Solution Construction for the Nonlinear Heat Transfer Problem in a Cylindrical Porous Fin

Martins‐Costa, Maria Laura; Sarmento, Vinícius Vendas; Gama, Rogério Pazetto Saldanha da; Gama, Rogério Martins Saldanha da

doi:10.1615/jpormedia.2022040580

Cited by 5 publications

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“…For instance, Martins-Costa et al [11] obtained the temperature distribution in porous fins by minimizing a convex functional. Martins-Costa et al [12] constructed a solution for the nonlinear problem arising from natural convection and thermal radiation in cylindrical porous fins from a sequence of linear problems, using the parameters suggested by Gorla and Bakier [13].…”

Section: Introductionmentioning

confidence: 99%

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A Variational Formulation for Fins with Nonzero Contact Thermal Resistance at the Base

Gama

Sarmento

et al. 2023

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This paper considers the steady-state heat transfer process in a fin with a Robin boundary condition at the base (instead of the usual Dirichlet boundary condition at the base). Robin boundary condition models the effect of the thermal resistance between the base of the fin and the surface on which the fin is placed. This work presents an equivalent minimum principle, represented by a convex and coercive functional, ensuring the solution’s existence and uniqueness. In order to illustrate the use of the proposed functional for reaching approximations, the heat-transfer process in a trapezoidal fin considering a piecewise linear approximation is simulated. The appendix presents a case in which the exact solution in a closed form has been achieved.

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Section: Introductionmentioning

confidence: 99%

“…In addition, f is not a linear function of T . For a cylindrical porous fin, considering only natural convection, it becomes [12,13]:…”

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confidence: 99%

A Variational Formulation for Fins with Nonzero Contact Thermal Resistance at the Base

Gama

Sarmento

et al. 2023

Axioms

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A methodology using a non-increasing sequence applied in the solution of heat transfer problems

Sarmento,

Martins-Costa,

Saldanha da Gama

2023

Applications in Engineering Science

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Heat transfer in heat sinks: An analytical approach based on integral transforms

Corrêa,

Chalhub

2023

Thermal Science and Engineering Progress

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Solution Construction for the Nonlinear Heat Transfer Problem in a Cylindrical Porous Fin

Cited by 5 publications

References 0 publications

A Variational Formulation for Fins with Nonzero Contact Thermal Resistance at the Base

A Variational Formulation for Fins with Nonzero Contact Thermal Resistance at the Base

A methodology using a non-increasing sequence applied in the solution of heat transfer problems

Heat transfer in heat sinks: An analytical approach based on integral transforms

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