# Optimal design of multi-layer thermal protection of variable thickness

Optimal design of multi-layer thermal protection of variable thickness <jats:sec><jats:title content-type="abstract-subheading">Purpose</jats:title><jats:p>The presented paper aims to consider algorithm for optimal design of multilayer thermal insulation.</jats:p></jats:sec><jats:sec><jats:title content-type="abstract-subheading">Design/methodology/approach</jats:title><jats:p>Developed algorithm is based on a sequential quadratic programming method.</jats:p></jats:sec><jats:sec><jats:title content-type="abstract-subheading">Findings</jats:title><jats:p>2D mathematical model of heat transfer in thermal protection was considered in frame of thermal design of spacecraft. The sensitivity functions were used to estimate the Jacobean of the object functions.</jats:p></jats:sec><jats:sec><jats:title content-type="abstract-subheading">Research limitations/implications</jats:title><jats:p>Design of distributed parameter systems and shape optimization may be thought of as geometrical inverse problems, in which the positions of free boundaries are determined along with the spatial variables. In such problems, the missing data (i.e. the position of boundaries) are compensated for by the presence of the so-called inverse problem additional conditions. In the case under consideration, such conditions are constrains on the temperature values at the discrete points of the system.</jats:p></jats:sec><jats:sec><jats:title content-type="abstract-subheading">Practical implications</jats:title><jats:p>Results are presented how to apply the algorithm suggested for solving a practical problem – thickness sampling for a thermal protection system of advanced solar probe.</jats:p></jats:sec><jats:sec><jats:title content-type="abstract-subheading">Originality/value</jats:title><jats:p>The procedure proposed in the paper to solve a design problem is based on the method of quadratic approximation of the initial problem statement as a Lagrange formulation. This has allowed to construct a rather universal algorithm applicable without modification for solving a wide range of thermal design problems.</jats:p></jats:sec> http://www.deepdyve.com/assets/images/DeepDyve-Logo-lg.png International Journal of Numerical Methods for Heat & Fluid Flow CrossRef

# Optimal design of multi-layer thermal protection of variable thickness

International Journal of Numerical Methods for Heat & Fluid Flow , Volume 27 (5): 1040-1055 – May 2, 2017

## Optimal design of multi-layer thermal protection of variable thickness

### Abstract

<jats:sec><jats:title content-type="abstract-subheading">Purpose</jats:title><jats:p>The presented paper aims to consider algorithm for optimal design of multilayer thermal insulation.</jats:p></jats:sec><jats:sec><jats:title content-type="abstract-subheading">Design/methodology/approach</jats:title><jats:p>Developed algorithm is based on a sequential quadratic programming method.</jats:p></jats:sec><jats:sec><jats:title content-type="abstract-subheading">Findings</jats:title><jats:p>2D mathematical model of heat transfer in thermal protection was considered in frame of thermal design of spacecraft. The sensitivity functions were used to estimate the Jacobean of the object functions.</jats:p></jats:sec><jats:sec><jats:title content-type="abstract-subheading">Research limitations/implications</jats:title><jats:p>Design of distributed parameter systems and shape optimization may be thought of as geometrical inverse problems, in which the positions of free boundaries are determined along with the spatial variables. In such problems, the missing data (i.e. the position of boundaries) are compensated for by the presence of the so-called inverse problem additional conditions. In the case under consideration, such conditions are constrains on the temperature values at the discrete points of the system.</jats:p></jats:sec><jats:sec><jats:title content-type="abstract-subheading">Practical implications</jats:title><jats:p>Results are presented how to apply the algorithm suggested for solving a practical problem – thickness sampling for a thermal protection system of advanced solar probe.</jats:p></jats:sec><jats:sec><jats:title content-type="abstract-subheading">Originality/value</jats:title><jats:p>The procedure proposed in the paper to solve a design problem is based on the method of quadratic approximation of the initial problem statement as a Lagrange formulation. This has allowed to construct a rather universal algorithm applicable without modification for solving a wide range of thermal design problems.</jats:p></jats:sec>

/lp/crossref/optimal-design-of-multi-layer-thermal-protection-of-variable-thickness-SNye0hyFaU
Publisher
CrossRef
ISSN
0961-5539
DOI
10.1108/hff-03-2016-0112
Publisher site
See Article on Publisher Site

### Abstract

<jats:sec><jats:title content-type="abstract-subheading">Purpose</jats:title><jats:p>The presented paper aims to consider algorithm for optimal design of multilayer thermal insulation.</jats:p></jats:sec><jats:sec><jats:title content-type="abstract-subheading">Design/methodology/approach</jats:title><jats:p>Developed algorithm is based on a sequential quadratic programming method.</jats:p></jats:sec><jats:sec><jats:title content-type="abstract-subheading">Findings</jats:title><jats:p>2D mathematical model of heat transfer in thermal protection was considered in frame of thermal design of spacecraft. The sensitivity functions were used to estimate the Jacobean of the object functions.</jats:p></jats:sec><jats:sec><jats:title content-type="abstract-subheading">Research limitations/implications</jats:title><jats:p>Design of distributed parameter systems and shape optimization may be thought of as geometrical inverse problems, in which the positions of free boundaries are determined along with the spatial variables. In such problems, the missing data (i.e. the position of boundaries) are compensated for by the presence of the so-called inverse problem additional conditions. In the case under consideration, such conditions are constrains on the temperature values at the discrete points of the system.</jats:p></jats:sec><jats:sec><jats:title content-type="abstract-subheading">Practical implications</jats:title><jats:p>Results are presented how to apply the algorithm suggested for solving a practical problem – thickness sampling for a thermal protection system of advanced solar probe.</jats:p></jats:sec><jats:sec><jats:title content-type="abstract-subheading">Originality/value</jats:title><jats:p>The procedure proposed in the paper to solve a design problem is based on the method of quadratic approximation of the initial problem statement as a Lagrange formulation. This has allowed to construct a rather universal algorithm applicable without modification for solving a wide range of thermal design problems.</jats:p></jats:sec>

### Journal

International Journal of Numerical Methods for Heat & Fluid FlowCrossRef

Published: May 2, 2017

### References

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