# RD-E: 5300 Thermal Analysis

A heat source moved on one plate. Heat exchanged between a heatsource and a plate through contact, also between a plate and theatmosphere (water) through convective flux.

## Options and Keywords Used

- /HEAT/MAT
- /CONVEC
- /IMPTEMP
- /INTER/TYPE7
- /MAT/LAW2 (PLAS_JOHNS)
- Boundary conditions (/BCS)
- Imposed displacement (/IMPDISP)

## Input Files

Refer to Access the Model Files to download the required model file(s).

The model files used in this example are available in:

/radioss/example/53_thermal_analysis

## Model Description

Units: mm, ms, g, N, and MPa

**Material Properties**- Initial density
- 2.8 x 10
^{-3}$\left[\frac{\text{g}}{{\text{mm}}^{3}}\right]$ - Young's modulus
- 70000 $\left[\mathrm{MPa}\right]$
- Poisson ratio
- 0.33
- Yield stress
- 206 $\left[\mathrm{MPa}\right]$
- Hardening parameter
- 450 $\left[\mathrm{MPa}\right]$
- Hardening exponent
- 0.5
- Room temperature
- 298 $\left[\text{K}\right]$
- Specific heat $\rho {C}_{p}$
- 2.51
- Initial temperature for heat source
- 800 [K] and for plate: 398 [K]
- Thermal conductivity coefficient AS
- 0.23

### Model Method

/HEAT/MAT is an additional material law card used to describe the material thermal character. So the material ID in the material law in /MAT and in /HEAT/MAT must be the same. The thermal parameter defined in /HEAT/MAT will recover the same parameters which are defined in the material law.

Heat capacity provides heat and mass the ability to change the temperature. In engineering and science, it is recommended to use specific heat capacity, which is heat capacity divided by mass, $$\left[\frac{\text{J}}{\text{kg}\cdot \text{K}}\right]$$ in SI unit. Heat capacity is $${C}_{p}=897\left[\frac{\text{J}}{\mathrm{kg}\cdot \text{K}}\right]=897\left[\frac{\text{N}\cdot \text{mm}}{\text{g}\cdot \text{K}}\right]$$ for aluminum. Refer to Material Constants in the Theory Manual Appendices for more information on heat capacity of ordinary material.

For the thermal conductivity coefficient AS, $$0.23\left[\frac{\text{N}\cdot \text{mm}}{\text{ms}\cdot \text{mm}\cdot \text{K}}\right]$$. Thermal conductivity $$k=230\left[\frac{\text{W}}{\text{m}\cdot \text{K}}\right]=0.23\left[\frac{\text{N}\cdot \text{mm}}{\text{ms}\cdot \text{mm}\cdot \text{K}}\right]$$ for aluminum, and constant thermal conductivity. Set $$BS=0$$. Since thermal conductivity $$k=AS+BS\ast T$$, then $$k=AS$$, in this case.

(1) | (2) | (3) | (4) | (5) | (6) | (7) | (8) | (9) | (10) |
---|---|---|---|---|---|---|---|---|---|

/CONVEC/convec_ID/unit_ID |
|||||||||

convec_flux_title |
|||||||||

surf_ID_{T} |
fct_ID_{T} |
sens_ID |
|||||||

Ascale_{x} |
Fscale_{y} |
T_{start} |
T_{stop} |
H |

`fct_ID`

_{T}(Figure 4).

Where, `H` is the heat transfer coefficient between structural
component and its surrounding infinite room with unit $$\left[\frac{\text{J}}{\text{s}\cdot {\text{m}}^{\text{2}}\cdot \text{K}}\right]$$ . In general, the convective heat transfer
coefficient for water (free convection) is about 20 - 100 $$\left[\frac{\text{J}}{\text{s}\cdot {\text{m}}^{\text{2}}\cdot \text{K}}\right]$$ and water (forced convection) is about 50 - 10000 $$\left[\frac{\text{J}}{\text{s}\cdot {\text{m}}^{\text{2}}\cdot \text{K}}\right]$$. Forced convection in water is $$H=500\left[\frac{\text{J}}{\text{s}\cdot {\text{m}}^{\text{2}}\cdot \text{K}}\right]=5\text{e}-4\left[\frac{\text{N}\cdot \text{mm}}{\text{s}\cdot {\text{mm}}^{\text{2}}\cdot \text{K}}\right]$$.

In /INTER/TYPE7, heat exchange between the heat source and plate
during the contact, is defined `K`_{the}=1 to activated
heat transfer between main and secondary.

`I`

_{the}= 1

(1) | (2) | (3) | (4) | (5) | (6) | (7) | (8) | (9) | (10) |
---|---|---|---|---|---|---|---|---|---|

K_{the} |
fct_ID_{K} |
T_{int} |
I_{the_form} |
Ascale_{K} |
|||||

F_{rad} |
D_{rad} |
Fheat_{s} |
Fheat_{m} |

`I`_{the_form} set to 1 for
heat exchange between all pieces in contact.

- Define constant heat exchange coefficient using
`K`_{the}($$\left[\frac{\text{W}}{{\text{m}}^{2}\cdot \text{K}}\right]$$ in SI unit). In this case,`fct_ID`_{K}= 0. - If
`fct_ID`_{K}$\ne $ 0, the heat exchange coefficient is the function of contact pressure using this curve and`K`_{the}is the scale factor.

Set `Fheat`_{s} and
`Fheat`_{m} to 0, to not consider
heat friction.

## Results

- Nodal N641 is not under trace. The temperature changed, only due to convection with water.
- Nodal N1034, N958 and N1708 are under trace. At first the temperature decreased before the heat source began, due to convection with water, and then increased, due to the heat exchange from the heat source through contact. Once the heat source is removed, the temperature decreased again, due to the heat conduction inside the material and convection with water. So the slope of the temperature decrease is much larger than N641 (only convection).