Numerical Simulation of Spray Cooling Pond Performance

1987 ◽  
Vol 109 (2) ◽  
pp. 179-185 ◽  
Author(s):  
N. Moussiopoulos
Keyword(s):  
Mathematical Model ◽  
Differential Equations ◽  
Present Model ◽  
Field Measurements ◽  
Equation System ◽  
Spray Cooling ◽  
Cooling Pond ◽  
Dependent Variables ◽  
Model Temperature ◽  
Good Agreement

A mathematical model for predictions of the performance of spray cooling ponds is presented. In contrast to previous methods, the present model requires neither empirical information from field measurements nor an adaptation of model constants. The airflow is described by partial differential equations for the vorticity and the stream function. Turbulence is taken into account by a modified version of the k-ε model. Temperature and humidity of air are obtained by solving appropriate transport differential equations. The equation system is solved by means of a finite difference method. The utilized numerical algorithm has been proved to be reasonably accurate. Predicted distributions for the dependent variables are presented for a circular spray cooling pond and the case of zero wind velocity. Results for the thermal performance of this pond are in good agreement with observations.

Nonlinear Dynamics of the Bombardier Beetle

1999 ◽  
Author(s):  
Richard H. Rand ◽  
Erika T. Wirkus ◽  
J. Robert Cooke
Keyword(s):  
Nonlinear Dynamics ◽  
Mathematical Model ◽  
Differential Equations ◽  
Equilibrium Point ◽  
Defense Mechanism ◽  
Fluid Pressure ◽  
Pulsed Jet ◽  
Dependent Variables

Abstract This work investigates the dynamics by which the bombardier beetle releases a pulsed jet of fluid as a defense mechanism. A mathematical model is proposed which takes the form of a pair of piece wise continuous differential equations with dependent variables as fluid pressure and quantity of reactant. The model is shown to exhibit an effective equilibrium point (EEP). Conditions for the existence, classification and stability of an EEP are derived and these are applied to the model of the bombardier beetle.

scholarly journals A Simple Mathematical Model of Cyclic Circadian Learning

2014 ◽  
Vol 2014 ◽  
pp. 1-9
Author(s):  
J. Šimon ◽  
M. Bulko
Keyword(s):  
Mathematical Model ◽  
Differential Equations ◽  
Learning Process ◽  
Memory Retention ◽  
Simple Mathematical Model ◽  
Prior Learning ◽  
Mnemonic Devices ◽  
Concurrent Processes ◽  
Mathematical Operations ◽  
Good Agreement

This paper deals with the derivation of a simple mathematical model of cyclic learning with a period of 24 hours. Various requirements are met with an emphasis and approach which relies on simple mathematical operations, the prediction of measurable quantities, and the creation of uncomplicated processes of calibration. The presented model can be used to answer questions such as the following.Will I be able to memorize a given set of information? How long will it take to memorize information? How long will I remember the information that was memorized?The model is based on known memory retention functions that are in good agreement with experimental results. By the use of these functions and by formalism of differential equations, the concurrent processes of learning and forgetting are described mathematically. The usability of this model is limited to scenarios where logical bonds (connections to prior learning) are not created and mnemonic devices cannot be utilized during the learning process.

scholarly journals Mathematical Model of VOCs Emission in Three-layer Building Materials

2021 ◽  
Vol 257 ◽  
pp. 03047
Author(s):  
Zhehua Du ◽  
Xin Lin
Keyword(s):  
Experimental Data ◽  
Boundary Layer ◽  
Mathematical Model ◽  
Building Materials ◽  
Present Model ◽  
Transfer Resistance ◽  
Model Predictions ◽  
Layer Resistance ◽  
Boundary Layer Resistance ◽  
Good Agreement

A simple mathematical model is proposed to account for emissions of Volatile Organic Compounds (VOCs) from three-layer building materials. The model considers both the diffusion within three layer building materials and the mass transfer resistance through the air boundary layer. A general solution method based on Laplace transform is presented. Compared to other models capable of accounting for emissions of VOCs from multi layer building materials, the present model is fully analytical instead of being numerical. The present model was validated by the experimental data from the specially designed test. The results indicated that there was a good agreement between the model predictions and the experimental data. It can also be seen from calculation that model ignoring the boundary layer resistance cannot fully reflect the real situation.

Numerical Analysis and Control of Gas Carburizing under Changes in Gas Compositions

2006 ◽  
Vol 522-523 ◽  
pp. 589-594 ◽  
Author(s):  
Yujiro Yokoyama ◽  
Tomoyuji Mizukoshi ◽  
Itsuo Ishigami ◽  
Tateo Usui
Keyword(s):  
Mathematical Model ◽  
Carbon Steel ◽  
Carbon Content ◽  
Present Model ◽  
Low Carbon Steel ◽  
Carbon Potential ◽  
Low Carbon ◽  
Gas Carburizing ◽  
And Control ◽  
Good Agreement

Low carbon steel, S15CK, was carburized at 1203K up to 12.93ks in a commercial furnace where RX gas converted from propane was employed as carrier gas. Gas compositions in the furnace were changed intentionally; consequently carbon potential changed from 0.8 to 1.2 mass%. The carbon content profiles were determined by a succession of grindings and carbon analyses of the ground surfaces with a vacuum type emission spectrometer. A mathematical model for calculation of carbon content profiles is proposed to describe carburizing behavior under time-variant gas compositions in a furnace. The calculated profiles were in good agreement with the experimental ones except the surface and its vicinity. This result indicates that the present model can be applied to gas carburizing in the furnace where gas compositions were changed.

Thermal Performance of Spray Cooling Ponds at Zero Wind Velocity

1987 ◽  
Vol 109 (1) ◽  
pp. 212-217
Author(s):  
N. Moussiopoulos ◽  
G. Ernst
Keyword(s):  
Water Vapor ◽  
Numerical Solution ◽  
Wind Velocity ◽  
Air Temperature ◽  
Thermal Performance ◽  
Present Model ◽  
Spray Cooling ◽  
Vapor Transfer ◽  
Water Vapor Transfer ◽  
Good Agreement

The present model allows predictions of the thermal performance of spray cooling ponds in the case of zero wind velocity. Droplet cooling is described by modeling of the heat and water vapor transfer to the air. Temperature and humidity of air are obtained by the numerical solution of transport differential equations. Detailed results are presented and discussed. Predictions are in good agreement with the observed thermal performance of spray cooling ponds. Results are utilized for a check of assumptions made by NTU models.

Theoretical and experimental research on slip and uplift of the timber-concrete composite beam

BioResources ◽  
2020 ◽  
Vol 15 (3) ◽  
pp. 7079-7099
Author(s):  
Jianying Chen ◽  
Guojing He ◽  
Xiaodong (Alice) Wang ◽  
Jiejun Wang ◽  
Jin Yi ◽  
...  
Keyword(s):  
Differential Equations ◽  
Deformation Theory ◽  
Concrete Slab ◽  
Theoretical Calculations ◽  
Structural Element ◽  
Structural Efficiency ◽  
Theoretical Investigations ◽  
New Type ◽  
Interlayer Slip ◽  
Good Agreement

Timber-concrete composite beams are a new type of structural element that is environmentally friendly. The structural efficiency of this kind of beam highly depends on the stiffness of the interlayer connection. The structural efficiency of the composite was evaluated by experimental and theoretical investigations performed on the relative horizontal slip and vertical uplift along the interlayer between composite’s timber and concrete slab. Differential equations were established based on a theoretical analysis of combination effects of interlayer slip and vertical uplift, by using deformation theory of elastics. Subsequently, the differential equations were solved and the magnitude of uplift force at the interlayer was obtained. It was concluded that the theoretical calculations were in good agreement with the results of experimentation.

Glycemia monitoring

1998 ◽  
Vol 2 ◽  
pp. 23-30
Author(s):  
Igor Basov ◽  
Donatas Švitra
Keyword(s):  
Diabetes Mellitus ◽  
Mathematical Model ◽  
Numerical Methods ◽  
Differential Equations ◽  
Blood Sugar ◽  
Self Regulation ◽  
Physiological System ◽  
Non Linear ◽  
The Mathematical Model

Here a system of two non-linear difference-differential equations, which is mathematical model of self-regulation of the sugar level in blood, is investigated. The analysis carried out by qualitative and numerical methods allows us to conclude that the mathematical model explains the functioning of the physiological system "insulin-blood sugar" in both normal and pathological cases, i.e. diabetes mellitus and hyperinsulinism.

The mathematical modelling of corrosion in hot dip galvanized steel reinforced concrete

2011 ◽  
Vol 2 (1) ◽  
pp. 1-12
Author(s):  
A. Hegyi ◽  
H. Vermeşan ◽  
V. Rus
Keyword(s):  
Mathematical Model ◽  
Reinforced Concrete ◽  
Numerical Model ◽  
Equation System ◽  
Galvanized Steel ◽  
Steel Reinforced Concrete ◽  
Numeric Model ◽  
Physical And Mathematical Models ◽  
Physical Phenomena ◽  
The Mathematical Model

Abstract In this paper we wish to present the numerical model elaborated in order to simulate some physical phenomena that influence the general deterioration of steel, whether hot dip galvanized or not, in reinforced concrete. We describe the physical and mathematical models, establishing the corresponding equation system, the initial and boundary conditions. We have also presented the numeric model associated to the mathematical model and the numeric methods of discretization and solution of the differential equations system that describes the mathematical model.

A Compact Model for Spherical Rough Contacts

2004 ◽  
Author(s):  
M. Bahrami ◽  
M. M. Yovanovich ◽  
J. R. Culham
Keyword(s):  
Pressure Distribution ◽  
Entire Range ◽  
Present Model ◽  
Numerical Solutions ◽  
Contact Radius ◽  
Bulk Deformation ◽  
Dimensional Parameters ◽  
Maximum Contact ◽  
Good Agreement ◽  
Key Parameter

The contact of rough spheres is of high interest in many tribological, thermal, and electrical fundamental analyses. Implementing the existing models is complex and requires iterative numerical solutions. In this paper a new model is presented and a general pressure distribution is proposed that encompasses the entire range of spherical rough contacts including the Hertzian limit. It is shown that the non-dimensional maximum contact pressure is the key parameter that controls the solution. Compact expressions are proposed for calculating the pressure distribution, radius of the contact area, elastic bulk deformation, and the compliance as functions of the governing non-dimensional parameters. The present model shows the same trends as those of the Greenwood and Tripp model. Correlations proposed for the contact radius and the compliance are compared with experimental data collected by others and good agreement is observed.

scholarly journals Ultrasonic Waves in Bubbly Liquids: An Analytic Approach

Mathematics ◽  
2021 ◽  
Vol 9 (11) ◽  
pp. 1309
Author(s):  
P. R. Gordoa ◽  
A. Pickering
Keyword(s):  
Mathematical Model ◽  
Partial Differential Equations ◽  
Differential Equations ◽  
Acoustic Waves ◽  
Elliptic Functions ◽  
Coupled System ◽  
Ultrasonic Waves ◽  
Partial Differential ◽  
Special Cases ◽  
Spherical Bubbles

We consider the problem of the propagation of high-intensity acoustic waves in a bubble layer consisting of spherical bubbles of identical size with a uniform distribution. The mathematical model is a coupled system of partial differential equations for the acoustic pressure and the instantaneous radius of the bubbles consisting of the wave equation coupled with the Rayleigh–Plesset equation. We perform an analytic analysis based on the study of Lie symmetries for this system of equations, concentrating our attention on the traveling wave case. We then consider mappings of the resulting reductions onto equations defining elliptic functions, and special cases thereof, for example, solvable in terms of hyperbolic functions. In this way, we construct exact solutions of the system of partial differential equations under consideration. We believe this to be the first analytic study of this particular mathematical model.

Sign in / Sign up

Export Citation Format

Share Document