The Joule‐Thomson effect on the thermoelectric conductors

Consiglieri, Luisa

doi:10.1002/zamm.200800108

Cited by 5 publications

(14 citation statements)

References 12 publications

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“…Let us consider the following problem that extends the thermoelectric problems, which were introduced in [10,11], in the sense of that the thermoelectric coefficient is assumed to be a given but arbitrary nonlinear function. The electrical current density j and the energy flux density J = q + φj, with q being the heat flux vector, satisfy    ∇ · j = 0 in Ω −j · n = g on Γ N j · n = 0 on Γ    ∇ · J = 0 in Ω J · n = 0 on Γ N −J · n = f λ (θ)|θ| ℓ−2 θ − γ(θ)θ ℓ−1 e on Γ, (1) for ℓ ≥ 2.…”

Section: Introductionmentioning

confidence: 99%

Radiative effects for some bidimensional thermoelectric problems

Consiglieri¹

2015

Advances in Nonlinear Analysis

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There are two main directions in this paper. One is to find sufficient conditions to ensure the existence of weak solutions to thermoelectric problems. At the steady-state, these problems consist of a coupled system of elliptic equations of the divergence form, commonly accomplished with nonlinear radiation-type conditions on at least a nonempty part of the boundary of a C 1 domain. The model under study takes the thermoelectric Peltier and Seebeck effects into account, which describe the Joule-Thomson effect. The proof method makes recourse of a fixed point argument. To this end, well-determined estimates are our main concern. The paper is in the second direction for the derivation of explicit W 1,p -estimates (p > 2) for solutions of nonlinear radiation-type problems, where the leading coefficient is assumed to be a discontinuous function on the space variable. In particular, the behavior of the leading coefficient is conveniently explicit on the estimate of any solution.2010 Mathematics Subject Classification. 80A17, 78A30, 35R05, 35J65, 35J20, 35B65.

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Section: Introductionmentioning

confidence: 99%

Radiative effects for some bidimensional thermoelectric problems

Consiglieri¹

2015

Advances in Nonlinear Analysis

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“…Let us extend the existence results whose can be found in [10]. The first main theorem states the existence of weak solutions to the problem under study, strengthening the assumption (H2), i.e.…”

Section: Remark 22mentioning

confidence: 73%

“…The thermoelectric problem under study reads (see its derivation in [10,25]) (P) Find the pair temperature-potential (θ, φ) such that − ∇ · (k∇θ) = σ(·, θ)α(·, θ)(α(·, θ) + ∂α ∂T (·, θ)θ)|∇θ| 2 + +σ(·, θ)(2α(·, θ) + ∂α ∂T (·, θ)θ)∇θ · ∇φ + σ(·, θ)|∇φ| 2 + g in Ω,…”

Section: Introductionmentioning

confidence: 99%

A limit model for thermoelectric equations

Consiglieri¹

2011

Ann Univ Ferrara

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We analyze the asymptotic behavior corresponding to the arbitrary high conductivity of the heat in the thermoelectric devices. This work deals with a steady-state multidimensional thermistor problem, considering the Joule effect and both spatial and temperature dependent transport coefficients under some real boundary conditions in accordance with the Seebeck-Peltier-Thomson cross-effects. Our first purpose is that the existence of a weak solution holds true under minimal assumptions on the data, as in particular nonsmooth domains. Two existence results are studied under different assumptions on the electrical conductivity. Their proofs are based on a fixed point argument, compactness methods, and existence and regularity theory for elliptic scalar equations. The second purpose is to show the existence of a limit model illustrating the asymptotic situation.Comment: 20 page

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“…Consider the case of dimension n = 2. For t, s > 1, using the Hölder inequality in (8) if t ′ ≤ 2, in (6) if t ′ > 2, and in (7) for any s > 1, we have…”

Section: H 1 -Solvabilitymentioning

confidence: 99%

Explicit Estimates for Solutions of Mixed Elliptic Problems

Consiglieri

2014

International Journal of Partial Differential Equations

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We deal with the existence of quantitative estimates for solutions of mixed problems to an elliptic second-order equation in divergence form with discontinuous coefficients. Our concern is to estimate the solutions with explicit constants, for domains in R ( ≥ 2) of class 0,1 . The existence of ∞ and 1, estimates is assured for = 2 and any < /( − 1) (depending on the data), whenever the coefficient is only measurable and bounded. The proof method of the quantitative ∞ estimates is based on the De Giorgi technique developed by Stampacchia. By using the potential theory, we derive 1, estimates for different ranges of the exponent depending on the fact that the coefficient is either Dini-continuous or only measurable and bounded. In this process, we establish new existences of Green functions on such domains. The last but not least concern is to unify (whenever possible) the proofs of the estimates to the extreme Dirichlet and Neumann cases of the mixed problem.

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The Joule‐Thomson effect on the thermoelectric conductors

Cited by 5 publications

References 12 publications

Radiative effects for some bidimensional thermoelectric problems

Radiative effects for some bidimensional thermoelectric problems

A limit model for thermoelectric equations

Explicit Estimates for Solutions of Mixed Elliptic Problems

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