# Heat Transfer Between Radiating Concentric Cylinders

In this application, AcuSolve is used to simulate the heat transfer due to radiation between concentric cylinders. The inner and outer cylinders are held at constant temperature and are defined to be radiation surfaces. AcuSolve results are compared with analytical results for temperature as described in Incropera (2006). The close agreement of AcuSolve results with analytical results validates the ability of AcuSolve to model cases with radiation heat transfer requiring view factor computation.

## Problem Description

The simulation was performed as a two dimensional problem by constructing a volume mesh that contains a single layer of elements normal to the radial and circumferential directions.

## AcuSolve Results

## Summary

The AcuSolve solution compares well with analytical results for heat transfer due to radiation between two concentric cylinders. In this application, an arbitrary material is subjected to a heat flux that is calculated based on the view factors within the model. As a result of radiative heat flux a temperature distribution between the two cylinders develops. The AcuSolve solution for the temperature as a function of radius matches well compared to the analytical solution.

## Heat Transfer Between Radiating Concentric Cylinders

AcuConsole database file: <your working directory>\annulus_radiation\annulus_radiation.acs

Global

- Problem Description
- Analysis type - Steady State
- Temperature equation - Advective Diffusive
- Radiation equation- Enclosure

- Auto Solution Strategy
- Convergence tolerance -
`0.0001` - Relaxation Factor-
`0.4` - Flow- off
- Enclosure radiation- on

- Convergence tolerance -
- Material Model
- Material
- Conductivity
- Type - Constant
- Conductivity-
`1.0`

- Conductivity

- Material
- Emissivity Model
- Grey Body
- Emissivity-
`0.03778`

- Emissivity-
- Black Body
- Emissivity-
`1.0`

- Emissivity-

Model

- Grey Body
- Volumes
- Medium
- Element Set
- Medium - Fluid
- Material model- Material

- Element Set

- Medium
- Surfaces
- ID
- Simple Boundary Condition
- Type- Wall
- Temperature BC type- Value
- Temperature-
`773.0`K

- Radiation Surface
- Type- Wall
- Emissivity model- Grey Body

- Simple Boundary Condition
- Max_Z
- Simple Boundary Condition
- Type- Symmetry

- Radiation Surface
- Type- Wall
- Emissivity model- Black Body

- Simple Boundary Condition
- Min_Z
- Simple Boundary Condition
- Type- Symmetry

- Radiation Surface
- Type- Wall
- Emissivity model- Black Body

- Simple Boundary Condition
- OD
- Simple Boundary Condition
- Type- Wall
- Temperature BC type- Value
- Temperature-
`300.0`K

- Radiation Surface
- Type- Wall
- Emissivity model- Grey Body

- Simple Boundary Condition

- ID

## References

F. P. Incropera and D. P. DeWitt. "Fundamentals of Heat Transfer - Sixth Edition". John Wiley & Sons. New York. 2006.