coefficient. The problem’s model is formulated in the form of partial differential equations (PDEs), transformed via similarity transformation into nonlinear ordinary differential equations (ODEs). Applying the finite difference method yields the solution to reduced equations. EMHD Darcy–Forchheimer flow and nanofluid dynamics are combined in cutting-edge technology. This is important for many industrial and technical applications. Moreover, providing a strong computational framework provides a precise simulation of the flow behavior. By providing insights into the intricate interactions between electromagnetic forces, porous medium effects, and variable thermal conductivity in nanofluids flow across a stretched sheet, this study makes an essential contribution to the science of fluid dynamics. This research is very significant and enlightening for researchers and professionals who are interested in the design and optimization of heat transfer systems. The fluid flow is examined thoroughly and graphically, and the relationship between the profiles of velocity, temperature, and concentration and other important physical limitations is investigated. The effect of various physical parameters on concentration, velocity, temperature, skin friction, Nusselt number and heat flow coefficient is verified and examined using graphs and tables.

MHD Mixed Convection Flow Over a Permeable Vertical Flat Plate Embedded in a Darcy–Forchheimer Porous Medium

AbstractThe purpose of this paper is to describe the stead MHD mixed convection flow over a permeable vertical flat plate embedded in a Darcy–Forchheimer porous medium. Using appropriate similarity variables, the partial differential equations are transformed into ordinary (similar) differential equations, which are numerically solved using the bvp4c function in MATLAB. The numerical results are used to present graphically and in tables, illustrations of the reduced skin friction, reduced Nusselt number, velocity, and temperature profiles. Dual (upper and lower branch) solutions are discovered in this exciting analysis. Although numerous studies on the mixed convection past a vertical plate embedded in a fluid-saturated porous medium exist, none of the researchers have focused on the Darcy–Forchheimer flow with asymptotic solutions. The behavior of the flow and heat transfer has been thoroughly analyzed with the variations in governing parameters, such as Darcy–Forchheimer $$G,$$ G , suction/injection $$S$$ S , MHD $$M,$$ M , and mixed convection $$\lambda$$ λ parameters.

Numerical discretization of a Darcy–Forchheimer flow with variable density and heat transfer

In this paper, we study a heat transfer scenario in Darcy–Forchheimer porous media with variable density. The block-centered finite difference method is applied to discretize the non-isothermal flow equations governing the system. Specifically, the pressure field is modeled using the nonlinear Darcy–Forchheimer formulation, while the density and temperature are described by convection-dominated diffusion equations, which are treated via the characteristic method. Theoretical analyses are rigorously developed for pressure, velocity, density, temperature, and auxiliary flux across non-uniform grids. Several numerical experiments are carried out to illustrate the merits of our method by comparing numerical results to analytical solutions.

Homogeneous–Heterogeneous reactions on Darcy–Forchheimer flow of SWCNTs/MWCNTs over a bidirectional Riga plate with nonlinear radiation and non-uniform heat source/sink

Homogeneous–Heterogeneous reactions on Darcy–Forchheimer flow of SWCNTs/MWCNTs over a bidirectional Riga plate with nonlinear radiation and non-uniform heat source/sink

Finite difference analysis for entropy optimized nanomaterial Darcy-Forchheimer flow with homogeneous and heterogeneous reactions

Hybrid nanoliquids are not underestimated for their involvement in microelectronics, transportation, coolant processes, ships, biological processes and power generation. Hence motivation for current work is to examine homogeneous-heterogeneous reactions in entropy optimized flow by curved sheet stretched with nonlinear velocity. Trihybrid nanoliquid is synthesized through 2 % of ferrous oxides(Fe3O4), 2 % of silver(Ag) and 2 % of copper(Cu). Kerosene oil is employed as the base fluid. These specific kinds of nanoparticles are taken into consideration because of their numerous applications in heat dissipation, air filters, dynamic sealing, biosensors and catalysts process. Kerosene oil may have applications in many different domains such as energy storage, cleaning agent, portable heaters, fuel additive and industrial lubricants. Darcy-Forchheimer model is employed. Analysis in presence of radiation, dissipation, Ohmic heating, entropy generation and heat generation/absorption are organized. Unlike the previous considerations, the thermal expression here consists of impacts through Darcy-Forchheimer relation. Adequate transformations are implemented. Computations have been arranged by applying finite difference technique (FDM) using MATLAB. Quantities for physical interest are addressed. The presented analysis may have relevance for solar systems, chemical reacting processes, cooling towers and polymer data processes. The conclusions are also organized for important key findings. It is noticed that trihybrid nanomaterial has more entropy rate when compared with hybrid and classical nanoliquids when volume fraction is chosen as 2 % for trihybrid fluid. It is proposed that the ability to transfer heat is enhanced when nanoparticles are added to conventional fluids. Decay in concentration is noticed for both homogeneous and heterogeneous parameters. Reduction for Bejan number is noticed through homogeneous diffusion factor. Comparison with previous study is also presented and found great consensus between them.

Characteristics of unsteady thermo-bioconvection chemical reactive stagnation point flow of trihybrid nanofluid around rotating sphere with Oxytactic Microorganisms

The present study is to highlight the significance of viscous dissipation, Joule heating and magnetic field on the stagnation point Darcy-Forchheimer flow of THNF (trihybrid nanofluid) around a spinning sphere containing Oxytactic and gyrotactic microorganisms. The analysis also includes the effects of heat generation and higher-order chemical reaction. A trihybrid nanofluid consisting of water (H2O) as the base fluid and TiO2,Cu and Fe3O4 nanoparticles is used. The Hamilton–Crosser model of trihybrid nanofluid is used in this work to compare their respective performance. This model is applicable to the optimization and design of sophisticated cooling systems where effective heat transfer is necessary, like electronic cooling, nuclear reactors, and high-performance heat exchangers. This model is used in biomedical engineering to comprehend drug delivery systems where exact control over reactions and fluid dynamics is required. Oxytactic microorganisms are important because they help break down contaminants in environmental engineering and wastewater treatment procedures. The fundamental system of the PDEs (partial differential equations) and the pertinent BCs (boundary conditions) have been transformed for computation using a few appropriate transformations. The numerical estimations for the appropriate system of differential equations are derived by employing the shooting approach (Bvp4c). Extensive studies are conducted to examine the effects of pertinent limitations on the rates of heat transfer, mass transfer, density of Oxytactic and gyrotactic microorganisms for both hybrid and trihybrid nanofluid. Among the various findings of this investigation is the observation that a higher Oxytactic and gyrotactic microorganisms Schmidt numbers result in a slower trihybrid nanofluid and hybrid nanofluid Oxytactic and gyrotactic microorganism's distributions. By increasing the value of Peclet number up to 7% the values of local density gyrotactic microorganisms enhance up to 9% .

Buoyancy effects on Darcy-Forchheimer flow of thermally radiated hybrid SiO2-TiO2/CH3OH nanofluid

Buoyancy effects on Darcy-Forchheimer flow of thermally radiated hybrid SiO2-TiO2/CH3OH nanofluid

Passive control of bio-convective flow on Eyring–Powell nanofluid over a slippery surface with activation energy and magnetic impact

The current communication deliberates the consequences of the Darcy–Forchheimer flow of Eyring–Powell nanofluid past a slippery surface containing activation energy and motile microorganisms. The flow is influenced by the consequences of Brownian motion, thermal radiation, the Cattaneo–Christov heat-mass flux theory, and thermophoresis. The framed flow models are transformed into ordinary derivative equations by adopting appropriate conversion variables. The transformed equations are numerically tackled by using the bvp4c scheme in MATLAB. The study is remarkable for its comprehensive analysis of the interplay of several flow factors, such as the Forchheimer number, Richardson number, bioconvection Rayleigh number, radiation, thermophoresis, Brownian motion, thermal and mass relaxation time parameters. The outcomes are visualized through tables and diagrams, which provide significant insights into the intricate physical mechanisms involved in this multifaceted subject. Evidently, the velocity profile declines when there is a rise in the buoyancy ratio parameter and the opposite trend is obtained for the Richardson number. The temperature grows when there is a larger magnitude of the thermophoresis parameter and it reduces for greater values of the time relaxation parameter. The activation energy and mass relaxation parameters enhance the concentration profile. The microbe density increases when enhancing the quantity of Peclet number and it declines for bioconvection Lewis number.

Entropy analysis of Darcy-Forchheimer flow of Reiner-Rivlin A12O3–Cu/engine oil based hybrid nanofluid between two rotating disks

This paper analyzes the flow of the Reiner-Rivlin hybrid nanofluid, considering the magnetic field and varying thermal conductivity between two spinning disks. Appropriate similarity variables are used to transform all dimensional equations into dimensionless form. A semi-analytical homotopy analysis approach applied to solve dimensionless equations and velocity profiles, temperature distribution, Nusselt number, skin friction, entropy generation, and Bejan number are presented graphically. Some key outcomes include that axial and tangential velocities decreases when porosity parameters increase. Additionally, higher Eckert number when varying from 1 to 1.3, increases the temperature near the center of the two disks from 1.02 to 1.18. The heat transfer rate goes up from 10.2767 to 10.3043 when thermal conductivity rises from 0.1 to 0.7. The entropy generation grows in proportion to the Brinkman number, Reynolds number, and the porosity parameter values. This research might enhance cooling, lubrication, and thermal management in automotive, aerospace, and biomedical industries.

Analysis of Darcy–Forchheimer flow of magnetized hybrid nanofluid (MoS 2+ZnO/E) with non-linear heat source and quartic autocatalytic chemical reaction

In this article, an effort is made to analyze the 3 − D flow of hybrid nanofluid over a rotating stretching sheet. The hybrid nanofluid contains engine oil as a base fluid amalgamated with nano-particles Mo S 2 and ZnO . The flow is assumed to pass through a Darcy–Forchheimer medium subjected to the influence of an inclined magnetic field. In addition, heat radiation, Joule heating, viscous dissipation, nonlinear heat source, and quartic autocatalytic chemical reaction are applied to discourse heat and mass transfer features. The PDEs representing the physical problem are converted to ODEs with the introduction of similarity transformations. The solution of the problem is determined numerically by using MATLAB built-in bvp4c method. The proposed mathematical model’s validation is ascertained by comparing it with an earlier study in limiting case. In this regard, an excellent consensus is accomplished. The current investigation reveals that the flow along axial direction gets retarded by enhancing the values of rotational parameter, inertial parameter, and magnetic parameter, whereas the flow along radial direction gets accelerated. The increasing value of angle of inclination admirably resists the motion of nanofluid and hybrid nanofluid. The concentration profile gets decreased under the increasing influence of inclination angle and Schmidt number while it enhances for homogeneous reaction parameter. The enhancing values of rotational parameter, solid volume fraction and temperature, and exponential dependent heat generation parameters enhance the value of Nusselt number.

Darcy–Forchheimer modelling on unsteady MHD convection flow of a hybrid nanofluids (CNTs–Al2O3/H2O) over a stretching sheet

AbstractThe present article provides a detailed analysis of the Darcy–Forchheimer flow of hybrid nanofluid past a porous stretching sheet. The carbon nanotubes and Al2O3 (aluminium oxide) are used to synthesize hybrid nanofluid. The nanoparticles of carbon nanotubes have attained fame to enhance the thermo‐physical features of fluid particles. The inclusion of nanoparticles of multi‐wall carbon nanotube (MWCNTs)/single‐wall carbon nanotubes (SWCNTs) and alumina in water past a stretching sheet by the magnetic field, thermal radiation, heat dissipation as well as slip conditions is computationally explored. The hybrid nanofluid flow experiences the unsteady non‐Darcy relation across two‐dimensional stretchable surface. At first, the governing partial differential equations of the projected modelling are in non‐dimensional and to attain the ordinary differential equations via the appropriate dimensionless similarity transformations and are then computationally explored by bvp4c MATLAB solver. The pertinent parameters of the associated model are demonstrated by the graphical profiles and tables. Furthermore, magnetic parameter, porosity parameter and inertia coefficient parameter tend to retards the flow pattern of hybrid nanofluid. The SWCNTs‐alumina/water experiences more resistive force as compared to the MWCNTs‐alumina/water. Higher values of Forchheimer parameter retards velocity profile as MWCNTs‐alumina/water flow overshoots SWCNTs‐/alumina water. The enhancement of volume fraction of MWCNTs and SWCNTs enhanced the rate of heat transfer throughout the fluid region.

Darcy-Forchheimer MHD micropolar water based hybrid nanofluid flow, heat and mass transfer features past on stretching/shrinking surface with slip and radiation effects

Hybrid nanofluids (HNF) play a vital role in enhancing the heat transfer characteristics of all types of traditional fluids, both in industrial and experimental applications. In this regard, the laminar two-dimensional (2D) boundary layer magnetohydrodynamic (MHD) Darcy-Forchheimer flow, heat transfer, and mass transfers characteristics of Cu–MoS2/micropolar water-based hybrid nanofluid have been considered over a stretching/shrinking surface. The thermal radiation and partial slip effects are considered in a porous medium. The governing partial differential equations (PDEs) are transformed into ordinary differential equations (ODEs) using appropriate similarity transformations. The equations are numerically solved using the shooting method in Maple software, and dual solutions are obtained for different ranges of the applied parameters. The effects of the different physical parameters and nanoparticle volume fractions on velocity, microrotation, temperature, and concentration profiles along with skin friction, couple stress, Nusselt and Sherwood numbers are examined. The main findings of this study show that the velocity profiles decrease with an increase in the suction, the Darcy-Forchheimer number, velocity slip, magnetic and micromaterial parameters, while oppositely, it increases with an increase in nanoparticle volume fractions. Moreover, an increase in the magnetic field, nanoparticle volume fractions, and thermal radiation increases the temperature profiles, while an increase in the Prandtl number, suction, and thermal slip parameters decreases it. An increase in nanoparticle volume fractions decreases skin friction, the couple stress coefficient, and the Nusselt number, but increases the Sherwood number with the variation of suction.

Supervised machine learning computing paradigm to measure melting and dissipative effects in entropy induced Darcy–Forchheimer flow with ternary-hybrid nanofluids

This study investigates the change in thermophysical characteristics of Darcy–Forchheimer flow of tri-hybrid nanofluid (THNF) over stretchable porous skin. Machine learning (ML) technique is employed to compare thermal exchange of water-based hybrid nanofluid (HNF), composed of aluminum oxide (Al2O3) and silicon dioxide (SiO2) with THNF by introducing copper oxide (CuO) nanoparticles in HNF. Flow rate profile, dissipation effect, and entropy generation are analyzed with novel, time, and cost-effective evaluation technique. By using similarity parameters, the governing system of partial differential equations (PDEs) is transformed to a system of ordinary differential equations (ODEs). Finite difference method is used for dataset generation by the aid of Python environment, then neural fitting computation technique is utilized for optimized results. Turbulence and randomness are incorporated in the present nonlinear mathematical model which is tackled by artificial intelligence (AI)-based Levenberg Marquardt Neural-Network Algorithms (LMNA), to produce optimized outputs. Velocity, temperature, and entropy profile are evaluated against various influencing factors, such as Forchheimer value, porosity, melting parameter, radiation, Prandtl, Eckert, and Brinkmann coefficient. Numerical and AI-generated outputs and errors graphs with complete neural network training scheme, are portrayed to draw the effective concluding inferences. Enhanced results are beneficial for industrial and engineering production units, for efficient thermal management.

Numerical heat transfer enhancement in MHD boundary layer flow with Darcy-Forchheimer Bioconvection Nanofluid

Scientists have harnessed the diverse capabilities of nanofluids to solve a variety of engineering and scientific problems due to high-temperature predictions. The contribution of nanoparticles is often discussed in thermal devices, chemical reactions, automobile engines, fusion processes, energy results, and many industrial systems based on unique heat transfer results. Examining bioconvection in non-Newtonian nanofluids reveals diverse applications in advanced fields such as biotechnology, biomechanics, microbiology, computational biology, and medicine. This study investigates the enhancement of heat transfer with the impact of magnetic forces on a linearly stretched surface, examining the two-dimensional Darcy-Forchheimer flow of nanofluids based on blood. The research explores the influence of velocity, temperature, concentration, and microorganism profile on fluid flow assumptions. This investigation utilizes blood as the primary fluid for nanofluids, introducing nanoparticles like zinc oxide and titanium dioxide (. The study aims to explore their interactions and potential applications in the field of biomedicine. In order to streamline the complex scheme of partial differential equations (PDEs), boundary layer assumptions are employed. Through appropriate transformations, the governing partial differential equations (PDEs) and their associated boundary conditions are transformed into a dimensionless representation. By employing a local non-similarity technique with a second-degree truncation and utilizing MATLAB’s built-in finite difference code (bvp4c), the modified model’s outcomes are obtained. Once the calculated results and published results are satisfactorily aligned, graphical representations are used to illustrate and analyze how changing variables affect the fluid flow characteristics problems under consideration. In order to visualize the numerical variations of the drag coefficient and the Nusselt number, tables have been specially designed. Velocity profile of -blood and -blood decreases for increasing values of and , while temperature profile increases for increasing values of and . Concentration profile decreases for increasing values of , and microorganism profile increases for increasing values of . For rising values of and the drag coefficient increases and the Nusselt number decreases for rising values of and The model introduces a novel approach by conducting a non-similar analysis of the Darchy-Forchheimer bioconvection flow of a two-dimensional blood-based nanofluid in the presence of a magnetic field.Scientists have harnessed the diverse capabilities of nanofluids to solve a variety of engineering and scientific problems due to high-temperature predictions. The contribution of nanoparticles is often discussed in thermal devices, chemical reactions, automobile engines, fusion processes, energy results, and many industrial systems based on unique heat transfer results. Examining bioconvection in non-Newtonian nanofluids reveals diverse applications in advanced fields such as biotechnology, biomechanics, microbiology, computational biology, and medicine. This study investigates the enhancement of heat transfer with the impact of magnetic forces on a linearly stretched surface, examining the two-dimensional Darcy-Forchheimer flow of nanofluids based on blood. The research explores the influence of velocity, temperature, concentration, and microorganism profile on fluid flow assumptions. This investigation utilizes blood as the primary fluid for nanofluids, introducing nanoparticles like zinc oxide and titanium dioxide (. The study aims to explore their interactions and potential applications in the field of biomedicine. In order to streamline the complex scheme of partial differential equations (PDEs), boundary layer assumptions are employed. Through appropriate transformations, the governing partial differential equations (PDEs) and their associated boundary conditions are transformed into a dimensionless representation. By employing a local non-similarity technique with a second-degree truncation and utilizing MATLAB’s built-in finite difference code (bvp4c), the modified model’s outcomes are obtained. Once the calculated results and published results are satisfactorily aligned, graphical representations are used to illustrate and analyze how changing variables affect the fluid flow characteristics problems under consideration. In order to visualize the numerical variations of the drag coefficient and the Nusselt number, tables have been specially designed. Velocity profile of -blood and -blood decreases for increasing values of and , while temperature profile increases for increasing values of and . Concentration profile decreases for increasing values of , and microorganism profile increases for increasing values of . For rising values of and the drag coefficient increases and the Nusselt number decreases for rising values of and The model introduces a novel approach by conducting a non-similar analysis of the Darchy-Forchheimer bioconvection flow of a two-dimensional blood-based nanofluid in the presence of a magnetic field.

Comparative approach of Darcy–Forchheimer flow on water based hybrid nanofluid ([formula omitted]) and mono nanofluid ([formula omitted]) over a stretched surface with injection/suction

The hybrid nanofluids are crucial for enhancing heat transfer efficiency in different technological and industrial operations like nuclear reactor cooling, fuel cells, drug delivery systems, etc. Taking this factor into account, the current investigation focused on the MHD Darcy–Forchheimer flow of water-based hybrid nanofluid (Cu-Al2O3) and mono nanofluid (Cu) past a stretched surface with injection/suction. Additionally, the investigation focuses on analyzing the consequences of nonlinear thermal radiation and heat consumption/generation. The governing higher-order PDEs are rehabilitated into ODEs through a suitable transformation process. Finally, we solve these equations using the quantitative approach of the Bvp4c algorithm in MATLAB and visualize the results in tables and graphs. Our study revealed that the intensified magnetic field, porosity, and injection/suction parameters suppress the fluid velocity. The fluid heat is enhanced when intensifying the radiation, and nanoparticles volume fraction parameters. Augmenting the magnetic field parameter results in a reduction in the skin friction coefficient. It is also found that the highest dwindling percentage of the skin friction coefficient is 24% (HNF), 33.38% (NF), and 25.70% (VF) when the magnetic field parameter changes from 0 to 1. The largest growing percentage of the local Nusselt number is 34.02% (HNF), 36.75% (NF) and 39.52 (VF), which occurs when the suction/injection parameter is modified from −0.3 to 0.

Radiative flow of cross ternary hybrid nanofluid (MoS2,TiO2, Ag/CMC-water) in a Darcy Forchheimer porous medium over a stretching cylinder with entropy minimization

Stretching cylinders play a crucial role in the plastic and metal extrusion processes. This current investigation is to examine the Darcy Forchheimer flow of Carboxymethyl cellulose (CMC)/water-based tri-hybrid nanofluid through a stretching cylinder. A composite of ternary hybrid nanofluid containing MoS2, TiO2 and Ag with CMC-water-based fluid has been added to the Crossflow model. The equations regulating motion and the equation for entropy generation are both formulated using cylindrical coordinates. The governing partial differential equations (PDEs) equations have been transformed into an ordinary differential equations (ODEs) system using a similar scaling operation. Afterward, the BVP4c function employs the finite difference method and then implements the Lobatto IIIa formula. To fully understand how the flow behaves close to the cylinder's surface, the effects of these various factors on the number of entropy generation, Bejan number, the speed of the flow, the temperature and concentration distributions have been carefully studied. The result reveals that enhancing the values of Weissenberg number We and the porosity parameter declines the velocity profile. An increment in the curvature parameter β declines the velocity gradient and temperature distribution. In addition, enhancement in the radiation parameter escalates the entropy minimization and Bejan number. Furthermore, the impact of drag friction, heat, and mass are displayed in tabular form and elaborated suitably. The outcomes are authenticated with previously published literature for accuracy and authenticity.

Numerical tackling for MHD Darcy-Forchheimer flow of water-based CNTs in a rotating frame with homogeneous-heterogeneous reactions: An artificial neural network approach

Numerous scientific fields rely heavily on rotating flows, such as jet engine design, geophysical flows, turbine engineering, vacuum cleaner design, and many others. Prior research on rotational flow has largely disregarded the impact of viscous dissipation and homogeneous-heterogeneous responses. The present study investigates the Darcy-Forchheimer flow of carbon nanotubes (CNTs) in a rotating frame caused by a biaxial stretched plate with heat consumption and radiation. Furthermore, the mass transport mechanism is treated in terms of homogeneous-heterogeneous chemical reactions. The equations governing the flow are reduced into ordinary differential equations by using appropriate transforms. An advanced computational technique, bvp4c, has been used to provide precise numerical solutions.The computation of the resulting systems is also performed using an artificial neural network (ANN) and also the machine learning study shows a high correlation between the numerical and ANN findings, with a mean squared error (MSE) of 0.000053 for SWCNT and 0.000268 for MWCNT. A comprehensive investigation of several parameters yields both graphical and numerical outcomes. It has been discovered that larger values of the Forchheimer number and porosity parameter result in the decay of fluid velocities. The x − direction skin friction coefficient reduced 50% and the y − direction skin friction coefficient improved 46% when the magnetic field enhanced 200%. The 200% porosity parameter leads to reducing the local Nusselt number by 22% for both CNTs.

Numerical simulation of Darcy–Forchheimer flow of Casson ternary hybrid nanofluid with melting phenomena and local thermal non-equilibrium effects

The Casson fluid flow over a stretching sheet is studied in this work in the presence of porous media with melting heat transfer and chemical reaction, combining nanoparticles of Ti4Al6V,AA7072 and AA7075 with a base fluid of sodium alginate (NaAlg). The porous medium Darcy Forchheimer effect is included in the momentum equation. Through the effects of melting, the process of heat transfer is described. In order to explore the features of heat transmission in the absenteeism of LTECs (local thermal equilibrium conditions), the current study employs a mathematical model that has been simplified. For both the solid and liquid phases, the LTNE model yields two different fundamental thermal gradients. This proposed model compares the YOM (Yamada-Ota model) and XM (Xue model), two well-known trihybrid nanofluid models, in terms of performance. After applying the proper transformations, modulated non-linear PDEs (partial differential equations) are simplified in ODEs (ordinary differential equations) and the bvp4c method is used to solve them numerically. A graphic discussion of the relevant factors' significance on the pertinent fields has been presented. It is observed that the Casson ternary hybrid nanofluid temperature and velocity distributions predominate at higher melting parameter. The solid phase's heat transport rate rises with an upsurge in the interphase heat transfer parameter.