The paper deals with a problem of deriving reliable and convenient models for the viscous suspension films of variable rate flows. The contribution and novelty of this work lies in the fact that a general concept is presented for the mathematical model of the formation of nonlinear waves in the film flows containing a dispersed solid phase, an asymptotic analysis is given, and a set of the main control parameters has been established. Unlike the previous works, this paper focuses specifically on clearly identifying the control parameters and deriving the general control equation. The decisive role of the special control parameter depending on the viscosity of the suspension near the support wall has been established. The work is theoretical in nature, but the developed model can be adapted for calculations of specific technological processes, since it contains the main physical characteristics of suspensions and the necessary parameters for calculation.
This study investigates the effects of slip conditions and magnetic effects on the oscillatory flow of a Jeffrey fluid within an elastic tube. The perturbation method is employed to derive analytical solutions for the flow characteristics, and Gill's fourth-order method is used to solve the differential equation for the pressure numerically along with the initial conditions. The graphs illustrate how the Womersley, slip velocity, elasticity, Jeffrey, and magnetic parameters affect the mean pressure drop and modulus of wall shear stress. The results reveal that increasing the magnetic field strength and Womersley parameter, the wall shear stress rises in rigid and elastic tubes. Additionally, the slip condition modifies the velocity profile, enhancing fluid motion near the walls. The findings provide insight into the complex interplay of rheology, geometry, and magnetic forces in physiological oscillatory flows.
In this study we have evaluated the potential of locally sourced clays from the Patos region to be used as base material for water-based drilling fluids in the Patos-Marinza oil field. Four drilling fluid formulations with densities ranging from 1.05 to 1.20 g/cm³ were prepared and tested for density, suspension stability, sedimentation, sand content, filtration, and rheological behavior. The results show that while Patos clays provide acceptable rheological properties and low hydraulic resistance, they have relatively high filtration values and sand content, which may lead to serious problems. In order to overcome this disadvantage, we may need to use additives and filter the clay before use. From an economic perspective, the higher clay dosage and processing costs make them less competitive than imported bentonite under current conditions. However, their favorable flow characteristics suggest potential for use in deeper wells or alternative applications, provided further optimization is carried out.
Complex dynamic systems are characterized by the presence of memory effects and a multi-level hierarchy of relaxation times at various stages of transport processes. Therefore, reliable models of transport phenomena in such systems necessarily include a nonlocality factor due to the aftereffects of disturbances at different time stages of the process. At the same time, control parameters in models describing such dynamic systems can also change at different rates over different time intervals under the influence of external influences and relaxation processes that alter the system's structure. This factor is not always taken into account when constructing a process model. In this paper, a new heuristic model for accounting the impact of disturbances on the model structure and the appropriate control equation for describing the memory effects and the changes in the system's dynamic characteristics have been submitted. The novelty of the approach lies in the new concept for building the model, according to which the manifestation of after-effects can be caused by the memory effects formed, in turns, as a result of a change in the depth of potential wells corresponding to the stationary states of the system during the model process. Such an approach provides mathematical tools for studying bifurcation phenomena in a dynamic system described by a two-parameter model. The details of the new concept and the scheme for deriving the control equation are given. This article is theoretical in nature; the concept is based on general physical considerations. The results of conducted researches and the novel model will nevertheless can find application in engineering practice in the design of various technological processes.
Managing aquatic systems needs a good prediction of water movement or the degradation of organic compounds. These phenomena are simulated using mathematical models that represent the structure and function of the systems, serving as tools for hypothesis testing and forecasting. This work reviews the mathematical models used to describe aquatic systems such as rivers, lakes, reservoirs, groundwater systems, aquifers, and watersheds.
Heavy crude oil production remains challenging mainly because of its high viscosity and complex non-Newtonian flow behaviour, which can reduce reservoir performance. Under these conditions, conventional recovery methods are often insufficient, necessitating enhanced oil recovery (EOR) techniques. This study focuses on the use of diluents, which reduce viscosity and improve production efficiency. Laboratory measurements under surface conditions indicate viscosity reductions of 50–99%, depending on diluent concentration and temperature. This paper examines diluent injection in the Visoka oilfield, Albania—a field with high-viscosity, non-Newtonian crude. The injection of light hydrocarbons alters the crude oil’s rheological behaviour, allowing easier flow near the wellbore and during surface handling, while also contributing to reservoir pressure maintenance. Similar behaviour has been observed in other heavy oil fields. The results from the Visoka oilfield indicate higher recovery rates and improved well performance. Further investigation under reservoir conditions could help refine these strategies.
This study investigates the magnetohydrodynamic (MHD) flow, heat, and mass transfer of a pseudoplastic (non-Newtonian) nanofluid within a mixed convection channel. The analysis focuses on the coupled effects of temperature-dependent activation energy and variable electrical conductivity, governed by the Wiedemann-Franz law. An adaptive multi-step differential transform method (AM-DTM) is employed to solve the governing non-linear equations. The solutions characterize the behavior of a tabbed bolus, the velocity maximum, and the spatial distributions of velocity, temperature, and nanoparticle concentration. Model validation is achieved through numerical comparison with nearest published results. Key findings indicate that elevated temperature- and concentration-dependent electrical conductivity enhances the potential energy of nanoparticles. This effect increases the temperature of the interior channel walls by 3–5 °C, a mechanism with potential applications for sustainable thermal management in building envelopes. Furthermore, modulation of thermophoresis and Brownian motion parameters provides effective control over the maximum flow velocity, thereby optimizing heat transfer rates. This optimization is directly relevant to improving thermal regulation in advanced solar cell systems. The absorption and transfer of solar thermal energy are critical in numerous industrial and architectural applications. The integration of nanofluids within building envelopes represents an innovative passive cooling strategy for sustainable architecture.
This paper proposes a numerical study of a turbulent flow around an inclined square obstacle in a channel. The objective of this work is to examine the effect of the obstacle inclination (θ) on the boundary layer separation. The two-dimensional unsteady Reynolds-averaged Navier-Stokes equations (2D-URANS) were solved by the finite volume method using the shear stress transport k- model ((SST-(k-ω)) for turbulence closure. Validation is carried out with available experimental data and large eddy simulation (LES) results of the no inclined case (θ=0∘). Six obstacle inclinations in the range 0∘ ≤θ≤45 ∘, for Reynolds number Re=3000, are examined. The results show that the Strouhal number (St) increases linearly until it reaches a maximum value (St = 0.145) for a critical angle (θ = 15°), then decreases below this value.
The study of unsteady stability of underwater structures and constructions operating under the influence of various wave processes is a pressing task for the purposes of their safe operation. This paper considers the problem of unsteady radial oscillations of an elastic spherical layer in an ideal fluid. Nonstationary wave processes in an infinite space of an ideal fluid are investigated for unsteady radial oscillations of the elastic spherical layer and within the layer. An analytical solution to the problem is constructed in the image space of the Laplace transform over time. Exact expressions were obtained for the coefficients of component series of the displacement and the stress tensor, as well as for the hydrodynamic parameters of the surrounding medium. Numerical results are calculated for the steel-water, aluminum-water, and aluminum-glycerin systems. The results of the numerical experiments are analyzed. The results of this work can be used in shipbuilding, aircraft manufacturing, and in the design of underwater reservoirs.
A numerical study was conducted to check heat transfer performance by a hybrid nanofluid ((Al2O3-Cu) / H2O) through a shallow heated cavity. The governing equations are solved by the finite volume method using a one-point closure turbulence model. The Maxwell-Garnett (MG) and Brinkman models are applied, respectively, for the computation of the conductivity and viscosity of the nanofluid. The results are specifically for turbulent flows for Reynolds number Re ranging between 2.104 and 6.104 . A percentage selection was made for a wide range of copper (10%Cu50%) and volume fraction of the nanoparticles between 0 and =5%. Heat transfer along the cavity bottom wall is strongly influenced by the Reynolds number and the volume fraction of all types of nanofluids. The high thermal conductivity of hybrid nanofluids justifies their efficiency in comparison with single nanofluids for heat transfer processes. The local Nusselt number is least in all recirculation zones, reaching peak values at stagnation points. The Nusselt number augments with the Reynolds number and volume fraction of all types of nanofluids (single or hybrid). Hybrid nanofluids improve heat transfer more than single nanofluids.
Excitation of streamwise structures in the boundary layer with combustion has been investigated for the first time. It is revealed that intense hydro-dynamic and thermal streamwise structures arise inside the boundary layer with diffusion flame as a result of external streamwise vorticity. It is found that the spanwise temperature inhomogeneity is much higher than the velocity inhomogeneity.
This paper investigates the a posteriori error estimates associated with the Darcy–Forchheimer problem under pressure boundary conditions. The problem is discretized using finite element methods and an iterative scheme is recalled along with its corresponding convergence properties. We then derive a posteriori error estimates, where the error between the exact and approximate solutions is bounded by two types of indicators: one related to the discretization and the other to the iteration process. Finally, we present several numerical experiments using the adaptive mesh method to highlight the effectiveness of the proposed approach.
We develop a compact analytical model for steady, axisymmetric flow of a power-law (non-Newtonian) fluid through a rotating, converging horizontal hollow cone. Extending the approach of [1], the model incorporates temperature-dependent rheology and particle loading through a generalized consistency index, and accommodates wall friction via Navier-slip and frictional boundary conditions on the rotating cone. The governing continuity, momentum, and energy equations are formulated in spherical coordinates and simplified under viscous-dominated asymptotic (low Reynolds number and large Ekman number). A nondimensional scaling argument justifies omission of Coriolis and centrifugal accelerations in the leading-order balance, and the azimuthal momentum equation reduces to a local torque-consistency condition that represents the distributed torque required to sustain steady rotation. The reduced formulation exposes the coupled influence of rotation, wall friction, temperature, and particulate concentration on shear rates and apparent viscosity, and identifies parameter regimes where higher-order corrections are required.
The paper explores a mathematical model for the anomalous solute transport within a porous medium. This model encompasses the mass balance equation and the kinetic equation. To solve the problem, a numerical algorithm for computer experimentation is developed on the basis of the finite difference method. Based on numerical results, the main characteristics of solute transport in a porous medium are established. Influences of model parameters on the transport and deposition of suspended particles of suspension in porous media are analysed. The anomalies of solute transport and the multi-stage nature of deposition kinetics can induce effects that differ from those typically observed in the normal solute transport with single-stage particle deposition kinetics.
The existing research investigates the comparative behavior of circumferential pressure distribution in a hydrodynamic journal bearing operating at rotational speeds of 250, 500, and 750 RPM under varying loads of 0, 0.25, and 0.50 kg for all 360o. Experimental analysis was conducted using SAE 15W30 lubricant to evaluate the influence of operating parameters on pressure distribution characteristics. Results reveal that rotational speed exerts a more dominant influence on pressure development compared to load, with the highest pressure observed at 750 RPM. The maximum fluid film pressure consistently occurred between 120° and 150°, located within the converging wedge region (90°–270°) where the lubricant film thickness is minimal. The study confirms that increasing load enhances the bearing’s peak pressure and load-carrying capacity, while higher speeds improve hydrodynamic pressure generation and lubrication performance. ANOVA analysis further validates these findings, indicating that Angle is the most influential parameter, followed by Speed and Load, all with statistically significant effects (p < 0.05). The strong effect sizes confirm the robustness of the experimental model and the reliability of the observed results.
In this study, flows around generic missiles were computationally modeled and analyzed using a coupled density-based solver, OpenFOAM-HiSA. The issues regarding the modeling procedures, e.g., turbulence modeling, were addressed, and analyses were conducted in subsonic, transonic, and supersonic ranges. The obtained numerical results were compared with the previously published measurements and predictions of other researchers. It was observed that the calculated drag coefficient values were in fairly good agreement with the measurements. Especially, using the SST turbulence model produced better results than using the Spalart-Allmaras model. In addition, the obtained flow pattern was qualitatively similar to the previously published calculation data. With this validated model, the flow field and the drag variation with respect to the freestream Mach number were investigated. Furthermore, the flow around a modified missile geometry was analyzed, and the results were examined comparatively. Hence, the drag reduction mechanism due to geometric modifications could be explained.
The current research focuses on the flow around cylinders with different cross sections (circle, semi-circle, rectangle, triangle, trapezoid, and two airfoils: NACA0040 and NACA4412), which is experimentally and numerically investigated. The primary objective of this research is to examine the impact of the geometry on the vortex shedding downstream of a smooth and stationary shape, and the aerodynamic loads are to be determined as well. The experimental investigations are carried out in an instrumented subsonic wind tunnel. The numerical computations are carried out using OpenFOAM, a finite volume method-based open-source CFD software. The governing equations are the Unsteady Averaged Navier Stokes equations, where the turbulence is modeled by the two-equation SST K- model; for this purpose, different Reynolds numbers are considered: Re = 10, 100, 200, and 1000. The obtained results show that the variation of the contact surface and the geometry has a strong effect on both the various physical parameters and the vortex detachment in the downstream flow.
Based on a series of laboratory experiments on a unique installation for upward filtration lifting of solutions of water-soluble salts of nonferrous metals, the regularities of mass transfer and surface deposition at the evaporative barrier have been obtained. It was found that the intensity of evaporation has a linear tendency to decrease with time, which is associated with changes in the porosity of the massif in the aeration zone. Redistribution of vertical zonality of salt deposition concentration in the surface zone of the array is possible by controlling the evaporation intensity. Regularities of salt concentration distribution in different levels of the massif have been established, which forms the basis of the mathematical model of the fluid-mass transfer process.
The paper explores the nonlinear dynamics of drill strings under stochastic factors and external influences by providing its comprehensive analysis. These studies are motivated by the need to improve the safety and efficiency of drilling operations in complicated conditions. The authors model the dynamics of drill strings from the perspective of the randomness of the processes involved, enabling a broader range of operational modes for drilling equipment to be considered, as well as enhancing the accuracy and efficiency of optimal decision-making. The nonlinear dynamics of the drill string are examined under the influence of random factors and environmental conditions. The mathematical model of the drill string describes its planar vibrations accounting for the initial curvature of the string, external loads, fluid flow around the string, and frictional forces against the wellbore walls. The randomness of the effects is taken into account through the friction coefficient. Stochastic terms derived using the prior probability distribution, which allows the application of Shannon’s maximum entropy principle, are employed in the study. A numerical experiment is conducted to identify instability zones of the drill string motion. The study relies on the Galerkin method and partial discretization method. The influence of random factors on the drill string stability is revealed.
This paper aims to create efficient techniques to optimize the weight of wind turbine blades. A new mathematical model has been introduced, applying boundary element methods. Hypersingular integral equations have been used to calculate the dynamic pressure acting on the blade. The finite Hadamard part of the hypersingular integral has been received analytically over an arbitrary flat polygon. A revised version of the nonlinear programming method has been developed, which incorporates adaptive management techniques to optimize the procedures. The proposed optimization method uses several methods, called hybrids. A criterion has been specified by which the most effective hybrids are selected for the current search for an extremum. This criterion includes information characterizing a changing situation. The computer simulation results indicate that the wind turbine blade with the minimal weight has been achieved. Additionally, the proposed method will be extended to include the strength and dynamic analysis of wind turbines with a vertical axis of rotation.
