Theoretical Model of Crater Wear

1971 ◽  
Vol 93 (4) ◽  
pp. 1051-1056 ◽  
Author(s):  
Yong-Son Lee
Keyword(s):  
Diffusion Coefficient ◽  
Theoretical Model ◽  
Temperature Distribution ◽  
Boundary Conditions ◽  
Second Law ◽  
Crater Wear ◽  
One Dimensional ◽  
Step Functions ◽  
Contact Surfaces ◽  
Infinite Media

A one dimensional mass diffusion equation including the first derivatives with respect to the coordinates in Fick’s second law is considered. The diffusion coefficient is also considered, as a function of temperature distribution in a semi-infinite media under certain boundary conditions. Since the boundary conditions for both temperature and concentration on the contact surfaces are not a well defined function, the solutions are approximated by dividing the boundary conditions into several well defined functions, such as step functions, and then superimposed. The results obtained by the present analysis are compared with the empirical results of other investigators.

Modeling of Moisture Transport Into an Electronic Enclosure Using the Resistor-Capacitor Approach

2018 ◽  
Vol 140 (3) ◽  
Author(s):  
Ž. Staliulionis ◽  
H. Conseil-Gudla ◽  
S. Mohanty ◽  
M. Jabbari ◽  
R. Ambat ◽  
...  
Keyword(s):  
Diffusion Coefficient ◽  
Moisture Transport ◽  
Initial Conditions ◽  
Computation Time ◽  
Second Law ◽  
Temperature Changes ◽  
One Dimensional ◽  
Isothermal Conditions ◽  
Rc Circuit ◽  
The Impact

Abstract The aim of this paper is to model moisture ingress into a closed electronic enclosure under isothermal and non-isothermal conditions. As a consequence, an in-house code for moisture transport is developed using the Resistor-Capacitor (RC) method, which is efficient as regards computation time and resources. First, an in-house code is developed to model moisture transport through the enclosure walls driven by diffusion, which is based on the Fick's first and second law. Thus, the model couples a lumped analysis of moisture transport into the box interior with a modified one-dimensional (1D) analogy of Fick's second law for diffusion in the walls. Thereafter, under non-isothermal conditions, the moisture RC circuit is coupled with the same configuration of thermal RC circuit. The paper concerns the study of the impact of imperfections in the enclosure for the whole diffusion process. Moreover, a study of the impact of wall thickness, different diffusion coefficient, and initial conditions in the wall for the moisture transport is accomplished. Comparison of modeling and experimental results showed that the RC model is very applicable for simple and rough enclosure design. Furthermore, the experimental and modeling results indicate that the imperfections, with certain limits, do not have a significant effect on the moisture transport. The modeling of moisture transport under non-isothermal conditions shows that the internal moisture oscillations follow ambient temperature changes albeit with a delay. Although, moisture ingress is slightly dependent on ambient moisture oscillations; however, it is not so dominant until equilibrium is reached.

scholarly journals Mathematical Study of Temperature Distribution in Human Dermal Part during Physical Exercises

2017 ◽  
Vol 12 (1) ◽  
pp. 63-76
Author(s):  
Dil Bahadur Gurung ◽  
Dev Chandra Shrestha
Keyword(s):  
Temperature Distribution ◽  
Boundary Conditions ◽  
Heat Equation ◽  
Metabolic Rate ◽  
Model Equation ◽  
Neumann Boundary ◽  
Neumann Boundary Conditions ◽  
Mathematical Study ◽  
One Dimensional ◽  
Physical Exercises

The purpose of this paper is to model metabolic rate that governs the behavior exhibited by various exercises over the period. This model equation is used in one dimensional Pennes’ bio-heat equation to study the temperature distribution in dermal part of tissue layers due to various exercises. The appropriate Dirichlet and Neumann boundary conditions are used. The solution of the bio-heat equation is then obtained using FEM technique and the simulated results are presented graphically. Journal of the Institute of Engineering, 2016, 12(1): 63-76 

A 1+1D Thermal Dynamic Model of a Li-Ion Battery Cell

2010 ◽  
Author(s):  
Matteo Muratori ◽  
Ning Ma ◽  
Marcello Canova ◽  
Yann Guezennec
Keyword(s):  
Temperature Distribution ◽  
Boundary Conditions ◽  
Thermal Management ◽  
Cooling System ◽  
Heat Diffusion ◽  
Li Ion Battery ◽  
Battery Cell ◽  
Heat Diffusion Equation ◽  
One Dimensional ◽  
Li Ion

Li-ion batteries are today considered the prime solution as energy storage system for EV/PHEV/HEV, due to their high specific energy and power. Since their performance, life and reliability are influenced by the operating temperature, great interest has been devoted to study different cooling solutions and control algorithms for thermal management. In this context, this paper presents a computationally efficient modeling approach to characterize the internal temperature distribution of a Li-ion battery cell, conceived to serve as a tool to aid the design of cooling systems and the development of thermal management systems for automotive battery packs. The model is developed starting from the unsteady heat diffusion equation, for which an analytical solution is obtained through the integral transform method. First, a general one-dimensional thermal model is developed to predict the temperature distribution inside a prismatic Li-ion battery cell under different boundary conditions. Then, a specific case with convective boundary conditions is studied with the objective of characterizing a cell cooled by a forced air flow. To characterize the effects of the cooling system on the temperature distribution within the cell, the one-dimensional solution is then extended to a 1+1D model that accounts for the variability of the boundary conditions in the flow direction. The calibration and validation of the specific model presented will be presented, adopting a detailed 2D FEM simulator as a benchmark.

Initial-boundary value problems for the one-dimensional linear advection–dispersion equation with decay

2020 ◽  
Vol 75 (8) ◽  
pp. 713-725 ◽  
Author(s):  
Guenbo Hwang
Keyword(s):  
Boundary Conditions ◽  
Dirichlet Boundary ◽  
Boundary Value ◽  
Initial Boundary ◽  
Initial Boundary Value Problems ◽  
One Dimensional ◽  
Advection Dispersion ◽  
Asymptotically Periodic ◽  
The One ◽  
Initial Boundary Value

AbstractInitial-boundary value problems for the one-dimensional linear advection–dispersion equation with decay (LAD) are studied by utilizing a unified method, known as the Fokas method. The method takes advantage of the spectral analysis of both parts of Lax pair and the global algebraic relation coupling all initial and boundary values. We present the explicit analytical solution of the LAD equation posed on the half line and a finite interval with general initial and boundary conditions. In addition, for the case of periodic boundary conditions, we show that the solution of the LAD equation is asymptotically t-periodic for large t if the Dirichlet boundary datum is periodic in t. Furthermore, it can be shown that if the Dirichlet boundary value is asymptotically periodic for large t, then so is the unknown Neumann boundary value, which is uniquely characterized in terms of the given asymptotically periodic Dirichlet boundary datum. The analytical predictions for large t are compared with numerical results showing the excellent agreement.

scholarly journals Pair-correlation ansatz for the ground state of interacting bosons in an arbitrary one-dimensional potential

2021 ◽  
Vol 11 (1) ◽  
Author(s):  
Przemysław Kościk ◽  
Arkadiusz Kuroś ◽  
Adam Pieprzycki ◽  
Tomasz Sowiński
Keyword(s):  
Boundary Conditions ◽  
Ground State ◽  
Pair Correlation ◽  
Contact Interactions ◽  
One Dimensional ◽  
Particle Correlations ◽  
Variational Scheme ◽  
Full Control ◽  
Arbitrary Shapes

AbstractWe derive and describe a very accurate variational scheme for the ground state of the system of a few ultra-cold bosons confined in one-dimensional traps of arbitrary shapes. It is based on assumption that all inter-particle correlations have two-body nature. By construction, the proposed ansatz is exact in the noninteracting limit, exactly encodes boundary conditions forced by contact interactions, and gives full control on accuracy in the limit of infinite repulsions. We show its efficiency in a whole range of intermediate interactions for different external potentials. Our results manifest that for generic non-parabolic potentials mutual correlations forced by interactions cannot be captured by distance-dependent functions.

scholarly journals Anomalous Diffusion with an Apparently Negative Diffusion Coefficient in a One-Dimensional Quantum Molecular Chain Model

Symmetry ◽  
2021 ◽  
Vol 13 (3) ◽  
pp. 506
Author(s):  
Sho Nakade ◽  
Kazuki Kanki ◽  
Satoshi Tanaka ◽  
Tomio Petrosky
Keyword(s):  
Diffusion Coefficient ◽  
Diffusion Constant ◽  
Mean Square Displacement ◽  
Second Law Of Thermodynamics ◽  
Molecular Chain ◽  
Chain Model ◽  
Phase Mixing ◽  
One Dimensional ◽  
The One ◽  
Negative Diffusion

An interesting anomaly in the diffusion process with an apparently negative diffusion coefficient defined through the mean-square displacement in a one-dimensional quantum molecular chain model is shown. Nevertheless, the system satisfies the H-theorem so that the second law of thermodynamics is satisfied. The reason why the “diffusion constant” becomes negative is due to the effect of the phase mixing process, which is a characteristic result of the one-dimensionality of the system. We illustrate the situation where this negative “diffusion constant” appears.

scholarly journals On a stochastic Burgers equation with Dirichlet boundary conditions

2003 ◽  
Vol 2003 (43) ◽  
pp. 2735-2746 ◽  
Author(s):  
Ekaterina T. Kolkovska
Keyword(s):  
Weak Solution ◽  
Boundary Conditions ◽  
Dirichlet Boundary ◽  
Burgers Equation ◽  
Martingale Problem ◽  
Weak Limit ◽  
Dirichlet Boundary Conditions ◽  
One Dimensional ◽  
Stochastic Burgers Equation ◽  
The One

We consider the one-dimensional Burgers equation perturbed by a white noise term with Dirichlet boundary conditions and a non-Lipschitz coefficient. We obtain existence of a weak solution proving tightness for a sequence of polygonal approximations for the equation and solving a martingale problem for the weak limit.

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