An upper bound for the steady-state temperature for a class of heat conduction problems wherein the thermal conductivity is temperature dependent

Gama, Rogério Martins Saldanha da; Corrêa, Eduardo Dias; Martins‐Costa, Maria Laura

doi:10.1016/j.ijengsci.2013.04.002

Cited by 16 publications

(1 citation statement)

References 9 publications

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“…In reference [13], Afrin et al provided an estimate for the temperature distribution, in a context of variable thermal conductivity, with the aid of a Kirchhoff transformation, by means of a Hadamard factorization, relating the front and back surface temperature as infinite product of polynomials. Reference [14] provides an a priori upper bound estimate for cases in which the thermal conductivity is a linear function of the temperature.…”

Section: Introductionmentioning

confidence: 99%

A Linear Approach Suitable for a Class of Steady-State Heat Transfer Problems with Temperature-Dependent Thermal Conductivity

Gama

Pazetto

2021

Mathematical Problems in Engineering

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This work presents an useful tool for constructing the solution of steady-state heat transfer problems, with temperature-dependent thermal conductivity, by means of the solution of Poisson equations. Specifically, it will be presented a procedure for constructing the solution of a nonlinear second-order partial differential equation, subjected to Robin boundary conditions, by means of a sequence whose elements are obtained from the solution of very simple linear partial differential equations, also subjected to Robin boundary conditions. In addition, an a priori upper bound estimate for the solution is presented too. Some examples, involving temperature-dependent thermal conductivity, are presented, illustrating the use of numerical approximations.

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Section: Introductionmentioning

confidence: 99%

A Linear Approach Suitable for a Class of Steady-State Heat Transfer Problems with Temperature-Dependent Thermal Conductivity

Gama

Pazetto

2021

Mathematical Problems in Engineering

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Existence, uniqueness and construction of the solution of the energy transfer problem in a rigid and non-convex blackbody with temperature-dependent thermal conductivity

Gama

2015

Z. Angew. Math. Phys.

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In this paper, we study the steady-state (coupled) conduction-radiation heat transfer phenomenon in a non-convex opaque blackbody with temperature-dependent thermal conductivity. The mathematical description consists of a nonlinear partial differential equation subjected to a nonlinear boundary condition involving an integral operator that is inherently associated with the non-convexity of the body. The unknown is the absolute temperature distribution. The problem is rewritten with the aid of a Kirchhoff transformation, giving rise to linear partial differential equation and a new unknown. An iterative procedure is proposed for constructing the solution of the problem by means of a sequence of problems, each of them with an equivalent minimum principle. Proofs of convergence as well as existence and uniqueness of the solution are presented. An error estimate, for each element of the sequence, is presented too.Mathematics Subject Classification. 35J60 · 35J65.

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Time-domain finite element analysis to nonlinear transient responses of generalized diffusion-thermoelasticity with variable thermal conductivity and diffusivity

Guo

Tian

2017

International Journal of Mechanical Sciences

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An upper bound for the steady-state temperature for a class of heat conduction problems wherein the thermal conductivity is temperature dependent

Cited by 16 publications

References 9 publications

A Linear Approach Suitable for a Class of Steady-State Heat Transfer Problems with Temperature-Dependent Thermal Conductivity

A Linear Approach Suitable for a Class of Steady-State Heat Transfer Problems with Temperature-Dependent Thermal Conductivity

Existence, uniqueness and construction of the solution of the energy transfer problem in a rigid and non-convex blackbody with temperature-dependent thermal conductivity

Time-domain finite element analysis to nonlinear transient responses of generalized diffusion-thermoelasticity with variable thermal conductivity and diffusivity

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