A Two Dimensional Mathematical Model of Heat Propagation Equation and its Applications

2020 ◽  
Vol 31 (3) ◽  
pp. 338-354
Author(s):  
Nassima Talbi ◽  
Anis Ben Dhahbi ◽  
Salah Boulaaras ◽  
Hadj Baltache ◽  
Mohammad Alnegga
Keyword(s):  
Mathematical Model ◽  
Heat Propagation ◽  
Two Dimensional ◽  
Propagation Equation

scholarly journals A Two-Dimensional Mathematical Model of Heat Propagation Equations and Their Significance for Soil Temperature

Symmetry ◽  
2019 ◽  
Vol 11 (4) ◽  
pp. 478 ◽  
Author(s):  
Anis Dhahbi ◽  
Salah Boulaaras ◽  
Taha Radwan ◽  
Nadia Mezouar ◽  
Khaled Zennir ◽  
...  
Keyword(s):  
Mathematical Model ◽  
Soil Temperature ◽  
Heat Propagation ◽  
Two Dimensional ◽  
Mathematical Problems ◽  
Different Depths ◽  
Spatial Method ◽  
The Stability ◽  
Academic Year ◽  
Real Experimental Data

In the context of the development of the research project (Boulaaras et al.) which was supported by the Deanship of Scientific Research of Qassim University under the Project No. 1140 during the academic year 2016/1437, this research will introduce a two dimensional mathematical model based on the finite elements spatial method combined with a finite differences time scheme applied to the diffusion equations. This model will be applied in the hypothetical example where the obtained results will be compared with the real experimental data. Such a comparison will allow to predict the soil temperature for different depths and at different time periods according to certain conditions on the weather and take into account the stability conditions of the used numerical method. It’s worthy of note that some of the concreted mathematical problems will be addressed by the experimental scientific theories of functional analysis and then the numerical simulation of the theoretical study will be provided thanks to sophisticated methods with more convergence and stability. This mathematical model would be reduced by means of physical measurement and also in charge of the physical cost.

Two Dimensional Unsteady State Mathematical Model for dispersion of Chlorine in Water in a Channel

2011 ◽  
Vol 3 (8) ◽  
pp. 503-505
Author(s):  
Jaipal Jaipal ◽  
◽  
Rakesh Chandra Bhadula ◽  
V. N Kala V. N Kala
Keyword(s):  
Mathematical Model ◽  
Two Dimensional ◽  
Unsteady State

Study on Grinding Force in Two-Dimensional Ultrasonic Grinding Nano-Ceramics

2010 ◽  
Vol 42 ◽  
pp. 204-208 ◽  
Author(s):  
Xiang Dong Li ◽  
Quan Cai Wang
Keyword(s):  
Mathematical Model ◽  
Ultrasonic Vibration ◽  
Contact Time ◽  
Reaction Force ◽  
Grinding Force ◽  
Two Dimensional ◽  
Indentation Fracture ◽  
Ultrasonic Grinding ◽  
The Impact ◽  
Ultrasonic Vibration Assisted Grinding

In this paper, the characteristic of grinding force in two-dimensional ultrasonic vibration assisted grinding nano-ceramic was studied by experiment based on indentation fracture mechanics, and mathematical model of grinding force was established. The study shows that grinding force mainly result from the impact of the grains on the workpiece in ultrasonic grinding, and the pulse power is much larger than normal grinding force. The ultrasonic vibration frequency is so high and the contact time of grains with the workpiece is so short that the pulse force will be balanced by reaction force from workpiece. In grinding workpiece was loaded by the periodical stress field, which accelerates the fatigue fracture.

Two-dimensional discrete mathematical model of tumor-induced angiogenesis

2009 ◽  
Vol 30 (4) ◽  
pp. 455-462
Author(s):  
Gai-ping Zhao ◽  
Er-yun Chen ◽  
Jie Wu ◽  
Shi-xiong Xu ◽  
M. W. Collins ◽  
...  
Keyword(s):  
Mathematical Model ◽  
Two Dimensional ◽  
Discrete Mathematical Model

A Numerical Study of Unsteady Natural Convection in a Rectangular Enclosure: The Effect of Compressibility

2004 ◽  
Author(s):  
K. M. Akyuzlu ◽  
Y. Pavri ◽  
A. Antoniou
Keyword(s):  
Mathematical Model ◽  
Stokes Equations ◽  
Numerical Study ◽  
Vertical Wall ◽  
Ideal Gas ◽  
Working Fluid ◽  
Two Dimensional ◽  
Algebraic Equations ◽  
Rectangular Enclosure ◽  
Circulation Patterns

A two-dimensional, mathematical model is adopted to investigate the development of buoyancy driven circulation patterns and temperature contours inside a rectangular enclosure filled with a compressible fluid (Pr=1.0). One of the vertical walls of the enclosure is kept at a higher temperature then the opposing vertical wall. The top and the bottom of the enclosure are assumed insulated. The physics based mathematical model for this problem consists of conservation of mass, momentum (two-dimensional Navier-Stokes equations) and energy equations for the enclosed fluid subjected to appropriate boundary conditions. The working fluid is assumed to be compressible through a simple ideal gas relation. The governing equations are discretized using second order accurate central differencing for spatial derivatives and first order forward finite differencing for time derivatives where the computation domain is represented by a uniform orthogonal mesh. The resulting nonlinear equations are then linearized using Newton’s linearization method. The set of algebraic equations that result from this process are then put into a matrix form and solved using a Coupled Modified Strongly Implicit Procedure (CMSIP) for the unknowns (primitive variables) of the problem. A numerical experiment is carried out for a benchmark case (driven cavity flow) to verify the accuracy of the proposed solution procedure. Numerical experiments are then carried out using the proposed compressible flow model to simulate the development of the buoyancy driven circulation patterns for Rayleigh numbers between 103 and 105. Finally, an attempt is made to determine the effect of compressibility of the working fluid by comparing the results of the proposed model to that of models that use incompressible flow assumptions together with Boussinesq approximation.

Analysis and modeling of an inverted pendulum system

2021 ◽  
Author(s):  
Keyword(s):  
Mathematical Model ◽  
Nonlinear System ◽  
Inverted Pendulum ◽  
System Analysis ◽  
Dimensional System ◽  
Two Dimensional ◽  
System Operation ◽  
Pendulum System ◽  
Inverted Pendulum System ◽  
Two Dimensional System

A nonlinear system, which consists of an inverted pendulum mounted on a cart with an electric drive, is considered. A mathematical model is created, its analysis and modeling of the investigated two-dimensional system operation is carried out. Keywords mathematical model; inverted pendulum; system analysis; state space

MATHEMATICAL MODEL OF TWO-DIMENSIONAL LAYERED PRESSURE FLOW IN THE AUGER CHANNEL

2018 ◽  
Author(s):  
А.В. ГУКАСЯН ◽  
В.С. КОСАЧЕВ ◽  
Е.П. КОШЕВОЙ
Keyword(s):  
Mathematical Model ◽  
Analytical Solution ◽  
Cross Section ◽  
Dynamic Pressure ◽  
Two Dimensional ◽  
Flow Dynamic ◽  
Pressure Flow ◽  
Rectangular Channels ◽  
Wide Range ◽  
Pressure Characteristics

Получено аналитическое решение двумерного слоистого напорного течения в канале шнека, позволяющее моделировать расходно-напорные характеристики прямоугольных каналов шнековых прессов с учетом гидравлического сопротивления формующих устройств и рассчитывать расходно-напорные характеристики экструдеров в широком диапазоне геометрии витков как в поперечном сечении, так и по длине канала. Obtained the analytical solution of two-dimensional layered pressure flow in the screw channel, allow to simulate the flow-dynamic pressure characteristics of rectangular channels screw presses taking into account the hydraulic resistance of the forming device and calculate the mass flow-dynamic pressure characteristics of the extruders in a wide range of the geometry of the coils, as in its cross section and along the length of the channel.

Dynamic Stability of Hovercraft in Heave

1970 ◽  
Vol 37 (4) ◽  
pp. 895-900 ◽  
Author(s):  
H. J. Davies ◽  
G. A. Poland
Keyword(s):  
Mathematical Model ◽  
Dynamic Behavior ◽  
Dynamic Stability ◽  
Equilibrium Position ◽  
Forced Oscillation ◽  
Dynamic Equilibrium ◽  
Forced Oscillations ◽  
Two Dimensional ◽  
Oscillation Characteristics ◽  
Nonlinear Nature

The regimes of flow governing the dynamic behavior of a two-dimensional mathematical model of an edge-jet Hovercraft in heaving motion are described and the equations associated with such regimes derived. Both the free and forced-oscillation characteristics are studied. The nonlinear nature of the system manifests itself, in the case of the forced oscillations, as a shift in the dynamic equilibrium position resulting in a loss of mean hoverheight.

Numerical Simulation of Subsea Cluster Manifold Installation by the Sheave Method

2018 ◽  
Author(s):  
Yu Zhao ◽  
Yingying Wang ◽  
Liwei Li ◽  
Chao Yang ◽  
Yang Du ◽  
...  
Keyword(s):  
Numerical Simulation ◽  
Mathematical Model ◽  
South China Sea ◽  
Deep Sea ◽  
High Reliability ◽  
Two Dimensional ◽  
Complex Environment ◽  
Lumped Mass ◽  
Lumped Mass Method ◽  
The Mathematical Model

The sheave installation method (SIM) is an effective and non-conventional method to solve the installation of subsea equipment in deep water (>1000m), which has been developed to deploy the 175t Roncador Manifold I into 1,885 meters water depth in 2002. With the weight increment of subsea cluster manifold, how to solve its installation with the high reliability in the deep sea is still a great challenge. In this paper, the installation of the 300t subsea cluster manifold using the SIM is studied in the two-dimensional coordinate system. The mathematical model is established and the lumped mass method is used to calculate the hydrodynamic forces of the wireropes. Taking into account the complex environment loads, the numerical simulation of the lowering process is carried out by OrcaFlex. The displacement and vibration of the subsea cluster manifold in the z-axis direction and the effective tension at the top of the wireropes can be gotten, which can provide guidance for the installation of the cluster manifold in the South China Sea.

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