Petrov-Galerkin finite element approach to coupled heat and fluid flow

Argyris, John; Laxander, Armin; Szimmat, J.

doi:10.1016/0045-7825(92)90146-b

Cited by 18 publications

(10 citation statements)

References 6 publications

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“…Following the work of Brooks and Hughes [15], and Argyris [16], finite element method was utilized to solve the governing equations and to discretize the computational domain. Four nodes of quadrilateral elements were used for the numerical discretization.…”

Section: Methodsmentioning

confidence: 99%

“…The advection term in momentum and energy equations was formulated by using the Streamline Upwind/Petrov-Galerkin (SUPG) approach. All field variables were converged, and the following condition was used to declare convergence: (16) is any degree of freedom (DOF) of general field variables. The convergence monitor represents the sum of changes of a variable calculated from the result between the current iteration and previous iteration divided by the sum of the current values.…”

Section: Methodsmentioning

confidence: 99%

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Thermal Analysis of a Channel Containing Multiple Heated Obstacles With Localized Heat Generations

Alawadhi

2004

IEEE Trans. Comp. Packag. Technol.

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This paper studies conjugate heat transfer for two-dimensional, developing flows over an array of multiple rectangular obstacles with localized heat generations. The paper focuses on the spatial distributions of Nusselt number and temperature along the solid/fluid interface, as well as the maximum temperature of the obstacles. The results are compared to uniform heat generation configuration to validate the approach of approximating the local heat generation as uniform. Finite element technique is utilized to solve the governing equations, along with boundary conditions for a wide range of Reynolds numbers and obstacles' thermal conductivities. At certain conditions, the numerical results showed that the uniform heat generation approach could lead to a significant analysis error. When the obstacles' thermal conductivity and Reynolds number are low, the uniform heat generation approach becomes invalid. The average Nusselt number and maximum temperature of the obstacles for the localized heat generation configuration are fully documented.Index Terms-Conjugate heat transfer, finite element technique, Nusselt number, Reynolds number, solid/fluid interface, thermal conductivity.

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Section: Methodsmentioning

confidence: 99%

Section: Methodsmentioning

confidence: 99%

Thermal Analysis of a Channel Containing Multiple Heated Obstacles With Localized Heat Generations

Alawadhi

2004

IEEE Trans. Comp. Packag. Technol.

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“…FEMs present spurious numerical oscillations, which give a failure result associated with the classical Galerkin formulations of viscous incompressible Navier-Stokes equations [91]. The Petrov-Galerkin method was widely used to solve coupled equations of flow and heat transfer [92][93][94][95][96] and also employed to prevent these potential numerical instabilities [81,97,98].…”

Section: Three-dimensional Modelsmentioning

confidence: 99%

A brief history of the filling simulation of injection moulding

Cardozo

2008

Proceedings of the Institution of Mechanical Engineers, Part C:

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Injection moulding is one of the most important manufacturing processes for mass production of complex plastic parts. The quality of injection moulded parts depends not only on the material, shape, and function of the part design, but also on how the material is processed during moulding. Traditional design approaches based on intuition, prior experience, and trial-and-error methodology have been becoming less efficient and effective. With advances in numerical modelling and computer simulation techniques, there have been tremendous efforts made to develop computer simulation tools to facilitate injection moulding design and process set-up. This paper reviews the history of research and development in the filling simulation of injection moulding. The existing models are classified into three categories: one-dimensional models, 2.5D models, and three-dimensional models. The basic features and relative key techniques about these models have been discussed. The techniques of tacking the moving flow front have also been presented. It is then followed by conclusions and discussions of these mentioned models.

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“…Finite element methods present spurious numerical oscillations, which give a failure result associated with the classical Galerkin formulations of viscous incompressible Navier-Stokes equations [84]. The Petrov-Galerkin method was widely used to solve coupled equations of flow and heat transfer [85][86][87][88][89] and also employed to prevent these potential numerical instabilities [90,91].…”

Section: The Connector Elementmentioning

confidence: 99%

Three Models of the 3D Filling Simulation for Injection Molding: A Brief Review

Cardozo

2008

Journal of Reinforced Plastics and Composites

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This article reviews the state-of-the-art research and development in the 3D filling simulation of injection molding, most notably the different models. The article organizes prior studies into three sequential categories, namely, mid-plane models, surface models, and solid models. In the mid-plane models, the arbitrary planar mid-plane is used to represent the three-dimensional geometry of the part. Their model and formulation are presented based on the Hele—Shaw approximation. The article further discusses the main disadvantage of the mid-plane models, which introduces the surface models. The surface models represent a three-dimensional part with a boundary or skin mesh on the outside surfaces of a solid geometric model. This kind of model still adopts the Hele—Shaw approximation, but can avoid the re-modeling of the mid-plane. Subsequently, the situations that cannot be accurately predicted using the Hele—Shaw approximation are discussed, in which a full 3D simulation has become a promising solution. The leading 3D simulation approaches are summarized, including the finite element method, the finite volume method, the control-volume-based finite-element-method, and the boundary element method. The tracking algorithms of the melt fronts are also described.

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Petrov-Galerkin finite element approach to coupled heat and fluid flow

Cited by 18 publications

References 6 publications

Thermal Analysis of a Channel Containing Multiple Heated Obstacles With Localized Heat Generations

Thermal Analysis of a Channel Containing Multiple Heated Obstacles With Localized Heat Generations

A brief history of the filling simulation of injection moulding

Three Models of the 3D Filling Simulation for Injection Molding: A Brief Review

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