Axisymmetric transient solutions of the heat diffusion problem in layered composite media

Azeez, Mohammed F. Abdul; Vakakis, Alexander F.

doi:10.1016/s0017-9310(99)00386-5

Cited by 16 publications

(4 citation statements)

References 11 publications

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“…where λ is the eigenvalue associated with the homogeneous boundary problem partial differential equation (PDE). Note that λ > 0 and that λ is not unique (Abdul Azeez & Vakakis, 2000;Mikhailov & Özisik, 1986). The solution for τ i is straightforward:…”

Section: Transient Heat Equation With Homogeneous Boundary Conditionsmentioning

confidence: 99%

“…In Cartesian coordi-nates, examples of applications of these techniques are Salt (1983) and Mikhailov & Özisik (1986) (orthogonal expansion technique in slabs) as well as Haji-Sheikh & Beck (2002) (Green function). In cylindrical coordinates, example works are Abdul Azeez & Vakakis (2000) (integral transform) and Milošević & Raynaud (2004) (orthogonal expansion in cylinders).…”

Section: Introductionmentioning

confidence: 99%

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Transient multipole expansion for heat transfer in ground heat exchangers

Prieto

Cimmino

2020

Science and Technology for the Built Environment

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A transient multipole method for short-term simulations of ground heat exchangers (GHEs) is presented. The two-dimensional unsteady heat equation over a GHE cross-section is separated into two problems: (i) a transient heat equation with homogeneous boundary conditions, and (ii) a steady-state heat equation with nonhomogeneous boundary conditions. An eigenfunction expansion is proposed for the solution of the transient heat equation, where the treatment of boundary conditions is considered by a multipole expansion of the eigenfunctions. A singular value decomposition is applied to extract the eigenvalues of the problem. The solution of the steady-state heat equation is obtained from a multipole expansion. The proposed method is validated against reference results for the evaluation of the eigenvalues and for the steady-state temperature field. The complete transient solution is validated against finite element analysis simulations. The proposed method is meshless, and its accuracy is only dependent on the evaluation of eigenvalues and on the number of terms in each of the multipole expansions.

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Section: Transient Heat Equation With Homogeneous Boundary Conditionsmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

Transient multipole expansion for heat transfer in ground heat exchangers

Prieto

Cimmino

2020

Science and Technology for the Built Environment

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“…Heat transfer in structural materials, e.g. wood and laminated metal sheets, and crystals is another flourishing field where anisotropic diffusion equation is generally applied [8][9][10]. Interestingly, in the recent years, anisotropic diffusion equation finds its application in the field of imaging, e.g.…”

Section: Introductionmentioning

confidence: 99%

Modeling anisotropic diffusion using a departure from isotropy approach

Ge¹,

Yap²,

Zhang

et al. 2013

Computers & Fluids

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There are a large number of finite volume solvers available for solution of isotropic diffusion equation. This article presents an approach of adapting these solvers to solve anisotropic diffusion equations. The formulation works by decomposing the diffusive flux into a component associated with isotropic diffusion and another component associated with departure from isotropic diffusion.This results in an isotropic diffusion equation with additional terms to account for the anisotropic effect. These additional terms are treated using a deferred correction approach and coupled via an iterative procedure. The presented approach is validated against various diffusion problems in anisotropic media with known analytical or numerical solutions. Although demonstrated for twodimensional problems, extension of the present approach to three-dimensional problems is straight forward. Other than the finite volume method, this approach can be applied to any discretization method.

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“…Our initial motivation of this study was time scales for multilayer reaction diffusion, extending composite diffusion work [12][13][14][15][16][17][18][19]. However, time scale analysis of reaction diffusion through a single-layer has not been adequately studied, and so is presented here.…”

Section: Introductionmentioning

confidence: 99%