Search Results (42)

In the present study, an effort was made to determine the effects of a porous matrix with different viscosities on the dynamic and static behaviors of rough short journal bearings taking into account the action of a squeezing film under varying loads without journal rotation. The micropolar fluid was regarded as a lubricant that contained microstructure additives in both the porous region and the film region. By applying Darcy’s law for micropolar fluids through a porous matrix and stochastic theory related to uneven surfaces, a standardized Reynolds-type equation was extrapolated. Two scenarios with a stable and an alternating applied load were analyzed. The impacts of variations in viscosity, the porous medium, and roughness on a short journal bearing were examined. We inspected the dynamic and static behaviors of the journal bearing. We found that the velocity of the journal center with a micropolar fluid decreased when there was a cyclic load, and the impact of variations in the viscosity and porous matrix diminished the load capacity and pressure in the squeeze film and increased the velocity of the journal center. Full article

In this article, a numerical method is proposed and investigated for an initial boundary value problem governed by a fractional differential generalization of the nonlinear transient filtration law which describes fluid motion in a porous medium. This type of equation is widely used to describe complex filtration processes such as fluid movement in horizontal wells in fractured geological formations. To construct the numerical method, a high-order approximation formula for the fractional derivative in the sense of Caputo is applied, and a combination of the finite difference method with the finite element method is used. The article proves the uniqueness and continuous dependence of the solution on the input data in differential form, as well as the stability and convergence of the proposed numerical scheme. The linearization of nonlinear terms is carried out by the Newton method, which allows for achieving high accuracy in solving complex problems. The research results are confirmed by a series of numerical tests that demonstrate the applicability of the developed method in real engineering problems. The practical significance of the presented approach lies in its ability to accurately and effectively model filtration processes in shale formations, which allows engineers and geologists to make more informed decisions when designing and operating oil fields. Full article

Porous medium models are commonly used in Computational Fluid Dynamics (CFD) to simulate flow through permeable screens of various types. However, the setup of these models is often limited to replicating a pressure drop in cases where fluid inflow is orthogonal to the screen. In this work, a porous medium formulation that employs a non-diagonal Forchheimer tensor is presented. This formulation is capable of reproducing both the pressure drop and flow deflection under varying inflow angles for complex screen geometries. A general method to determine the porous model coefficients valid for both diagonal and non-diagonal Forchheimer tensors is proposed. The coefficients are calculated using a nonlinear least-squares optimisation based on an analytical solution of a special case of the Navier–Stokes equations. The applicability of the proposed method is evaluated in four different scenarios supplemented by local CFD simulations of permeable screens: wire mesh, perforated screens, air louvers, and expanded mesh panels. The practical application of this method is demonstrated in the modelling of windbreaks and permeable double-skin facades, which typically employ the aforementioned types of porous screens. Full article

In this work, we investigate isothermal MHD motions of a large class of rate type fluids through a porous medium between two infinite horizontal parallel plates when a differential expression of the non-trivial shear stress is prescribed on the boundary. Exact expressions are provided for the dimensionless steady state velocities, shear stresses and Darcy’s resistances. Obtained solutions can be used to find the necessary time to touch the steady state or to bring to light certain characteristics of the fluid motion. Graphical representations showed the fluid moves slower in presence of a magnetic field or porous medium. In addition, contrary to our expectations, the volume flux across a plane orthogonal to the velocity vector per unit width of this plane is zero. Finally, based on a simple remark regarding the governing equations of velocity and shear stress for MHD motions of incompressible generalized Burgers’ fluids between infinite parallel plates, provided were the first exact solutions for MHD motions of these fluids when the two plates apply oscillatory or constant shear stresses to the fluid. This important remark offers the possibility to solve any isothermal MHD motion of these fluids between infinite parallel plates or over an infinite plate when the non-trivial shear stress is prescribed on the boundary. As an application, steady state solutions for MHD motions of same fluids have been developed when a differential expression of the fluid velocity is prescribed on the boundary. Full article

One of the modern, recently developed mathematical approaches for modeling various complex chaotic processes (the bacteria migration is apparently one of them), is the application of fractional differential equations. Introduction of fractional derivatives is also a very effective approach for investigation of the reactive processes (growth of bacteria in our case). Our recent advances in application of fractional differential equations for modeling the anomalous transport of reactive and non-reactive contaminants (see our recent publications in the References) allow us to expect that the anomalous transport of growing bacteria can also be effectively described by the models with fractional derivatives. Based on these modern approaches, utilizing fractional differential equations, in this paper we developed a reliable mathematical model that could be properly calibrated and, consequently, provide an adequate description of the growing bacteria transport. This model accounts for the memory effects in the bacteria transport due to the random character of bacteria trapping and release by the porous matrix. Two types of bacteria in the saturated porous medium are considered: mobile and immobile bacteria. Bacteria in the mobile phase are migrating in the fluid and have the velocity of the bulk flow, whereas bacteria in the immobile phase are the bacteria that are captured by the porous matrix. These bacteria have zero velocity and can cause clogging of some pores (therefore, porosity is possibly not constant). Examining different conventional models and comparing computations based on these models, we show that this extremely complex character of bacteria transport cannot be described by the traditional approach based on classical partial differential equations. In this paper we suggest fractional differential equations as a simple but very effective tool that can be used for constructing the proper model capable of simulating all the above-mentioned effects associated with migration of alive bacteria. Using this approach, a reliable model of the growing bacteria transport in the porous medium is developed and validated by comparison with experimental laboratory results. We proved that this novel model can be properly linearized and calibrated, so that an excellent agreement with available experimental results can be achieved. This simple model can be used in many applications, for example, as a part of more general mathematical models for predicting the outcomes of the bioremediation of contaminated soils. Full article

Various researchers in the field of engineering have used porous media for many years. The present paper studies heat enhancement using two different types of porous media. In the first type, porous metal foam media was used experimentally and numerically for heat extraction. The porous medium was replaced with a porous structure using the Gyroid model and the triply periodic minimum surfaces technique in the second type. The Darcy–Brinkman model combined with the energy equation was used for the first type, whereas Navier–Stokes equations with the energy equation were implemented for the second type. The uniqueness of this approach was that it treated the Gyroid as a solid structure in the model. The two types were tested for different heat fluxes and different flow rates. A comparison between the experimental measurements and the numerical solution provided a good agreement. By comparing the performance of the two types of structure, the Gyroid structure outperformed the metal foam for heat extraction and uniformity of the temperature distribution. Despite an 18% increase in the pressure drop in the presence of the Gyroid structure, the performance evaluation criteria for the Gyroid are more significant when compared to metal foam. Full article

The paper concerns a nonlinear second-order parabolic evolution equation, one of the well-known objects of mathematical physics, which describes the processes of high-temperature thermal conductivity, nonlinear diffusion, filtration of liquid in a porous medium and some other processes in continuum mechanics. A particular case of it is the well-known porous medium equation. Unlike previous studies, we consider the case of several spatial variables. We construct and study solutions that describe disturbances propagating over a zero background with a finite speed, usually called ‘diffusion-wave-type solutions’. Such effects are atypical for parabolic equations and appear since the equation degenerates on manifolds where the desired function vanishes. The paper pays special attention to exact solutions of the required type, which can be expressed as either explicit or implicit formulas, as well as a reduction of the partial differential equation to an ordinary differential equation that cannot be integrated in quadratures. In this connection, Cauchy problems for second-order ordinary differential equations arise, inheriting the singularities of the original formulation. We prove the existence of continuously differentiable solutions for them. A new example, an analog of the classic example by S.V. Kovalevskaya for the considered case, is constructed. We also proved a new existence and uniqueness theorem of heat-wave-type solutions in the class of piece-wise analytic functions, generalizing previous ones. During the proof, we transit to the hodograph plane, which allows us to overcome the analytical difficulties. Full article

Recent developments in the 3D printing of metals are attracting many researchers and engineers. Tailoring a porous structure using triply periodic minimum surfaces is becoming an excellent approach for cooling electronic equipment. The availability of metallic 3D printing encourages researchers to study cooling systems using porous media. In the present article, we designed a porous structure using a gyroid model produced using 3D printing. Porous aluminum has a 0.7, 0.8, and 0.9 porosity, respectively. The porous medium is tested experimentally using distilled fluid as the cooling liquid, while the structure is subject to bottom heating with a heat flux of 30,000 W/m². A different inlet velocity from 0.05 m/s to 0.25 m/s is applied. On the numerical side, the porous medium is modeled as a porous structure, and only the Navier–Stokes equations and the energy equation were solved using the finite element technique. In addition, an excellent agreement between the experimental measurement and numerical calculation, an optimum porosity of 0.8 was obtained. The performance evaluation criterion led us to believe that pressure drop plays a significant role in heat enhancement for this type of gyroid structure. As the porosity increases, the boundary layer becomes more noticeable. Full article

Steel storage tanks are widely used in different fields. Most of these tanks contain hazardous materials, which may lead to disasters and environmental damage for any design errors. There are many reasons which cause the failure of these tanks such as excessive base plate settlement, shear failure of soil, liquid sloshing, and buckling of the tank shell. In this study, five models of above-ground steel storage tanks resting over different types of clay soils (medium-stiff clay, stiff clay, and very stiff clay soils) are analyzed using the finite element program ADINA under the effect of static and dynamic loading. The soil underneath the tank is truly simulated using a 3D solid (porous media) element and the used material model is the Cam-clay soil model. The fluid in the tank is modeled depending on the Navier–Stokes fluid equation. Moreover, the earthquake record used in this analysis is the horizontal component of the Loma Prieta Earthquake. The analyzed tanks are circular steel tanks with the same height (10 m) and different diameters (ranging from 15 m to 40 m). The soil under the tanks has a noticeable effect on the dynamic behavior of the studied tanks. The tanks resting over the medium-stiff clay (the weakest soil) give a lower permanent settlement after the earthquake because of its low elastic modulus which leads to the absorption of the earthquake waves in comparison to the other types of soil. There are 29.6% and 35.6% increases in the peak dynamic stresses under the tanks in the cases of stiff clay and very stiff clay soils, respectively. The maximum values of the dynamic vertical stresses occur at a time around 13.02 s, which is close to the peak ground acceleration of the earthquake. Full article

The sustainable exploitation of groundwater resources is a multifaceted and complex problem, which is controlled, among many other factors and processes, by water flow in porous soils and sediments. Modeling water flow in unsaturated, non-deformable porous media is commonly based on a partial differential equation, which translates the mass conservation principle into mathematical terms. Such an equation assumes that the variation of the volumetric water content ($\theta$) in the medium is balanced by the net flux of water flow, i.e., the divergence of specific discharge, if source/sink terms are negligible. Specific discharge is in turn related to the matric potential (h), through the non-linear Darcy–Buckingham law. The resulting equation can be rewritten in different ways, in order to express it as a partial differential equation where a single physical quantity is considered to be a dependent variable. Namely, the most common instances are the Fokker–Planck Equation (for $\theta$), and the Richards Equation (for h). The other two forms can be given for generalized matric flux potential ($\Phi$) and for hydraulic conductivity (K). The latter two cases are shown to limit the non-linearity to multiplicative terms for an exponential K-to-h relationship. Different types of boundary conditions are examined for the four different formalisms. Moreover, remarks given on the physico-mathematical properties of the relationships between K, h, and $\theta$ could be useful for further theoretical and practical studies. Full article

Combustion in a porous medium can be beneficial for enhancing reaction rate and temperature uniformity. Therefore, considering the combination with oxy-fuel combustion can address some shortcomings in oxy-fuel burners, a cylindrical two-layer porous burner model is established based on OpenFOAM in this paper. A two-temperature equation model is adopted for the simulation of the heat transfer process. The CH₄ skeletal kinetic mechanism is adopted for complex chemistry integration based on OpenSMOKE++. Corresponding experimental methods were used for complementary studies. The walls of the burner are wrapped with three types of thermal insulation materials to present different levels of heat loss. The results show that considering the convection and radiative heat loss of the burner wall, the temperature near the wall is reduced by more than 300 K compared to the adiabatic condition. As a result, the flame propagation speed and CO oxidation rate slowed down. The stable range will be destructively narrowed by more than 50%, and CO emissions will increase by more than 10 times. These defects will be aggravated by increasing the diameter of the burner. It is observed that when the diameter of the burner increases from the initial 5 cm to 10 cm, the effect of heat loss on the stable range is insignificant. Full article

The main purpose of this work is to completely solve two motion problems of some differential type fluids when velocity or shear stress is given on the boundary. In order to do that, isothermal MHD motions of incompressible second grade fluids over an infinite flat plate are analytically investigated when porous effects are taken into consideration. The fluid motion is due to the plate moving in its plane with an arbitrary time-dependent velocity or applying a time-dependent shear stress to the fluid. Closed-form expressions are established both for the dimensionless velocity and shear stress fields and the Darcy’s resistance corresponding to the first motion. The dimensionless shear stress corresponding to the second motion has been immediately obtained using a perfect symmetry between the governing equations of velocity and the non-trivial shear stress. Furthermore, the obtained results provide the first exact general solutions for MHD motions of second grade fluids through porous media. Finally, for illustration, as well as for their use in engineering applications, the starting and/or steady state solutions of some problems with technical relevance are provided, and the validation of the results is graphically proved. The influence of magnetic field and porous medium on the steady state and the flow resistance of fluid are graphically underlined and discussed. It was found that the flow resistance of the fluid declines or increases in the presence of a magnetic field or porous medium, respectively. In addition, the steady state is obtained earlier in the presence of a magnetic field or porous medium. Full article

The problem considered in this paper is a steady micropolar fluid flow in porous media between two plates. This model can be used to describe the flow of some types of fluids with microstructures, such as human and animal blood, muddy water, colloidal fluids, lubricants and chemical suspensions. Fluid flow is a consequence of the constant pressure gradient along the flow, while two parallel plates are fixed and have different constant temperatures during the fluid flow. Perpendicular to the flow, an external magnetic field is applied. General equations of the problem are reduced to ordinary differential equations and solved in the closed form. Solutions for velocity, microrotation and temperature are used to explain the influence of the external magnetic field (Hartmann number), the characteristics of the micropolar fluid (coupling and spin gradient viscosity parameter) and the characteristics of the porous medium (porous parameter) using graphs. The results obtained in the paper show that the increase in the additional viscosity of micropolar fluids emphasizes the microrotation vector. Moreover, the analysis of the effect of the porosity parameter shows how the permeability of a porous medium can influence the fluid flow and heat transfer of a micropolar fluid. Finally, it is shown that the influence of the external magnetic field reduces the characteristics of micropolar fluids and tends to reduce the velocity field and make it uniform along the cross-section of the channel. Full article

The time-independent performance of a micropolar nanofluid under the influence of magneto hydrodynamics and the existence of a porous medium on a stretching sheet has been investigated. Nano-sized particles were incorporated in the base fluid because of their properties such as their extraordinary heat-enhancing ability, which plays a very important role in modern nanotechnology, cooling electronic devices, various types of heat exchangers, etc. The effects of Brownian motion and thermophoresis are accounted for in this comprehensive study. Using similarity conversion, the leading equations based on conservation principles are non-dimensionalized with various parameters yielding a set of ODEs. The numerical approach boundary value problem fourth-order method (bvp4c) was implemented as listed in the MATLAB computational tool. The purpose of this examination was to study and analyze the influence of different parameters on velocity, micro-rotation, concentration, and temperature profiles. The primary and secondary velocities reduced against the higher inputs of boundary concentration, rotation, porosity, and magnetic parameters, however, the base fluid temperature distribution grows with the increasing values of these parameters. The micro-rotation distribution increased against the rising strength of the Lorentz force and a decline is reported against the growing values of the micropolar material and rotational parameters. Full article

In the present study, the three-parameter one-dimensional vertical infiltration equation recently proposed by Poulovassilis and Argyrokastritis is examined. The equation includes the saturated hydraulic conductivity (K_s), soil sorptivity (S), and an additional parameter c; it is valid for all infiltration times. The c parameter is a fitting parameter that depends on the type of porous medium. The equation is characterized by the incorporation of the exact contribution of the pressure head gradient to flow during the vertical infiltration process. The application of the equation in eight porous media showed that it approaches to the known two-parameter Green–Ampt infiltration equation for parameter c = 0.300, while it approaches to the two-parameter infiltration equation of Talsma–Parlange for c = 0.750, which are the two extreme limits of the cumulative infiltration of soils. The c parameter value of 0.500 can be representative of the infiltration behavior of many soils for non-ponded conditions, and consequently, the equation can be converted into a two-parameter one. The determination of K_s, S, and c using one-dimensional vertical infiltration data from eight soils was also investigated with the help of the Excel Solver application. The results showed that when all three parameters are considered as adjustment parameters, accurate predictions of S and K_s are not achieved, while if the parameter c is fixed at 0.500, the prediction of S and K_s is very satisfactory. Specifically, in the first case, the maximum relative error values were 33.29% and 39.53% for S and K_s, respectively, while for the second case, the corresponding values were 13.25% and 17.42%. Full article