Eckert Number Ec Research Articles

Paradigm on Levenberg–Marquardt neural algorithm analysis of heat conduction optimization for ternary hybrid nanofluid with entropy generation

AbstractThe significance of the present article is to enhance the thermal management and energy efficiency of complex engineering infrastructures such as energy storage systems, modern electric vehicles, thermal insulations, heavy‐duty machinery, and production units. This research aims to understand the intricate relationship between the thermal conductivity performance of ternary () hybrid nanomaterial and entropy generation to optimize material design and efficacy. A synergetic combination of three distinct nanomaterials silicon dioxide, ferric oxide, and titanium oxide with ethylene glycol and water in the ratio 3:2 as a base solvent is comprised of contributing unique thermophysical properties. To elucidate the impact of this hybrid composition on thermal conductivity, various factors are analyzed. The advanced computational technique of Artificial intelligent feed‐forward neural network (AIFFNN) is utilized. The problem governed the system of PDEs, which is transformed into ODEs by dimensionless similarity. Adams method provided the dataset which is filtered and embedded into Marquardt–Levenberg Algorithm (LMA). The study examines the role of nanomaterial constituents, morphology, and boundary conditions on thermal performance and entropy generation. Graphical analysis of velocity, temperature, and entropy is provided with respect to varying parameters, including surface absorption (λ), magnetic strength (Tesla M), radiation parameter (Rd), Brownian motion (Br), and Eckert number (Ec). The findings have practical significance for optimizing material design in engineering and industrial applications.

Modeling of Electric MHD Flow of Nanoparticles in a CMC-Water Based Casson Hybrid Nanofluid over a Porous Medium

The principal focus of this exploration is to study the computationally simulate the combined convection of CMC-water-based Casson hybrid nanofluid through a stretching sheet with electric magnetic force in a porous medium. Copper (Cu) and Silver (Ag) nanoparticles are included to enhance the heat transfer performance of CMC-water. The physical problem is formulated with mathematical PDEs, and to solve this, initially we used similarity transformation technique to reduce the PDEs into ODEs, then Runge-Kutta Fehlberg method (RKFM) of order four with shooting technique is adopted for further reduction from the non-linear ODEs to first order DEs. The influence of key parameters such as the magnetic field parameter (M), porous medium parameters (K), electric field factor (E), radiation parameter (Nr), permeability parameter (λ), Casson parameter (β), and Eckert number (Ec) on relevant physical quantities is illustrated through tables and graphical visualizations. The impact of these parameters on velocity and temperature profiles, as well as on the skin friction coefficient and Nusselt number of the nanofluid, is observed. Our results indicate that an increase in the Casson parameter values leads to a decrease in the velocity of the host fluid in the case of opposite flow, and a similar behavior is observed with the nanoparticle porous medium parameter (K) in the case of assisting flow. Furthermore, the use of the Runge-Kutta Fehlberg Method (RKFM) is found to be more accurate and reliable in dealing with the problem studied in this work.

Thermal dynamics of nanoparticle aggregation in MHD dissipative nanofluid flow within a wavy channel: Entropy generation minimization

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

Optimizing heat transfer with electro-osmotic ciliated propulsion in a non-uniform canals with Cu-blood characteristics considering thermal casson nano fluid

Electroosmosis peristaltic flows find promising applications in electro-fluid thrusters in space propulsion, polymer injection systems, ion exchange membrane designs, microbe fuel cells, biochip fabrication and fossil fuel energy process. In light of this, the current work aims to investigate blood based electroosmotic peristaltic flow in a ciliated, non-uniform propagation channel when copper nanoparticles are present. For that purpose, mathematical modeling is done in two dimensional frame and then governing partial differential equations are simplified and converted in ordinary differential equations using dimensionless quantities and long wave length and low Reynolds number approximations. In result we got coupled nonlinear boundary value problem that is solved numerically using three-stage Lobatto IIIa formula known as bvp4c invoking shooting technique. Peristaltic ciliated waves are thought to pass along the channel wall. The properties of both fluid phase and particle phase flow are modeled and investigated. Plotting against various parameters, streamline contours, temperature contours, concentration and temperature profiles, and pressure rise graphs are examined in-depth from a physical perspective. The obtained results revealed that concentration profile α upsurges for rising values of Casson fluid parameter β, nanoparticle volume fraction ϕ and flow rate Q while it drops with an increase in particulate volumetric fraction C, Eckert number Ec, Soret number Sr, Schmidt number Sc and viscosity constant. A decrease in temperature is also caused by an increase in the volumetric percentage of nanoparticles. In the pumping portion, there is a decrease in pressure rise; however, this decrease changes to an increase in the increased pumping zone.

Analyzing heat transfer behavior in two-dimensional Darcy–Forchheimer porous medium using magnetized nanoparticles

This study investigates the two-dimensional boundary layer flow and heat transfer of an incompressible fluid over a plate embedded in a Darcy–Forchheimer porous medium of magnetite ternary hybrid ferrofluid in the presence of suction or injection. It uniquely includes the effects of thermal radiation and viscous dissipation in the energy equation, offering a comprehensive analysis of the phenomena involved. The research focuses on three nanoparticle (NP) combinations of ferrofluid particles ( Fe 3 O 4 ) and metal oxide NPs ( CuO / TiO 2 ) dispersed in an aquatic base fluid with different volume fractions. The governing nonlinear partial differential equations are transformed into ordinary differential equations via similarity transformations and solved using the Runge–Kutta-based shooting technique. The study evaluates key physical quantities, such as the skin friction coefficient and Nusselt number, and examines the effects of dimensionless parameters, including the absorbent Reynolds number (Re), expansion ratio (α), Peclet number (Pe), Eckert number (Ec), NP volume fractions ( φ 1 , φ 2 , and φ 3 ) , porous medium parameter (r), and Darcy-porous medium parameter (F), on velocity and temperature profiles. The results indicate that increasing the porous medium parameters r and F leads to opposite shear stress effects in the dual-porosity medium. Higher Peclet number (Pe) and Eckert number (Ec) values enhance heat transfer rates within the thermal boundary layers. Moreover, elevated Reynolds number (Re) and expansion ratio (α) values result in opposing radial velocity profiles within the momentum boundary layers. This comprehensive analysis provides valuable insights into the complex interactions governing ternary ferrofluid flow and thermal performance in dual-porosity media, contributing to advancements in fluid system applications.

Numerical and semi-analytical approaches for heat transfer analysis of ternary hybrid nanofluid flow: A comparative study

This study presents a meticulous investigation into the intricate dynamics of a Fe3O4(25%)–Al2O3(50%)–ZnO(25%)/water ternary hybrid nanofluid within the framework of the Darcy–Forchheimer model, inclusive of heat source and suction/injection phenomena on two stretching surfaces. The governing partial differential equations are transformed into ordinary differential equations by strategically applying similarity variables. These equations are then solved using the efficient analytical approach of the Homotopy Analysis Method (HAM) and numerically using the implicit finite difference-based Keller Box Method (KBM). We further compare the solutions obtained through HAM with the numerical results from the KBM approach. The inquiry discerns those pivotal parameters such as porosity (Pm) and magnetic (M) amplifying the velocity profile (g), while parameters including Reynolds number (Re), inertia coefficient (Fr), rotational (Ro), and stretching (α) manifest diminishing effects. Furthermore, the study reveals a direct correlation between temperature escalation and the amplification of Eckert number (Ec), magnetic (M), radiation (R), heat source (Q), and stretching (α) parameters. In the case of suction applied to the lower and upper surfaces, the velocity profiles f′ and g, decrease whereas for injection, the opposite trend is observed. When there is suction at the upper surface the temperature profile decreases, but for suction at the upper surface the same increases. However, when there is injection, a reverse pattern is observed. Compared to water, suspension of nanoparticles with a 5% volume fraction of spheres, cylinders, platelets, and blades achieves 13%, 23%, 27%, and 36% heat transfer rates, respectively. This research provides crucial insights into nanofluid flow and heat transfer, with significant implications for various technological applications.

Optimisation of MHD flow within trapezoidal cavity containing hybrid nanofluid by artificial neural network

PurposeThis study aims to numerically investigate heat transport in a trapezoidal cavity using hybrid nanoparticles (Ag-$Al_2O_3$). Unlike previous studies, this one covers magnetohydrodynamics, joule heating with viscous dissipation, heat absorption and generation. The left and right sides of the chasm are frigid. The upper wall heats, whereas the bottom wall remains adiabatic.Design/methodology/approachAfter reducing the system of dimensional equations to dimensionless equations, the authors use the Galerkin finite element method to solve them numerically. Geometric parameters affect heating efficiency; thus, the authors use flow metrics such as the Reynold number Re, magnetic parameter M, volume fraction coefficient, heat absorption and Eckert number Ec. The authors use the finite volume method to solve the governing equations after converting them to dimensionless form. The authors also try the artificial neural network method to predict the innovative cavity’s heat response in future scenarios. Transition state charts, regression analysis, MSE and error histograms accelerate, smooth and accurately converge solutions.FindingsAs the magnetic parameter and Eckert number increase, the enclosure emits more heat. As Reynold and volume fraction coefficients rise, the Nusselt number falls. It rose as magnetic, Eckert and heat absorption characteristics increased. The average Nusselt number rises with Reynolds and volume fraction coefficients. The magnetic, Eckert and heat absorption characteristics have inverse values.Originality/valueThis study numerically investigates heat transport in a trapezoidal cavity using hybrid nanoparticles (Ag-$Al_2O_3$). Unlike previous studies, this one covers MHD, joule heating with viscous dissipation, heat absorption and generation. The left and right sides of the chasm are frigid. The upper wall heats, whereas the bottom wall remains adiabatic.

Numerical performance of Hall current and Darcy-forchheimer influences on dissipative Newtonian fluid flow over a thinner surface

Present problem concerns may be found in a wide variety of various industries and can takes a shape of round toroid's, cones, cylinders, domes (Axisymmetric shape), and other shapes as well. When it comes to actual applications, they are represented by aerosol cans, submarine pressure hulls, cooling towers, offshore drilling rigs, radomes, nuclear reactors, and other similar objects. The aim of this research is to improve the performance of MHD flow using Darcy-Forchheimer, viscous dissipation, porous and a heat source. The viscous convective permeable flow flowing over a bullet-shaped item is examined. Using similarity transforms, the structure of nonlinear differential equations are converted into dimensionless ODEs. Employing bvp4c shooting technique to decrypt the findings. Influences of physical entities on velocity and temperature were sketched and briefly described. Physical behaviors of skin friction and heat transfer rates are explored. The fluid velocity drops for Eckert number Ec as ε < 1.0, and rises as ε > 1.0, The fluid velocity improves with Darcy-Forchhemier parameter Fr when stretching ratio ε < 1.0 or = 1 or >1.0. The enhancement of fluid temperature is observed with enhanced Ec. A enhance in the Darcy-Forchhemier parameter Fr associated with improvement in skin-friction. In the absence of viscous dissipation, hall current, porous and Dacy-Forchhemier influences, the outcomes are in splendid covenant with those of previous studies.

Unsteady magnetohydrodynamic tri-hybrid nanofluid flow past a moving wedge with viscous dissipation and Joule heating

This study aims to boost thermal convection through careful selection and adjustment of nanomaterial volumes, focusing on the unsteady magnetohydrodynamic flow past a moving wedge with viscous dissipation and Ohmic heating in a ternary nanofluid of alumina (Al2O3), copper oxide (CuO), and copper (Cu) in water. Employing mathematical modeling and numerical analysis via MATLAB's BVP4C, it explores how discharge concentration influences flow characteristics and identifies critical conditions for single or dual solutions. Key parameters such as motion and wedge parameters, Eckert number, magnetic strength, and nanoparticle volume ratios were scrutinized for their impact on fluid dynamics and heat transfer. Results show enhanced convective thermal transfer with increased nanoparticle hybridity and volume fraction, alongside suction/injection parameter (S), unsteadiness parameter (A), Eckert number (Ec), and magnetic parameter (M), albeit decreasing with wedge angle adjustments. Stability analysis revealed the stability of the initial solution vs the instability of the secondary. Introducing a novel time variable, τ=cAt(1−ct), this research demonstrates that at λ=−4.7(a leftward wedge) with a 0.04 nanoparticle volume fraction, ternary and hybrid nanofluids significantly outperform mono nanofluid, achieving thermal efficiency gains of 25.6% and 7.5%, respectively. This foundation underscores the potential of optimized nanofluid mixtures for advanced heat transfer applications.

Porosity and heat transfer analysis of nanofluids due to rotating-stretching disk with Joule heating

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

Unsteady MHD flow analysis of hybrid nanofluid over a shrinking surface with porous media and heat generation: Computational study on entropy generation and Bejan number

The use of hybrid nanofluids in real-world situations is essential for enhancing the efficiency of heat transmission, especially in cooling semiconductor technology and industrial processes. The entropy generation on unsteady Al2O3-Cu/H2O hybrid nanofluid flow over a three-dimensional shrinking sheet is addressed numerically in this study, taking into account the effects of magnetohydrodynamic (MHD), nonlinear thermal radiation, porous media, heat generation, viscous dissipation, joule heating, and convective conditions. Using well-known non-similarity transformations, the model is carefully converted from partial differential equations (PDEs) to ordinary differential equations (ODEs). Afterwards, the behaviors of critical physical characteristics are uncovered across different parameter configurations by a numerical solution using the finite difference technique in bvp4c MATLAB. The velocity profiles of hybrid nanofluid grow proportionately with increases in the values of ϕ2,M,A,K and λ parameters. As Rd,θw,Ec,Bi,H and ϕ2 increase, the temperature of the hybrid nanofluid rises, but as M and A increase, the temperature falls. The local skin friction in both the x and y- directions is increased by enhancing the unsteadiness A, nanoparticle volume fraction ϕ2, magnetic M, porous media K, and the ratio of strain rate λ parameter on the shrinking surface. The local Nusselt number is improved by cumulative the unsteadiness A, nanoparticle volume fraction ϕ2, magnetic M, and Biot number Bi parameter in the direction of a shrinking surface, while the Nusselt number decreases when Eckert number Ec, thermal radiation Rd, heat production H, and temperature ratio θw are improved. An upsurge in the magnetic parameter leads to the development of entropy generation. Increasing levels of the magnetic parameters led to a reduction in the Bejan number. At a nanoparticle volume fraction of 1 % and a nonlinearity radiation scenario, where the unsteadiness values are 0.5, the Nusselt number for hybrid nanofluid shows an estimated improvement of 10.55 % compared to regular nanofluid.

MHD flow of blood-based hybrid nanofluid through a stenosed artery with thermal radiation effect

The MHD flow of a blood-based hybrid nanofluid with thermal radiation and stenosis effects is explored in this study. Gold (Au) and Copper (Cu) hybrid nanoparticles are assumed to be distributed in the blood. Relevant governing equations are established and appropriately normalized. The Caputo fractional-order derivative is used to convert the transient terms of normalized equations into time-fractional forms, which are then semi-analytically solved using the Laplace transform method to yield complex forms of modified Bessel functions. The concentrated matrix exponential (CME) approach is used to numerically determine approximate inverse Laplace transforms of the updated equations. The distribution patterns of velocity, temperature, and concentration are evaluated graphically. The results showed that the fractional-order derivative and the height of stenosis greatly influence the velocity, temperature and concentration profiles. We also observed that both velocity and temperature decreased with increasing values of Ha. Temperature rises with increasing values of the thermal radiation parameter (Ra) and the Eckert number (Ec) whilst concentration is enhanced with rising values of the chemical reaction parameter (Cr) and the Schmidt number (Sc). Our numerical results show that relevant parameters have considerable influences on skin friction, Nusselt number, and Sherwood number, which are important for understanding blood mobility, heat and mass transfer dynamics, and treating cardiovascular illnesses. Our results are also essential for controlling blood flow, temperature and delivery of drugs to diseased arteries in the human body.

The significant role of Darcy–Forchhiemer with integrated hybrid nanoparticles (Graphene and TiO 2) on dusty nanofluid flow subjected to heat conduction

The thermal analysis of two-phase models that deal with the fluid and dusty phases has been considered. This study instigates the flow of a non-miscible, dusty hybrid nanofluid over a stretching cylinder with Darcy–Forchheimer permeability in the presence of thermal radiation. The mathematical model is based on the single-phase nanofluid model, which features modified thermophysical characteristics. This innovative flow model explores how important it is to enhance the concentration of dust particles in fluid dynamics. Hybrid nanoparticles are substituted for nanoparticles in a conventional case to accelerate the heat transfer rate of the fluid. Therefore, in this study, the magnetohydrodynamic flow of hybrid nanofluids and heat transfer of non-Newtonian dusty fluids with suspensions of hybrid nanoparticles have been examined. The appropriate dimensionless variables are used to convert the governing periodic model into a non-dimensional form. The finite-difference-based bvp5c algorithm is used through Matlab for numerical analysis of the set of obtained ordinary differential equations. The graphs explored the influences of relatable factors over the profiles of mass, heat, and velocity transfers. It is observed that with intensifying values of Eckert number (Ec) and Biot number (Bi), the temperature of both phases increased at a significant level, and the velocity decreased with increasing intensity of the magnetic field. The computational results of velocity, core temperature, and intensity dispersion are significant for both aspects. Furthermore, it is observed that both the fluid and dust phases exhibit declining behavior as a result of the impact of porosity, mass concentration, and magnetism on the flow stream. Moreover, it is noticed that both the dust phase temperature θ p ( η ) and fluid phase temperature θ ( η ) intensified with the high intensity of magnetic field and thermal radiation. The missile nozzles, nuclear power plants for aerospace and gaseous-core nuclear rocket systems, and the radiation are considered for evaluating heating significance.

Unfolding some numerical solutions for the magnetohydrodynamics Casson–Williamson nanofluid flow over a stretching surface

Abstract This research focuses on exploring the significance of chemical reactions and thermal radiation on the magnetohydrodynamic (MHD) flow of a Casson–Williamson nanofluid (CWNF) over a stretching sheet. The objective is to comprehend how these factors influence the flow and heat transfer. A mathematical model, comprising partial differential equations adjusted into ordinary differential equations (ODEs) via utilizing some transformation. These ODEs are then tackled by MATLAB’s BVP4C method, which is part of the finite difference technique. Results are verified by comparison with existing literature and are depicted visually and in tabular format. Additionally, the study explores the effects of external factors such as magnetic fields and the Lewis number on parameters like Nusselt number, friction factor, and Sherwood number. Furthermore, heat generation in MHD CWNF is analyzed, along with a thorough evaluation of heat transfer near a stretching sheet with a permeable layer. The findings suggest that growing Brownian motion factor (Nb) and thermophoresis coefficient (Nt) enhance the rate of heat transfer, signifying improved heat transfer rates. Similarly, higher Nt values are associated with enhanced Sherwood numbers, indicating better mass transfer. Conversely, higher Nb values lead in lower local Sherwood numbers. Physically, an increase in Brownian motion causes significant displacement of nanofluid particles, boosting their kinetic energy and thereby enhancing heat generation within the boundary layer. It is noted that the Eckert number (Ec) reflects the impact of different Ec values on temperature distribution. As Ec increases, there is a proportional increase in fluid temperature due to frictional heating, which stores heat energy within the fluid. This effect becomes more pronounced for non-linear stretching surfaces, demonstrating the response of the thermal region to viscous dissipation. Viscous dissipation has the potential to enhance convective heat transfer, leading to amplified temperature distribution and thickening of the thermal layer.

MHD peristaltic two-phase Williamson fluid flow, heat and mass transfer through a ureteral tube with microliths: Electromagnetic therapy simulation

The ureter typically experiences a frequency of one to five peristaltic contractions per minute. However, it is important to note that these contractions can be disrupted by various physical and mechanical irritants. Ionic contents in the urine make it electrically conducting and responsive to electromagnetic body forces. MHD can be deployed in bio magnetic therapy to control or mitigate symptoms associated with peristaltic pumping in the urinary system. This article therefore focuses on the hydromagnetic effects on flow patterns of urine with debris (monoliths). The mechanism of urine flow is largely coordinated by the kidneys. The flow inside the ureter is interrupted by microliths, which are generated by the sedimentation of excretory products. To simulate this, a two-phase formulation is adopted, comprising the electromagnetic urological viscous fluid phase and the particulate phase for solid grains. The peristaltic propulsion of two-phase liquid in the ureter is simulated as a sinusoidal wave propagation of incompressible non-Newtonian fluid. The Williamson viscoelastic model is deployed for the rheology. Heat transfer is also included with Soret thermo-diffusion and viscous heating effects. Long wave and low Reynolds number approximations are employed based on lubrication theory. The mass, momentum, energy and concentration conservation equations with associated boundary conditions are rendered non-dimensional via appropriate scaling transformations. A numerical solution is achieved via BVP4C MATLAB quadrature. Graphical visualizations of the velocity, temperature and concentration (solid grains) are given for the influence of suspension parameter ( ζ ), Hartmann number (M), Prandtl number (Pr), Weissenburg number (We), particle volume fraction (C), Eckert number (Ec), Soret number (Sr), Schmidt number (Sc). The novelty of the present work is therefore the simultaneous consideration of a generalized two-phase model, wall slip, non-Newtonian characteristics, cross diffusion, viscous dissipation, mass diffusion, magnetic body force and curvature effects in peristaltic urological transport, which has not been undertaken previously. The detailed simulations reveal that the flow velocity is reduced due to the presence of solid particles and the channel curvature, in comparison to the flow in an unobstructed channel devoid of solid particles. Enhancing the hydrodynamic slip parameter speeds up the movement of particles and fluid near the channel walls, boosts wall skin friction, raises pressure difference in the pumping area, and amplifies bolus magnitudes.The rise in peristaltic pumping results in a reduction in solid particle concentration, which is significant phenomena.This theoretical approach may aid in treating conditions such as Urinary Tract Infections (UTIs). The computations effectively demonstrate that significant manipulation of urological pumping characteristics can be achieved with an electromagnetic field. Some new features of two-phase ureteral dynamics are highlighted as relevant to magnetic therapy techniques, which may be beneficial to clinicians.

Neural network and thermodynamic optimization of magnetized hybrid nanofluid dissipative radiative convective flow with energy activation

This article, motivated by hybrid magnetic coating manufacturing developments, utilizes a neural network-based computational program to study the dynamics of hybrid magnetic nanofluids with entropy generation. A new physico-chemo-mathematical model has been presented to simulate the hybrid magnetic nano-coating flow along a stretching surface to a porous medium with viscous heating. A Rosseland flux model is used for radiation heat transfer and Darcy’s model for the isotropic porous medium. The stretching sheet is porous, and wall suction or injection are possible. A robust neural network has been deployed to optimize the physical parameters controlling the transport characteristics of hybrid nanofluids. Specifically, two hybrid nanoparticle combinations are addressed, namely graphite oxide (GO)-molybdenum disulfide ( Mo S 2 ) and copper (Cu)-silicon dioxide ( Si O 2 ), both with engine oil as the base fluid. The dimensional boundary layer model is transformed via suitable scaling variables from a partial differential system into a dimensionless non-linear coupled ordinary differential system. The transformed boundary value problem is solved numerically with the BVP4C subroutine in the symbolic software MATLAB, which achieves exceptional accuracy. Validation with previous simpler studies is conducted and a good correlation is obtained. The neural network optimization analysis incorporates Bayesian regularization as the training algorithm. The Bejan entropy generation minimization (EGM) analysis shows that with increasing radiation parameter R d , both entropy generation rate and Bejan number are increased. Furthermore, an elevation in Brinkman number Br leads to an upsurge in entropy generation rate and a downtrend in the Bejan number. The numerical solution of the boundary value problem reveals that with an increment in nanoparticle solid volume fraction φ 2 , magnetic parameter M , inverse permeability parameter ϵ , surface injection parameter ( s < 0 ) , Eckert number Ec and radiation parameter R d and with a decrement in suction parameter ( s > 0 ) and Prandtl number Pr , there is a strong enhancement in temperature magnitude and thermal boundary layer thickness. With greater nanoparticle solid volume fraction φ 2 , magnetic parameter M , inverse permeability parameter ϵ , suction parameter s and a reduction in thermal buoyancy parameter λ , strong flow deceleration is induced, and momentum boundary layer thickness is increased. The skin friction coefficient is substantially boosted with lower values of magnetic parameter M , inverse permeability parameter ϵ , suction parameter s and higher values of thermal buoyancy parameter λ . There is a significant decrement also computed in Nusselt number with a greater radiation parameter R d . The simulations provide a good benchmark for future extensions that may consider non-Newtonian behavior.

Numerical simulation of heat transfer and entropy generation due to the nanofluid natural convection with viscous dissipation in an inclined square cavity

In this work, the effects of viscous dissipation on heat transfer and entropy generation of the nanofluid natural convection in an inclined square cavity are numerically investigated. A fractional-step semiimplicit finite difference algorithm based on the projection method on a staggered grid is proposed to solve the laminar natural convection problem, which has the advantage of larger time steps. The square cavity is filled with a nanofluid composed of (Cu) copper nanoparticles and water. and the viscous dissipative behavior of the mixture flow is not negligible. The studied parameters are Rayleigh number Ra ( 10 4 and 10 5 ), Eckert number Ec ( 0 − 2 ), the volume fraction of solid particles ϕ ( 0 − 0.06 ), and inclination angle of square cavity α ( 0 − π / 2 ). The Prandtl number is fixed to Pr = 6.2 . The results show that at any inclination angle, the increase in viscous dissipation leads to weakened heat transfer on the hot wall, enhanced heat transfer on the cold wall, and weakened flow in the square cavity. For the base solution without nanoparticles, the Eckert number has the greatest impact, with its effects on the average Nusselt number on the hot wall, maximum streamfunction, and average Nusselt number on the cold wall being ∼13, 0.15, 18.69%, and at Ra = 10 4 , and 12, 0.5, 28.87% at Ra = 10 5 , respectively. Research on entropy generation shows that as Eckert number increases, the entropy generation due to heat transfer increases, while due to fluid friction decreases. As the Rayleigh number increases, the effect of viscous dissipation increases. As the inclination angle increases, the effects of volume fraction and Eckert number weaken. Adding solid particles can effectively weaken the effect of viscous dissipation.

Numerical investigation of MHD mixed-convective flow and heat transfer within immiscible micropolar and nanofluids in a vertical channel

ABSTRACT This paper analyzed the influence of the Brownian motion and thermophoresis on the behavior of microrotation, linear velocity profile, heat transfer, mass diffusion upon a mixed convective flow of two non-miscible nanofluids in a vertical channel in the presence of a transverse magnetic field and temperature gradient. In the OY axis direction, the modified and coupled Navier-Stokes and nanoparticle volume fraction equations are solved using similarity variables. The solution is carried out and highlights non-dimensional numbers and parameters such as Hartmann number (Ha), Prandtl number (Pr), Eckert number (Ec), Reynolds number (Re), and non-analogous Grashof number (Grc) used in cases of mass transfer caused by natural convection and a concentration gradient. Additionally, the Grashof number (Gr) of heat transfer is used as a function of temperature gradients. The material parameter (K), thermophoresis parameter (MT), Brownian motion parameter (MB), etc. are considered. The algorithm of the final equations is plotted using the bvp4c function in @Matlab software, providing insightful graphs that demonstrate motivating effects on nanofluid flow behavior. The ascending and descending curves of velocity profiles are positively influenced by Lorentz force, thermophoretic phenomenon, and Brownian movement, thereby enhancing heat transfer. The results are thoroughly discussed and compared to previous studies.

Bioconvective flow analysis of non-Newtonian fluid over a porous curved stretching surface

The aim of current investigation is to explore the two-dimensional Darcy flow of second grade fluid with homogenous and heterogeneous reactions toward a porous curved stretching surface. The thermal features the bioconvective flow are observed with the impact of joule heating, nonlinear thermal radiation, and non-uniform heat source/sink. The thermal stratification conditions are imposed on the boundary of the surface with magnetic field which is normal to surface. Flow model momentum and energy equations are converted into the system of nonlinear ordinary differential equations with some appropriative transformation. These nonlinear equations are tackled numerically with the utilization of Bvp4c approach. The graphical and tabulated results are obtained and discussed thoroughly. It is noticed that for the larger Darcy-Forchheimer number F, porosity parameter [Formula: see text], and Hartman number M, the fluid velocity decreases, while curvature parameter [Formula: see text] exhibits the reverse trend on the velocity field. Further, increment in the fluid temperature is observed by the escalation of the Hartman number M and Eckert number Ec, because more resistance produces larger energy in the fluid. This research contributes to understanding the complex interplay of parameters governing fluid dynamics and thermal behavior near porous curved surfaces, shedding light on the impact of various factors on velocity and temperature distributions.

Model-based comparative analysis of MHD stagnation point flow of hybrid nanofluid over a stretching sheet with suction and viscous dissipation

The effects of steady MHD stagnation point flow with viscous dissipation over a permeable stretching surface are examined. The fluid water is infused with Al 2 O 3 − Cu hybrid nanofluid particles. Magnetohydrodynamics (MHDs), suction with viscous dissipation reveals a mechanism for the transmission of heat and flow. Many different thermal conductivity models, such as the Hamilton–Crosser, Yamada–Ota, and Xue models are utilized to learn more about the thermophysical properties of hybrid nanoparticles. By using the boundary layer approximation, the partial differential equations may be transformed into ordinary differential equations (ODEs), which are linked and highly nonlinear. This is accomplished by employing a separate set of equations. Mathematica is used to find the numerical solution by applying the Runge-Kutta (RK-IV) technique to the coupled system in question. Visualization of the resulting numerical data shows the velocity, temperature, and skin friction. There have also been discoveries about the local heat transfer rate. Afterwards, the data is presented in tables and discussed. Suction S is studied together with magnetism M , Eckert number Ec , and the nanoparticle volume fraction toward stretching to better understand the performance of flow, heat transfer within these systems. According to the findings of this investigation, the stretching sheet offers a novel approach. When compared to the Hamilton–Crosser and Xue models of hybrid nanofluid, the Yamada–Ota model of the hybrid nanofluid achieves higher heat transfer rates than the other two models combined for mass suction. Also, the tri-models demonstrate growing tendencies to growing the volume fraction rate of Al 2 O 3 − Cu / H 2 O hybrid nanoparticles. Furthermore, the hybrid nanoparticles performance is superior to that of conventional nanofluids.