Control Volume Based Finite Element Research Articles

Cu and Al2O3-based hybrid nanofluid flow through a porous cavity

Abstract In this study, the (Cu and Al2O3/water) hybrid nanofluid flow is carried out in a porous cavity. The thermophysical structures of solid materials are used from the available literature to improve the thermal performance of the base fluid. The mathematical model as a porous cavity is mainly used in the distillation process and is vital for the storage of thermal energy. The magnetic field is also employed perpendicular to the flow field and the impact of the magnetic parameter examined versus fluid motion. Similarity variables are used to transform governing equations as simplified partial differential equations. The model is solved using the control volume-based finite element method. Boussinesq–Darcy force is employed for the motion of the fluid flow, and the Koo–Kleinstreuer–Li model is used to assess the characteristics of the hybrid nanofluids. The roles of the Hartmann number, Rayleigh number, porosity factor in the porous medium, and drag fin improve traditional fluids’ thermal distribution presentation. Recent results predict that the two different kinds of nanoparticles speed up the heat transfer through the porous cavity. The percentage analysis shows that the hybrid nanofluids (Cu and Al2O3/water) are prominent in improving traditional fluids’ thermal distribution. Finally, the grid sensitivity test is also carried out for hybrid nanoparticles to demonstrate that the results are asymptotically coherent.

Simulation for magnetic force impact on nanomaterial transportation through a porous closed curved container as a multi physics problem

It is a practical application to use porous zones for cooling systems of magnetic sensors. The importance of MHD (Magnetohydrodynamic) on the irreversibility of liquid within a chamber consisting of porous zone has been incorporated in current article. CVFEM (Control Volume based Finite Element Method) has been employed to model the simplified model obtained after employing the vorticity formula. Outputs indicated that the intensity of nanomaterial circulation increases as Ra increases, while it decreases with the inclusion of a magnetic field, which converts the heat transmission mode to conduction, and due to the appearance of a stretching eddy, the heat plume is removed. A reduction in permeability reflects an increase in the exergy drop, which means greater thermal irreversibility. A nonessential impact on the Bejan number (Be) distribution was reported with altering Darcy number (Da) if the buoyancy force was negligible. Regardless of the changing maximum magnitude of Be, augmenting Da results in lower Be. Due to the dependence of Nusselt number (Nu) on the inner surface temperature, Hartmann number (Ha) has a reverse relation with Nu, which means a lower cooling rate with the inclusion of Ha.

Thermal and flow calculations of platen superheater in large scale CFB boiler

Circulating Fluidized Bed (CFB) boilers are desirable technology to utilize solid fuels, operate within a wide load range, and promote the high flexibility in burning a wide range of coal and other solid fuels, keeping high efficiency and low gaseous pollution. The paper presents thermal and flow modeling results of steam superheater operated in the large-scale coal-fired CFB boiler, both in steady and transient states. The mathematical model of the superheater wall was developed using Control Volume-based Finite Element Method. The heat transfer coefficient as the sum of radiative and convective heat transfer coefficients was considered in the presented approach to modeling thermal processes in a circulating fluidized bed. The overall heat transfer coefficient was computed for the analyzed type of the boiler at full load and steady-state conditions using available measuring data and results obtained using Computational Fluid Dynamics (CFD) modeling. Depending on the modeling approach adopted in the CFD model, the heat transfer coefficient at full boiler load varies between 159.96 and 189.63 W/(m2·K). In the analyzed period of boiler start-up, results of steam outlet temperature (455 °C–485 °C), heat transfer coefficients on the flue-gas side (100 W/(m2∙K) and 120 W/(m2∙K)), and heat transfer coefficients on the steam-side (925–2008 W/(m2∙K)) vary with time. The methods presented in the paper can be applied to modeling transient flow and thermal processes in superheaters with complicated flow arrangements. The advantage of the proposed method is a short computing time compared to detailed and complex 3D models. The developed model of the superheater with the transfer coefficient determination methods can be used to perform calculations in the full range of boiler load, both during steady and transient boiler operation.

A hybrid finite element model for non-isothermal two-phase flow in deformable porous media

This paper presents a numerical method to model the coupled thermo-hydro-mechanical (THM) processes in porous media saturated with two immiscible fluids. The basic equations of the system have been derived based on the averaging theory, considering skeleton deformation, two-phase fluid flow, and heat transport. As applying the standard Galerkin finite element method (GFEM) to solve this system of partial differential equations may lead to oscillatory results for saturation and temperature profiles, a hybrid numerical solution is proposed. In this frame, the GFEM is combined with a control volume based finite element (CVFE) approach, and a streamline upwind control volume finite element (SUCVFE) scheme, respectively for the mechanical, hydraulic and thermal part of the system. The CVFEM has been adopted to provide a smooth saturation profile by ensuring local mass conservation, while the streamline upwind scheme has been applied to remove the spurious temperature oscillation by adding stabilizing terms to the thermal part of the system. The CVFE and SUCVFE formulations have been derived using a similar approach as the standard FE practice in the context of weighted residual technique, but using different weighting functions. This will significantly facilitate the implementation of the proposed model in existing FE codes. Accuracy and efficiency of the proposed method have been justified using several numerical examples and comparing the results with available analytical or numerical solutions.

Comparison of collocated methods of MCIM and PWIM for different solution algorithms in CVFEM

The pressure-velocity coupling method of MCIM (Mass Corrected Interpolation Method) and different solution algorithms of this method were previously developed and tested for steady and unsteady incompressible flows. But the effect of under-relaxation factors in cell-face velocities and the main equations never have been investigated. On the other hand, this method and its different algorithms never have been compared with similar and more common methods in the formulation of primitive variables and non-staggered grid arrangements. In this paper, the accuracy, performance, and computational efficiency of the different solution algorithms of MCIM are compared with the well-known PWIM (Pressure Weighted Interpolation Method) of Rhie & Chow. In this study, a fully coupled, segregated approach without any pressure correction and SIMPLE-like segregated algorithms are proposed for two methods of MCIM and PWIM on the control volume-based finite element (CVFEM) framework. Also, for each method, the proper under-relaxation factors for the main equations and cell-face velocities are introduced. The accuracy and performance of the proposed algorithms are demonstrated by solving different steady and unsteady benchmark problems, and the results of both methods for different algorithms are compared. The results indicate that the both methods have spatial 2nd-order accuracy approximately and are not very different from each other. The results also show that the numerical dissipation of the MCIM is much less than PWIM. Comparing the computational cost of the different algorithms of both methods shows that the coupled algorithm of the MCIM for steady and unsteady problems with different time steps and various grid numbers is at least 10% better than other algorithms.

Study of Compact Heat Exchangers Operating in Self-Sustained Oscillatory Flows

Abstract Computer codes were developed to study the performance of compact heat exchangers (CHEs) operating in self-sustained oscillatory flow (SSOF) regimes. The methods were based on a control volume-based finite element (CVFEM) method for geometric discretization and the explicit first stage, single diagonal coefficient, diagonally implicit, Runge–Kutta (ESDIRK) method for temporal discretization. The developed codes were validated for both steady and unsteady cases. A study of nine geometrically related domains of flat tubes in staggered configurations was performed. Grid independence was established subject to double cyclic conditions—periodically fully developed flow and heat transfer in the stream-wise direction and cyclic or repeating flow and heat transfer in the cross-stream direction. The maximum Reynolds number was established at approximately 2000 for the cases studied to avoid the turbulent flow regime. Parameters of interest like Nusselt number, friction factor, and pumping power were calculated for steady and SSOF regimes. An approach was proposed to determine critical Reynolds number (Recrit) for the SSOFs such that for Reynolds number below Recrit the flow remains steady, and above Recrit, the flow exhibits the characteristics of SSOFs before finally transitioning to fully turbulent conditions. The results indicated a sensitivity of performance parameters to transverse spacing but not to longitudinal spacing.

CVFEM modeling of fluid flow induced by convective heat transfer from a hot pipe buried in soil

In this investigation, fluid flow numerical evaluation induced by convective heat transfer due to a buried hot pipe in the soil is performed. The numerical method implemented is the control volume-based finite element method (CVFEM). The physical domain consists of a circular pipe enclosed in a square cylinder. The temperature of the enclosure upper wall was kept uniform cold while remaining walls were insulated. The research was conducted by fixed non-dimensional parameters, that is, porosity (e), location of pipe (K), Prandtl number (Pr), permeability (K (X, Y)), Darcy number (Da), and the Rayleigh number (Ra). The simulation of porous medium was performed by the application of Brinkman-extended Darcy model. Results are illustrated through isotherm and streamlines. The results depicted that the effect of Darcy on the average Nusselt number (Nuave), at larger Ra, is more noticeable. Additionally, Da reduction causes suppression in the fluid flow and, in addition, less heat transfer among the hot pipe and enclosure. The non-homogeneity reduces the Nu over the hot pipe. Moreover, the value of pipe location, as well as its radius, significantly affects the pipe heat transferring.

Numerical simulation of hydrothermal features of Cu–H2O nanofluid natural convection within a porous annulus considering diverse configurations of heater

The purpose of the current study is to numerically investigate the effects of shape factors of nanoparticles on natural convection in a fluid-saturated porous annulus developed between the elliptical cylinder and square enclosure. A numerical method called the control volume-based finite element method is implemented for solving the governing equations. The modified flow and thermal structures and corresponding heat transfer features are investigated. Numerical outcomes reveal very good grid independency and excellent agreement with the existing studies. The obtained results convey that at a certain aspect ratio, an increment in Rayleigh and Darcy numbers significantly augments the heat transfer and average Nusselt number. Further, enhancement of Rayleigh number increases the velocity of nanofluid, while that of aspect ratio of the elliptical cylinder shows the opposite trend.

Analysis of hybrid nanofluid behavior within a porous cavity including Lorentz forces and radiation impacts

We investigate the hybrid nanofluid convection transportation within a permeable medium in appearance of an externally applied magnetic force by modeling it through control volume-based finite element method. To employ the permeability effect terms, one term was added in momentum and radiation was involved to show the diverse states of nanoparticles. The impact of Darcy and Rayleigh as well as magnetic and radiation parameters on the nanofluid performance is investigated and presented. We observe that the conduction mode enhances with higher values of Ha. Nusselt number Nu augments with the consideration of radiation source term. The addition of Lorentz force makes the conduction mode more sensible. The agreement with the published results makes us more confident about the validity of our numerical computations.

Simulation Examination for Nanoparticle Flow in a Permeable Enclosure via CVFEM Involving MHD Effect

In the present investigation, innovative complex porous enclosure is chosen to simulate the MHD (magnetohydrodynamic) natural convection. One side of porous cavity packed with radiative nanofluid (CuO–water) has curve-shaped triangular wave pattern. To gain insight into outputs, CVFEM (control volume-based finite element method) has been used. Nanofluid behavior is inspected by employing two-temperature model for solid matrix and nanoliquid and KKL model for effective properties of nanofluid with an extensive range of key parameters acting as Hartmann number, radiation parameter, buoyancy impact, phase interacting heat transfer factor. Not only imposing magnetic field but also wavy surface and dispersion of nanomaterial have been considered in the current paper. New numerical approach has been utilized to demonstrate the behavior of nanomaterial through the porous tank. Interrelation of average Nusselt number with involved parameters is also proposed. Outcomes reveal that radiation term has straightforward association with Nusselt number. Greater vortex generates with the rise in shape factor.

Numerical framework for simulating bio-species transport in microfluidic channels with application to antibody biosensors

Diagnosis is a fundamental stage in health care and medical treatment. Microfluidic biosensors and lab-on-a-chip devices are amongst the few practical tools for achieving this goal. A new computational code, specifically for designing microfluidic-integrated biosensors is developed, the details of which is presented in this work. This new approach is developed using control-volume based finite-element (CVFEM) method and solves bio-recognition chemical reactions and full Navier–Stokes equations. The results of the proposed platform are validated against the experimental data for a microfluidic based biosensor, where excellent agreement is achieved. The properties of the biosensor, sample, buffer fluid and even the microfluidic channel can easily be modified in this platform. This feature provides the scientific community with the ability to design a specific biosensor for requested point-of-care applications.•A new approach is developed using control-volume based finite-element (CVFEM) method for investigating flow inside a microfluidic-integrated biosensor. It is also used to study the influence of surface functionalization on binding cycle.•The proposed model solves bio-recognition chemical reactions as well as full Navier–Stokes and energy equations. Experimental-based or personalized equations of the chemical reactions and flow behaviour are adoptable to this code.•The developed model is Fortran-based and has the potential to be used in both industry and academia for biosensing technology.

The influence of hybrid nanoparticle (Fe3O4 + MWCNT) transportation on natural convection inside porous domain

In this study, hybrid nanofluid free convection has been simulated within a permeable domain involving Lorentz effect. To solve and simulate the problem, Control Volume-based Finite Element Method (CVFEM) method is applied. In addition, the non-Darcy model has been used to apply permeable condition in equations. The influence of hybrid nanoparticles (Fe3O4[Formula: see text][Formula: see text][Formula: see text]MWCNT) inside water as base fluid has been studied. Meanwhile, source term of radiation impact has been described for different nanoparticle shapes. The impacts of substantial variables such as Darcy number, radiation factor, magnetic strength and Rayleigh number on nanofluid behavior were fully revealed. It can be concluded that enhancing permeability factor can improve the Nusselt number but reverse behavior can be reported for Lorentz forces.

Entropy generation and economic analyses in a nanofluid filled L-shaped enclosure subjected to an oriented magnetic field

Natural convected heat transportation attributes can be elaborated better using entropy generation analysis. In current framework, we scrutinized magnetized Al2O3-H2O nanomaterial natural convection based on entropy generation and L-shaped cavity. Non-dimensional forms of governing expressions are computed through Control Volume-based Finite Element Method (CVFEM). Entropy generation number is calculated. Features of active parameters e.g. Rayleigh number, nanoparticles volume-fraction, nanoparticle shape, Hartmann number, magnetic field angle and aspect ratio versus average heat transportation rate (Nusselt number) and the entropy generation number are investigated. For the first time, an economic analysis is introduced for evaluating the performance of the enclosure with consideration cost of nanofluid. Also, in order to assess the performance of the enclosure, six criteria are introduced which two of them are based on the cost of nanofluids. The results were compared with references and a good compromise was seen. According to the results, both the entropy generation number and average heat transportation rate rise when Rayleigh number upsurges. The average heat transportation rate rises with ascending the nanoparticle volume-fraction whereas the entropy generation number declines when nanoparticles concentration ascends. The entropy generation number decreases 15.14% and 8.15% for Ha=25 and Ha=75, respectively, when ϕ increases from 0 to 0.1.

The influence of different shapes of nanoparticle on Cu–H[formula omitted]O nanofluids in a partially heated irregular wavy enclosure

In this work, a complex nature structure is presented to deal with the flow and heat transfer characteristics of Cu–H2O nanofluid within the irregular triangular enclosure. Influences of the various shape of Cu nanoparticles are also considered to deal with this mechanism. The irregular side (sinusoidal) of the triangular cavity is partially heated from the bottom. A fixed magnetic field is horizontally applied to the enclosure. The governing equations are derived in the form of nonlinear coupled partial differential equations comprising energy, momentum, and continuity equations. These equations are firstly nondimensionalized before being numerically simulated via Control Volume based Finite Element Method (CVFEM). The relation among the diverse parameters is defined in the form of correlation for Nusselt number. The study concludes that the heat transfer rate is ascended owing to the ascendant in Rayleigh number and descended owing to the ascendant in Hartmann number. Particle shape factor also plays a crucial role in the heat transfer rate within and at the surface of the enclosure.

Natural Convection Analysis in a Cavity with an Inclined Elliptical Heater Subject to Shape Factor of Nanoparticles and Magnetic Field

The objective of the present study is to peruse the natural convection in the cavity containing inclined elliptical heater under shape factor of nanoparticles and magnetic field. The control volume-based finite element method is used for solving conservation equations. Numerical results show very good grid independency and very good compromise with other works. The result shows the heat transfer grows via mounting nanofluid volume fraction. The increment of Ra number also leads the heat transfer to ascend. Heat transfer of nanofluid with three different shapes of nanoparticles is studied, and results show the platelet nanoparticle is better than the other ones. The influence of magnetic field on heat transfer is also investigated and discussed. The obtained outcomes represent that at a certain Rayleigh number, the average Nusselt number descends with the ascendant of Hartmann number. Finally, the new correlation is reported for calculating the Nu number in these geometries.

Numerical analysis of entropy generation of a nanofluid in a semi-annulus porous enclosure with different nanoparticle shapes in the presence of a magnetic field

One of the important problems in the field of heat transfer is the investigation of natural convection heat transfer in cavities. The next step is the study of entropy generation. The object of the present work is the investigation of the entropy generation in a semi-annulus porous cavity filled with Cu-water nanofluid in the presence of a magnetic field. The outer and inner semi-circular walls are kept at constant temperatures whereas the two other walls are insulated. Firstly, the governing equations (i.e. continuity, momentum and energy equations) are numerically solved by the Control Volume based Finite Element Method (CVFEM) and then the entropy generation number is calculated. The effects of the Rayleigh number, Darcy number, Hartmann number, angle of magnetic field, the nanoparticle volume fraction, the particle shape and the angle of turn for the enclosure, number and amplitude of undulation in the wavy wall on the entropy generation number are investigated. Also, a new criterion for the evaluation of cavity thermal performance is defined that is called ECOP. The results were compared with those of the literature and good agreement was observed. The results show that the Nusselt number and entropy generation number increase as the Rayleigh number and the nanoparticle volume fraction increase. Also, the entropy generation number decreases with increasing the Hartmann number whereas it increases as the Darcy number increases.

Entropy generation in a nanofluid-filled semi-annulus cavity by considering the shape of nanoparticles

One of the important problems in the field of heat transfer is the investigation of natural convection heat transfer in the cavities. The next step is study of entropy generation. The object of the present work is investigation of the entropy generation in a semi-annulus cavity filled with Cu–water nanofluid. The outer and inner semicircular walls are kept at constant temperatures, whereas the two other walls are insulated. Firstly, the governing equations (i.e., continuity, momentum and energy equations) are numerically solved by the control volume-based finite element method, and then, the entropy generation number is calculated. The effects of the Rayleigh number, the nanoparticle volume fraction, the particle shape and the angle of turn for the enclosure on the entropy generation number are investigated. Also, a new criterion for the evaluation of cavity thermal performance is defined that is called ECOP. The results were compared with those of the literature, and good agreement was observed. The results show that the Nusselt number and entropy generation number increase as the Rayleigh number and the nanoparticle volume fraction increase.

Quantifying numerically forecast size effects in the free vibration of heterogeneous beams

This paper reports on the influence that a periodic microstructure has on the unconstrained flexural vibration of geometrically similar but differently sized heterogeneous beam samples. A numerical investigation was conducted by finite element analysis (FEA) incorporating the detailed heterogeneity to identify and quantify any effect of beam size on the transverse modal frequencies when the microstructural scale is comparable to the overall size. Finite element models of the macroscopic beam samples were created by firstly specifying microstructural scale unit cells containing a single void or inclusion using ANSYS Mechanical APDL and then repeatedly regenerating these as required. Four beam sizes consisting of one, two, three or four layers of unit cells were created while the length to depth aspect ratio was kept constant for all sizes. Void or inclusion volume fraction was also altered while keeping the homogenised mass and stiffness properties of each beam fixed. The influence of the beam boundary texture on the results was also investigated. The ANSYS results were compared to the analytical solution for a conventional Timoshenko beam and a nonlocal Timoshenko beam. Using the nonlocal Timoshenko analysis, the Eringen small length scale coefficients were estimated but found to be size dependent. Numerical predictions obtained from a novel control volume based finite element (CVFEM) procedure incorporating micropolar constitutive behaviour were therefore matched to the ANSYS results and thereby used to identify the two additional constitutive parameters featuring in planar micropolar elasticity theory, namely the characteristic length in bending and coupling number.

Heat transfer by natural convection of Fe3O4-water nanofluid in an annulus between a wavy circular cylinder and a rhombus

Researchers in modern science always attempt to find new techniques to optimize the performance of energy devices through heat transfer enhancement. It comes to the knowledge that such enhancement can be done with the help of nanofluids. Therefore, the present study is aimed to investigate the role of natural convection and thermal radiation on thermo-hydrodynamics of nanofluid heat transfer in an annulus between a wavy circular cylinder and a rhombus enclosure subject to a uniform magnetic field. A new model for viscosity called magnetic field dependent (MFD) viscosity is used. Mathematical formulation of the current physical model is based on the continuity, momentum and energy equations. Numerical simulation of the reduced problem is done with the help of Control Volume based Finite Element Method (CVFEM). The impacts of controlling physical parameters, for instance, Rayleigh number, radiation parameter, Hartmann number, aspect ratio, shape factor of nanoparticles and solid volume fraction of nanoparticles on thermo-hydrodynamics of flow are studied. The quantities of physical interest are graphically presented and discussed in detail. From the present study it becomes apparent that the local heat transfer rate decreases with an increase in aspect ratio in the absence of Hartmann number. In addition, for decreasing values of aspect ratio, the space for fluid flow inside enclosure becomes wider.

Natural Convection of Fe3O4-Ethylene Glycol Nanouid under the Impact of Electric Field in a Porous Enclosure

Free convection of Fe3O4-Ethylene glycol nanofluid in existence of Coulomb forces is studied. Effect of thermal radiation is taken into account. Properties of nanofluid are varied with supplied voltage and shape of nanoparticles. The bottom wall is considered as positive electrode. Control Volume based Finite Element Method is used to obtain the results, which are the roles of Darcy number (Da), radiation parameter (Rd), Rayleigh number (Ra), nanofluid volume fraction (ϕ), and supplied voltage (Δφ). Results indicate that Nusselt number is an enhancing function of supplied voltage and Darcy number. Maximum values for temperature gradient are occurred for platelet shape nanoparticles.