scholarly journals New Thermal-Conductivity Constitutive Matrix in Fourier’s Law for Heat Transfer Using the Cell Method

2019 ◽  
Vol 9 (21) ◽  
pp. 4521
Author(s):  
González-Domínguez ◽  
Monzón-Verona ◽  
García-Alonso
Keyword(s):  
Heat Transfer ◽  
Thermal Conductivity ◽  
Finite Element Method ◽  
Thermal Conduction ◽  
Computational Method ◽  
The Finite Element Method ◽  
Cell Method ◽  
Tetrahedral Meshes ◽  
The Matrix ◽  
Constitutive Matrix

In this paper, a new constitutive matrix Mτ for thermal conduction, for tetrahedral meshes, in a steady state thermal regime is developed through a new algebraic methodology, using the Cell Method as a computational method, which is included in the finite formulation. The constitutive matrix defines the behavior of solids when they are under a thermal potential. The results are compared with those obtained for the same problem by means of the constitutive matrix Mλ developed previously, taking in both cases with a 2D axisymmetric model as reference, calculated with the finite element method. The errors obtained with the new matrix Mτ are of the order of 0.0025%, much lower than those obtained with the matrix Mλ.

scholarly journals New Constitutive Matrix in the 3D Cell Method to Obtain a Lorentz Electric Field in a Magnetic Brake

Sensors ◽  
2018 ◽  
Vol 18 (10) ◽  
pp. 3185 ◽  
Author(s):  
José Monzón-Verona ◽  
Pablo González-Domínguez ◽  
Santiago García-Alonso
Keyword(s):  
Magnetic Field ◽  
Finite Element Method ◽  
Finite Element ◽  
Computer Applications ◽  
The Finite Element Method ◽  
Cell Method ◽  
Hall Sensors ◽  
Constitutive Matrix ◽  
The Magnetic Field ◽  
Made In

In this work, we have obtained a new constitutive matrix to calculate the induced Lorentz electric current of in a conductive disk in movement within a magnetic field using the cell method in 3D. This disk and a permanent magnet act as a magnetic brake. The results obtained are compared with those obtained with the finite element method (FEM) using the computer applications Getdp and femm. The error observed is less than 0.1173%. Likewise, a second verification has been made in the laboratory using Hall sensors to measure the magnetic field in the proximity of the magnetic brake.

scholarly journals Prediction of Heat Transfer Characteristics of the Carbonized Layer of Resin-Based Ablative Material Based on the Finite Element Method

2019 ◽  
Vol 2019 ◽  
pp. 1-14
Author(s):  
Junjie Gao ◽  
Jijun Yu ◽  
Haitao Han ◽  
Daiying Deng
Keyword(s):  
Heat Transfer ◽  
Thermal Conductivity ◽  
Finite Element Method ◽  
Finite Element ◽  
Thermal Conductivity Coefficient ◽  
Carbon Deposition ◽  
Random Model ◽  
The Finite Element Method ◽  
Heat Transfer Characteristics ◽  
Transfer Characteristics

The microstructure of the carbonized layer of the low-density resin-based ablative thermal insulation material is observed, and multiscale unit cell models are established for the residual carbon deposition mode of a carbonization process, and then the thermal conductivity coefficient is predicted using the finite element method. The heat transfer characteristics of a carbonized material are discussed and studied. The results show that among the several models established, the thermal conductivity coefficient obtained by the cross-linked model of matrix carbonization is more accurate, and the deviation compared with the experimental results is within 20%, which is more consistent with the actual heat transfer mechanism. At the same time, the finite element random model is used to predict the thermal conductivity coefficient. The results show that the deviation between the numerical results and the experimentally measured thermal conductivity coefficient of the carbonized layer is within 10%, showing that the accuracy of the finite element random model is significantly higher than that of the dual-scale unit cell model. The carbon deposition model can accurately predict the heat transfer characteristics of the carbonized layer.

scholarly journals Coupled THM and Matrix Stability Modeling of Hydroshearing Stimulation in a Coupled Fracture-Matrix Hot Volcanic System

2018 ◽  
Vol 2018 ◽  
pp. 1-15 ◽  
Author(s):  
Yong Xiao ◽  
Jianchun Guo ◽  
Hehua Wang ◽  
Lize Lu ◽  
John McLennan ◽  
...  
Keyword(s):  
Heat Transfer ◽  
Thermal Conduction ◽  
Dominant Role ◽  
Injection Well ◽  
Time Step ◽  
Volcanic System ◽  
Induced Stress ◽  
The Matrix ◽  
Matrix Stability ◽  
The Stability

A coupled thermal-hydraulic-mechanical (THM) model is developed to simulate the combined effect of fracture fluid flow, heat transfer from the matrix to injected fluid, and shearing dilation behaviors in a coupled fracture-matrix hot volcanic reservoir system. Fluid flows in the fracture are calculated based on the cubic law. Heat transfer within the fracture involved is thermal conduction, thermal advection, and thermal dispersion; within the reservoir matrix, thermal conduction is the only mode of heat transfer. In view of the expansion of the fracture network, deformation and thermal-induced stress model are added to the matrix node’s in situ stress environment in each time step to analyze the stability of the matrix. A series of results from the coupled THM model, induced stress, and matrix stability indicate that thermal-induced aperture plays a dominant role near the injection well to enhance the conductivity of the fracture. Away from the injection well, the conductivity of the fracture is contributed by shear dilation. The induced stress has the maximum value at the injection point; the deformation-induced stress has large value with smaller affected range; on the contrary, thermal-induced stress has small value with larger affected range. Matrix stability simulation results indicate that the stability of the matrix nodes may be destroyed; this mechanism is helpful to create complex fracture networks.

Teaching the Finite Element Method As a Design Tool for Mechanical Engineering

1993 ◽  
Author(s):  
T. R. Grimm
Keyword(s):  
Finite Element Method ◽  
Finite Element ◽  
Solution Process ◽  
Thinking Skills ◽  
Design Tool ◽  
Basic Solution ◽  
The Finite Element Method ◽  
The Matrix ◽  
Analysis Of Results ◽  
Element Method

Abstract The importance of the finite element method as an engineering tool for design and analysis is emphasized in a senior level elective course taught at Michigan Technological University. The course emphasizes hands-on experience with computers and the pre- and post-analysis of results to establish confidence in solutions obtained. The students learn by using the finite element method to “solve” several design projects, rather than by being told about the method without significant actual experience. They also learn about the basis of the method, including formation of the matrix equations required and the numerical methods used in their solution. Intelligent use of the method requires that engineers understand both the mechanics of how to apply the method, i.e modeling requirements, and the limitations imposed by the basic solution process. The course provides the students with important experience in using the powerful finite element method as a design tool. It requires a strong background of fundamentals and stimulates the problem solving thinking skills so essential to industry.

scholarly journals Efficient Alternative for Construction of the Linear System Stemming from Numerical Solution of Heat Transfer Problems via FEM

2016 ◽  
Vol 2016 ◽  
pp. 1-7 ◽  
Author(s):  
Estaner Claro Romão
Keyword(s):  
Heat Transfer ◽  
Finite Element Method ◽  
Finite Element ◽  
Linear System ◽  
Numerical Solution ◽  
The Finite Element Method ◽  
Numerical Application ◽  
System Building ◽  
Efficient Alternative ◽  
Transfer Problems

This paper proposes an efficient alternative to construction of the linear system coming from a solution via the Finite Element Method that is able to significantly decrease the time of construction of this system. From the presentation of the methodology used and a numerical application it will be clear that the purpose of this work is to be able to decrease 6-7 times (on average) the linear system building time.

scholarly journals Design and Implementation of a Laboratory Equipment for Studying Heat Transfer by Conduction

2019 ◽  
Vol 11 (1) ◽  
pp. 153-156
Author(s):  
István Padrah ◽  
Judit Pásztor ◽  
Rudolf Farmos
Keyword(s):  
Heat Transfer ◽  
Thermal Conductivity ◽  
Heat Conduction ◽  
Thermal Conduction ◽  
Transfer Mechanism ◽  
Measuring Instrument ◽  
Heat Transfer Mechanism ◽  
Laboratory Equipment ◽  
Insulating Materials ◽  
Design And Implementation

Abstract Thermal conduction is a heat transfer mechanism. It is present in our everyday lives. Studying thermal conductivity helps us better understand the phenomenon of heat conduction. The goal of this paper is to measure the thermal conductivity of various materials and compare results with the values provided by the manufacturers. To achieve this we assembled a measuring instrument and performed measurements on heat insulating materials.

Computer Modelling of Temperature Distribution in Brake Drums for Fade Assessment

1988 ◽  
Vol 202 (4) ◽  
pp. 257-264 ◽  
Author(s):  
V T V S Ramachandra Rao ◽  
H Ramasubramanian ◽  
K N Seetharamu
Keyword(s):  
Heat Transfer ◽  
Finite Element Method ◽  
Temperature Distribution ◽  
Present Model ◽  
Computer Modelling ◽  
Convective Heat Transfer Coefficient ◽  
The Finite Element Method ◽  
Data Logging ◽  
Brake Drum ◽  
Predicted Values

Simulation of the temperature distribution in a brake drum of a commercial truck is carried out using the finite element method. Verification of the predicted values is done using an inertia dynamometer with a data logging system. The effect of variable convective heat-transfer coefficient and the effect of contact area are also studied. From the investigation it is concluded that the present model can be used for the simulation of temperature distribution in rigid brake drums during a fade test.

Influence of Shape of Nanoparticles on Nanofluid Hydrothermal Behavior

2018 ◽  
pp. 331-388
Keyword(s):  
Heat Transfer ◽  
Thermal Conductivity ◽  
Finite Element Method ◽  
Finite Element ◽  
Stream Function ◽  
Shape Factor ◽  
Control Volume ◽  
Flow And Heat Transfer ◽  
Shape Of Nanoparticles ◽  
Stream Function Formulation

The shape of nanoparticles can change the thermal conductivity of nanofluid. So, the effect of shape factor on nanofluid flow and heat transfer has been reported in this chapter. Governing equations are presented in vorticity stream function formulation. Control volume-based finite element method (CVFEM) is utilized to obtain the results. Results indicate that platelet shape has the highest rate of heat transfer.

The Finite-Element Method—Part I

1989 ◽  
Author(s):  
Shiro Kobayashi ◽  
Soo-Ik Oh ◽  
Taylan Altan
Keyword(s):  
Heat Transfer ◽  
Finite Element Method ◽  
Finite Element ◽  
Ritz Method ◽  
Approximate Solutions ◽  
Plane Elasticity ◽  
Heat Transfer Analysis ◽  
Deformation Analysis ◽  
The Finite Element Method ◽  
Element Method

The concept of the finite-element procedure may be dated back to 1943 when Courant approximated the warping function linearly in each of an assemblage of triangular elements to the St. Venant torsion problem and proceeded to formulate the problem using the principle of minimum potential energy. Similar ideas were used later by several investigators to obtain the approximate solutions to certain boundary-value problems. It was Clough who first introduced the term “finite elements” in the study of plane elasticity problems. The equivalence of this method with the well-known Ritz method was established at a later date, which made it possible to extend the applications to a broad spectrum of problems for which a variational formulation is possible. Since then numerous studies have been reported on the theory and applications of the finite-element method. In this and next chapters the finite-element formulations necessary for the deformation analysis of metal-forming processes are presented. For hot forming processes, heat transfer analysis should also be carried out as well as deformation analysis. Discretization for temperature calculations and coupling of heat transfer and deformation are discussed in Chap. 12. More detailed descriptions of the method in general and the solution techniques can be found in References [3-5], in addition to the books on the finite-element method listed in Chap. 1. The path to the solution of a problem formulated in finite-element form is described in Chap. 1 (Section 1.2). Discretization of a problem consists of the following steps: (1) describing the element, (2) setting up the element equation, and (3) assembling the element equations. Numerical analysis techniques are then applied for obtaining the solution of the global equations. The basis of the element equations and the assembling into global equations is derived in Chap. 5. The solution satisfying eq. (5.20) is obtained from the admissible velocity fields that are constructed by introducing the shape function in such a way that a continuous velocity field over each element can be denned uniquely in terms of velocities of associated nodal points.

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