As I wrote earlier, if new idea's arise I would pick up this thread again.

For several reasons I did not find any reason to do new Lugano based calculations nor find the time to continue studying atom theory as I intended.

But in between I did a new investigative calculation on the second MFMP thermal dogbone test.

The calculation is based on the DB_test3_TC test.

Note that this calculation is indicative, not exact due to the unknown heat distribution in the MFMP dogbone for the used power of 300 Watt.

see : https://drive.google.com/drive…xJkjesxe4kXzczVnlfajhjbDQ

We start with a calculation on the heater coil of the MFMP dogbone.

Specifications are :

Diameter 11.1 mm

Windingen under ribs : 76.5

From the coil specificatione we derive a total wire length under the ribs of 265.05 cm

Total wire length in the dogbone : 273.05 cm (two times 4 cm in the end caps added)

This means that 265.05/273.05 = 0.971 of total coil power is dissipated under the ribs

(Did not take into account the heater wire length outside the dogbone since it is not known)

From the DB_test3 we use for our calculation the last value for the 300 watt applied power.

(sample number 147)

The important data :

Optris temperature-----------------505.4 degree C

Applied power------------------------300.24 Watt

The power under the ribs is now calcualted as 0.971 x 300.24 = 291.5 Watt

We have 10 measurement sections, thus the power per rib section = 29.15 watt

For the temperature of 505.4 degree C with an ambient temperature of 17.5 degree C the calculated convective heat transfer coefficient is 13.49

Due to the ribs being close which reduces the convective heat transfer we have to correct this with a factor 0.735 which brings the value to 0.735 x 13.49 = 9.92

(The value of 0.735 was interpolated from two CFD simulations)

Area of a section is 0.00263 m^2.

Thus the disspated convective power is 9.92 x 0.00263 x (505.4 - 17.5) = 12.73 Watt

Radiated power 29.15 -12.73 = 16.42 Watt (Discarding the limited lateral power dissipation)

We now us the following formula to calculate the emissivity

See for an explanation of the formula :

Rossi Lugano/early demo's revisited. (technical)

E = σ x Af x e x Fbg x { 1/(1 - (1-Fbg)(1-e))} x T^4

with---E--------Radiated energy (11.84 Watt)

---------σ--------Stefan-Boltzmann constant (5.67·10-8 W/m2K4)

---------Af-------Fin area of a section (0.00263 m^2)

---------e--------Emissivity

---------Fbg-----View factor of ribs to background ( 0.572 )

---------T--------Temperature (Kelvin) ( 505.40 + 273.15 = 778.55 K )

Before we apply the formula we have to correct the Optris temperature reading due to the increase in apparent emissivity caused by the reflection between the ribs.

The apparent emissivity is

e' = e /(1 - (1-Fbg)(1-e))

For the used Optris in band emissivity setting of 0.95 the apparent emssivity becomes 0.97.

The relationship between temperature and n value as used in the formula given by Optris is given in the following post :

Rossi Lugano/early demo's revisited. (technical)

Applying this to the formula given by Optris we find that the real temperature was 499 degree C (772.15 K) with a value of n = 2.311.

Filling in the found values in the above equation for the radiated energy we find for the emissivity a value of 0.41.

This calculated indicative value is much lower then the broad band emissivity value of Alumina for the temperature of 499 degree C, the value being 0.65.

This becomes clear if we plot this value in the graph of the broad band emissivity as a function of temperature for Alumina.

This is shown in the following figure :

The much lower calculated emissivity then that of Alumina indicates that the MFMP dogbone was not casted of pure (> 98 %) Alumina, but instead must have contained other components or being based on an other type ceramic.

The question is then if the MFMP as a part of their test did check if their Dogbone was casted conform their material specification.

Note :

As a verification I did a FEM simulation with broad band emissivities set at a value of 0.41 at the middle of the dogbone and got simulated center temperatures of 497 degree C, close to the 499 C calculated from the Optris. It confirms that to get a temperature of about 499 C the emissivity has to be much lower then that of Alumina.