The heating of a stream of particles by thermal counter radiation

2021 ◽  
Vol 30 (2) ◽  
pp. 15-22
Author(s):  
N. L. Poletaev
Keyword(s):  
Heat Capacity ◽  
Temperature Distribution ◽  
Numerical Solutions ◽  
Combustion Products ◽  
Monodisperse Particles ◽  
Problem Model ◽  
One Dimensional ◽  
Simplifying Assumptions ◽  
Black Surface ◽  
Analytical Assessment

Introduction. It is accepted that the depth of heating of the dust/gas/air mixture by the radiation of combustion products SR is equal to the length LR of the free path of radiation in the mixture. Numerical simulation of combustion of a gas-air mixture that has inert particles, taking into account the re-radiation of heat by heated particles of the fresh mixture, led to ratio SR >> LR. In this work, the analytical assessment of ratio χS = SR/LR is performed.One-dimensional problem model. The co-authors determined stationary temperature distribution over the flow of initially cold monodisperse particles suspended in vacuum. Particle velocity V is directed toward a heat-radiating, absolutely black surface that is permeable by particles. Simplifying assumptions are used: radiation consists of two oppositely-directed flows of electromagnetic energy; interaction between particles and radiation is described in the approximation of geometric optics; the temperature inside the particle is the same. Problem solving. It is shown that χS is determined by V=Vcp / (εT 0,5, σTb)3 , where cp, εT, σ, Tb are, respectively, heat capacity per unit volume of the suspended matter, integral emissivity of the particle material, the Stefan-Boltzmann constant, and the surface temperature. For ≤ 2.8, re-emission can be neglected: χS ≈ 1. At ≤ 1.2, temperature distribution regulates re-emission: χS ≈ 5 –1/(2 – εT) >> 1.Solution discussion. The analytical solution satisfactorily describes the available numerical solutions and experimental data for the case of combustion of a dust/gas/air mixture after specifying the parameters of a simplified model: the radiating surface should be understood as the flame front, Tb is the combustion temperature, and cp is the overall heat capacity of the mixture. The estimate ≤ 1.2 indicates the final high temperature of the gas suspension, the possibility of its autoignition far from the flame, and the need to change initial assumptions when simulating re-emission.Conclusions. Analytical evaluations make it possible to employ ratios SR >> LR and SR ≈ LR for the suspension over a thermal radiation source in vacuum. Conditions for the application of the results of simplified simulation of re-emission to the combustion of a dust/gas/air mixture are formulated.

Numerical Solutions of Transients in Pneumatic Networks—Transmission-Line Calculations

1968 ◽  
Vol 35 (3) ◽  
pp. 588-595 ◽  
Author(s):  
S. Tsao
Keyword(s):  
Wave Propagation ◽  
Transmission Lines ◽  
Numerical Solutions ◽  
Navier Stokes ◽  
Damping Factor ◽  
Temperature Profiles ◽  
Hypothetical Case ◽  
One Dimensional ◽  
Simplifying Assumptions ◽  
Energy Equations

Equations governing the damped wave propagation along transmission lines are obtained from the Navier-Stokes and energy equations by making certain simplifying assumptions. The flow considered is essentially one-dimensional. However, radial variations of the velocity and temperature profiles must be considered, because the damping factor is directly dependent on them. The equations are integrated by numerical methods. A hypothetical case is computed as an example.

One-dimensional laminar flame propagation with an enthalpy gradient

1961 ◽  
Vol 261 (1304) ◽  
pp. 53-78 ◽  
Keyword(s):  
Numerical Solutions ◽  
Laminar Flame ◽  
Plug Flow ◽  
Combustion Products ◽  
Radiative Heat Loss ◽  
Decomposition Products ◽  
One Dimensional ◽  
Combustible Gas ◽  
Gradient Parameter ◽  
Negative Gradient

Exact numerical solutions of the flame equations are presented for a class of one-dimensional pre-mixed steady flames propagating in the presence of an enthalpy gradient. It is shown that a positive enthalpy gradient increases the flame speed whereas a negative gradient decreases it to zero, the latter result occurring at a finite value of the dimensionless enthalpy-gradient parameter. The physical significance of the results is discussed quantitatively for the following cases: Flow of a combustible gas in to a hot plug : flow of a combustible gas in to a cold plug; the ‘sandwich burner’ (flame between two cooled plugs); radiative heat loss from the combustion products; burning of a condensed-phase propellant in an atmosphere with which the decomposition products can react chemically. It is shown that some of these conditions lead to the existence of two possible burning velocities, and to conditions under which the flame will be extinguished.

scholarly journals Tornado-type stationary vortex with nonlinear term due to moisture transport

2010 ◽  
Vol 4 (1) ◽  
pp. 77-82 ◽  
Author(s):  
P. B. Rutkevich ◽  
P. P. Rutkevych
Keyword(s):  
Tropical Cyclones ◽  
Shooting Method ◽  
Nonlinear Term ◽  
Numerical Solutions ◽  
Variable Temperature ◽  
Slow Rotation ◽  
Nonlinear Phenomenon ◽  
One Dimensional ◽  
Stationary Vortex ◽  
General Possibility

Abstract. Tornado vortex is believed to be essentially nonlinear phenomenon; and the puzzle to choose the nonlinear term(s) responsible for its formation is still unresolved. In the present work we consider the nonlinear term associated with atmosphere humidity, by introducing variable temperature gradient depending on the vertical velocity of the fluid. Such term is able to yield energy to the system and is very suitable for such a problem. Other nonlinear terms are neglected, assuming slow rotation, or in other words a "weak" tornado approximation. We consider one-dimensional radial boundary problem, and use a modificaiton of shooting method to satisfy boundary conditions at large radii. Obtained numerical solutions of the nonlinear differential equation qualitatively agree with the observed atmosphere vortices (tornados, tropical cyclones). The obtained results show general possibility of existence of unstable motion even in convectively stable atmosphere stratification.

Analysis of Heat, Mass, and Momentum Transfer in the Rain Zone of Counterflow Cooling Towers

1999 ◽  
Vol 121 (4) ◽  
pp. 751-755 ◽  
Author(s):  
E. de Villiers ◽  
D. G. Kro¨ger
Keyword(s):  
Momentum Transfer ◽  
Cooling Tower ◽  
Mechanical Energy ◽  
Performance Evaluations ◽  
Cooling Towers ◽  
Droplet Deformation ◽  
One Dimensional ◽  
Mechanical Energy Loss ◽  
Simplifying Assumptions ◽  
Semi Empirical

The rate of heat, mass, and momentum transfer in the rain zone of three counterflow cooling tower geometries is analyzed using simplifying assumptions and numerical integration. The objective of the analysis is to generate equations for use in a one-dimensional mathematical cooling tower performance evaluations. Droplet deformation is taken into account and momentum transfer is calculated from the air flow’s mechanical energy loss, caused by air-droplet interaction. A comparison of dimensionless semi-empirical equations and experimental data demonstrates the method’s capability to predict the pressure drop in a counterflow rain zone.

Diffusion-Limited Cell Dehydration: Analytical and Numerical Solutions for a Planar Model

1999 ◽  
Author(s):  
Alexander V. Kasharin ◽  
Jens O. M. Karlsson
Keyword(s):  
Analytical Solution ◽  
Numerical Solutions ◽  
Planar System ◽  
One Dimensional ◽  
Diffusion Limited ◽  
Dimensional Diffusion ◽  
Constant Diffusivity ◽  
A Cell ◽  
Cell Dehydration ◽  
The One

Abstract The process of diffusion-limited cell dehydration is modeled for a planar system by writing the one-dimensional diffusion-equation for a cell with moving, semipermeable boundaries. For the simplifying case of isothermal dehydration with constant diffusivity, an approximate analytical solution is obtained by linearizing the governing partial differential equations. The general problem must be solved numerically. The Forward Time Center Space (FTCS) and Crank-Nicholson differencing schemes are implemented, and evaluated by comparison with the analytical solution. Putative stability criteria for the two algorithms are proposed based on numerical experiments, and the Crank-Nicholson method is shown to be accurate for a mesh with as few as six nodes.

Magnetic properties of manganese based one-dimensional spin chains

2015 ◽  
Vol 44 (46) ◽  
pp. 19812-19819 ◽  
Author(s):  
K. S. Asha ◽  
K. M. Ranjith ◽  
Arvind Yogi ◽  
R. Nath ◽  
Sukhendu Mandal
Keyword(s):  
Heat Capacity ◽  
Magnetic Properties ◽  
Magnetic Susceptibility ◽  
Spin Chains ◽  
One Dimensional

Magnetic susceptibility and heat capacity of three manganese based structures are measured and modeled with one-dimensional antiferromagnetic chains.

scholarly journals Dissociation and recombination in the electrolyte flow model

2021 ◽  
Vol 2090 (1) ◽  
pp. 012076
Author(s):  
A Shobukhov ◽  
H Koibuchi
Keyword(s):  
Flow Model ◽  
Numerical Solutions ◽  
Stable Equilibrium ◽  
Steady State Solution ◽  
System Of Equations ◽  
Constant Flow ◽  
Dimensional Model ◽  
Electrolyte Flow ◽  
One Dimensional ◽  
Dilute Aqueous Solution

Abstract We propose a one-dimensional model for the dilute aqueous solution of NaCl which is treated as an incompressible fluid placed in the external electric field. This model is based on the Poisson-Nernst-Planck system of equations, which also contains the constant flow velocity as a parameter and considers the dissociation and the recombination of ions. We study the steady-state solution analytically and prove that it is a stable equilibrium. Analyzing the numerical solutions, we demonstrate the importance of dissociation and recombination for the physical meaningfulness of the model.

scholarly journals Data visualization and distinct features extraction of the comet Ison 2013

2019 ◽  
Vol 12 (24) ◽  
pp. 122-128
Author(s):  
Salman. Z. Khalaf
Keyword(s):  
Temperature Distribution ◽  
Data Visualization ◽  
Features Extraction ◽  
Maximum Intensity ◽  
Distribution Fitting ◽  
One Dimensional ◽  
Mathematical Equations ◽  
Distinct Features

The distribution of the intensity of the comet Ison C/2013 is studied by taking its histogram. This distribution reveals four distinct regions that related to the background, tail, coma and nucleus. One dimensional temperature distribution fitting is achieved by using two mathematical equations that related to the coordinate of the center of the comet. The quiver plot of the gradient of the comet shows very clearly that arrows headed towards the maximum intensity of the comet.

One-dimensional consolidation of multilayered aquifer systems with viscoelastic properties induced by time-dependent groundwater drawdown

2021 ◽  
pp. qjegh2021-073
Author(s):  
Weitao Yang ◽  
Jin Xu
Keyword(s):  
Viscoelastic Properties ◽  
Numerical Solutions ◽  
Pore Water Pressure ◽  
Water Pressure ◽  
Time Dependent ◽  
Analytical Models ◽  
Consolidation Process ◽  
One Dimensional ◽  
Groundwater Drawdown ◽  
Aquifer Systems

Most analytical and semi-analytical models for pumping-induced land subsidence invoke the simplifying assumptions regarding characteristics of geomaterials, as well as the pattern of drawdown response to pumping. This paper presents an analytical solution for one-dimensional consolidation of the multilayered soil due to groundwater drawdown, in which viscoelastic property and time-dependent drawdown are taken into account. The presented solution is developed by using the boundary transformation techniques. The validity of the proposed solution is verified by comparing with a degenerated case for a single layer, as well as with the numerical solutions and experimental results for a two-layer system. The difference between the average consolidation degree Up defined by hydraulic head and that Us defined by total settlement is discussed. The detailed parametric studies are conducted to reveal the effects of viscoelastic properties and drawdown patterns on the consolidation process. It is revealed that while the effect of different drawdown response patterns is significant during the early-intermediate stages of consolidation, the viscoelastic properties may have a more dominant influence on long-term consolidation behavior, depending on the values of the material parameters, which are reflected in both the deformation process of soil layers and the dissipation of excess pore-water pressure.

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