**MFMP dogbone thermal versus applied power. A case study**

In post #445 in this forum thread we have shown that for the second MFMP dogbone thermal test the applied electrical power differs largely from the calulated thermal power.

This can be possibly due to one of the following reasons :

Wrong power measurement

Wrong temperature measurement

Emissivity of the casting material is different

Concerning the power measurement we can state that for the first MFMP dogbone thermal test we are able to calculate from the posted data the heater coil resistance for each setting.

This resistance has about the same value for each run and calculating the wire resistance from the supplied heater coil winding data gives about the same value.

Thus it is likely that the power measurments of the MFMP where correct.

Concerning the temperature measurment we know that at least during one of the MFMP thermal tests the temperatures where measured with the Optris thermal camera and the Williamson pyrometer.

Both where in close agreement and as such the measured temperatures with the Optris are supposed to be (near) accurate.

The differences between applied power and calculated thermal power can also be explained if the emissivity of the material used to cast the dogbone is much lower then that for standard alumina.

This possibility will now be investigated in this case study.

Using the data in post #445 a rough estimate was made by which factor the emissivities of the 900 Watt run had to be lowered to bring the applied power in line with the total thermal power.

This factor was about .7 . This means that emissivities for the high temperatures would have been closer to .30 then to the .45 for the ribbed area.

The question now is which ceramic material can have such low emissivity values. A likely candidate is Magnesia (Magnesium Oxide, MgO).

Total emissivity of magnesia as a function of temperaure is given in the following figure which was taken from the

"**HANDBOOK OF THE INFRARED OPTICAL PROPERTIES OF AL2O3, CARBON, MGO, AND ZrO2, VOLUME 1" by Milo E. Whitson, Jr. (1975)**

For magnesia the handbook gives the following figure :

The dots in the figure are representing measured emissivities by several sources. As can be seen there is a wide spread between those measured values.

The curve represents the curve fit for all these measurements. The curve is in the document also presented as a table and we take that data as a starting point .

We now do a linear transformation on the published emissivity values of magnesia such that for the MFMP dogbone thermal tests for 500, 700 and 900 Watt the applied power is about in agreement with the thermal power. The translation used was :

ε' = 1.02 x ε - 0.04

The part of the original curve between 200K and 1800K together with the translated curve is given in the following figure :

The new curve has almost the same shape as the original curve but is somewhat lower but falls largely within the upper and lower limits shown by the measurements dots in the first figure.

We now apply the translated emissivity values of magnesia to our calculations of the thermal powers of the MFMP 500, 700 and 900 Watt runs and determine the difference between applied powers and thermal powers.

The table below shows the differences between the calculated applied power and thermal power for both the original calculation with alumina and for the translated magnesia curve

Run-------------Difference alumina (%)----------Difference magnesia (%)

500 Watt-----------------16.3-----------------------------------0.94

700 Watt-----------------27.3-----------------------------------0.09

900 Watt-----------------33.9-----------------------------------0.95

Conclusion of this case study is that the large differences between the applied and calculated thermal powers of the MFMP dogbone thermal test almost disappear if the MFMP dogbone was casted from a lower emssivity ceramic then alumina. Especially magnesia is a good candidate to bring applied and calculated thermal powers in line.

Note that if instead of alumina magnesia or an other low emissivity ceramic was used it would also result in the higher surface temperatures measured during the MFMP test.

Update for typo error : Constant factor in emissivity translation is -.04 instead of -.03

Update 08-11-2018 : Added Excel sheet with calculation