Search Results (59)

In this paper, we consider the unsteady flow of a compressible micropolar fluid between two moving, thermally isolated parallel plates. The fluid is characterized as viscous and thermally conductive, with polytropic thermodynamic properties. Although the mathematical model is inherently three-dimensional, we assume that the variables depend on only a single spatial dimension, reducing the problem to a one-dimensional formulation. The non-homogeneous boundary conditions representing the movement of the plates lead to moving domain boundaries. The model is formulated in mass Lagrangian coordinates, which leads to a time-invariant domain. This work focuses on numerical simulations of the fluid flow for different configurations. Two computational approaches are used and compared. The first is based on the finite difference method and the second is based on the Faedo–Galerkin method. To apply the Faedo–Galerkin method, the boundary conditions must first be homogenized and the model equations reformulated. On the other hand, in the finite difference method, the non-homogeneous boundary conditions are implemented directly, which reduces the computational complexity of the numerical scheme. In the performed numerical experiments, it was observed that, for the same accuracy, the Faedo–Galerkin method was approximately 40 times more computationally expensive compared to the finite difference method. However, on a dense numerical grid, the finite difference method required a very small time step, which could lead to an accumulation of round-off errors. On the other hand, the Faedo–Galerkin method showed the convergence of the solutions as the number of expansion terms increased, despite the higher computational cost. Comparisons of the obtained results show good agreement between the two approaches, which confirms the consistency and validity of the numerical solutions. Full article

The article proposes several classes of exact solutions to the Oberbeck–Boussinesq equations to describe convective flows of micropolar fluids. The possibility of using families of exact solutions for convective flows of classical incompressible fluids to micropolar incompressible fluids is discussed. It is shown that the three-dimensional Oberbeck–Boussinesq equation for describing steady and unsteady flows of micropolar fluids satisfies the class of Lin–Sidorov–Aristov exact solutions. The Lin–Sidorov–Aristov ansatz is characterized by a velocity field with a linear dependence on two spatial coordinates. These coordinates are called horizontal or longitudinal. The coefficients of the linear forms of the velocity field depend on the third coordinate (vertical or transverse) and time. The pressure field and the temperature field are described using quadratic forms. Generalizations of the Ostroumov–Birikh class are considered a special case of the Lin–Sidorov–Aristov family for describing unidirectional flows and homogeneous shear flows. An overdetermined system of Oberbeck–Boussinesq equations is investigated for describing non-homogeneous shear flows of non-trivial complex topology in 3D metric space. A compatibility condition is obtained in the Lin–Sidorov–Aristov class. Finally, a class of exact solutions with a vector velocity field that is nonlinear in part of the coordinates is presented in our analysis; such partially invariant solutions correspond to theoretical findings regarding symmetric/asymmetric properties of flow fields in solutions topology in a part of the existence appropriate for symmetry for the obtained invariant solutions. Full article

The present study investigates the entropy generation of chemically reactive micropolar hybrid nanoparticle motion with mass transfer. Magnetic oxide (Fe₃O₄) and copper oxide (CuO) nanoparticles were mixed in water to form a hybrid nanofluid. The governing equations for velocity, concentration, and temperature are transformed into ordinary differential equations along with the boundary conditions. In the fluid region, the heat balance is kept conservative with a source/sink that relies on the temperature. In the case of radiation, there is a differential equation along with several characteristic coefficients that transform hypergeometric and Kummer’s differential equations by a new variable. Furthermore, the results of the current problem can be discussed by implementing a graphical representation with different factors, namely the Brinkman number, porosity parameter, magnetic field, micropolar parameter, thermal radiation, Schmidt number, heat source/sink parameter, and mass transpiration. The results of this study are presented through graphical representations that depict various factors influencing the flow profiles and physical characteristics. The results reveal that an increase in the magnetic field leads to a reduction in velocity and entropy production. Furthermore, temperature and entropy generation rise with a stronger radiation parameter, whereas the Nusselt number experiences a decline. This study has several industrial applications in technology and manufacturing processes, including paper production, polymer extrusion, and the development of specialized materials. Full article

Understanding shear flow behavior in compressible, viscous, micropolar real gases is essential for both theoretical advancements and practical engineering applications. This study develops a comprehensive model that integrates micropolar fluid theory with compressible flow dynamics to accurately describe the behavior of real gases under shear stress. We formulate the governing equations by incorporating viscosity and micropolar effects and transform the obtained system into the mass Lagrangian coordinates. Two numerical methods, Faedo–Galerkin approximation and finite-difference methods, are used to solve it. These methods are compared using several benchmark examples to assess their accuracy and computational efficiency. Both methods demonstrate good performance, achieving equally precise results in capturing essential flow characteristics. However, the finite-difference method offers advantages in speed, stability, and lower computational demands. This research bridges gaps in existing models and establishes a foundation for further investigations into complex flow phenomena in micropolar real gases. Full article

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 work, we analyze a spherically symmetric 3D flow of a micropolar, viscous, polytropic, and heat-conducting real gas. In particular, we take as a domain the subset of $R^3$ bounded by two concentric spheres that present solid thermoinsulated walls. Also, here, we consider the generalized equation of state for the pressure in the sense that the pressure depends, as a power function, on the mass density. The model is based on the conservation laws for mass, momentum, momentum moment, and energy, as well as the equation of state for a real gas, and it is derived first in the Eulerian and then in the Lagrangian description. Through the application of the Faedo–Galerkin method, a numerical solution to a corresponding problem is obtained, and numerical simulations are performed to demonstrate the behavior of the solutions under various parameters and initial conditions in order to validate the method. The results of the simulations are discussed in detail. Full article

The convective micropolar fluid flow over a permeable shrinking sheet in the presence of a heat source and thermal radiation with the magnetic field directed towards the sheet has been studied in this paper. The mathematical formulation considers the partial slip condition at the sheet, allowing a realistic representation of the fluid flow near the boundary. The governing equations for the flow, heat, and mass transfer are formulated using the conservation laws of mass, momentum, angular momentum, energy, and concentration. The resulting nonlinear partial differential equations are transformed into a system of ordinary differential equations using suitable similarity transformations. The numerical solutions are obtained using robust computational techniques to examine the influence of various parameters on the velocity, temperature, and concentration profiles. The impact of slip effects, micropolar fluid characteristics, and permeability parameters on the flow features and heat transfer rates are thoroughly analyzed. The findings of this investigation offer valuable insights into the behavior of micropolar fluids in free convection flows over permeable shrinking sheets with slip, providing a foundation for potential applications in various industrial and engineering processes. Key findings include the observation that the velocity profile overshoots for assisting flow with decreasing viscous force and rising magnetic effects as opposed to opposing flow. The thermal boundary layer thickness decreases due to buoyant force but shows increasing behavior with heat source parameters. The present result agrees with the earlier findings for specific parameter values in particular cases. Full article

This paper studies the large time behavior of solutions to the 2D micropolar equations with linear damping velocity. It is proven that the global solutions have rapid time decay rates ${\parallel \nabla \omega \parallel }_{L^2}+{\parallel \nabla u\parallel }_{L^2}\le C{(1+t)}^{-\frac{3}{2}}$ and ${\parallel u\parallel }_{L^2}\le C{(1+t)}^{-\frac{3}{2}},{\parallel \omega \parallel }_{L^2}\le C{(1+t)}^{-1}$. The findings are mainly based on the new observation that linear damping actually improves the low-frequency effect of the system. The methods here are also available for complex fluid models with linear damping structures. Full article

This study investigates the magnetohydrodynamics of a micropolar fluid consisting of a hybrid nanofluid with mixed convection effects. By using the dimensionless set of variables, the resulting equations of ordinary differential equations are solved numerically using the bvp4c solver in MATLAB. In the present work, the water-based alumina–copper hybrid nanofluid is analytically modeled with modified thermophysical properties. The study reveals that the highest critical value of opposing flow is the hybrid nanofluid (ϕ₁ = ϕ₂ = 2%). By comparing the hybrid nanofluid with Cu–water nanofluid (ϕ₁= 0%, ϕ₂= 1%) as well as water (ϕ₁= 0%, ϕ₂= 0%), hybrid nanoparticle volume fraction enhances the dynamic viscosity performance and surface shear stress. In addition, the augmentation of the nanoparticle volume fraction and magnetic field parameter will increase the physical quantities Re_x^1/2 C_f, Re_x M_x, and Re_x^−1/2 Nu_x. The result from the stability inquiry discloses that the first solution is more physically stable and trustworthy. It is proven that magnetohydrodynamics could contribute to controlling the fluid flow in a system, i.e., engineering operations and the medical field. In addition, this theoretical research can be a benchmark for experimental research. 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 current study delivers a numerical investigation on the performance of heat transfer and flow of micropolar fluid in porous Darcy structures with isothermal and isoflux walls (boundary conditions) of a stretching sheet. The dynamics and mechanism of such fluid flows are modelled by nonlinear partial differential equations that are reduced to a system of nonlinear ordinary differential equations by utilizing the porosity of medium and similarity functions. Generally, the explicit or analytical solutions for such nonlinear problems are hard to calculate. Therefore, we have designed a computer or artificial intelligence-based numerical technique. The reliability of neural networks using the machine learning (ML) approach is used with a local optimization technique to investigate the behaviours of different material parameters such as the Prandtl number, micropolar parameters, Reynolds number, heat index parameter, injection/suction parameter on the temperature profile, fluid speed, and spin/rotational behaviour of the microstructures. The approximate solutions determined by the efficient machine learning approach are compared with the classical Runge–Kutta fourth-order method and generalized finite difference approximation on a quasi-uniform mesh. The accuracy of the errors lies around 10⁻⁸ to 10⁻¹⁰ between the traditional analytical solutions and machine learning strategy. ML-based techniques solve different problems without discretization or computational work, and are not subject to the continuity or differentiability of the governing model. Moreover, the results are illustrated briefly to help implement microfluids in drug administering, elegans immobilization, and pH controlling processes. Full article

These days, heat transfer plays a significant role in the fields of engineering and energy, particularly in the biological sciences. Ordinary fluid is inadequate to transfer heat in an efficient manner, therefore, several models were considered for the betterment of heat transfer. One of the most prominent models is a single-phase nanofluid model. The present study is devoted to solving the problem of micropolar fluid with a single-phase model in a channel numerically. The governing partial differential equations (PDEs) are converted into nonlinear ordinary differential equations (ODEs) by introducing similarity transformation and then solved numerically by the finite difference method. Response surface methodology (RSM) together with sensitivity analysis are implemented for the optimization analysis. The study reveals that sensitivity of the skin friction coefficient (Cf_x) to the Reynolds number (R) and magnetic parameter (M) is positive (directly proportional) and negative (inversely proportional) for the micropolar parameter. 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

Boosting the heat transfer rate in a base fluid is of interest to researchers; many traditional methods have been utilized to do this. One significant way is using nanofluid to boost thermal performance. This investigation sought to improve the transmission of a thermal above-stretching inclined surface over an upper surface to be influenced by the magnetic field $B_0$ along the microgravity $g*\left(\tau \right)=g_0(1+acos\left(\pi \omega t\right))$. The G-jitter impacts were analyzed for three colloidal fluids flow; the mono micropolar nanofluid (alumina/water), micropolar hybrid nanofluid (alumina–titanium)/water, and micropolar trihybrid nanofluid (alumina–titanium–silicon)/water. Using suitable transformation, the governing formulation was changed into an ordinary differential equation. In a Matlab script, a computational code was composed to evaluate the impacts of the involved parameters on fluid dynamics. The fluid flow motion and thermal performance for the trihybrid case were greater than the mono and hybrid nanofluid cases subject to a microgravity environment. The fluid velocity and microrotation function decreased in opposition to the magnetic parameter’s increasing strength, but with an increasing trend in the fluid temperature function. Fluctuations in the velocity gradient and heat flow gradient increased as the modulation amplitude increased. Full article

The utilization of hybrid nanofluids (HNs) to boost heat transfer is a promising area of study, and thus, numerous scientists, researchers, and academics have voiced their admiration and interest in this area. One of the main functions of nanofluids is their dynamic role in cooling small electrical devices such as microchips and associated gadgets. The major goal of this study is to perform an analysis of the buoyancy flow of a shrinking/stretching sheet, whilst considering the fascinating and practical uses of hybrid nanofluids. The influence of a nonlinear heat source/sink induced by a micropolar fluid is also inspected. Water-based alumina and copper nanoparticles are utilized to calculate the fine points of the fluid flow and the features of heat transfer. The governing equations are framed with acceptable assumptions and the required similarity transformations are used to turn the set of partial differential equations into ordinary differential equations. The bvp4c technique is used to solve the simplified equations. Dual solutions are presented for certain values of stretching/shrinking parameters as well as the mixed convective parameter. In addition, the shear stress coefficient in the first-branch solution (FBS) escalates and decelerates for the second-branch solution (SBS) with the superior impact of the magnetic parameter, the mass transpiration parameter, and the solid nanoparticles volume fraction, while the contrary behavior is seen in both (FB and SB) solutions for the larger values of the material parameter. Full article