# EXACT SOLUTION OF HEAT CONDUCTION IN A TWO-DOMAIN COMPOSITE CYLINDER WITH AN ORTHOTROPIC OUTER LAYER.

## Abstract

The transient exact solution of heat conduction in a two-domain composite cylinder is developed using the separation of variables technique. The inner cylinder is isotropic and the outer cylindrical layer is orthotropic. Temperature solutions are obtained for boundary conditions of the first and second kinds at the outer surface of the orthotropic layer. These solutions are applied to heat flow calorimeters modeling assuming that there is heat generation due to nuclear reactions in the inner cylinder. Heat flow calorimeter simulations are carried out assuming that the inner cylinder is filled with plutonium oxide powder. The first objective in these simulations is to predict the onset of thermal equilibrium of the calorimeter with its environment. Two types of boundary conditions at the outer surface of the orthotropic layer are used to predict thermal equilibrium. The procedure developed to carry out these simulations can be used as a guideline for the design of calorimeters. Another important application of these solutions is on the estimation of thermophysical properties of orthotropic cylinders. The thermal conductivities in the vertical, radial and circumferential directions of the orthotropic outer layer can be estimated using this exact solution and experimental data. Simultaneous estimation of the volumetric heat capacitymore »

- Authors:

- Publication Date:

- Research Org.:
- Los Alamos National Lab., NM (US)

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

- OSTI Identifier:
- 767432

- Report Number(s):
- LA-UR-00-5289

TRN: US0102873

- DOE Contract Number:
- W-7405-ENG-36

- Resource Type:
- Conference

- Resource Relation:
- Conference: Conference title not supplied, Conference location not supplied, Conference dates not supplied; Other Information: PBD: 1 Nov 2000

- Country of Publication:
- United States

- Language:
- English

- Subject:
- 47 OTHER INSTRUMENTATION; 22 GENERAL STUDIES OF NUCLEAR REACTORS; THERMAL CONDUCTION; CYLINDERS; CALORIMETERS; DESIGN; BOUNDARY CONDITIONS; HEAT FLUX; NUCLEAR REACTIONS; PLUTONIUM OXIDES; RECOMMENDATIONS; SPECIFIC HEAT; THERMAL DIFFUSIVITY; THERMAL EQUILIBRIUM

### Citation Formats

```
C. AVILES-RAMOS, and C. RUDY.
```*EXACT SOLUTION OF HEAT CONDUCTION IN A TWO-DOMAIN COMPOSITE CYLINDER WITH AN ORTHOTROPIC OUTER LAYER.*. United States: N. p., 2000.
Web.

```
C. AVILES-RAMOS, & C. RUDY.
```*EXACT SOLUTION OF HEAT CONDUCTION IN A TWO-DOMAIN COMPOSITE CYLINDER WITH AN ORTHOTROPIC OUTER LAYER.*. United States.

```
C. AVILES-RAMOS, and C. RUDY. Wed .
"EXACT SOLUTION OF HEAT CONDUCTION IN A TWO-DOMAIN COMPOSITE CYLINDER WITH AN ORTHOTROPIC OUTER LAYER.". United States.
doi:. https://www.osti.gov/servlets/purl/767432.
```

```
@article{osti_767432,
```

title = {EXACT SOLUTION OF HEAT CONDUCTION IN A TWO-DOMAIN COMPOSITE CYLINDER WITH AN ORTHOTROPIC OUTER LAYER.},

author = {C. AVILES-RAMOS and C. RUDY},

abstractNote = {The transient exact solution of heat conduction in a two-domain composite cylinder is developed using the separation of variables technique. The inner cylinder is isotropic and the outer cylindrical layer is orthotropic. Temperature solutions are obtained for boundary conditions of the first and second kinds at the outer surface of the orthotropic layer. These solutions are applied to heat flow calorimeters modeling assuming that there is heat generation due to nuclear reactions in the inner cylinder. Heat flow calorimeter simulations are carried out assuming that the inner cylinder is filled with plutonium oxide powder. The first objective in these simulations is to predict the onset of thermal equilibrium of the calorimeter with its environment. Two types of boundary conditions at the outer surface of the orthotropic layer are used to predict thermal equilibrium. The procedure developed to carry out these simulations can be used as a guideline for the design of calorimeters. Another important application of these solutions is on the estimation of thermophysical properties of orthotropic cylinders. The thermal conductivities in the vertical, radial and circumferential directions of the orthotropic outer layer can be estimated using this exact solution and experimental data. Simultaneous estimation of the volumetric heat capacity and thermal conductivities is also possible. Furthermore, this solution has potential applications to the solution of the inverse heat conduction problem in this cylindrical geometry. An interesting feature of the construction of this solution is that two different sets of eigenfunctions need to be considered in the eigenfunction expansion. These eigenfunctions sets depend on the relative values of the thermal diffusivity of the inner cylinder and the thermal diffusivity in the vertical direction of the outer cylindrical layer.},

doi = {},

journal = {},

number = ,

volume = ,

place = {United States},

year = {Wed Nov 01 00:00:00 EST 2000},

month = {Wed Nov 01 00:00:00 EST 2000}

}