Applications in Transient Heat Conduction

“…Substitution of equation (16) into equation (15) results in a set of non-linear ordinary di erential equations (17) where the capacity matrix C is deÿned as (18) and matricesˆ andQ are assemblies of column vectorsF j andq j , respectively. It should be noted that, despite the non-linearity of the problem at hand, matrices H, G, and C are constant and depend only on the geometry.…”

Section: Dual Reciprocitymentioning

confidence: 99%

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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“…To this aim, two di erent step-by-step procedures, which are indicated as procedures 1 and 2, are analysed in the following (see [5]). …”

Section: Discretization In Space and Time And Marching Solution Procementioning

confidence: 99%

Implementation of a symmetric boundary element method in transient heat conduction with semi-analytical integrations

Carini

Diligenti

Salvadori

1999

Int. J. Numer. Meth. Engng.

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SUMMARYA time-convolutive variational hypersingular integral formulation of transient heat conduction over a 2-D homogeneous domain is considered. The adopted discretization leads to a linear equation system, whose coe cient matrix is symmetric, and is generated by double integrations in space and time. Assuming polynomial shape functions for the boundary unknowns, a set of compact formulae for the analytical time integrations is established. The spatial integrations are performed numerically using very e cient formulae just recently proposed. The competitiveness from the computational point of view of the symmetric boundary integral equation approach proposed herein is investigated on the basis of an original computer implementation.

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Applications in Transient Heat Conduction

Cited by 21 publications

References 11 publications

On the Spline Collocation Method for the Single-Layer Heat Operator Equation

On the Spline Collocation Method for the Single-Layer Heat Operator Equation

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

Implementation of a symmetric boundary element method in transient heat conduction with semi-analytical integrations

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