Asymptotic analysis of the nonsteady micropolar fluid flow through a system of thin pipes revisited: Boundary-layer-in-time effects

In this paper, we analyze the time‐dependent flow of an incompressible micropolar fluid in a multiple‐pipe system. Motivated by the applications, we assume that the pipes have circular cross‐section and that the ratio between pipes' thickness and its length is small, denoted by the parameter . Far from the junction, the fluid exhibits different behavior depending on the magnitude of the viscosity coefficients with respect to the small parameter . Focusing on the critical case described by the strong coupling between velocity and microrotation, the complete asymptotic expansion of the solution (up to an arbitrary order) is built. To improve the accuracy of the asymptotic approximation, we introduce the boundary layer correctors near the pipes' ends and take into account the interior layer correction in the vicinity of the junction as well. The convergence is also proved via error estimates, providing the rigorous justification of the proposed effective model.

We consider the nonsteady flow of a micropolar fluid in a thin (or long) curved pipe via rigorous asymptotic analysis. Germano's reference system is employed to describe the pipe's geometry. After writing the governing equations in curvilinear coordinates, we construct the asymptotic expansion up to a second order. Obtained in the explicit form, the asymptotic approximation clearly demonstrates the effects of pipe's distortion, micropolarity and the time derivative. A detailed study of the boundary layers in space is provided as well as the construction of the divergence correction. Finally, a rigorous justification of the proposed effective model is given by proving the error estimates.

The linear and nonlinear stability analyses of micropolar fluid flow in a horizontal porous layer heated from below in the presence of throughflow is numerically investigated. The Brinkman model is considered to govern the micropolar fluid flow within the porous region. The main purpose of the present study is to investigate the behavior of the subcritical region for micropolar fluid parameters in the presence of throughflow. The energy approach is used to analyze nonlinear stability, whereas the normal mode scheme is used to investigate linear stability. The obtained eigenvalue problems related to linear and nonlinear stability analyses are solved numerically using the bvp4c routine in MATLAB. Finally, the critical thermal Rayleigh number is determined for the given values of the governing parameters. It is observed that the subcritical area decreases as the Darcy number (Da), micropolar parameter (m), and absolute value of throughflow parameter (|Pe|) decrease. Furthermore, there is no subcritical gap in the absence of the throughflow effect for micropolar fluid flow, which is a good agreement for the linear and nonlinear thresholds.

Integrated electro-thermomechanical analysis of nonuniformly chip-powered microelectronic system

In the considered problem, we presented a model for the flow of immiscible fluids (non-Newtonian and Newtonian) through the cylindrical pipe. Cylindrical pipe is constituted by two porous cylindrical shell enclosing a cylindrical cavity. Non-Newtonian (micropolar) fluid is flowing through the middle porous cylindrical shell, and other immiscible Newtonian fluids are flowing through the cavity and outer porous cylindrical shell. The flow of fluid through the outer porous cylindrical shell and cavity is governed by well-known Brinkman and Stoke’s equation, respectively. However, the flow of micropolar fluid through the middle porous cylindrical shell is governed by the field equation given by Eringen (Springer, Berlin, 2001). An analytical solution of the problem has been obtained by using the justified boundary conditions. The effects of various non-dimensional parameters such as permeability parameters, micropolar parameter, and viscosity ratio on the linear flow velocity, microrotational flow velocity and flow rate are examined graphically. The results are validated with the help of previously established result.

PurposeThe purpose of this paper is to simulate with in-depth reconstruction of existing geometry a process of cooling of the aircraft engine in pusher configuration, which is more problematic than usually used, tractor configuration. Moreover, a complex thermal and fluid flow analysis is necessary to verify that an adequate cooling is ensured and that temperatures in the engine nacelle are maintained within the operating limits.Design/methodology/approachMethodology used in this research is based on computational fluid dynamics tools to model adequately the internal and the external flow, to find the state of cooling system and research the results of baffles modification inside the engine cover. Additionally, two types of the cover with different sizes of inlets and outlets are tested.FindingsThe results showed the influence of baffles modifications and changes in inlets and outlet sizes on the mass flow rate and temperature distributions inside the engine nacelle. The best configuration of air inlets and outlets was determined.Practical implicationsThe method used in the research is the safest method in testing of such cases, provided the proper approach in modeling is taken. The collaboration of internal and external flow is crucial and should not be replaced with assumed flow rate through inlet and outlet area. The obtained results will help in future studies on cooling systems of engines in pusher configuration.Originality/valueThe work presents original results obtained by the authors during a complex fluid flow and heat transmission analysis and is a part of the design project of the OSA patrol aircraft.

For three-dimensional finite element analysis of transient fluid flow with free-surface, a new marker surface method is proposed, in which the fluid flow is represented by the marker surface composed of marker elements instead of marker particles used in the marker particle method. This also involves an adaptive grid that is created under a new criterion of element categorization of filling states and the locations in the total region at each time step. The marker surface is used in order to represent the free-surface accurately, as well as to decrease the memory and computation time, and to effectively display the predicted three-dimensional free-surface. By using the adaptive grid in which the elements, finer than those in internal and external regions, are distributed in the surface region through refinement and coarsening procedures, the analysis of three-dimensional transient fluid flow with free-surface is achieved more efficiently. Through three-dimensional analysis of two kinds of problems using several grids, the efficiency of the proposed marker surface method and the adaptive grid are verified. Copyright © 1999 John Wiley & Sons, Ltd.

Analysis of fluid flow and particle transport in evaporating droplets exposed to infrared heating

The present study has been produced to analyze the steady state, laminar and Newtonian fluid flow via the rectangular channel with three equal spaced inclined perforated plates with screen boundary conditions settled at angles from $ - \frac{\pi }{4}$ to $\frac{\pi }{4}$ with κ = 2.2 and η = 0.78. The leading two-dimensional incompossible Navier-Stokes equations are solved by applying the finite element method with least square Galerkin’s scheme using the commercial software COMSOL MultiPhysics 5.4. In the first step, results are contrasted by measuring the stream-wise velocity at the exit wall of the channel with the asymptotic solution provided by Elder [1], which was built on the analysis of fluid flow through the single screen. In the 2nd step we are going to present the velocity contours with surface plot and pressure drop arrow plot in the whole domain vs the inclination of the screens. Finally, dragging forces are calculated at the three perforated plates in terms of angle. The research is significant because it contributed interpolated equations of the maximum velocity at the exit, maximum pressure in the domain and drag force applied by the single screen in terms of inclination.

Fluid flow analyses and investigations of associated structural variations in rock formations are important due to the complex nature of rocks and the high heterogeneity that exists within fluid-rock systems. Variations in fluid-rock parameters need to be ascertained over time with continuous or cyclic fluid injection into subsurface rocks for enhanced oil recovery and other subsurface applications. This Review introduces the use of the core flooding-nuclear magnetic resonance (NMR) technique for analysis of combined fluid flow and structural features in subsurface fluid-rock systems. It presents a summary of the results realized by various researchers in this area of study. The influence of several conditions, such as geochemical interactions, wettability, inherent heterogeneities in fluid flow and rock properties, and variations in these parameters, is analyzed. We investigate NMR measurements for both single fluid phase saturation and multiphase saturation. Additionally, the processes for identifying and distinguishing different fluid phases are emphasized in this study. Furthermore, capillary pressure and its influence on fluid-rock parameters are also discussed. Although this study emphasizes subsurface rocks and enhanced oil recovery, the experimental combination is also extended to core flooding using several other injection fluids and porous media. Finally, research gaps pertaining to core flooding-NMR systems regarding fluid flow, structural changes, fluid-rock systems, and instrumentation are pointed out. Transient flow analysis involving structural variations is suggested for future work in this regard.

The micropolar fluid theory augments the laws of classical continuum mechanics by incorporating the effects of fluid molecules on the continuum. So, the micropolar theory has been able to explain many phenomena at micro and nano scales. In this paper, a finite element formulation for the numerical analysis of micropolar laminar fluid flow is developed. In order to validate the results of the FE formulation, analytical solution of the Poiseuille flow of micropolar fluid in a microchannel is presented, and an excellent agreement between the results of the analytical solution and those of the FE formulation is observed. It is shown that the micropolar viscosity and the length scale parameter have significant roles on changing the flow characteristics. Then, the behavior of an incompressible viscous fluid flow in a lid-driven square cavity is investigated. The obtained results are compared to the results reported in the literature, and an excellent agreement is observed.

Various experimental observations have demonstrated that the classical fluid theory is incapable of explaining many phenomena at micro and nano scales. On the other hand, micropolar fluid dynamics can naturally pick up the physical phenomena at these scales owing to its additional degrees of freedom caused by incorporating the effects of fluid molecules on the continuum. Therefore, one of the aims of this paper is to investigate the applicability of the theory of micropolar fluids to modeling and calculating flows in circular microchannels depending on the geometrical dimension of the flow field. Hence, a finite element formulation for the numerical analysis of micropolar laminar fluid flow is developed. In order to validate the results of the FE formulation, the analytical and exact solution of the micropolar Hagen–Poiseuille flow in a circular microchannel is presented, and an excellent agreement between the results of the analytical solution and those of the FE formulation is observed. It is also shown that the micropolar viscosity and the length scale parameter have significant roles on changing the flow characteristics. Then, the behavior of an incompressible viscous fluid flow such as blood flow in a stenosed artery, having multiple kinds of stenoses, is investigated. The obtained results are compared to the results reported in the literature, and an excellent agreement is observed.

This study presents the optimization design process of a segment ball valve that involves the reduction of the flow resistance coefficient and the satisfaction of the strength requirement. Numerical analysis of fluid flow and structural analysis have been performed to predict the flow resistance coefficient and the maximum stress of a segment ball valve. In this study, a segment ball valve incorporating the advantages of a ball valve and a butterfly valve has been devised. In general, ball valves are installed in a pipe system where tight shut off is required. Butterfly valves having smaller end-to-end dimension than ball valve can be installed in narrow spaces in a pipe system. The metamodels for the shape design of a segment ball valve are built by the response surface method and the Kriging interpolation model.

This paper presents finite element analysis of non-Newtonian fluid flow in 2-d branching channel. The Galerkin method and mixed finite element method are used. Here the fluid is considered as incompressible, non-Newtonian fluid with Oldyord differential-type constitutive equation. The non-linear algebraic equation system which is formulated with finite element method is solved by means of continuous differential method. The results show that finite element method is suitable for the analysis of non-Newtonian fluid flow with complex geometry.

Removing geometric details from the computational domain can significantly reduce the complexity of downstream task of meshing and simulation computation, and increase their stability. Proper estimation of the sensitivity analysis error induced by removing such domain details, called defeaturing errors, can ensure that the sensitivity analysis fidelity can still be met after simplification. In this paper, estimation of impacts of removing arbitrarily constrained domain details to the analysis of incompressible fluid flows is studied with applications to fast analysis of incompressible fluid flows in complex environments. The derived error estimator is applicable to geometric details constrained by either Dirichlet or Neumann boundary conditions, and has no special requirements on the outer boundary conditions. Extensive numerical examples were presented to demonstrate the effectiveness and efficiency of the proposed error estimator.