# Sensitivity Analysis and Uncertainty Propagation in a General-Purpose Thermal Analysis Code

## Abstract

Methods are discussed for computing the sensitivity of field variables to changes in material properties and initial/boundary condition parameters for heat transfer problems. The method we focus on is termed the ''Sensitivity Equation Method'' (SEM). It involves deriving field equations for sensitivity coefficients by differentiating the original field equations with respect to the parameters of interest and numerically solving the resulting sensitivity field equations. Uncertainty in the model parameters are then propagated through the computational model using results derived from first-order perturbation theory; this technique is identical to the methodology typically used to propagate experimental uncertainty. Numerical results are presented for the design of an experiment to estimate the thermal conductivity of stainless steel using transient temperature measurements made on prototypical hardware of a companion contact conductance experiment. Comments are made relative to extending the SEM to conjugate heat transfer problems.

- Authors:

- Publication Date:

- Research Org.:
- Sandia National Labs., Albuquerque, NM (US); Sandia National Labs., Livermore, CA (US)

- Sponsoring Org.:
- US Department of Energy (US)

- OSTI Identifier:
- 9700

- Report Number(s):
- SAND99-2058C

TRN: AH200125%%143

- DOE Contract Number:
- AC04-94AL85000

- Resource Type:
- Conference

- Resource Relation:
- Conference: 3rd ASME/JSME Joint Fluids Engineering Conference, San Francisco, CA (US), 07/18/1999--07/22/1999; Other Information: PBD: 4 Aug 1999

- Country of Publication:
- United States

- Language:
- English

- Subject:
- 36 MATERIALS SCIENCE; FIELD EQUATIONS; HEAT TRANSFER; PERTURBATION THEORY; SENSITIVITY; SENSITIVITY ANALYSIS; STAINLESS STEELS; TEMPERATURE MEASUREMENT; THERMAL ANALYSIS; THERMAL CONDUCTIVITY; TRANSIENTS

### Citation Formats

```
Blackwell, Bennie F., and Dowding, Kevin J.
```*Sensitivity Analysis and Uncertainty Propagation in a General-Purpose Thermal Analysis Code*. United States: N. p., 1999.
Web.

```
Blackwell, Bennie F., & Dowding, Kevin J.
```*Sensitivity Analysis and Uncertainty Propagation in a General-Purpose Thermal Analysis Code*. United States.

```
Blackwell, Bennie F., and Dowding, Kevin J. Wed .
"Sensitivity Analysis and Uncertainty Propagation in a General-Purpose Thermal Analysis Code". United States. https://www.osti.gov/servlets/purl/9700.
```

```
@article{osti_9700,
```

title = {Sensitivity Analysis and Uncertainty Propagation in a General-Purpose Thermal Analysis Code},

author = {Blackwell, Bennie F. and Dowding, Kevin J.},

abstractNote = {Methods are discussed for computing the sensitivity of field variables to changes in material properties and initial/boundary condition parameters for heat transfer problems. The method we focus on is termed the ''Sensitivity Equation Method'' (SEM). It involves deriving field equations for sensitivity coefficients by differentiating the original field equations with respect to the parameters of interest and numerically solving the resulting sensitivity field equations. Uncertainty in the model parameters are then propagated through the computational model using results derived from first-order perturbation theory; this technique is identical to the methodology typically used to propagate experimental uncertainty. Numerical results are presented for the design of an experiment to estimate the thermal conductivity of stainless steel using transient temperature measurements made on prototypical hardware of a companion contact conductance experiment. Comments are made relative to extending the SEM to conjugate heat transfer problems.},

doi = {},

journal = {},

number = ,

volume = ,

place = {United States},

year = {1999},

month = {8}

}