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Heat exchange plays an important role in hydrodynamical systems, which is an interesting topic in theory and application. In this paper, the authors consider the global stability of steady supersonic Rayleigh flows for the one-dimensional compressible Euler equations with heat exchange, under the small perturbations of initial and boundary conditions in a finite rectilinear duct. [ABSTRACT FROM AUTHOR]

Atherosclerosis is a leading cause of death worldwide. Making matters worse, nearly 463 million people have diabetes, which increases atherosclerosis-related inflammation. Diabetic patients are twice as likely to have a heart attack or stroke. In this paper, we consider a simplified mathematical model for diabetic atherosclerosis involving LDL, HDL, glucose, insulin, free radicals (ROS), β cells, macrophages and foam cells, which satisfy a system of partial differential equations with a free boundary, the interface between the blood flow and the plaque. We establish the existence of small radially symmetric stationary solutions to the model and study their stability. Our analysis shows that the plague will persist due to hyperglycemia even when LDL and HDL are in normal range, hence confirms that diabetes increase the risk of atherosclerosis. [ABSTRACT FROM AUTHOR]

Atherosclerosis is a leading cause of death worldwide. Making matters worse, nearly 463 million people have diabetes, which increases atherosclerosis-related inflammation. Diabetic patients are twice as likely to have a heart attack or stroke. In this paper, we consider a simplified mathematical model for diabetic atherosclerosis involving LDL, HDL, glucose, insulin, free radicals (ROS), β cells, macrophages and foam cells, which satisfy a system of partial differential equations with a free boundary, the interface between the blood flow and the plaque. We establish the existence of small radially symmetric stationary solutions to the model and study their stability. Our analysis shows that the plague will persist due to hyperglycemia even when LDL and HDL are in normal range, hence confirms that diabetes increase the risk of atherosclerosis.

The Boltzmann equation is a fundamental kinetic equation that describes the dynamics of dilute gas. In this paper we study the regularity of both dynamical and steady Boltzmann equations in a strictly convex domain with the Cercignani-Lampis (C-L) boundary condition. The C-L boundary condition describes the intermediate reflection law between diffuse reflection and specular reflection via two accommodation coefficients. We construct a local weighted C¹ dynamical solution using repeated interaction through the characteristic. When we assume small fluctuation to the wall temperature and accommodation coefficients, we construct weighted C¹ steady solution. [ABSTRACT FROM AUTHOR]

The understanding of fluid flow and heat transfer (HT) through a rotating curved duct (RCD) is important for different engineering applications. The available literature improved the understanding of the fluid flow and HT through a large-curvature rotating duct. However, the comprehensive knowledge of fluid flow and HT through an RCD with small curvature is little known. This numerical study aims to perform fluid flow characterization and HT through an RCD with curvature ratio 0.001. The spectral based numerical approach investigates the effects of rotation on fluid flow and HT for the Taylor number -1000 ≤ Tr ≤ 1500. A constant pressure gradient force, the Dean number Dn = 100, and a constant buoyancy force parameter, the Grashof number Gr = 500 are used for the numerical simulation. Fortran code is developed for the numerical computations and Tecplot software is used for the post-processing purpose. The numerical study investigates steady solutions and a structure of two-branches of steady solutions is obtained for positive rotation. The transient solution reports the transitional flow patterns and HT through the rotating duct, and two- to four-vortex solutions are observed. In case of negative rotation, time-dependent solutions show that the Coriolis force exhibits an opposite effect to that of the curvature so that the flow characteristics exhibit various flow instabilities. The numerical result shows that convective HT is increased with the increase of rotation and highly complex secondary flow patterns influence the overall HT from the heated wall to the fluid. To validate the numerical results, a comparison with the experimental data is provided, which shows that a good agreement is attained between the numerical and experimental investigations. [ABSTRACT FROM AUTHOR]

In this paper, a numerical study on centrifugal instability with convective heat transfer through a curved square duct is presented by using a spectral method, and covering a wide range of the Dean number (0< Dn ≤ 5000) for a tightly coiled square duct of curvature 0.5 The outer and bottom walls of the duct are heated while cooling from the inner and the ceiling. The main objective of this study is to expose combined effects of centrifugal and buoyancy forces on fluid flows through a curved channel. For this purpose, solution structure of the steady solutions is obtained first. As a result, four branches of symmetric/asymmetric steady solutions are obtained. Linear stability of the steady solutions is then investigated. It is found that only the first branch is linearly stable while the other branches are linearly unstable. Unsteady flow behavior, obtained by time evolution calculations, shows that the steady-state flow turns into chaotic flow via periodic and multiperiodic flows, if Dn is increased. Typical contours of secondary flow pattern, stream-wise velocity distribution and temperature profiles are obtained at several values of Dn and it is found that the flow consists of asymmetric two- to four-vortex solutions. The present study shows that convective heat transfer is significantly enhanced by the secondary flow; and the chaotic flow, which occurs at large Dn’s, enhances heat transfer more effectively than the steady-state or periodic solutions. Finally, a comparison between the numerical and experimental investigations has been made, and it is found that there is a good agreement between the numerical and experimental investigations. [ABSTRACT FROM AUTHOR]

The steady solutions of solitary waves are studied through the use of the Irrotational Green–Naghdi (IGN) equations for an incompressible and inviscid fluid. The steady solutions are obtained by Newton–Raphson method. We consider the solitary gravity waves of H / h  = 0.30, 0.50, 0.70, 0.79, 0.8296, 0.833199 (where H is the wave amplitude and h is the water depth). Some experiments are conducted to test the results of the IGN equations. In particular, we focus on the wave profile and velocity field. We find that for the cases of the solitary waves of H / h  ≤ 0.79, the IGN-5 results agree very well with the Euler solutions. For the solitary waves that close to the maximum amplitude, the converged IGN results are presented. It is also shown that high level IGN results on wave speed agree well with the results obtained by others. [ABSTRACT FROM AUTHOR]

The study of the stability of a dynamical system described by a set of partial differential equations (PDEs) requires the computation of unstable states as the control parameter exceeds its critical threshold. Unfortunately, the discretization of the governing equations, especially for fluid dynamic applications, often leads to very large discrete systems. As a consequence, matrix based methods, like for example the Newton–Raphson algorithm coupled with a direct inversion of the Jacobian matrix, lead to computational costs too large in terms of both memory and execution time. We present a novel iterative algorithm, inspired by Krylov-subspace methods, which is able to compute unstable steady states and/or accelerate the convergence to stable configurations. Our new algorithm is based on the minimization of the residual norm at each iteration step with a projection basis updated at each iteration rather than at periodic restarts like in the classical GMRES method. The algorithm is able to stabilize any dynamical system without increasing the computational time of the original numerical procedure used to solve the governing equations. Moreover, it can be easily inserted into a pre-existing relaxation (integration) procedure with a call to a single black-box subroutine. The procedure is discussed for problems of different sizes, ranging from a small two-dimensional system to a large three-dimensional problem involving the Navier–Stokes equations. We show that the proposed algorithm is able to improve the convergence of existing iterative schemes. In particular, the procedure is applied to the subcritical flow inside a lid-driven cavity. We also discuss the application of Boostconv to compute the unstable steady flow past a fixed circular cylinder (2D) and boundary-layer flow over a hemispherical roughness element (3D) for supercritical values of the Reynolds number. We show that Boostconv can be used effectively with any spatial discretization, be it a finite-difference, finite-volume, finite-element or spectral method. [ABSTRACT FROM AUTHOR]

The mathematical property of one-dimensional steady solution for reverse smolder waves in the context of a model that permits both fuel-rich and fuel-lean has been studied using the method of analysis. Based on the equations and the boundary conditions some asymptotic properties of the solution at infinity are proved. It is shown that the value of oxygen or the mass of fuel (corresponding to the fuel-rich case and the fuel-lean case, respectively) tends to zero, and the temperature approaches to a fixed value. This is confirmed by other authors using large activation energy asymptotic methods. [ABSTRACT FROM AUTHOR]