scholarly journals A Generalized Analytical Model for Joule Heating of Segmented Wires

2018 ◽  
Vol 140 (7) ◽  
Author(s):  
Vivekananthan Balakrishnan ◽  
Toan Dinh ◽  
Hoang-Phuong Phan ◽  
Dzung Viet Dao ◽  
Nam-Trung Nguyen
Keyword(s):  
Temperature Distribution ◽  
Analytical Solution ◽  
Joule Heating ◽  
Numerical Solutions ◽  
Analytical Data ◽  
Experimental Studies ◽  
Governing Equations ◽  
Steady State Temperature ◽  
The One ◽  
Good Agreement

This paper presents an analytical solution for the Joule heating problem of a segmented wire made of two materials with different properties and suspended as a bridge across two fixed ends. The paper first establishes the one-dimensional (1D) governing equations of the steady-state temperature distribution along the wire with the consideration of heat conduction and free-heat convection phenomena. The temperature coefficient of resistance of the constructing materials and the dimension of the each segmented wires were also taken into account to obtain analytical solution of the temperature. COMSOL numerical solutions were also obtained for initial validation. Experimental studies were carried out using copper and nichrome wires, where the temperature distribution was monitored using an IR thermal camera. The data showed a good agreement between experimental data and the analytical data, validating our model for the design and development of thermal sensors based on multisegmented structures.

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.

scholarly journals Complex Variable Meshless Manifold Method for Elastic Dynamic Problems

2016 ◽  
Vol 2016 ◽  
pp. 1-8 ◽  
Author(s):  
Hongfen Gao ◽  
Gaofeng Wei
Keyword(s):  
Analytical Solution ◽  
Complex Variable ◽  
Meshless Method ◽  
Numerical Solutions ◽  
Least Square ◽  
Dynamic Problems ◽  
Finite Covering ◽  
Moving Least Square ◽  
Elastic Dynamics ◽  
Good Agreement

Combining the finite covering technical and complex variable moving least square, the complex variable meshless manifold method can handle the discontinuous problem effectively. In this paper, the complex variable meshless method is applied to solve the problem of elastic dynamics, the complex variable meshless manifold method for dynamics is established, and the corresponding formula is derived. The numerical example shows that the numerical solutions are in good agreement with the analytical solution. The CVMMM for elastic dynamics and the discrete forms are correct and feasible. Compared with the traditional meshless manifold method, the CVMMM has higher accuracy in the same distribution of nodes.

scholarly journals An Equal-Strain Analytical Solution for the Radial Consolidation of Unsaturated Soils by Vertical Drains considering Drain Resistance

2018 ◽  
Vol 2018 ◽  
pp. 1-9 ◽  
Author(s):  
Feng Zhou ◽  
Zheng Chen ◽  
Xudong Wang
Keyword(s):  
Analytical Solution ◽  
Unsaturated Soils ◽  
Ground Surface ◽  
Matrix Analysis ◽  
Governing Equations ◽  
Vertical Drains ◽  
Ground Surface Settlement ◽  
Parametric Studies ◽  
Strain Model ◽  
Good Agreement

Developing an analytical solution for the consolidation of unsaturated soils remains a challenging task due to the complexity of coupled governing equations for air and water phases. This paper presents an equal-strain model for the radial consolidation of unsaturated soils by vertical drains, and the effect of drain resistance is also considered. Simplified governing equations are established, and an analytical solution to calculate the excess pore-air and pore-water pressures is derived by using the methods of matrix analysis and eigenfunction expansion. The average degrees of consolidation for air and water phases and the ground surface settlement are also given. The solutions of the equal-strain model are verified by comparing the proposed free-strain model with the equal-strain model, and reasonably good agreement is obtained. Moreover, parametric studies regarding the drain resistance effect are graphically presented.

scholarly journals Study of Unsteady Flow in a Heat Exchanger by the Method of Characteristics

1992 ◽  
Vol 114 (4) ◽  
pp. 459-463 ◽  
Author(s):  
Yuan Mao Huang
Keyword(s):  
Heat Exchanger ◽  
Unsteady Flow ◽  
Transfer Rate ◽  
Method Of Characteristics ◽  
Governing Equations ◽  
One Dimensional ◽  
The Method Of Characteristics ◽  
Improvement Factor ◽  
The One ◽  
Good Agreement

The one-dimensional, unsteady flow in an air-to-air heat exchanger is studied. The governing equations are derived and the method of characteristics with the uniform interval scheme is used in the analysis. The effect of the fin improvement factor on the air temperature in the heat exchanger and the heat transfer rate of the heat exchanger, and air properties in the heat exchanger are analyzed. The numerical results are compared and show good agreement with the available data.

scholarly journals Numerical Solution Strategies in Permeation Processes

2021 ◽  
Vol 413 ◽  
pp. 29-46
Author(s):  
Axel von der Weth ◽  
Daniela Piccioni Koch ◽  
Frederik Arbeiter ◽  
Till Glage ◽  
Dmitry Klimenko ◽  
...  
Keyword(s):  
Analytical Solution ◽  
Ad Hoc ◽  
Numerical Solutions ◽  
Matrix Multiplication ◽  
Transport Processes ◽  
Time Step ◽  
Stability Range ◽  
The Stability ◽  
The One ◽  
Crank Nicolson

In this work, the strategy for numerical solutions in transport processes is investigated. Permeation problems can be solved analytically or numerically by means of the Finite Difference Method (FDM), while choosing the Euler forward explicit or Euler backwards implicit formalism. The first method is the easiest and most commonly used, while the Euler backwards implicit is not yet well established and needs further development. Hereafter, a possible solution of the Crank-Nicolson algorithm is presented, which makes use of matrix multiplication and inversion, instead of the step-by-step FDM formalism. If one considers the one-dimensional diffusion case, the concentration of the elements can be expressed as a time dependent vector, which also contains the boundary conditions. The numerically stable matrix inversion is performed by the Branch and Bound (B&B) algorithm [2]. Furthermore, the paper will investigate, whether a larger time step can be used for speeding up the simulations. The stability range is investigated by eigenvalue estimation of the Euler forward and Euler backward. In addition, a third solver is considered, referred to as Combined Solver, that is made up of the last two ones. Finally, the Crank-Nicolson solver [9] is investigated. All these results are compared with the analytical solution. The solver stability is analyzed by means of the Steady State Eigenvector (SSEV), a mathematical entity which was developed ad hoc in the present work. In addition, the obtained results will be compared with the analytical solution by Daynes [6,7].

scholarly journals A modification of the CABARET scheme for numerical simulation of multicomponent gaseous flows in two-dimensional domains

2015 ◽  
pp. 436-445
Author(s):  
А.В. Данилин ◽  
А.В. Соловьев ◽  
А.М. Зайцев
Keyword(s):  
Numerical Simulation ◽  
Initial Conditions ◽  
Experimental Studies ◽  
Two Dimensional ◽  
Governing Equations ◽  
Cabaret Scheme ◽  
Gaseous Flows ◽  
Multicomponent Gas ◽  
Good Agreement ◽  
Made In

Предложен явный численный алгоритм для расчета течений смесей идеальных газов в двумерных областях. Приведены физическая модель и уравнения движения смеси в консервативной и характеристической формах. Дискретизация уравнений движения произведена по методике Кабаре. Алгоритм испытан на задачах о прохождении ударной волны в воздухе через неоднородности из легкого и тяжелого газов, начальные условия для которых адаптированы из рассмотренных другими авторами натурных и численных экспериментов. Показано хорошее совпадение расчетов по предложенному алгоритму с результатами этих экспериментов. An explicit numerical algorithm for calculation of two-dimensional motion of multicomponent gas mixtures is proposed. A physical model as well as conservative and characteristic forms of governing equations are given. The discretization of the governing equations is made in accordance with the CABARET (Compact Accurately Boundary Adjusting-REsolution Technique) approach. The proposed algorithm is tested on problems of air shock waves passing through dense and dilute volume inhomogeneities with initial conditions adopted from numerical and experimental studies of other authors. A good agreement between the results of these studies and those obtained by the CABARET approach is shown.

Natural Convection in a Rectangular Porous Cavity With One Permeable Endwall

1983 ◽  
Vol 105 (4) ◽  
pp. 803-808 ◽  
Author(s):  
M. Haajizadeh ◽  
C. L. Tien
Keyword(s):  
Theoretical Study ◽  
Numerical Solutions ◽  
Constant Pressure ◽  
Experimental System ◽  
Governing Equations ◽  
Porous Cavity ◽  
Steady State Temperature ◽  
Shallow Cavity ◽  
Higher Temperature ◽  
Water Saturated

This paper describes a theoretical and experimental study of two-dimensional, buoyancy-driven flow in a rectangular porous cavity with one permeable endwall. Connected to a constant temperature tank, the permeable end allows for natural recharge and discharge of the saturating fluid. The other vertical endwall is impermeable and maintained at a constant but higher temperature, thus inducing a buoyancy-driven flow. The theoretical study includes an asymptotic analysis developed for a shallow cavity with one permeable endwall and the numerical solutions of the power-law difference representation of the full governing equations. The experimental system consists of water-saturated glass beads packed in a rectangular cavity with a length-to-height aspect ratio of 3.17, for which the Rayleigh number can vary up to 120. Measurements were made of the steady-state temperature distribution in the cavity and the heat transfer rate from the impermeable endwall. It is shown that the constant pressure and temperature assumptions at the permeable wall, as employed in the theoretical analysis, satisfactorily predict the experimental data. Results are also compared with those existing in the literature.

Vibration Analysis of a Sensor-Integrated Ball Bearing

2000 ◽  
Vol 122 (4) ◽  
pp. 384-392 ◽  
Author(s):  
Brian T. Holm-Hansen ◽  
Robert X. Gao
Keyword(s):  
Condition Monitoring ◽  
Ball Bearing ◽  
Numerical Solutions ◽  
Experimental Studies ◽  
Force Sensor ◽  
Deep Groove ◽  
Bearing Condition Monitoring ◽  
Deep Groove Ball Bearing ◽  
On Line ◽  
Good Agreement

This paper presents an analysis of the vibrational behavior of a deep groove ball bearing with a structurally integrated force sensor. The miniaturized force sensor, accommodated within a slot on the bearing’s outer ring, provides on-line condition monitoring capability to the bearing. Analytical and finite element models were developed to predict the sensor output due to bearing dynamic load and rotational speed variations. Experimental studies were conducted on a ball bearing to validate the analytical and numerical solutions. Good agreement was found between the model-predicted sensor outputs and the experimental results. The findings validated the approach of integrated-sensing for on-line bearing condition monitoring. [S0739-3717(00)00203-8]

A Study of Photo-Thermoelastic Wave in Semiconductor Materials With Spherical Holes Using Analytical-numerical Methods

2021 ◽  
Author(s):  
Faris S. Alzahrani ◽  
Ibrahim Abbas
Keyword(s):  
Finite Difference ◽  
Analytical Solution ◽  
Finite Difference Method ◽  
Difference Method ◽  
Numerical Solutions ◽  
Governing Equations ◽  
Thermoelastic Wave ◽  
Spherical Cavities ◽  
Implicit Finite Difference ◽  
Implicit Finite Difference Method

Abstract Analytical and numerical solutions are two basic tools in the study of photothermal interaction problems in semiconductor medium. In this paper, we compare the analytical solutions with the numerical solutions for thermal interaction in semiconductor mediums containing spherical cavities. The governing equations are given in the domain of Laplace transforms and the eigenvalues approaches are used to obtained the analytical solution. The numerical solutions are obtained by applying the implicit finite difference method (IFDM). A comparison between the numerical solutions and analytical solution are presented. It is found that the implicit finite difference method (IFDM) is applicable, simple and efficient for such problems.

Optimal Perturbation Iteration Method for Solving Nonlinear Heat Transfer Equations

2017 ◽  
Vol 139 (7) ◽  
Author(s):  
Sinan Deniz
Keyword(s):  
Heat Transfer ◽  
Temperature Distribution ◽  
Iteration Method ◽  
Numerical Solutions ◽  
Nonlinear Differential Equations ◽  
Optimal Perturbation ◽  
Transfer Equations ◽  
Better Than ◽  
Good Agreement ◽  
Distribution Equation

In this paper, the new optimal perturbation iteration method (OPIM) is introduced and applied for solving nonlinear differential equations arising in heat transfer. The effectiveness of the proposed method will be tested by considering two specific applications: the temperature distribution equation in a thick rectangular fin radiation to free space and cooling of a lumped system with variable specific heat. Comparing different methods shows that the results obtained by optimal perturbation iteration method are very good agreement with the numerical solutions and perform better than the most existing analytic methods.

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