Boundary element analysis of nonlinear transient heat conduction problems

Kikuta, M.; Togoh, H.; Tanaka, Masataka

doi:10.1016/0045-7825(87)90066-1

Cited by 11 publications

(1 citation statement)

References 11 publications

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“…For instance, heat transfer by radiation and temperature interchange between objects have been studied using a combination of finite element and Galerkin methods [10]. Conduction heat transfer cases were also investigated using the boundary element method [11]. Furthermore, the finite difference method has also been used with Laplace transform to estimate the heat transfer through glass pane with down-flowing water film [12].…”

Section: Introductionmentioning

confidence: 99%

Modeling glass cooling mechanism with down-flowing water film via the smoothed particle hydrodynamics

Abdoh

Ademiloye

Liew

2020

Computer Methods in Applied Mechanics and Engineering

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This paper presents a new attempt to investigate the cooling mechanism of glass panes with down-flowing water film during fire outbreak by simulating the heat energy conservation equation using smoothed particle hydrodynamics (SPH) method. The nature of meshfree SPH method used allows us to predict the temperature distribution efficiently in continuous flow problems in contrast with mesh-based methods. To validate and show the efficiency of the proposed SPH model, the results from our simulation at specific conditions were compared with experimental measurements and results from commercial software packages. Furthermore, the new SPH model is utilized to simulate the effects of heat flux variation, down-flowing velocity and thickness of water film on temperature distribution of glass during fire. The developed SPH model is well able to describe glass cooling under different conditions. The computational results show that the rate of cooling increases when velocity or thickness of down-flowing water film increases. However, the glass temperature increases when heat flux increases.

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Section: Introductionmentioning

confidence: 99%

Modeling glass cooling mechanism with down-flowing water film via the smoothed particle hydrodynamics

Abdoh

Ademiloye

Liew

2020

Computer Methods in Applied Mechanics and Engineering

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Transient non-linear heat conduction-radiation problems?a boundary element formulation

Blobner

Ecki

Kühn

1999

Int. J. Numer. Meth. Engng.

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SUMMARYA novel boundary-only formulation for transient temperature ÿelds in bodies of non-linear material properties and arbitrary non-linear boundary conditions has been developed. The option for self-irradiating boundaries has been included in the formulation. Heat conduction equation has been partially linearized by Kirchho 's transformation. The result has been discretized by the dual reciprocity boundary element method. The integral equation of heat radiation has been discretized by the standard boundary element method. The coupling of the resulting two sets of equations has been accomplished by static condensation of the radiative heat uxes arising in both sets. The ÿnal set of ordinary di erential equations has been solved using the Runge-Kutta solver with automatic time step adjustment. The algorithm proved to be robust and stable. Numerical examples are included.

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Boundary elements for non‐linear heat conduction problems

Wrobel¹,

Brebbia²

1988

Commun. appl. numer. methods

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SUMMARYBoundary element formulations employing time-independent fundamental solutions are becoming popular for treating transient problems described by parabolic or hyperbolic partial differential equations. This paper describes the extension of one such formulation, named the dual reciprocity boundary element method, to non-linear transient heat conduction problems with temperature-dependent material parameters and boundary conditions of the radiative type. The original non-linear diffusion equation is solved in a transform space, where it appears in a pseudo-linear form, since it contains a modified time variable which is itself a function of position. The problem is solved by using an iterative algorithm of the Newton-Raphson type.

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Boundary element analysis of nonlinear transient heat conduction problems

Cited by 11 publications

References 11 publications

Modeling glass cooling mechanism with down-flowing water film via the smoothed particle hydrodynamics

Modeling glass cooling mechanism with down-flowing water film via the smoothed particle hydrodynamics

Transient non-linear heat conduction-radiation problems?a boundary element formulation

Boundary elements for non‐linear heat conduction problems

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