Heat conduction in nuclear fuel by the Kirchhoff transformation

Tomatis, Daniele

doi:10.1016/j.anucene.2013.01.048

Cited by 21 publications

(10 citation statements)

References 9 publications

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“…The Kirchhoff transformation [18] is the common approach to transform Eq. (1c) into a linear diffusion equation by applying (2a), namely Then, the solution of (2c) has been performed by, series expansion [4], separation of variables [19,20], homotopyperturbation method [22], etc.…”

Section: Problem Formulationmentioning

confidence: 99%

On the integral-balance approach to the transient heat conduction with linearly temperature-dependent thermal diffusivity

Fabre

Hristov

2016

Heat Mass Transfer

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relationship (Eqs. 9, 10) (m 2 /s) bCoefficient in Eq. (24b) which should be defined trough the initial condition δ (t = 0) = 0 C p Specific heat capacity (J/kg) E L (n, β, t) Squared-error function in accordance with the Langford criterion (Eq. 34) E LT (n, β, t) Squared-error function in accordance with the Langford criterion (Eq. 35) E Mq (p, β, t) Squared-error function in accordance with the Langford criterion and fixed flux BC problem (Eq. 76) e LT (n, β, t) Squared-error sub-function in accordance with the Langford criterion (Eq. 35) e Lq (p, β) Squared-error sub-function in accordance with the Langford criterion and the fixed flux BC problem k Thermal conductivity (W/mK) k (T) Temperature-dependent thermal conductivity (W/mK) k 0 Thermal conductivity of the linear problem (β = 0) (W/mK) m Dimensionless parameter of the nonlinearity (power-law diffusivity) n Dimensionless exponent of the parabolic profile p Dimensionless exponent of the parabolic profile of the assumed profile used to solve Eq. (48) (m) Abstract Closed form approximate solutions to nonlinear transient heat conduction with linearly temperaturedependent thermal diffusivity have been developed by the integral-balance integral method under transient conditions. The solutions uses improved direct approaches of the integral method and avoid the commonly used linearization by the Kirchhoff transformation. The main steps in the new solutions are improvements in the integration technique of the double-integration technique and the optimization of the exponent of the approximate parabolic profile with unspecified exponent. Solutions to Dirichlet and Neumann boundary condition problems have been developed as examples by the classical Heat-balance integral method (HBIM) and the Double-integration method (DIM). Additional examples with HBIM and DIM solutions to cases when the Kirchhoff transform is initially applied have been developed. List of symbolsThermal diffusivity (m 2 /s) a 0 Thermal diffusivity of the linear problem (β = 0) (m 2 /s) a p Thermal diffusivity coefficient in the case of power-law non-linear

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Section: Problem Formulationmentioning

confidence: 99%

On the integral-balance approach to the transient heat conduction with linearly temperature-dependent thermal diffusivity

Fabre

Hristov

2016

Heat Mass Transfer

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“…Kirchhoff's transformation can be derived differential of Â with the dimensionless quantity r, according to Popov et al (2000) and Tomatis (2013).…”

Section: K(t )Dt As a New Variablementioning

confidence: 99%

Development of a steady-state sub-channel code for small reactor on the basis of combined cross momentum and non-linear conduction

Chen

Zhang

2015

Nuclear Engineering and Design

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“…1, pp. S377-S389 a linearization through the Kirchhoff transformation [8], Heat-balance integral method (HBIM) [9] with Dirichlet boundary condition of the model eq. (1) and transformation the variables φ = T m and τ = t/m [10].…”

Section: S378mentioning

confidence: 99%

Non-linear heat conduction with ramped surface heating ramp surface heating and approximate solution

Hristov

2020

THERM SCI

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Non-linear heat conduction with a power-law thermal diffusivity and ramped surface temperature has been solved by the double-integration technique of the integral-balance integral method. The case of a semi-infinite medium and infinite ramp of surface temperature has been considered as example demonstrating the versatility of the solution approach. The thermal penetration depth and solution behaviours with finite speeds have been analyzed.

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Heat conduction in nuclear fuel by the Kirchhoff transformation

Cited by 21 publications

References 9 publications

On the integral-balance approach to the transient heat conduction with linearly temperature-dependent thermal diffusivity

On the integral-balance approach to the transient heat conduction with linearly temperature-dependent thermal diffusivity

Development of a steady-state sub-channel code for small reactor on the basis of combined cross momentum and non-linear conduction

Non-linear heat conduction with ramped surface heating ramp surface heating and approximate solution

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