# Heat Transfer Between Concentric Cylinders with Heat Source

In this application, AcuSolve is used to simulate a 2D cable problem to demonstrate one way Flux-AcuSolve coupling. The 2D cable is used to demonstrate how the volumetric heat load conducts through a solid. AcuSolve results are compared with analytical results as described in Incropera (2006). The close agreement of AcuSolve results with analytical results validates the ability of AcuSolve to model cases with volumetric heat source applied on a solid volume.

## 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 the 2D solid conduction model case with volumetric heat source applied on a solid volume. In this application, the temperature within the cylinders is driven by a gradient along the outer and inner solid volumes, due to the volumetric heat source and fixed temperature. The AcuSolve solution for the temperature as a function of radius matches well compared to the analytical solution.

## Heat Transfer Between Concentric Cylinders with Heat Source

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

Global

- Problem Description
- Analysis type - Steady State
- Turbulence equation - Advective Diffusive
- Absolute temperature offset -
`273.15`

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

- Convergence tolerance -
- Material Model
- Insulation
- Density
- Type - Constant
- Conductivity -
`2702.0`

- Specific Heat
- Type - Constant
- Conductivity -
`908.0`

- Conductivity
- Type - Constant
- Conductivity -
`0.8`

Model

- Insulation
- Volumes
- Solid
- Element Set
- Medium - Solid
- Material model - Insulation

- Element Set
- SolidHeated
- Element Set
- Medium - Solid
- Material model - Insulation
- Total heat source - 1.46686 (applied through EMag Manager)

- Element Set

- Solid
- Surfaces
- +ZInner
- Simple Boundary Condition - (disabled, no BC needed)

- +ZOuter
- Simple Boundary Condition - (disabled, no BC needed)

- -ZInner
- Simple Boundary Condition - (disabled, no BC needed)

- -ZOuter
- Simple Boundary Condition - (disabled, no BC needed)

- InterfaceAll
- Simple Boundary Condition - (disabled, no BC needed)

- InterfaceInner
- Simple Boundary Condition - (disabled, no BC needed)

- InterfaceOuter
- Simple Boundary Condition - (disabled, no BC needed)

- OuterWall
- Simple Boundary Condition
- Type - Wall
- Temperature BC type - Value
- Temperature -
`20.0`K

- Simple Boundary Condition

- +ZInner

## References

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