The finite element method with heat transfer and fluid mechanics applications

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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Convective heat transfer analysis by the finite element method

Computer Methods in Applied Mechanics and Engineering ◽

10.1016/0045-7825(77)90024-x ◽

1977 ◽

Vol 12 (3) ◽

pp. 365-382 ◽

Cited By ~ 47

Author(s):

David K. Gartling

Keyword(s):

Heat Transfer ◽

Finite Element Method ◽

Finite Element ◽

Convective Heat Transfer ◽

Convective Heat ◽

Heat Transfer Analysis ◽

The Finite Element Method ◽

Element Method

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Prediction of the Heat-Insulating Crumb Rubber Brick Walls Design by the Finite Element Method

Advanced Materials Research ◽

10.4028/www.scientific.net/amr.805-806.1575 ◽

2013 ◽

Vol 805-806 ◽

pp. 1575-1582 ◽

Cited By ~ 1

Author(s):

Weerapol Namboonruang ◽

Rattanakorn Rawangkul ◽

Wanchai Yodsudjai ◽

Trakool Aramraks ◽

Nutthanan Suphadon

Keyword(s):

Heat Transfer ◽

Finite Element Method ◽

Finite Element ◽

Economic Factor ◽

Crumb Rubber ◽

The Finite Element Method ◽

Element Analysis ◽

Good Correspondence ◽

Soil Cement ◽

Element Method

Nowadays, materials used to construct house or building wall areconsidered not only in the physical material behaviour but also energy conscious and economic factor. Adding crumb rubber to the brick composite is one of many methods to develop the properties of bricks. As widely known,the finite element method (FEM) is a tool used for finding accurate solutions of the heat transfer equation of materials including the composite bricks. In this paper an investigation of the heat transfer of a soil cement brick containing crumb rubber particles, is presented and compared to results of finite element analysis (FEA) simulation. To determine the effect of crumb rubber to the heat transfer behaviour of soil cement brick, different volume fractions are varied by 10, 20, 30 and 40%. It was reported that a modelling application reveals good correspondence with the experimental results.

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Simulation of the Heat-Insulating Sludge Waste Rubber Composite Brick by the Finite Element Method (FEM)

Solid State Phenomena ◽

10.4028/www.scientific.net/ssp.280.451 ◽

2018 ◽

Vol 280 ◽

pp. 451-461

Author(s):

Weerapol Namboonruang ◽

Nutthanan Suphadon

Keyword(s):

Heat Transfer ◽

Finite Element Method ◽

Finite Element ◽

Economic Factor ◽

Raw Material ◽

The Finite Element Method ◽

Element Analysis ◽

Good Correspondence ◽

Sludge Waste ◽

Element Method

Recently, materials used to construct house or building wall are considered not only in the physical material behaviour but also energy conscious and economic factor. The possibility of utilization of the sludge waste obtained from the natural rubber manufacturing process as a raw material for producing composite brick was investigated. It has been widely known that the finite element method (FEM) is a tool used for finding accurate solutions of the heat transfer equation of materials including the composite bricks. In this work, study of the heat transfer of a composite brick containing rubber sludge waste (RSW) was showed and compared to results of finite element analysis (FEA) simulation. To determine the effect of rubber sludge waste to the heat transfer behaviour of composite brick with different volume fractions are varied by 10, 20, 30, 40 and 50%. It appeared that a FEA prediction showed good correspondence with the experimental results.

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