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 THERMO-HYDRAULIC FINITE ELEMENT MODELLING OF DISTRICT HEATING NETWORK BY THE UNCOUPLED APPROACH

2003 ◽  
Vol 9 (3) ◽  
pp. 153-162 ◽  
Author(s):  
Irena Gabrielaitienė ◽  
Rimantas Kačianauskas ◽  
Bengt Sunden
Keyword(s):  
Heat Transfer ◽  
Finite Element Method ◽  
Finite Element ◽  
Fluid Flow ◽  
District Heating ◽  
Multilayered Structure ◽  
The Finite Element Method ◽  
Flow And Heat Transfer ◽  
Transfer Problems ◽  
Element Method

The modelling of uncoupled fluid flow and heat transfer problems of a district heating network using the finite element method (FEM) is presented. Since the standard thermo-hydraulic pipe elements cannot be directly used for modelling insulation, the main attention was paid to discretisation of multilayered structure of pipes and surrounding by one-dimensional thermal elements. In addition, validity of the finite element method was verified numerically by solving fluid flow and heat transfer problems in district heating pipelines. Verification analysis involves standard single pipe problems and simulation of fragment of district heating in Vilnius. Pressure and temperature results obtained by finite element method are compared with those by other approaches.

scholarly journals Thermal Modelling of the Torrefaction Process Using the Finite Element Method

2021 ◽  
Vol 25 (1) ◽  
pp. 736-749
Author(s):  
Alok Dhaundiyal ◽  
Laszlo Toth
Keyword(s):  
Heat Transfer ◽  
Finite Element Method ◽  
Finite Element ◽  
Numerical Solution ◽  
Thermal Behaviour ◽  
Transfer Equation ◽  
Thermal Characteristic ◽  
Heating System ◽  
Heat Transfer Equation ◽  
The Finite Element Method

Abstract This paper focuses on the thermal characteristic of the torrefied pinecone pellets. The resistivity heating system was used for torrefaction purposes. The torrefaction was conducted at 523 K for different holding times of 5, 10 and 15 minutes. The thermal behaviour of the pinecone pellet was numerically predicted using the pdepe algorithm. A parabolic 2-D heat transfer equation was used to estimate the thermal profile across the pinecone. The effect of the interactive atmosphere was on the numerical solution was also examined. The pelletisation was performed using a ring-die at the temperature of 70 °C.

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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