Control Volume Finite Element Research Articles

The evaluation of error estimation for the Casson hybrid nanofluid flow in the uniform gap between two tubes for drug delivery applications

ABSTRACT Hybrid nanofluids are capable of being used as a carrier for delivering drugs to targeted areas in the body. For this purpose, the Casson hybrid nanofluids (HNFs) flow is suggested between the gap of two tubes. The study involves analyzing blood-based hybrid nanofluids (HNFs) that consist of silver (Ag) and titanium dioxide (TiO2) nanoparticles for applications of drug delivery. Titanium oxide nanoparticles, or TiO2 NPs, have strong photoactivity, low toxicity, and excellent biocompatibility, making them promising candidates for cancer treatment. The attractiveness of silver nanoparticles (AgNPs) for cancer therapy is due to their unique properties. Graphic representations are provided based on the simulations of non-dimensional velocity, temperature, and skin friction under physical parameter variations, for the applications of drug delivery are investigated and discussed. The control volume finite element method (CVFEM), is used to solve the problem. The new strategy of artificial neural networks (ANN) is also used to solve the transform equations. Nanoparticles increase drug stability and extend shelf life by protecting them from degradation or inactivation.

Artificial neural network analysis of the flow of nanofluids in a variable porous gap between two inclined cylinders for solar applications

Copper (Cu) nanoparticles (NPs) and polyvinyl alcohol (PVA) are utilized to enhance heat transfer (HT) which is used in the efficiency of solar energy systems. Copper nanoparticles have excellent thermal conductivity (TC) properties that enable them to conduct heat efficiently. In this arrangement, the gap between the two cylindrical channels is settled for the hybrid nanofluids (HNFs) flow in an inclined position that is favourable to sunlight. The nanomaterials consist of a mixture of PVA and Cu nanoparticles (NPs), to execute HNFs. Solar radiation is present on the hot side of the system. The porous gap between the two channels is considered variable which plays a crucial role in enhancing heat transfer and energy conversion. The varying permeability of the gap is adjusted to control the flow resistance and improve the stability of the system. It is observed that higher porosity allows for better convective heat transfer and reduced pressure drop. The transformed equations are solved through an artificial neural network (ANN) while the control volume finite element method (CVFEM) is also used to handle the governing equations. The Cu and PVA (HNF) improves solar radiation absorption and protects components, ultimately increasing the performance and efficiency of the systems.

Stable and locally mass- and momentum-conservative control-volume finite-element schemes for the Stokes problem

We introduce new control-volume finite-element discretization schemes suitable for solving the Stokes problem. Within a common framework, we present different approaches for constructing such schemes. The first and most established strategy employs a non-overlapping partitioning into control volumes. The second represents a new idea by splitting into two sets of control volumes, the first set yielding a partition of the domain and the second containing the remaining overlapping control volumes required for stability. The third represents a hybrid approach where finite volumes are combined with finite elements based on a hierarchical splitting of the ansatz space. All approaches are based on typical finite element function spaces but yield locally mass and momentum conservative discretization schemes that can be interpreted as finite volume schemes. We apply all strategies to the inf-sub stable MINI finite-element pair. Various test cases, including convergence tests and the numerical observation of the boundedness of the number of preconditioned Krylov solver iterations, as well as more complex scenarios of flow around obstacles or through a three-dimensional vessel bifurcation, demonstrate the stability and robustness of the schemes.

Numerical study of mass and heat transport within a ceramic porous tank

<p>In porous media, the thermal transfer phenomenon is widely applied in diverse energy-intensive industrial processes. This research paper aims to elucidate the simultaneous transfer of mass and heat within a ceramic porous tank. To simulate these transport phenomena, a numerical method is developed: Control Volume Finite Element Method (CVFEM), in conjunction with the utilization of a free mesh generator called Gmsh. The study showcases numerous simulation results that depict the transport phenomenon, such as the three-dimensional evolution of three parameters (temperature, saturation and pressure) during the heating of the ceramic tank. By employing this numerical model, a more comprehensive comprehension of these transport phenomena can be achieved.</p>

Production simulation and prediction of fractured horizontal well with complex fracture network in shale gas reservoir based on unstructured grid

In order to accurately simulate the productivity variation characteristics of fractured wells with complex fracture network in shale gas reservoir, based on the multiple migration mechanism of shale gas, the micro-seismic data and discrete fracture model were used to characterize the fracture geometry and complex boundary characteristics, and the comprehensive seepage mathematical model of fractured wells with complex fracture network was established based on the dual porosity-discrete fracture model, and the numerical solution was carried out by combining the unstructured grid and the control volume finite element method. The sensitivity analysis of the influence of key parameters such as fracture conductivity, physical property difference in composite area and Langmuir volume on the production performance of fractured horizontal wells is carried out. This study provides theoretical methods and calculation tools for accurate prediction of productivity change and optimization of production system of fractured horizontal wells with complex fracture network in shale gas reservoirs.

Irreversibility analysis through neural networking of the hybrid nanofluid for the solar collector optimization

Advanced techniques are used to enhance the efficiency of the energy assets and maximize the appliance efficiency of the main resources. In this view, in this study, the focus is paid to the solar collector to cover thermal radiation through optimization and enhance the performance of the solar panel. Hybrid nanofluids (HNFs) consist of a base liquid glycol (C3H8O2) in which nanoparticles of copper (Cu) and aluminum oxide (Al2O3) are doped as fillers. The flow of the stagnation point is considered in the presence of the Riga plate. The state of the solar thermal system is termed viva stagnation to control the additional heating through the flow variation in the collector loop. The inclusion of entropy generation and Bejan number formation are primarily conceived under the influence of physical parameters for energy optimization. The computational analysis is carried out utilizing the control volume finite element method (CVFEM), and Runge–Kutta 4 (RK-4) methods. (FEATool Multiphysics) software has been used to find the solution through (CVFEM). The results are further validated through a machine learning neural networking procedure, wherein the heat transfer rate is greatly upgraded with a variation of the nanoparticle's volume fraction. We expect this improvement to progress the stability of heat transfer in the solar power system.

3D Thermal Study of Double Partition Brick Drying

In porous media, heat and mass transfer is a classical model of transport and it is one of the most energy-intensive industrial processes with a wide variety of applications. This present paper is developed in order to explain the coupled heat and mass transfer that arise during drying process. A free mesh generator Gmsh is used and a 3-D unstructured Control Volume Finite Element Method (CVFEM) is employed to simulate the transport phenomena with a convective drying. Several simulation results, that depict the transport phenomenon inside a porous brick are presented and analyzed. Indeed, thanks to this numerical model, we can observe the three-dimensional distribution of temperature, liquid saturation and pressure during double partition brick drying.

Electro-enhanced natural convection analysis for an Al2O3-water-filled enclosure by considering the effect of thermal radiation

One of the most crucial topics in the thermal sciences is the analysis of how an external electric field affects the natural convection flow. In this study, the heat transfer of electro-hydrodynamic natural convection in an enclosure with a wavy hot wall is numerically studied. Al2O3-water nanofluid is considered as the working fluid, and furthermore, the effect of thermal radiation on the characteristics of fluid flow is simulated. Non-dimensional forms of governing equations are numerically solved using control volume finite element method. The effects of operational parameters such as Rayleigh number, nanoparticles volume-fraction, Lorentz force number, Eckert number, charge diffusivity number, and electric field number on the maximum absolute value of stream function and the average Nusselt number are investigated. Two new parameters are defined to evaluate the contribution of the electrical field and radiation effects on the fluid flow. The results show that ascends 7.95% when increases from 0 to 0.05 at Also, the values of and increase 27.6% and 37.2%, respectively, when goes up from 0 to 0.5 at The values of and decrease 48.7% and 27.1%, respectively, with decreasing the amplitude parameter from 0.1 to 0.3 at

Comparative analysis of the flow of the hybrid nanofluid stagnation point on the slippery surface by the CVFEM approach

In the present analysis,the stagnation point flow model is employedto evaluate the energy transient across the nanofluid using the comparative analysis. The consequences of slip surface are engaged to the momentum equation, to assess the lubrication. Hybride nanofluid has been synthesized by the dispersion of silver (Ag) and Titanium oxide (TiO2), in two different solvents (H2O and C2H6O2), having a great deal of interest in the field of advancement and innovation. The flow mechanismis formulated in the form of a nonlinear set of PDEs with an additional impact of a magnetic field, thermal radiation, and natural convection.As a principal contribution, a specific type of thermophysical model based on thermal conductivity and viscosity is used in the present study with slip boundary conditions. The modeled system of equations is processed by the Numerical Runge Kutta (RK-4) procedure. The accuracy of the observation is checked using the control volume finite element method (CVFEM). The influence of Cf and Nu is estimated according to the characteristics of the flow rate. Drag force and heat transmission velocity are displayed for optimization with the modeled parameters. The results are authenticated by prior studies and a decent level of coherence is demonstrated.

Numerical Investigation of Heat Transfer Inside Participating Media: Built Thermal Environment Application

This paper is devoted to studying the effect of volumetric radiation on coupled convection and radiation heat transfer in a participating two-dimensional enclosure with emitting absorbing and scattering medium which is a crucial criterion in design of built thermal environment. Radiative information is gotten by resolving RTE (the radiative transfer equation) by means of CVFEM (the Control Volume Finite Element Method). Temperature, density and velocity fields are calculated using the mesoscopic two double population lattice Boltzmann approach. Results are validation of results with existing works in literature and the proposed approach was found to be numerically stable, efficient and accurate.

Ferrofluid treatment with insertion of electric field inside a porous cavity considering forced convection

The electro-hydrodynamic (EHD) ferrofluid flow through a porous square shaped enclosure is simulated with different shapes of nanomaterial in the presence of constant heat flux. The flow is governed by coupled partial differential equations and is simulated with the well-established computational technique of control volume finite element method (CVFEM). The effects of the enhancing medium permeability and electric field strength on the flow are displayed through contour plots of streamlines and isotherms. The calculations are performed for different governing parameters namely, porosity, applied electric field , radiation effect , and nanomaterial shape factor over the Nusselt number . It is found that the medium augmenting permeability depreciates the ferrofluid streaming in the absence as well as in the presence of the applied electric field. The temperature of the ferrofluid augments with the medium increasing porosity in the absence of an external electric field, while an opposite effect is observed on the temperature in the presence of the electric field. The enhancement in the medium porosity makes the ferrofluid flow more regular in the absence as well as in the presence of an external electric field.

Production performance simulation of a horizontal well in a shale gas reservoir considering the propagation of hydraulic fractures

In recent years, shale gas has become an important energy source due to its abundant reserves. Due to their extremely tight initial properties, shale gas reservoirs require the use of the multi-stage fractured horizontal well (MFHW) technique to break the shale rock, activate closed natural fractures, and form a complex fracture network. In this study, to solve the issue of how to describe the fracture network's geometry and to predict the production performance accurately, a model that couples the fracture propagation with the fracturing fluid and proppant flow in a horizontal wellbore and hydraulic fractures is established. The displacement discontinuity method (DDM) and finite volume method are used to iteratively obtain numerical simulations of the fracture propagation. The accuracy of the fracture propagation model is verified through comparison with analytical and numerical models. Then, the coupled continuous media and discrete fracture network model considering multiscale flow mechanisms in shale is developed, which is solved numerically using the control volume finite element method (CVFEM) and unstructured tri-prism grids. Finally, the numerical simulation models are successfully applied to synthetic and field cases, sensitivity analysis is conducted to evaluate the influences of the proppant injection, stress anisotropy and distribution of the natural fractures on the fracture propagation and production performance of the MFHW in a shale gas reservoir.

A hybrid pressure approximation in the control volume finite element method for multiphase flow and transport in heterogeneous porous media

We present a new hybrid pressure formulation applied to the control volume finite element (CVFE) method to model multiphase flow and transport in highly heterogeneous porous media. The formulation effectively captures sharp saturation changes in the presence of discontinuous material properties by employing a discontinuous pressure approximation at material interfaces. The heterogeneous porous medium is divided into sub-domains within which material properties are uniform or smoothly varying. By construction, the resultant control volume dual mesh is restricted within a sub-domain. The artificial mass leakage across material property boundaries observed in classical CVFE methods is therefore circumvented. The approach applies the robust continuous pressure approximation in the rest of the computational domain; the discontinuous approximation is applied only at the sub-domain boundaries. The discontinuous parameters necessary to achieve mass conservative solutions, locally and globally, are described. We demonstrate the accuracy and efficiency of the new approach by comparison with the classical continuous CVFE method on various examples of heterogeneous domains as well as establishing the convergence of the numerical method. The proposed hybrid formulation significantly outperforms the accuracy and efficiency of classical CVFE methods that use the same order of approximation for modeling multiphase flow in heterogeneous porous media.

Research of the thermoelastic performance of the functionally graded sandwich slabs with convective-radiative boundary conditions based on FVM

<p indent="0mm">In this study, a two-dimensional control volume finite element method (CV-FVM) has been developed for the thermoelastic coupling problem of sandwich structures with functionally graded material core under a convection-radiation heat transfer environment. Based on a four-node quadrilateral element, the discrete process of the governing equation and the nonlinear heat transfer boundary are given in detail. Based on the staggered grid technology, the variables are stored at the node of the element, and the material parameters are defined at the center of the element. To ensure the convergence of the temperature solution, the radiation heat transfer boundary condition is handled by the linearization technique. The numerical method developed in this study is validated for the heat conduction problem of sandwich structures with an exponential core. The results showed that CV-FVM results are consistent with the analytical solution. The influences of the geometric and physical parameters, such as the Biot number, radiation conduction coefficient, environmental temperature ratio, panel thickness, and gradient index of the functionally graded core, on the thermoelastic performance of the structure are investigated. The results showed that the Biot number of the heating surface has only a slight effect on the thermoelastic response of the structure, whereas the Biot number of the cooling surface has a significant effect on the thermoelastic response. The cooling surface is more sensitive to the change in the environmental temperature than the heating surface. For sandwich structures with an exponential core, increasing the thickness of the upper panel can reduce the large gradient change of the stress at the junction between the upper panel and the core. The stress with a linear variation of the properties (<italic>p</italic> = 1) is smoother than that with a nonlinear variation of the properties (<italic>p</italic> = 0.1 and 10), and the large gradient change of the stress of the structure can be reduced significantly (<italic>p</italic> = 1).

Production Performance Simulation of the Fractured Horizontal Well Considering Reservoir and Wellbore Coupled Flow in Shale Gas Reservoirs

Unmodified original shale gas reservoirs have been demonstrated to have extremely low permeability, and the long horizontal drilling and hydraulic fracturing techniques are widely used to obtain economic gas production. However, these techniques can result in a nonlinear flow of fluids during transport through the multi-scale pore system and the complex fracture network around the horizontal well, as well as a two-phase gas-water flow during shale production. To solve these issues, in this paper, first, the complex fracture network around the horizontal well is characterized using the discrete main hydraulic fractures combined with composite regions with different properties. Then, the dual porosity media and discrete-fracture model are implemented to describe the nonlinear flow behavior in the multi-scale pore system, and a wellbore pressure drop model is established to characterize the transient two-phase gas–liquid flow in the different sections of the fractured horizontal well. Finally, the coupled reservoir wellbore flow model is fully implicitly solved using the control volume finite element method and unstructured tetrahedral grids. The results of the simulation model of a multi-stage fractured horizontal well in the shale of the Longmaxi Formation will help field engineers deeply understand gas and water production performance and the dynamics of wellbore and reservoir pressure, as well as optimize development schemes.

On Numerical Approximation of Diffusion Problems Governed by Variable-Exponent Nonlinear Elliptic Operators

We highlight the interest and the limitations of the L1-based Young measure technique for studying convergence of numerical approximations for diffusion problems of the variable-exponent p(x)- and p(u)- laplacian kind. CVFE (Control Volume Finite Element) and DDFV (Discrete Duality Finite Volume) schemes are analyzed and tested. In the situation where the variable exponent is log-Hölder continuous, convergence is proved along the guidelines elaborated in [Andreianov et al. Nonlinear Anal. 72, 4649–4660, 2010 & Nonlinear Anal. 73, 2–24, 2010] while investigating the structural stability of weak solutions for this class of PDEs. In general, the lack of density of the smooth functions in the energy space, related to the Lavrentiev phenomenon for the associated variational problems, makes it necessary to distinguish two notions of solutions, the narrow ones (the H-solutions) and the broad ones (the W-solutions). Some situations where approximation methods “select” the one or the other of these two solution notions are described and illustrated by numerical tests.

Development and deployment of a credible unstructured, six-DOF, implicit low-Mach overset simulation tool for wave energy applications

An unstructured, low-Mach, balanced-force, volume of fluid methodology is coupled to an implicit, six-DOF overset formulation for the simulation of wave-based renewable energy devices. We propose an overlapping unstructured mesh construct that affords a wave energy converter (WEC) geometry to move freely about a background domain. A control volume finite element (CVFEM) numerical discretization, which includes novel residual-based stabilization, is developed. Credibility of this simulation tool is established by code verification, which demonstrate design-order numerics on linear and quadratic conformal and overset meshes, and model validation. A CVFEM balanced-force method is applied to a static bubble configuration using conformal and mixed topology overset meshes, while an obstructed dam break case is used to establish the viability of the proposed numerical construct. A validation hierarchy that focuses on falling and rising spheres in quiescent flow showcases the stability of the overset and six-DOF coupling approach. Finally, a buoy validation case is presented that demonstrates the efficacy of the parallel, implicit overset approach for this challenging multiphase flow regime by including both low- and high-displacement configurations along with a large wave displacement numerical benchmark with and without mooring.

Heat Transfer Study in Cylindrical Cavity with Heat Absorption or Generation

Lattice Boltzmann mesoscopic (LBM) is applied to solve energy equation of a transient conduction radiation heat transfer problem in a two-dimensional cylindrical participating (absorbing, emitting and scattering) medium in the presence of heat generation/absorption coefficient. Control volume finite element method (CVFEM) formulation is used to obtain the radiative information. To study the effectiveness of the LBM-CVFEM combination on unsteady conduction-radiation problems in cylindrical media, the energy equation of the problem is also solved using the finite difference method (FDM) in which the CVFEM is used to compute radiative information. The effects of heat generation/absorption coefficient on temperature distributions in the medium are studied. Results of the present work are benchmarked against those available in the literature. The hybrid numerical model’s results are also compared with those obtained by the FDM-CVFEM combination. All the results presented in this work show that the present method is accurate and valuable for the analysis of cylindrically axisymmetric radiative heat transfer problems .

Computational modeling of a complex container with nanofluid carrier fluid and magnetic force

The porous curved container with magnetic force was examined in this article via control volume finite element method. To make a more convective flow, the water has been mixed with nano-sized particles and various shapes of powders were utilized. The momentum equations have been updated according to the Darcy law and adding magnetohydrodynamics (MHD) terms. Circular wall assimilates uniform heat flux, but the lobed surface maintains at T = T c. Moreover, the properties of operate fluid should be changed and single-phase formulation has been utilized. The verification procedure proved the good accuracy of the applied code. Utilizing blade shapes particles instead of m = 4.8 causes Nu to augment around 11.98%. Increasing gravity force makes Nu to elevate around 28.85%. With impose of MHD, the Nu declines to about 22.81%. Adding powders leads to the elevation of Nu around 43.06%.

A Peaceman-type well model for the 3D Control Volume Finite Element Method and numerical simulations of supercritical geothermal resource utilization

While supercritical geothermal resources receive increasing attention, it has so far remained unclear if and how they could be utilized. In order to provide a tool that can simulate both the natural transient evolution of a supercritical resource near a magma intrusion and its response to possible operation schemes, we augmented the CSMP++ simulation platform with a Peaceman-type well model. For the purpose of generic porous medium simulations of the supercritical resource’s response to direct production, injection or other operation schemes, only a single in-/outflow interval per well is considered and flow in the wellbore is not simulated. The model’s semi-analytical source/sink function accounts for the rapid change in pressure near the wells in the reservoir simulation. As the implementation is based on the 3D Control Volume Finite Element Method it allows the use of unstructured computational grids in order to be able to include geologically realistic geometries. We validate that the well model provides robust solutions of well pressures and rates. Such robust solutions are also obtained for supercritical conditions where water is highly compressible and, therefore, does not strictly fulfil the assumptions used in the derivation of the Peaceman model. To illustrate how a magma-related supercritical resource responds to well operation, we first simulate the evolution of a geothermal system around and above a 2 km deep, explicitly represented magma body. During the system’s hottest phase, ca. 2700 years after its initiation and during progressive inward cooling of the magma body, a well completion interval is activated at 2.1 to 2.2 km depth where temperatures then reach 420 to 490 °C. For the relatively low host rock permeability used in the model (10−15 m2), injection and production rates remain quite limited at several kg/s. Yet, the evolving patterns of temperature, enthalpy, density and flow rates provide some first insights into supercritical resource response to operation.