Integral technique solutions to a class of simple ablation problems

Vallerani, E.

doi:10.1007/bf02209512

Cited by 14 publications

(3 citation statements)

References 2 publications

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“…Zien [3] reported an integral approximate solution of ablation of a semi-infinite body with two types of time-dependent heat fluxes: power-law and exponential heat fluxes. The results were compared with Vallerani's [4] results based on the classical heat balance integral solutions first proposed by Goodman [5]. The results showed that the integral approximate solution used by Zien [3] is more accurate than the classical heat balance integral solutions, especially for a short time period at the beginning of the ablation.…”

Section: Introductionmentioning

confidence: 93%

An Integral Approximate Solution to Ablation of a Two-Layer Composite with a Temporal Gaussian Heat Flux

Yang

Zhang

Chen

2011

Heat Transfer Engineering

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Ablation is the most common approach for thermal management for reentry of the spacecraft to the atmosphere. An analytical solution of the ablation of a two-layer composite, which includes an ablative layer and a nonablative substrate, subject to a Gaussian heat flux is presented in this paper. The problem is divided into five stages and the temperature distributions in both layers in the five stages are obtained using an integral approximate method. The locations of ablation interface, thermal penetration depth, and ablation rate are obtained and the effects of Stefan number, subcooling parameter, thickness of the ablative material, and ratio of thermal diffusivities between two materials are investigated.

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Section: Introductionmentioning

confidence: 93%

An Integral Approximate Solution to Ablation of a Two-Layer Composite with a Temporal Gaussian Heat Flux

Yang

Zhang

Chen

2011

Heat Transfer Engineering

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“…Nevertheless, the exact solution provides tests for convergence, accuracy, and stability of results. As given by Akbari [19], using a time step of 0.5 s yields an error Downloaded by [University of Sussex Library] at 00:14 01 June 2016 Use is thus made of the HIM of Vallerani [3] and the MOM of Zien [4] for comparison. Both are in good agreement with the present results; see Figure 3a.…”

Section: Numerical Solution Strategiesmentioning

confidence: 99%

“…However, it is the numerical results in his paper that have often been referred to by others for comparison. Popular analytical solutions for the ablation problems use a heat balance integral method (HIM) and a moment method (MOM), which provide reasonably accurate results [2][3][4]. The problems can also be solved by a variational analysis [5][6][7].…”

Section: Introductionmentioning

confidence: 99%

Solution of Ablation and Combination of Ablation and Stefan Problems by a Source-and-Sink Method

Akbari

Hsieh

1994

Numerical Heat Transfer, Part A: Applications

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A source-and-sink metlwd has been developed for the solution of both ablation and combination of ablation and Stefan problems for a one-dimensional, subcooled medium imposed with both constant and time variant heat jlwc conditions. In this metlwd the problem is solved in a jix£d domain, so that the original heat jlwc condition imposed on the moving boundary is taken to be the condition imposed on the solid-vapor or liquid-vapor intelface. This jlwc condition can then be used together with the temperature at the interface to solve for the interface position as well as the condition imposed on the fixed boundary. Finally, these interface position and boundary conditions are used in the temperature equation to complete the solution. The method has been used successfuUy in solving seven examples encompassing one-, two-, and three-phase ablation with the boundary of the medium imPVsed with constant, linear, and quadratic jlwc conditions. Numerical solutions.for these examples as weU as the trends of the moving boundary positions are discussed in detail.

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A General Integral Method for one dimensional ablation

Venkateshan

Solaiappan

1990

Wärme- und Stoffübertragung

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Integral technique solutions to a class of simple ablation problems

Cited by 14 publications

References 2 publications

An Integral Approximate Solution to Ablation of a Two-Layer Composite with a Temporal Gaussian Heat Flux

An Integral Approximate Solution to Ablation of a Two-Layer Composite with a Temporal Gaussian Heat Flux

Solution of Ablation and Combination of Ablation and Stefan Problems by a Source-and-Sink Method

A General Integral Method for one dimensional ablation

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