Mathematical Model Of Fluid Flow Research Articles

Study on Three-dimensional Impinging Jet Flow and Heat Transfer of Dryer for Gravure Printing and Coating Machine

Drying system is the largest energy consumption of equipment parts of solvent-based printing and coating equipment. How to optimize to design the equipment is of the highlights of this research field. According to this demand, a mathematical model of fluid flow of the drying oven is developed. By building a testing platform and using RNG k-epsilon two-equation turbulence model in Fluent Software to analyze three-dimensional impinging jet flow and heat transfer process of hot air drying in conventional drying oven. The results show that the separation of some boundary layers and undesirable swirls, which result in the non-uniform velocity field and temperature field of hot air from nozzles and no promotion to the drying effect, because of unreasonable design of the drying oven.

A nonlinear mathematical model for fluid flow in low-permeability reservoirs and its effect on well production performance

Fluid flow in low-permeability reservoirs exhibits nonlinear behavior owing to the presence of nano-sized pores and strong fluid-solid interactions. The percolation velocity significantly deviates from that estimated by Darcy's law, particularly in regions with low-pressure gradients. Several modified Darcy's equations have been proposed to describe these nonlinear phenomena. However, existing flow models often suffer from practical limitations, such as complex formulations or challenging determination of parameters. To address this, non-Darcy flow behavior was investigated and a novel low-velocity-nonlinear flow equation that accounts for the boundary layer effect is presented. The curves with different coefficients are plotted and the sensitivity of the corresponding parameters are discussed. Moreover, considering that core flooding experiments fail to accurately reflect actual flow behavior in reservoirs, an inversion method based on genetic algorithm (GA) that utilizes bottomhole pressure (BHP) testing data to estimate the pending coefficients is introduced. Finally, the proposed nonlinear flow equation is applied, using the finite difference method (FDM), to simulate the production performance, including pressure distribution, production rate, and recovery factor of vertical and multi-fractured horizontal wells in low-permeability reservoirs. The results demonstrated significant deviations in reservoir pressure distribution from those estimated using Darcy's law, and the production rate and recovery factor of nonlinear flow were notably lower than those predicted by Darcy's flow law, albeit to varying degrees.

Thermo-poro-elastic analytical model of the heat extraction performance of EGS inlaid with multi-linked fractures

The existing analytical model of the heat extraction performance of EGS ignored the influences of both thermo-poro-elastic effect and multi-linked fractures. Therefore, a thermo-poro-elastic analytical model was proposed to simulate heat extraction performance of EGS inlaid with multi-linked fractures. First, the mathematical models of fluid flow, heat transfer, and fracture aperture variation were established based on the conservation of energy and mass. Second, the partial differential equations were converted to ordinary differential equations by Laplace transformation, and the analytical solutions of water and rock temperatures were obtained. Then, the proposed model was verified with the published single-fracture model, which has been demonstrated to be efficient. Finally, the influencing factors, including geothermal reservoir parameters, production parameters, thermo-poro-elastic effect, and fracture morphology, were systematically analyzed and discussed. The results indicated that both the thermo-poro-elastic effect and multi-linked fractures have significant influence on the heat extraction performance of the EGS. The thermo-poro-elasticity effect tends to cause the fracture aperture to increase. The heat extraction performance of the EGS inlaid with multi-linked fractures is much better than that of single fracture EGS. Compared to the uncoupled situation, the production temperature is lowered and the output energy is increased by the thermo-poro-elastic effect at a constant flow rate in the fracture due to the increase in injection rate caused by the increase in fracture aperture. With the increasing of initial fracture aperture, the production temperature gradually decreases, while the output energy first increases and then decreases, so that the optimal initial fracture aperture is 2 mm. The results can provide important guidance for the design and production of an EGS inlaid with multi-linked fractures.

Mathematical modeling of fluid flow and pollutant transport in a homogeneous porous medium in the presence of plate stacks

This study aims at investigating the numerical analysis of pollutant transport in homogeneous porous media with solid plate stacks. The investigation was performed for solid/impervious objects of the same size placed in homogeneous porous media. The pollutant transport equation (i.e., steady-state and time dependent advection-dispersion) chosen in mathematical modeling. Three cases arise on the basis of dispersion coefficients: (a) when dispersion is uniformly constant, (b) when dispersion depends upon magnitude of the velocity, and (c) when dispersion depends upon magnitude of the velocity and directional dispersivities, all these are discussed in detail. Generally, analytical solution of such problems doesn't exist, so all the work is done numerically. The governing partial differential equation of pollutant concentration is approximated by using finite difference technique. Central, one-sided, backward and forward finite difference formulae of the same order are used to discretize the domain.Simulations of velocity potential and stream function are approximated by Matlab software. Then equipotential lines and streamlines are visualized in the form of contours. Both, velocity potential and stream function are harmonic and satisfy Laplace's equation. Fluid flow lines and pollutant concentration are represented graphically for several parameters involved in the study.It is found that entrance/exit length, shape, hydraulic conductivity, the number and position of impervious objects affect the fluid flow and pollutant transport. However, there is no significant affect of heated objects on pollutant transport. Moreover, advection and dispersion depend upon permeability of porous media and properties of solid matrix.To authenticate the Matlab scheme of finite difference, it is verified that fluid as well as pollutant fluxes (in and out) are equal. Moreover, time-dependent problem converges to steady-state form after very long time.For monitoring or forecasting the build up of contamination concentration, the pollutant transport model is considerable. As this model is affected by different parameters which are discussed above, can helps to overcome the pollutant accumulation. The solid object is main key to lessen the contamination in the underground. If the entrance or leakage point of the domain is blocked by impermeable object or filled the vertical column with material of low hydraulic conductivity it ultimately slows down or even refrains the pollutant particles to pass through. The pollutant concentration is also minimized by injecting the bioremedial agents with the help of treatment columns.

Mathematical model of fluid flow in a channel with reabsorption at permeable walls

Mathematical model of fluid flow in a channel with reabsorption at permeable walls

Mathematical model of fluid flow along a straight through filled with a distributed flow from above

In a one-dimensional approximation and in the absence of friction forces, a mathematical model has been developed for the steady flow of an incompressible fluid along a straight line, for example, a drainage gutter, into which a distributed flow flows from above. The boundary condition missing for solving the system of equations of momentum and continuity is determined using the principle of minimum potential energy. For a rectangular chute, equations are obtained that allow one to calculate the distributions of the layer thickness and fluid velocity along the length of the chute with a plug at one end and without a plug, slope and without slope to the horizon, depending on the intensity of the incoming flow, the size of the chute, and the density of the liquid. This model, by means of a simple recalculation, can also be extended to the flow in a trough of a different cross-sectional profile. The results of the study can be applied to the calculation of external drainage systems.

Well-posedness and variational numerical scheme for an adaptive model in highly heterogeneous porous media

Mathematical modeling of fluid flow in a porous medium is usually described by a continuity equation and a chosen constitutive law. The latter, depending on the problem at hand, may be a nonlinear relation between the fluid's pressure gradient and velocity. The actual shape of this relation is normally chosen at the outset of the problem, even though, in practice, the fluid may experience velocities outside of its range of applicability. We propose here an adaptive model, so that the most appropriate law is locally selected depending on the computed velocity. From the analytical point of view, we show well-posedness of the problem when the law is monotone in velocity and show existence in one space dimension otherwise. From the computational point of view, we present a new approach based on regularizing via mollification the underlying dissipation, i.e., the power lost by the fluid to the porous medium through drag. The resulting regularization is shown to converge to the original problem using Γ-convergence on the dissipation in the monotone case. This approach gives rise to a variational numerical scheme which applies to very general problems and which we validate on three test cases.

Transportation of thermal and velocity slip factors on three-dimensional dual phase nanomaterials liquid flow towards an exponentially stretchable surface

The fundamental purpose of this research is to elaborate on slip boundary conditions and the flow of three-dimensional, stable, incompressible, rotating movements of nanoparticles lying across a stretchable sheet. The mathematical model for fluid flow is created using the assumptions stated above. The partial differentials are produced after utilizing boundary layer estimates. The partial differential governing equations are reduced into three coupled ordinary differential equations by using similarity transformations. After, applying transformations the system is solved numerically. Numerical results are approved with the help of the MATLAB bvp4c algorithm. The analysis shows that velocity and temperature are strongly dependent on essential parameters like stretching ratio, velocity slip, rotation, thermal slip parameter, and Prandtl number. Numerical values of distinct parameters on heat flux and skin friction factors are shown in a tabulated form. Partial velocity and thermal slip are applied to the temperature surface. The comparison among the nano-sized particles copper oxide and silver with water base nanofluid affecting velocity and temperature fields are used for analysis. Moreover, the Graphical depiction designates that the velocity and temperature spreading of the thermal slip parameter is increasing. It is observed that Ag-water is the best heat carrier as compared to CuO-water nanofluid.

A study on dual solutions for water-based hybrid nanofluids flowing through convergent channel with dissipative heat transport

Over the years, the fluid flows in conjunction with thermal transport between non-parallel surfaces having converging nature is of great significance due to their broad spectrum of applications, which include fluid flows through nozzles in petroleum engineering, blood flow in arteries, lubrication systems, automobile radiators, thermal pumps, and water purification processes. Additionally, hybrid nanofluid is a prolific topic because of its thermal properties and potentials which provide a better performance even compared with common nanofluid in optimizing heat transfer. Therefore, this article presents a numerical simulation to investigate the heat transport characteristics of hybrid nanofluids in Jeffery-Hamel flow through a convergent channel. The considered hybrid nanofluids are composed of Copper (Cu) and Graphene-oxide (Go) as suspended nanoparticles and water as base fluid. This analysis further includes the impacts of viscous dissipation and magnetic field. A mathematical model for fluid flow and heat transfer are constructed with the help of cylindrical polar coordinates. The governing equations are converted into a system of ordinary differential equations (ODEs) by Lie symmetry group transformation. A MATLAB code is exercise to get the numerical solutions for flow and thermal distributions. An interesting phenomenon is that dual solutions are obtained in the computation. Thus, a comprehensive discussion is included on the dual solutions for various involved variables. The current findings may be employed in petroleum science, r biomedical scientists, polymer industry, etc.

Organic fluid migration in low permeability reservoirs restricted by pore structure parameters

The flow of fluids in porous media is a complex but essential study; due to the limitation of experimental methods, the research on ultra-low velocity flow of fluids has been developing slowly. This paper investigated the flow of oil in shale through laboratory tests to explore the flow characteristics of organic fluids at ultra-low velocities in ultra-low permeability porous media; the experimental results show that the flow of organic fluids in a specific porous medium at ultra-low velocity still follow Darcy's law, which is different from the previous research that believed that the ultra-low velocity flow of fluids must be non-Darcy flow. However, the flow characteristics of fluids are not static and will change with external conditions (Ambient temperature or Confining pressure). Moreover, an improved mathematical model of fluid flow based on Poiseuille's law is deduced, which can be verified well by the calculation and experimental data. The model comprehensively considers the shale stress sensitivity and the effects of the boundary layer on the fluid flow. The boundary layer is cleverly calculated through the concept of shale oil occurrence and confirmed with molecular dynamics simulation results. The correlation analysis between the critical parameters in the model and the geological parameters shows that any material composition of porous media has a specific influence on the fluid flow characteristics, especially the effect of clay minerals, that cannot be ignored. The analysis results show that when the relative content of clay minerals is about 50%, the porous medium has a better flow capacity; When the relative content of brittle minerals is between 70% and 80%, it has a better compressive ability. Simultaneously, the organic matter content index TOC has a specific inhibitory effect on fluid flow. Therefore, determining the properties of porous media and the changes in the external conditions of porous media is of great significance for engineering practice (e.g., the development of shale oil).

Mathematical model of fluid flow in a double constricted tapered tube with permeable boundary

Abstract In this paper, a mathematical model for the steady laminar, incompressible and Newtonian fluid flow in a proximal renal tubule is presented. In this, the tubule is considered as a tapered tube with double constriction and permeable boundary. The impact of the fluid reabsorption across the tubule wall is assumed as the occurrence of exponentially decreasing flow at each cross-section. The present model is formulated through the Navier–Stokes equations, under the appropriate boundary conditions. A regular perturbation technique is used to obtain the approximate solutions. This study brings out the significant impacts of reabsorption coefficient (α) and tapered angle (ϕ) on the flow variables such as velocities, the drop in pressure, and wall shear stress are discussed through graphs. The streamlines are also plotted to understand the influence of the reabsorption and tapering phenomena on the flow.

Triple-Porosity and Dual-Permeability Productivity Prediction Model of CBM Wells Considering Complex Flow Regimes

The productivity evaluation of CBM wells can yield significant insights into exploring the patterns of CBM production, predicting the effectiveness of the CBM well and reservoir stimulation, optimizing the gas reservoir development program, and developing a reasonable production system, for the purpose of facilitating efficient development of CBM. In particular, to accurately evaluate CBM productivity, we should establish the corresponding mathematical model of fluid flow through porous media and productivity evaluation model based on a clear understanding of CBM occurrence states and mechanisms of its flow through porous media. After considering the effects of slip flow, Knudsen diffusion, surface diffusion, stress sensitivity, and matrix shrinkage on fluid mass transfer, we have put forward a triple-porosity and dual-permeability mathematical model to predict CBM productivity that incorporates matrix gas desorption, complex flow in matrix pores, and gas–water two-phase flow in a cleat system. In combination with reservoir characteristic parameters, a case study of Ma-26 well in the Mabidong block in the south of the Qinshui Basin, we carried out a numerical simulation of the productivity of a fractured CBM well and analyzed the effects (on production performance) of occurrence states, cleat system permeability, complex flow regimes in the matrix, Langmuir pressure, and Langmuir volume on production are provided. The results show that 1) in the initial drainage and production stage of CBM wells, both free gas and adsorbed gas are produced simultaneously, while adsorbed gas dominates the production in later stages; 2) the peak output and cumulative output of CBM wells increase significantly with the rise in cleat system permeability; 3) the increase of Langmuir pressure, volume, and matrix porosity are conducive to the increase of CBM production. The research has considerable reference value for work on mechanisms of CBM flow in porous media and post fracturing productivity evaluation of CBM and also provides a theoretical basis for fieldwork in CBM development.

A Nonlinear Mathematical Model for Fluid Flow in Low Permeability Reservoirs and its Effect on Well Production Performance

A Nonlinear Mathematical Model for Fluid Flow in Low Permeability Reservoirs and its Effect on Well Production Performance

Numerical Analysis of Conjugated Heat and Mass Transfer of Helical Hollow Fiber Membrane Tube Bank for Seawater Distillation

A numerical study on the conjugated heat-mass transfer of helical hollow fiber membrane tube bank (HFMTB) for seawater desalination was carried out. Physical and mathematical models of fluid flow, temperature and humidity distribution were constructed to investigate the influences of flow type, Reynolds number, and temperature on the conjugated heat-mass transfer performance of hollow fibers in the distillation membrane module. The conjugated heat-mass transfer characteristics of HFMTB were discussed by utilizing the friction coefficient, Nusselt number (Nu), and Sherwood number (Sh). Results demonstrate that a distillation efficiency enhancement of 29% compared to the straight HFMTB has been detected for four-helical HFMTB configuration, though the friction coefficient of such a module is about 4 times of their straight counterparts. The values of average Nu and Sh numbers are increasing with tube number, which improves distillation efficiency. The effect of flow type has been studied by employing the upstream and downstream flows to the double-helical HFMTB, demonstrating upstream flow type is more conducive to the heat-mass transfer process. Both the outlet air humidity (ω) and distillation efficiency (η) decrease with the air-side Reynolds number (Rea) and inlet air temperature in the helical HFMTB while increasing with the solution-side Reynolds number (ReS) and inlet solution temperature. Overall, the obtained results indicate that helical HFMTB applying upstream flow has great potential to achieve high-performance SGMD for seawater desalination. It is anticipated that the present work can assist in a better understanding of the membrane desalination process in HFMTB and thus provide theoretical suggestions for further optimization and development.

Numerical calculations of heat transfer during FC-72 flow in minichannels performed with ANSYS software

The main aim of the paper was to apply numerical calculations in ANSYS software to solve problems related to steady-state convective heat transfer during FC-72 flow in a minichannel heat sink. A mathematical model of fluid flow in a minichannel heat sink was proposed. Data from research conducted on the experimental stand with asymmetrically heated test section were selected. The element cooled by fluid flowing in minichannels was a thin foil. The distribution of temperature on the outer heated foil surface was measured using infrared thermography. Thermocouples and pressure meters were installed at the inlet and outlet of the minichannels. A CAD model was prepared with respect to the geometry of the test section. The mesh was created in ANSYS Mesher. A suitable model of turbulences was selected and materials temperature dependencies were considered. The iterative process of creating the model and comparing the results obtained by the CFD calculation was used to capture the fluid behavior. The velocity magnitudes and temperature distributions were presented as the main results of numerical calculations.

Mathematical Model of Fluid Flow and Solute Transfer in a Permeable Channel with Slip Velocity at the Boundaries

Mathematical Model of Fluid Flow and Solute Transfer in a Permeable Channel with Slip Velocity at the Boundaries

Forced convection heat transfer from a plate stack embedded in a homogeneous porous medium

The current paper examines some novel and interesting aspects of the mathematical modelling of fluid flow and forced convection heat transfer from a plate stack embedded in a homogeneous porous media. Time-dependent forced convection heat transfer from some cylinders embedded in groundwater are explored numerically using finite difference methods. An algorithm was developed about rectangular heated solid objects with the same size placed in an in-line arrangement in homogeneous porous media. Central and one-sided finite difference formulae are used to discretize the domain. Applying the mathematical model, continuity, momentum, and energy equations are solved by the finite difference methods. Generally, analytical solutions are not possible for such problems, so most of the work is done numerically. The numerical results for the two-dimensional velocity potential and stream function have been calculated and the resulting fluid and temperature contours are represented graphically for various values of the parameters involved (e.g. length of the entrance, the fluid flow rates, coefficient of thermal diffusion and advection in the observed long-time plume behaviour, effect of time and temperature on heat transfer, etc.). It is observed that fluid and heat fluxes and fluid velocity depend upon the size, shape, burial depth, position of heated objects, and positions of the entrance and exit of the homogeneous porous media. Moreover, the hydraulic conductivity of the porous medium affects the pressure drops, fluid velocity as well as the heat transfer rates.

Mathematical modelling of fluid flow in electromagnetically stirred weld pool

In this paper, a mathematical model has been proposed to study the relationship between electromagnetic stirring (EMS) weld parameters and the mode of fluid flow on grain refinement of AA 6060 weldments. For this purpose, fluid flow modelling using Navier-Stokes equation is described first, and then, the proposed mathematical approach has been discussed in detail. For demonstration, calculations to determine the fluid velocity in the weld pool of thin plate AA6060 were performed. The application of the model on the experimental results indicates that the best grain refinement is achieved at a transition mode from laminar to turbulent fluid flow.

Mathematical Modeling of Fluid Flow and Heat Transfer in Petroleum Industries and Geothermal Applications 2020

In this Special Issue, all aspects of fluid flow and heat transfer in geothermal applications, including the ground heat exchanger, conduction, and convection in porous media, are considered. The emphasis here is on mathematical and computational aspects of fluid flow in conventional and unconventional reservoirs, geothermal engineering, fluid flow and heat transfer in drilling engineering, and enhanced oil recovery (hydraulic fracturing, steam-assisted gravity drainage (SAGD), CO2 injection, etc.) applications.

Hydrodynamic Optimization of Coaxial Ground Heat Exchanger

Abstract A simple mathematical model of fluid flow is applied to determine the cross-sectional shape of a coaxial ground heat exchanger (CGHE) for which the friction pressure drop is minimal. Both laminar and turbulent flows of a Newtonian fluid are analyzed. The dimensionless form of the friction pressure losses is taken as the objective function, and the dimensionless internal diameter and wall thickness of the inner tube is adopted as decision variables, with the reference length taken to be the internal diameter of the external pipe. The resulting optimization problem is solved by means of a hybrid analytical-numerical method. The obtained solutions are generalized as two simple equations valid for laminar and turbulent flows, respectively. It is shown that the pressure losses in a coaxial ground heat exchanger with optimal cross section may be considerably smaller than the pressure losses for a nonoptimal one. The obtained results are significant for the global optimization of CGHEs, resulting in improved energy conservation of buildings and district heating systems.