Equivalent Flow Model Research Articles

Consequences of higher order chemical reaction on bioconvective carbon nanotubes flow implementing Buongiorno's model

In recent years, carbon nanotubes have been extensively explored based on numerous applications in fields such as carbon nanotube based electrodes, super capacitors, nanowires, sensors, coating with polymers, biomedical, and mechanical applications. Keeping in view the significance of carbon nanotubes in the heat transfer process in micro-electrochemical systems, this study is conducted to examine the heat transfer attributes of the carbon nanotubes using the mixture base working fluid. The focus of this investigation is to elaborate the consequence of higher chemical reactions on the bioconvective flow of carbon nanotubes. Additionally, modified Buongiorno's nanofluid model has been used, which undertakes thermophoresis and Brownian motion effects. Heated boundary condition has also been incorporated with the migration of motile microorganisms. The hybrid nanofluid mechanism has been followed in this work. Carbon nanotubes of single-layer and multi-layer have been used simultaneously with different working fluids, such as ethylene glycol (EG) and ethylene glycol/water (EG-water). Non-dimensional flow model equations have been tackled with the bvp-4c package. The obtained outcomes have been presented for distinct profiles and tabulated data sets for the surface skin friction and heat transfer coefficient. It has been observed that when the level of Brownian motion increases, the velocity profile decreases abruptly for SWCNT-MWCNT/EG as compared to SWCNT-MWCNT/EG-water hybrid nanofluid. Opposite behavior has been seen with raising values of magnetization. High Prandtl number decrease thermal boundary layer thickness for both types of hybrid nanofluids. The motile microorganism profile expands by raising the level of bioconvective Lewis number. Moreover, the outcomes of drag force and Nusselt number have been compared, and good agreement has been found.

Stagnation point flow of hybrid nanofluid flow passing over a rotating sphere subjected to thermophoretic diffusion and thermal radiation

The effects of thermal radiation and thermophoretic particles deposition (TPD) on the hybrid nanofluid (HNF) flow across a circling sphere have momentous roles in research and engineering. Such as electrical devices, projectiles, thermal conveyance, sheet production, renewable energy, and nuclear-powered plants. Therefore, the current study presents the stagnation point flow of HNF flows about an orbiting sphere. The HNF is organized with the accumulation of aluminum alloys (AA70772 and AA7075) nanoparticles in the water. The HNF flow model equations are changed into the non-dimensional form of ODEs through the similarity variables and then numerically solved through the parametric simulation. It has been perceived that the significance of the rotation factor boosts the velocity curve, while the flow motion drops with the increasing numbers of AA7072 and AA7075 nanoparticles. Furthermore, the addition of AA7072 and AA70775 nano particulates in water lessens with the temperature profile. The energy distribution rate in case of hybrid nanoliquid enhances from 3.87 to 13.79%, whereas the mass dissemination rate enhances from 4.35 to 11.24% as the nanoparticles concentration varies from 0.01 to 0.03.

A second-order conic approximation to solving the optimal power flow problem in bipolar DC networks while considering a high penetration of distributed energy resources

This article presents an optimal power flow (OPF) formulation based on the branch flow model for bipolar DC grids with asymmetric loading. The proposal considers the power injection formulation of the OPF to obtain the branch flow model equations that allow solving the power flow problem in bipolar DC networks. Furthermore, a nonlinear programming (NLP) optimization model is deduced and transformed into a second-order conic programming one, which involves convex optimization and guarantees a global optimum for the relaxed model, the uniqueness of this solution, and fast convergence. Finally, an approximation based on balanced operation is proposed to simplify the OPF. Several case studies in two test systems composed of 21 and 85 nodes with a bipolar structure demonstrate that the proposal is accurate, fast, and close to the exact solution of the NLP model when compared with competitive literature reports. All optimization models were implemented in the Python language.

Derivation and stability analysis of two-fluid model equations for bubbly flow with bubble oscillations and thermal damping

The two-fluid model with bubble oscillations, proposed by Egashira et al. (2004), can explain the properties of cavitating bubbly flow and pressure wave propagation in the bubbly liquid. However, the viscous effect as well as energy conservation leading to temperature changes inside the bubble with bubble oscillations have not yet been considered. Hence, this study aimed to incorporate the viscous (bulk viscosity and drag) and thermal effects to the previously proposed two-fluid model with bubble oscillations. Bulk viscosity was considered by averaging the shear stress term in the single-phase momentum conservation for a Newtonian fluid, and the drag was introduced by transforming the interfacial shear stress. We derived the averaged energy conservation for a general two-phase flow with a thermal conduction inside bubbles and heat transfer between the two phases, and limited this equation to that for a bubbly flow by closing the interfacial temperature gradient term via constitutive equations for a single bubble. Furthermore, we investigated the stability of our proposed one-dimensional model equations using the dispersion analysis. This analysis provided the following insight: (i) The difference in the temperature gradient models had a slight effect on the stability of the proposed model equations; (ii) the thermal conduction inside the bubbles was dominant in the thermal damping in bubbly flows rather than the heat transfer between the two phases; (iii) incorporating both the bulk viscosity and drag stabilized the proposed model equations. Our results provide insights into the development of mathematical models to investigate the thermal effects in bubbly flow with bubble oscillations, such as cavitating bubbly flow and wave propagation in bubbly liquids.

Theory and Semi-Analytical Study of Micropolar Fluid Dynamics through a Porous Channel

In this work, We are looking at the characteristics of micropolar flow in a porous channel that’s being driven by suction or injection. The working of the fluid is described in the flow model. We can reduce the governing nonlinear partial differential equations (PDEs) to a model of coupled systems of nonlinear ordinary differential equations using similarity variables (ODEs). In order to obtain the results of a coupled system of nonlinear ODEs, we discuss a method which is known as the differential transform method (DTM). The concern transform is an excellent mathematical tool to obtain the analytical series solution to the nonlinear ODEs. To observe beast agreement between analytical method and numerical method, we compare our result with the Rung-Kutta method of order four (RK4). We also provide simulation plots to the obtained result by using Mathematica. On these plots, we discuss the effect of different parameters which arise during the calculation of the flow model equations.

Efficient linear dual-medium model for production prediction

<p indent="0mm">Production prediction (PP) is the basis for assessing the fracturing effect and exploitation value of a reservoir. A reasonable, efficient, and accurate PP model is vital for exploiting unconventional gas reservoirs. Referring to microseism monitoring results, a new PP model was proposed based on the linear fracture-network assumption, which considers the distribution properties of fractures. The flow model equations were developed based on the dual-medium assumption. Then, the simulation and prediction program were developed by numerical methods, and a software platform was built. The results show that the proposed PP model outperforms the traditional tri-linear model. The main advantages are as follows: the theoretical basis of the proposed model is more reasonable, which is more consistent with the microseism monitoring results; the proposed PP model is more efficient, with a prediction time that is less than one-thousandth or even one ten-thousandth of that of the traditional model; and the proposed model has similar or higher accuracy than the traditional model. The proposed model can provide valuable guidance for predicting and assessing gas reservoir production, including shale and coalbed gas.

Alternative flow model of anisotropic porous media

Porous flow is typically analyzed by the Kozeny–Carman equation using geometric variables, such as hydraulic diameter and tortuosity. The hydraulic tortuosity was first described by Kozeny, and later redefined by Carman as the tortuosity square term in the Kozeny–Carman equation. However, the revised term correlating the flow velocity with path length square would be physically ambiguous. Moreover, the hydraulic diameter, which is directly correlated to the permeability and interstitial velocity in the Kozeny–Carman equation, is an isotropic constant property; thus, it should be verified whether the isotropic hydraulic diameter can reasonably correlate each anisotropic directional flow feature passing through heterogeneous complex media. Accordingly, the Kozeny–Carman equation was theoretically examined and experimentally verified in this study to obtain the proper correlation based on the definitions of truly equivalent diameter and tortuosity. Therefore, the effective variables of porous media were presented, and it confirmed that the effective diameter corresponded to the physically equivalent diameter of anisotropic porous media. Moreover, using the mass conservation relation, it was verified that Kozeny's tortuosity is exactly associated with the truly equivalent flow model, and then the Kozeny constant must be differently defined from the original Kozeny equation. Accordingly, the Kozeny–Carman equation was improved by appertaining either effective diameter or tortuosity, and the momentum conservation relation was used to verify it. The pore-scale simulations using 5-sorts of 25-series porous media models were performed to test the validity of derived effective variables and revised equations. Finally, the alternative flow model of anisotropic porous media was presented using equivalent geometric and frictional flow variables. Subsequently, their practical and more accurate estimations were achieved by introducing the concentric annulus flow model under the special hydraulic condition. The new variables and relations are expected to be usefully applied to various porous flow analyses, such as interstitial velocity estimations, geometric condition variations, flow regime changes, and anisotropic heat and multiphase flows.

System Dynamics and Graphical Interface Modeling of a Fig-Derived Micro-Producer Factory

This study started from a fig-derived product project in the 2022–2026 Strategic Plan from Sonora, Mexico, to develop technological solutions in complex environments and provide a global panorama from the industry to the prevailing situation in Valle del Mayo. A technological solution is based on a graphical interface to support decision-making in fig supply, production and distribution in the administration process, given that the main problem has been the lack of a processing plant with a sustainable approach. Four options were set up for nine producers—figs in syrup, dehydrated, marmalade, compost—based on the system dynamics methodology to solve the problem of factory installation. Six stages were followed: (1) mapping the system to determine variables and parameters; (2) constructing the causal diagram; (3) developing the flow and level diagram and model equations; (4) simulating and validating the current model; (5) designing policies and evaluating scenarios using a multi-criteria analysis; and (6) developing the graphical interface. The main conclusions show that fig-derived products and their distribution can feature in diverse markets in a graphics environment supported by complex mathematical models in the supply chain along with the capacity to generate income into utilities to support the decision of the physical factory prior to important investments.

A significant impact of Carreau Yasuda material near a zero velocity region

This goal of this study is to examine the incompressible steady 2D flow of MHD Carreau Yasuda model along with the heat generation and chemical reaction near a zero velocity region. The magnetic field and thermally conducting fluid towards a stretching cylinder are very significant due to its usage in the various manufacturing sector. Chemical reactions are widely practice in everyday life as turning nutrition into energy fuel for our body, food change, fireworks expulsions, removing grimes, photosynthesis, etc. The nonlinear flow model equations and their corresponding boundary conditions are changed into non-dimensional shape using similarity variables. The role of vital parameters is discussed with the assistance of MATLAB software by BVP4C method. It is concluded that the momentum increases for rising the curvature and stretching ratio parameter. This is examined that the heat field improves for rising behavior of the magnetic force, curvature coefficient and heat generation. The fluid concentration upsurges due to curvature and magnetic field parameter while reverse results shown due to chemical reaction parameter. We graphically investigate the impression of magnetic effect and chemical force for heat and mass profiles.

Study on Flow Model and Flow Equation of Shale Gas Based on Microflow Mechanism

Shale gas storage and permeability space is between nanometers and micrometers and has strong multiscale characteristics, resulting in highly complicated shale gas flow. Therefore, the development of shale gas needs to clarify the seepage mechanism of shale gas and establish a flow model and flow equation that can analyze shale gas flow. In this paper, based on the single nanotube model, combined with the Weiyuan-Changning shale gas demonstration zone of the target layer of the Longmaxi formation shale core high-pressure mercury pore throat test results, the contribution of seepage, diffusion, transition flow, and free molecular flow to shale gas flow was calculated. The contribution of seepage and diffusion is over 95%, and seepage and diffusion are the main flow pattern. Then, a shale gas seepage and diffusion coupled flow model and coupled flow equation were established. A method for calculating shale permeability and diffusion was proposed using the relationship between flow pressure and shale gas velocity. Finally, shale gas flow experiment analysis was carried out to verify that the established shale gas flow model and flow equation can describe the shale gas flow well. The result shows that the flow rate of shale gas is composed of seepage flow rate and diffusion flow rate. The seepage flow rate is proportional to the pseudopressure difference and proportionate to the low-pressure squared difference. The diffusion velocity is proportional to the difference in shale gas density, and the pressure difference in low pressure is proportional. As the pressure of a shale gas reservoir decreases, the proportion of diffusion flow increases. The research results enrich the understanding of shale gas flow; it also has particular reference significance to the development of shale gas reservoirs.

Insight into the Significance of Viscous Dissipation and Heat Generation/Absorption in Magneto-Hydrodynamic Radiative Casson Fluid Flow With First-Order Chemical Reaction

This study is an attempt to explore two-dimensional magneto-hydrodynamic Casson fluid flow with heat generation or absorption, chemical reaction, and viscous dissipation under the effect of thermal radiation. Prescribed surface temperature (PST) and prescribed heat flux (PHF) cases have been taken into account to investigate the problem. The constitutive relations for Casson fluid incorporated with suitable boundary layer approximation theory have been utilized to achieve the flow model equations. The obtained highly non-linear partial differential equations cannot be solved analytically, so we transform them into first-order differential equations, then tackle them with the boundary value problem (BVP-4c) technique in Matlab. Radiation increment decreases primary and secondary velocity profiles abruptly in both cases. Heat generation and absorption augmentation decrease the thermal and momentum boundaries for both studied cases. The skin coefficient for PHF cases has decreased 80% when compared with PST cases. The increment in Casson parameter has enhanced the Nusselt number by 75% for the PST case, whereas the decline in Nusselt number has doubled for the PHF case with the increase in magnetic field. It is concluded that, with the increment in Casson fluid, magnetic, radiation, and permeability parameter the Nusselt number has significantly increased for the PST case. However, for these parameters, an abrupt decline in Nusselt number has been observed for the PHF case. Results reported in this study for shear stress and Sherwood number are in complete agreement with already published previous work.

Mathematical modeling of mixed-traffic in urban areas

Transportation is the means of mobility. Due to the growth in the population, rising traffic on road, delay in the movement of vehicles and traffic chaos could be observed in urban areas. Traffic congestion causes many social and economic problems. Because of the convenience and the quickness, motor-bikes gradually become the main travel mode of urban cities. In this paper, we extend the Lighthill–Whitham–Richards (LWR) traffic flow model equation into the mixed-traffic flow of two entities: car and motor-bike in a unidirectional single-lane road segment. The flow of cars is modeled by the advection equation and the flow of motor-bikes is modeled by the advection-diffusion equation. The model equations for cars and motor-bikes are coupled based on total traffic density on the road section, and they are non-dimensionalized to introduce a non-dimensional number widely known as Péclet number. Explicit finite difference schemes satisfying the CFL conditions are employed to solve the model equations numerically to compute the densities of cars and motor-bikes. The simulation of densities over various time instants is studied and presented graphically. Finally, the average densities of cars and motor-bikes on the road section are calculated for various values of Péclet numbers and mixed-traffic behavior are discussed. It is observed that the mixed-traffic behavior of cars and motor-bikes depends upon the Péclet number. The densities of motor-bikes and cars in the mixed-traffic flow approach the equilibrium state earlier in time for smaller values of Péclet number whereas densities take longer time to approach the equilibrium for the greater values of Péclet number.

A high resolution numerical method for solving atmospheric models

We develop a numerical method to solve atmospheric model equations, which is a hybrid of the exponential time differencing (ETD) and the equation solving solution gradient (ESSG) method. The Coriolis force term due to geostrophic effects is handled by the ETD method and the convective flux balance terms are implemented by the ESSG method. In the ESSG method, gradients of solution variables are solved by their corresponding difference equations instead of interpolating from nearby solution values as in the conventional finite volume method. In this way, significant features of the model equations can be preserved and correctly considered to provide a reliable simulation. Feasibility of the proposed method is verified in a number of applications and shows it is more accurate than other common schemes, including the first-order upwind (UD) scheme and the second-order minimum modulus (minmod) scheme. We apply the method to a one-dimensional shock tube, a two-dimensional Riemann problem, and an atmospheric vortex flow. Our studies indicate that the exponential time differencing together with the equation solving solution gradient method provides very accurate simulations for the atmospheric flow model equations.

Computational analysis of heat and mass transfer in a micropolar fluid flow through a porous medium between permeable channel walls

Abstract The present work numerically investigates the mass and heat transport flow of micropolar fluid in a channel having permeable walls. The appropriate boundary layer approximations are used to convert the system of flow model equations in ODEs, which are then numerically treated with the quasi-linearization method along with finite difference discretization. This technique creates an efficient way to solve the complex dynamical system of equations. A numerical data comparison is presented which assures the accuracy of our code. The outcomes of various problem parameters are portrayed via the graphs and tables. The concentration and temperature accelerate with the impacts of the Peclet numbers for the diffusion of mass and heat, respectively. It is also found that the porosity of the medium has a substantial effect on the skin friction but low effect on the heat and mass transfer rates. Our results may be beneficial in lubrication, foams and aerogels, micro emulsions, micro machines, polymer blends, alloys, etc.

Numerical Study of Lorentz Force Interaction with Micro Structure in Channel Flow

The heat transfer Magnetohydrodynamics flows have been potentially used to enhance the thermal characteristics of several systems such as heat exchangers, electromagnetic casting, adjusting blood flow, X-rays, magnetic drug treatment, cooling of nuclear reactors, and magnetic devices for cell separation. Our concern in this article is to numerically investigate the flow of an incompressible Magnetohydrodynamics micropolar fluid with heat transportation through a channel having porous walls. By employing the suitable dimensionless coordinates, the flow model equations are converted into a nonlinear system of dimensionless ordinary differential equations, which are then numerically treated for different preeminent parameters with the help of quasi-linearization. The system of complex nonlinear differential equations can efficiently be solved using this technique. Impact of the problem parameters for microrotation, temperature, and velocity are interpreted and discussed through tables and graphs. The present numerical results are compared with those presented in previous literature and examined to be in good contact with them. It has been noted that the imposed magnetic field acts as a frictional force which not only increases the shear stresses and heat transfer rates at the channel walls, but also tends to rotate the micro particles in the fluid more rapidly. Furthermore, viscous dissipation may raise fluid temperature to such a level that the possibility of thermal reversal exists, at the geometric boundaries of the domain. It is therefore recommended that external magnetic fields and viscous dissipation effects may be considered with caution in applications where thermal control is required.

Approximate analytical solution for the flow of a Phan-Thien–Tanner fluid through an axisymmetric hyperbolic contraction with slip boundary condition

An analytic approximation for the flow of a linear Phan-Thien–Tanner model fluid through an axisymmetric semi-hyperbolic contraction is presented. Such an approximation allows us to compute velocity and pressure response for the flow through axisymmetric contraction geometries; in particular, we have considered here the semi-hyperbolic contraction, which is a geometry where an almost constant extension-rate is reached at different radial positions. In addition, we present a semi-analytic solution capable of representing the exponential version of the selected viscoelastic model; this solution was compared to the results of commercial software, demonstrating the excellent approximation level of the semi-analytic model proposed. Alternatively, for both approaches (linear and exponential Phan-Thien–Tanner), the flow model equations are solved by considering the Navier boundary condition, which allows these models to represent flows with some degree of slip at the geometry wall.

Rheological Parameter Analysis in Generalized Bulk Mixture Mass Flow Model

Pokhrel et al. recently developed a generalized quasi two-phase bulk mixture model for mass flow. This model has been constructed by employing full dimensional two-phase mass flow model equations. The model is a set of coupled partial differential equations which is characterized by some new mechanical and dynamical aspects of generalized bulk and shear viscosities, pressure, velocities and effective friction for the mixture where all these are evolving as functions of several dynamical variables, physical parameters, inertial and dynamical coefficients and drift factors. They formulated pressure and rate-dependent Coulumbviscoplastic rheology of the mixture mass flow to describe the model equation. Rheological behavior of the flow dynamics affects the whole dynamics of mixture mass flow. So, in this paper, the relations of mixture pressure and viscosity with respect to pressure drifts and solid volume fractions are studied to describe the rheological behavior of the generalized bulk mixture mass flow model. Moreover, the behaviour of mixture viscosities with respect to isotrophic drifts are also analyzed. We also present the simulation result for the time evolution of the drift induced full dynamical mixture pressure of the material exited from a silo gate that moves down slope along a channel.

A comparative study between linear and exponential stretching sheet with double stratification of a rotating Maxwell nanofluid flow

The aim of the current article is to investigate the rotating Maxwell nanofluid flow with double stratification and activation energy. The heat and mass transfer analysis is examined with the influence of variable thermal conductivity and thermophoretic effects. The flow analysis is presented over a linear / exponential stretching sheet. Theory of the boundary layer is considered to modify the flow model equations into the coupled ordinary differential equations. The numerical technique bvp4c Matlab is used to compute these coupled equations. It is found that both rotation and stretching has a remarkable impact on the velocity profile and temperature. The heat flux condenses for higher values of rotation parameter. The reduction occurred in the rate of heat and mass transfer by enlarging value of Deborah number. Further, augmentation of thermophoretic parameter produces the enhancement in the mass transfer rate. The novelty of the current problem is to analyzed the Maxwell nanofluid flow in the rotating frame with activation energy and thermophoretic effect. A relative analysis of current computations with prevailing literature revealed a remarkable agreement.

New Rate-Transient Analysis for Fractured Shale Gas Wells Using a Tri-linear Flow Model

Fractured shale gas wells often exhibit long-term linear flow. Previous studies have developed some linear flow models to analyse this behaviour. In this study, we developed a tri-linear flow model for simulating shale gas production. Our model does not assume that the length of secondary fractures is equal to the half-distance between adjacent hydraulic fractures, which is an improvement over previous tri-linear flow models. Based on the tri-linear flow model, we developed simplified equations for characterizing bilinear and linear flow regimes. Combining the tri-linear flow model and simplified equations, we developed a new rate-transient analysis (RTA) workflow to analyse shale gas production data. The new RTA workflow not only includes the identification of flow regimes and their analysis using a log-log plot of the reciprocal of production rate versus time, i.e., straight line analysis, but also history-matching. The results obtained from straight line analysis serve as additional constraints in history-matching. This helps to reduce the non-uniqueness issue of history-matching. The new RTA workflow was validated using two synthetic and five field examples.

Oldroyd-B nanofluid-flow between stretching disks with thermal slip and multiple flow features

This novel investigation deals with the thermal slip in magnetized axi-symmetric flow of Oldroyd-B liquid configured by infinite stretchable disks. With appliance of fundamental laws, the flow model equations are constructed. The governing flow equations are altered into no-dimensional form by using similarity quantities. The solution procedure is followed by using famous homotopy analysis technique. The convergence analysis is performed to evaluate the solution accuracy. The signifi?cance of flow parameters in the pattern of velocity, temperature and concentration are graphically illustrated. The novel numerical simulations for wall shear stress, Nusselt number, and Sherwood number are also performed at both surfaces of disks. It is noted the effects of relaxation time and retardation constants on radial and normal velocity components is opposite. The thermal slip parameters enhance the nanoparticles temperature. The concentration profile is decreases with Brown?ian motion parameter.