scholarly journals Mathematical Modeling of Liquid‐Junction Photovoltaic Cells: I . Governing Equations

1984 ◽  
Vol 131 (11) ◽  
pp. 2569-2574 ◽  
Author(s):  
Mark E. Orazem ◽  
John Newman
Keyword(s):  
Mathematical Modeling ◽  
Photovoltaic Cells ◽  
Governing Equations ◽  
Liquid Junction

Entropy Production as a Predictive Performance Measure: I — Turbomachinery

1999 ◽  
Author(s):  
David M. Paulus ◽  
Richard A. Gaggioli ◽  
William R. Dunbar
Keyword(s):  
Mathematical Modeling ◽  
Energy Conversion ◽  
Entropy Production ◽  
Predictive Performance ◽  
Performance Measure ◽  
Governing Equations ◽  
Compressor Performance

Abstract It is proposed that consideration be given to an alternative, streamlined manner for mathematical modeling of the performance of energy conversion and transfer equipment. We make the case, here, by application to compressors. It is advocated that, instead of using an expression for efficiency as one of the governing equations, performance can be accounted for directly, with entropy production. It is shown that (1) the modeling is more straightforward, using fewer relations, and (2) that compressor performance (e.g. maps) can be represented equally well.

On the Mathematical Modeling of Heat Transfer Characteristics of Turbulent Flames in Industrial Furnaces

2002 ◽  
Author(s):  
Essam E. Khalil
Keyword(s):  
Mathematical Modeling ◽  
Heat Transfer ◽  
Flow Pattern ◽  
Three Dimensional ◽  
Flow Regimes ◽  
Wall Heat Transfer ◽  
Governing Equations ◽  
Heat Transfer Characteristics ◽  
Combustion Chambers ◽  
Transfer Characteristics

The recent advances in numerical methods and the vast development of computers had directed the designers to better development and modifications to air flow pattern and heat transfer in combustion chambers. Extensive efforts are exerted to adequately predict the air velocity and turbulence intensity distributions in the combustor zones and to reduce the emitted pollution and noise abatement to ultimately produce quite and energy efficient combustor systems. The present work fosters mathematical modeling techniques to primarily predict what happens in three-dimensional combustion chambers simulating boiler furnaces, areo engines in terms of flow regimes and interactions. The present work also demonstrates the effect of chamber design and operational parameters on performance, wall heat transfer under various operating parameters. The governing equations of mass, momentum and energy are commonly expressed in a preset form with source terms to represent pressure gradients, turbulence and viscous action. The physical and chemical characteristics of the air and fuel are obtained from tabulated data in the literature. The flow regimes and heat transfer play an important role in the efficiency and utilization of energy. The results are obtained in this work with the aid of the three-dimensional program 3DCOMB; applied to axisymmetrical and three-dimensional complex geometry with and without swirl with liquid or gaseous fuels. The present numerical grid arrangements cover the combustion chamber in the X, R or Y and Z coordinates directions. The numerical residual in the governing equations is typically less than 0.001%. The obtained results include velocity vectors, turbulence intensities and wall heat transfer distributions in combusors. Examples of large industrial furnaces are shown and are in good agreement with available measurements in the open literature. One may conclude that flow patterns, turbulence and heat transfer in combustors are strongly affected by the inlet swirl, inlet momentum ratios, combustor geometry. Both micro and macro mixing levels are influential. The present modeling capabilities can adequately predict the local flow pattern and heat transfer characteristics in Complex combustors. Proper representation of the heat transfer and radiation flux is important in adequate predictions of large furnace performance.

scholarly journals 50 Years of the K-BKZ Constitutive Relation for Polymers

2013 ◽  
Vol 2013 ◽  
pp. 1-22 ◽  
Author(s):  
Evan Mitsoulis
Keyword(s):  
Mathematical Modeling ◽  
Constitutive Model ◽  
Particle Tracking ◽  
Constitutive Equations ◽  
Historical Perspective ◽  
Governing Equations ◽  
Dimensionless Numbers ◽  
Flow Problems ◽  
Polymer Flows ◽  
Method Of Solution

The K-BKZ constitutive model is now 50 years old. The paper reviews the connections of the model and its variants with continuum mechanics and experiment, presenting an up-to-date recap of research and major findings in the open literature. In the Introduction a historical perspective is given on developments in the last 50 years of the K-BKZ model. Then a section follows on mathematical modeling of polymer flows, including governing equations of flow, rheological constitutive equations (with emphasis on viscoelastic integral constitutive equations of the K-BKZ type), dimensionless numbers, and boundary conditions. The Method of Solution section reviews the major developments of techniques necessary for particle tracking and calculation of the integrals for the viscoelastic stresses in flow problems. Finally, selected examples are given of successful application of the K-BKZ model in polymer flows relevant to rheology.

scholarly journals Modelling of Permeation Grouting Through Soils

2020 ◽  
Vol 10 (1) ◽  
pp. 11-16
Author(s):  
S. B. Coskun ◽  
T. Tokdemir
Keyword(s):  
Mathematical Modeling ◽  
Numerical Simulation ◽  
Finite Element ◽  
Porous Medium ◽  
Capillary Pressure ◽  
Immiscible Fluids ◽  
Saturated Soils ◽  
Governing Equations ◽  
Permeation Grouting ◽  
Element Technique

AbstractIn this study, mathematical modeling of permeation grouting through fully saturated soil is proposed based on immiscible multiphase flow theory. Grout flow in the medium is modeled together with the existing water as the simultaneous flow of two immiscible fluids. In the model, the porous medium is assumed as isotropic and rigid, fluids are assumed as incompressible and capillary pressure is assumed as negligible. Governing equations are discretized using upstream weighted finite element technique and results show that, proposed models give good results and may be used in the numerical simulation of grouting through fully saturated soils.

scholarly journals Mathematical Modeling of Heavy Metal Percolation in Lube-Oil Contaminated Soil: A Case Study of Epe Automobile Mechanic Village

2020 ◽  
Vol 5 (2) ◽  
pp. 1-8
Author(s):  
O. Duduyemi ◽  
◽  
A.A. Moronkola ◽  
K.A. Adedeji
Keyword(s):  
Mathematical Modeling ◽  
Heavy Metals ◽  
Mathematical Model ◽  
Numerical Technique ◽  
Soil Surface ◽  
Governing Equations ◽  
Soil Columns ◽  
Transport And Transformation ◽  
Indiscriminate Disposal

Indiscriminate disposal of automobile lube-oil especially around mechanic workshops was evident by the inability of plants to grow in some batches of the operation environment. The relevance of certain heavy metals and their bio-toxic effect on man and the mechanisms of their biochemical activities were investigated. A mathematical model for the transport and transformation of solute contaminant through two cases of soil columns characteristics of clay and sandy from surface to the ground water was developed and the governing equations solved numerically by orthogonal numerical technique and simulated with computer algorithm. The result shows that at a depth of 20meter from the soil surface, the concentration decreases from about 0.075 kg/m3, while it decreased to about 0.01kg/m3. At a depth of about 90 meters from the surface, the concentration of lead remained the same at about 0.01 kg/m3. The major finding in the present study indicates that as time increases, the concentration of the lead increases. Also the higher the porosity of the soil the higher the concentration with time and as the depth increases, the concentration decreases. The analysis can help predict when the water table may become contaminated with leached heavy metals

The Application of Iteration and Functional Analysis in Numerical Calculation of Beams with Large Deformation

2011 ◽  
Vol 243-249 ◽  
pp. 6144-6149
Author(s):  
Jing Yan ◽  
Ya Wu Zeng ◽  
Rui Gao
Keyword(s):  
Mathematical Modeling ◽  
Functional Analysis ◽  
Bending Moment ◽  
Steady State Solution ◽  
Vertical Displacement ◽  
Axial Deformation ◽  
Governing Equations ◽  
Deflection Curve ◽  
Initial Value ◽  
Small Deflection

For the research of beam’s deformation, material mechanics uses equation of small deflection curve which neglects 1storder derivative of deflection and regards bending moment M is merely a function of abscissa x, and then gets the approximate solution of vertical displacement. However in some case, small deflection curve isn’t efficacious, so two methods come up in this paper to solve the accurate differential equation of beam’s deformation. This paper takes a slightness beam from temperature controlling device as an example and shows detailed process of mathematical modeling and solving. For iteration, firstly governing equations are founded, then an initial value is put into it to work out a new value, next see the new value as a new initial value and calculate again, by doing the operation repeatedly steady-state solution will be got in the end. For functional analysis, deflection equation is assumed as a kind of function containing some undetermined coefficients, then make it satisfy all the boundary conditions, and establish residual fonctionelle, by partial derivative operation to make the fonctionelle minimum, undetermined coefficients are estimated and deflection curve is got. At the end, impacts of gravity and axial deformation are discussed.

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