Explicit solutions for a non-classical heat conduction problem for a semi-infinite strip with a non-uniform heat source

Ceretani, Andrea N.; Tarzia, Domingo A.; Villa, L. T.

doi:10.1186/s13661-015-0416-3

Cited by 6 publications

(9 citation statements)

References 26 publications

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“…Problems of this type are related to the thermostat problem [21,29,30,31,32,34,35]. For example, we will use mathematical ideas developed for the one-dimensional case in [2,25,46,49,50] and for the n-dimensional case in [8,9,10]. The first paper connecting the nonclassical heat equation with a phase-change process (i.e.…”

Section: Introductionmentioning

confidence: 99%

Explicit solution for non-classical one-phase Stefan problem with variable thermal coefficients and two different heat source terms

Bollati¹,

Natale²,

Semitiel³

et al. 2022

Preprint

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A one-phase Stefan problem for a semi-infinite material is investigated for special functional forms of the thermal conductivity and specific heat depending on the temperature of the phase-change material. Using the similarity transformation technique, an explicit solution for these situations are showed. The mathematical analysis is made for two different kinds of heat source terms, and the existence and uniqueness of the solutions are proved.

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Section: Introductionmentioning

confidence: 99%

Explicit solution for non-classical one-phase Stefan problem with variable thermal coefficients and two different heat source terms

Bollati¹,

Natale²,

Semitiel³

et al. 2022

Preprint

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“…This problem is motivated by modeling the temperature in an isotropic medium with the average of non-uniform and nonlocal sources that provide a cooling or heating system, according to the properties of the function F with respect to the heat flow (y, s) → V (y, s) = u x (0, y, s) at the boundary S, see [11,13]. Some references on the subject are [6], where F 1 t t 0 u x (0, y, s) ds is replaced by F (u x (0, y, t)), or [7], where it is replaced by F t 0 u x (0, y, s) ds ; see also [4,14,23,24], where the semi-infinite case of this nonlinear problem with F (u x (0, y, t)) has been considered. The non-classical one-dimensional heat equation in a slab with fixed or moving boundaries was studied in [14,22].…”

Section: Introductionmentioning

confidence: 99%

“…Some references on the subject are [6], where F 1 t t 0 u x (0, y, s) ds is replaced by F (u x (0, y, t)), or [7], where it is replaced by F t 0 u x (0, y, s) ds ; see also [4,14,23,24], where the semi-infinite case of this nonlinear problem with F (u x (0, y, t)) has been considered. The non-classical one-dimensional heat equation in a slab with fixed or moving boundaries was studied in [14,22]. See also other references on the subject: [8]- [10], [12], [16]- [19].…”

Section: Introductionmentioning

confidence: 99%

A heat conduction problem with sources depending on the average of the heat flux on the boundary

Boukrouche¹,

Tarzia²

2020

Rev. Un. Mat. Argentina

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Motivated by the modeling of temperature regulation in some mediums, we consider the non-classical heat conduction equation in the domain D = R n−1 × R + for which the internal energy supply depends on an average in the time variable of the heat flux (y, s) → V (y, s) = ux(0, y, s) on the boundary S = ∂D. The solution to the problem is found for an integral representation depending on the heat flux on S which is an additional unknown of the considered problem. We obtain that the heat flux V must satisfy a Volterra integral equation of the second kind in the time variable t with a parameter in R n−1. Under some conditions on data, we show that a unique local solution exists, which can be extended globally in time. Finally in the one-dimensional case, we obtain the explicit solution by using the Laplace transform and the Adomian decomposition method.

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“…This problem is motivated by modeling the temperature in an isotropic medium with the average of non-uniform and non local sources that provide cooling or heating system, according to the properties of the function F with respect to the heat flow (y, s) → V (y, s) = u x (0, y, s) at the boundary S, see [11,13]. Some references on the subject are [6] where F 1 t t 0 u x (0, y, s)ds is replaced by F (u x (0, y, t)), or [7] where is replaced by F t 0 u x (0, y, s)ds ; see also [4], [14], [23], [24] where the semi-infinite case of this nonlinear problem with F (u x (0, y, t)) have been considered. The non-classical one-dimensional heat equation in a slab with fixed or moving boundaries was studied in [14], [22].…”

Section: Introductionmentioning

confidence: 99%

A Heat Conduction Problem with Sources Depending on the Average of the Heat Flux on the Boundary

Boukrouche¹,

Tarzia²

2019

Preprint

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Motivated by the modeling of temperature regulation in some mediums, we consider the non-classical heat conduction equation in the domain D = R n−1 × R + for which the internal energy supply depends on an average in the time variable of the heat flux (y, s) → V (y, s) = ux(0, y, s) on the boundary S = ∂D. The solution to the problem is found for an integral representation depending on the heat flux on S which is an additional unknown of the considered problem. We obtain that the heat flux V must satisfy a Volterra integral equation of second kind in the time variable t with a parameter in R n−1 . Under some conditions on data, we show that a unique local solution exists, which can be extended globally in time. Finally in the one-dimensional case, we obtain the explicit solution by using the Laplace transform and the Adomian decomposition method.

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Explicit solutions for a non-classical heat conduction problem for a semi-infinite strip with a non-uniform heat source

Cited by 6 publications

References 26 publications

Explicit solution for non-classical one-phase Stefan problem with variable thermal coefficients and two different heat source terms

Explicit solution for non-classical one-phase Stefan problem with variable thermal coefficients and two different heat source terms

A heat conduction problem with sources depending on the average of the heat flux on the boundary

A Heat Conduction Problem with Sources Depending on the Average of the Heat Flux on the Boundary

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