Simultaneous solution of the time dependent coupled continuity equations, heat conduction equations, and equations of motion for a system consisting of a neutral gas, an electron gas, and a four component ion gas

1970 ◽  
Vol 32 (5) ◽  
pp. 865-903 ◽  
Author(s):  
Peter Stubbe
Keyword(s):  
Heat Conduction ◽  
Equations Of Motion ◽  
Electron Gas ◽  
Time Dependent ◽  
Simultaneous Solution ◽  
Neutral Gas ◽  
Continuity Equations

scholarly journals Effect of an oscillating time-dependent pressure gradient on Dean flow: transient solution

2020 ◽  
Vol 9 (1) ◽  
Author(s):  
Basant K. Jha ◽  
Dauda Gambo
Keyword(s):  
Pressure Gradient ◽  
Initial Conditions ◽  
Fluid Velocity ◽  
Outer Cylinder ◽  
Time Dependent ◽  
Navier Stokes ◽  
Dean Flow ◽  
Continuity Equations ◽  
Riemann Sum ◽  
Flow Formation

Abstract Background Navier-Stokes and continuity equations are utilized to simulate fully developed laminar Dean flow with an oscillating time-dependent pressure gradient. These equations are solved analytically with the appropriate boundary and initial conditions in terms of Laplace domain and inverted to time domain using a numerical inversion technique known as Riemann-Sum Approximation (RSA). The flow is assumed to be triggered by the applied circumferential pressure gradient (azimuthal pressure gradient) and the oscillating time-dependent pressure gradient. The influence of the various flow parameters on the flow formation are depicted graphically. Comparisons with previously established result has been made as a limit case when the frequency of the oscillation is taken as 0 (ω = 0). Results It was revealed that maintaining the frequency of oscillation, the velocity and skin frictions can be made increasing functions of time. An increasing frequency of the oscillating time-dependent pressure gradient and relatively a small amount of time is desirable for a decreasing velocity and skin frictions. The fluid vorticity decreases with further distance towards the outer cylinder as time passes. Conclusion Findings confirm that increasing the frequency of oscillation weakens the fluid velocity and the drag on both walls of the cylinders.

scholarly journals Boussinesq modeling of surface waves due to underwater landslides

2013 ◽  
Vol 20 (3) ◽  
pp. 267-285 ◽  
Author(s):  
D. Dutykh ◽  
H. Kalisch
Keyword(s):  
Surface Waves ◽  
Shallow Water ◽  
Bottom Topography ◽  
Equations Of Motion ◽  
Boussinesq Equations ◽  
Time Dependent ◽  
Viscous Drag ◽  
Underwater Landslide ◽  
Landslide Mass ◽  
Run Up

Abstract. Consideration is given to the influence of an underwater landslide on waves at the surface of a shallow body of fluid. The equations of motion that govern the evolution of the barycenter of the landslide mass include various dissipative effects due to bottom friction, internal energy dissipation, and viscous drag. The surface waves are studied in the Boussinesq scaling, with time-dependent bathymetry. A numerical model for the Boussinesq equations is introduced that is able to handle time-dependent bottom topography, and the equations of motion for the landslide and surface waves are solved simultaneously. The numerical solver for the Boussinesq equations can also be restricted to implement a shallow-water solver, and the shallow-water and Boussinesq configurations are compared. A particular bathymetry is chosen to illustrate the general method, and it is found that the Boussinesq system predicts larger wave run-up than the shallow-water theory in the example treated in this paper. It is also found that the finite fluid domain has a significant impact on the behavior of the wave run-up.

scholarly journals Effect of Deformation on Semi–infinite Viscothermoelastic Cylinder Based on Five Theories of Generalized Thermoelasticity

2017 ◽  
Vol 6 (1) ◽  
pp. 17-35 ◽  
Author(s):  
D. K. Sharma ◽  
Himani Mittal ◽  
Sita Ram Sharma ◽  
Inder Parkash
Keyword(s):  
Heat Conduction ◽  
Laplace Transformation ◽  
Numerical Technique ◽  
Equations Of Motion ◽  
Generalized Thermoelasticity ◽  
Dynamical Problem ◽  
Infinite Cylinder ◽  
Matlab Software ◽  
Voigt Model ◽  
Laplace Transformations

We considera dynamical problem for semi-infinite viscothermoelastic semi infinite cylinder loaded mechanically and thermally and investigated the behaviour of variations of displacements, temperatures and stresses. The problem has been investigated with the help of five theories of the generalized viscothermoelasticity by using the Kelvin – Voigt model. Laplace transformations and Hankel transformations are applied to equations of constituent relations, equations of motion and heat conduction to obtain exact equations in transformed domain. Hankel transformed equations are inverted analytically and for the inversion of Laplace transformation we apply numerical technique to obtain field functions. In order to obtain field functions i.e. displacements, temperature and stresses numerically we apply MATLAB software tools. Numerically analyzed results for the temperature, displacements and stresses are shown graphically.

scholarly journals Symmetry analysis of rotating fluid

2005 ◽  
Vol 47 (1) ◽  
pp. 65-74 ◽  
Author(s):  
K. Fakhar ◽  
Zu-Chi Chen ◽  
Xiaoda Ji
Keyword(s):  
Steady State ◽  
Infinite Number ◽  
Special Function ◽  
Equations Of Motion ◽  
Time Dependent ◽  
Lie Theory ◽  
Rotating Fluid ◽  
Type Solution ◽  
Function Type ◽  
Basic Equations

AbstractThe machinery of Lie theory (groups and algebras) is applied to the unsteady equations of motion of rotating fluid. A special-function type solution for the steady state is derived. It is then shown how the solution generates an infinite number of time-dependent solutions via three arbitrary functions of time. This algebraic structure also provides the mechanism to search for other solutions since its character is inferred from the basic equations.

scholarly journals Mechanical aspects of the semicircular ducts in the vestibular system

2020 ◽  
Vol 114 (4-5) ◽  
pp. 421-442
Author(s):  
Mees Muller
Keyword(s):  
Brownian Motion ◽  
Vestibular System ◽  
Equations Of Motion ◽  
Complex Structure ◽  
Coupled System ◽  
Continuity Equations ◽  
Mathematical Expressions ◽  
Semicircular Ducts ◽  
Evolutionary Aspects ◽  
Instrumental Role

Abstract The semicircular ducts (SCDs) of the vestibular system play an instrumental role in equilibration and rotation perception of vertebrates. The present paper is a review of quantitative approaches and shows how SCDs function. It consists of three parts. First, the biophysical mechanisms of an SCD system composed of three mutually connected ducts, allowing endolymph to flow from one duct into another one, are analysed. The flow is quantified by solving the continuity equations in conjunction with the equations of motion of the SCD hydrodynamics. This leads to mathematical expressions that are suitable for further analytical and numerical analysis. Second, analytical solutions are derived through four simplifying steps while keeping the essentials of the coupled system intact. Some examples of flow distributions for different rotations are given. Third, the focus is on the transducer function of the SCDs. The complex structure of the mechano-electrical transduction apparatus inside the ampullae is described, and the consequences for sensitivity and frequency response are evaluated. Furthermore, both the contributions of the different terms of the equations of motion and the influence of Brownian motion are analysed. Finally, size limitations, allometry and evolutionary aspects are taken into account.

scholarly journals The role of heat conduction to the formation of [WC]-type planetary nebulae

2011 ◽  
Vol 7 (S283) ◽  
pp. 494-495
Author(s):  
Christer Sandin ◽  
Matthias Steffen ◽  
Ralf Jacob ◽  
Detlef Schönberner ◽  
Ute Rühling ◽  
...  
Keyword(s):  
Heat Conduction ◽  
Chemical Composition ◽  
Physical Properties ◽  
Planetary Nebulae ◽  
Time Dependent ◽  
Diffuse Emission ◽  
Hydrodynamic Models ◽  
X Ray ◽  
Central Stars

AbstractX-ray observations of young Planetary Nebulæ (PNe) have revealed diffuse emission in extended regions around both H-rich and H-deficient central stars. In order to also reproduce physical properties of H-deficient objects, we have, at first, extended our time-dependent radiation-hydrodynamic models with heat conduction for such conditions. Here we present some of the important physical concepts, which determine how and when a hot wind-blown bubble forms. In this study we have had to consider the, largely unknown, evolution of the CSPN, the slow (AGB) wind, the fast hot-CSPN wind, and the chemical composition. The main conclusion of our work is that heat conduction is needed to explain X-ray properties of wind-blown bubbles also in H-deficient objects.

scholarly journals Model Calculations of Solar Wind Expansion Including an Enhanced Fraction of Ionizing Electrons

1980 ◽  
Vol 91 ◽  
pp. 159-162
Author(s):  
E. F. Petelski ◽  
H. J. Fahr ◽  
H. W. Ripken
Keyword(s):  
Solar Wind ◽  
Impact Ionization ◽  
Hydrogen Atoms ◽  
Interstellar Gas ◽  
Model Calculations ◽  
Neutral Gas ◽  
Continuity Equations ◽  
Velocity Effect ◽  
Collective Interactions ◽  
Ionization Velocity

Collective interactions of the solar wind and newly ionized interstellar gas cause turbulent electron heating to ionizing energies analogous to laboratory experiments on the critical ionization velocity effect. Implications for solar wind and interstellar gas dynamics are calculated by simultaneously solving continuity equations for solar wind protons, interstellar hydrogen atoms, and energetic electrons. Electron impact ionization is shown to be practically as important as photoionization, giving rise to a stronger deceleration and heating of the distant solar wind, a weaker terminating shock, a smaller stand-off distance of the helio pause, and implying higher densities of the outer solar wind and the interstellar neutral gas.

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