Selected data for common materials on the Vapor Box project

Quantities that use the Mathematica “Quantity” functionality have the first letter in 𝓈𝒸𝓇𝒾𝓅𝓉.

The abbreviation for stainless steel 316 is SS.

(* some abbreviations for units *)
gpcc=Quantity["Grams"/(("Centimeters")^3)];
jpkgk=Quantity[1.0,"Joules"/("Kilograms""Kelvins")];
wpmk=Quantity["Watts"/("Meters""Kelvins")];

Typical density of 316 stainless steel from [1]

[1] https://www.azom.com/properties.aspx?ArticleID=863 
This page is also available at https://web.archive.org/web/20190225005937/https://www.azom.com/properties.aspx?ArticleID=863

ρSS=8. gpcc;

Density of mullite from [2]. We assume the ceramic heaters are made of mullite.

[2] https://accuratus.com/mullite.html.
 This page is also available at https://web.archive.org/web/20190225005700/https://accuratus.com/mullite.html

ρMullite=2.8 gpcc ;

Specific heat of stainless steel from the same azom.com page as above. I arbitrarily chose the lowest value.

𝒸SS=490 jpkgk;

Specific heat capacity of Mullite, from [3]. The multiplying a constant value for 𝒸Mullite, taken to be the highest encountered in the experiment, by the 𝒸MulliteTFactor allows a more sophisticated analysis that takes into account the lower specific heat capacity at lower temperatures.

[3] Hildmann, Bernd, and Hartmut Schneider. “Heat Capacity of Mullite-New Data and Evidence for a High-Temperature Phase Transformation.” Journal of the American Ceramic Society 87, no. 2 (2004): 227–234.

(* Temperature is in Kelvin *)
𝒸MulliteT[T_]:=Quantity[a+(10^(-5))b T + (10^4)c (T^(-2))+ 10 d (T^(-0.5))+(10^6)e (T^(-3)),"Joules"/("Grams""Kelvins")]/.{a->1.58816,b->-1.2254,c->-2.2240,d->-1.1142,e->2.487}//Evaluate;
𝒸Mullite=𝒸MulliteT[950];(*worst case scenario for highest specific heat *);
𝒸MulliteTFactor[TK_]:=((𝒸MulliteT[TK])/(𝒸Mullite))

Emissivity of stainless steel is estimated as 0.3, similar to that reported on page 61 of [4], for SS 316, “as received”, on first heating.
Coated and uncoated ceramic heater emissivities are from the Watlow High Temperature Heaters brochure, [5], page 439.

[4] Thermal radiative properties of selected materials / by W.D. Wood, H.W. Deem, and C.F. Lucks ; to Office of the Director of Defense Research and Engineering.
Columbus, Ohio : Defense Metals Information Center, Battelle Memorial Institute, 1962.

[5] https://transition.watlow.com/downloads/en/catalogs/high-temp.pdf
Also available at https://web.archive.org/web/20190225011854/https://transition.watlow.com/downloads/en/catalogs/high-temp.pdf

ϵSS=0.3;
ϵCeramicHeaterHighEmissivity=0.85;
ϵCeramicHeaterUncoatedSurfaces=0.6; (* at 800C *)

The temperature factor for the resistance of Kanthal wire. From [5], using data for Kanthal A.

[5] https://www.kanthal.com/globalassets/kanthal-global/products/resistance-heating-wire-and-strip/materials-physical-and-mechanical-properties-chart_alkrothal-nikrothal.pdf
Also available at https://web.archive.org/web/20190224231336/https://www.kanthal.com/globalassets/kanthal-global/products/resistance-heating-wire-and-strip/materials-physical-and-mechanical-properties-chart_alkrothal-nikrothal.pdf

ρElTemperatureFactorKanthal[Tc_]:=Interpolation[{{20,1},{250,1.01},{500,1.03},{800,1.05},{1000,1.06},{1200,1.06}},InterpolationOrder->1][Tc];

materialLib[ρ_,𝒸_,𝓀_,ϵ_]:=<|"ρ"->ρ,"𝒸"->𝒸,"𝓀"->𝓀,"ϵ"->ϵ,"𝓈"->ρ 𝒸|>;
materialLib["SS"]:=materialLib[ρSS,𝒸SS,I,ϵSS];

materialLib["CeramicHeater"]:=materialLib[ρMullite,𝒸Mullite,I,ϵCeramicHeaterHighEmissivity];
materialLib["CeramicHeaterUncoated"]:=materialLib[ρMullite,𝒸Mullite,I,ϵCeramicHeaterUncoatedSurfaces];
materialLib["Arbitraryϵ0.1"]:=materialLib[I,I,I,0.1];
materialLib["Arbitraryϵ0.2"]:=materialLib[I,I,I,0.2];

Thickness of sheet metal gauges

sheetGage[{"SS",g_}]:=sheetGageSS[g];

sheetGageSS["16th"]:=Quantity[0.0625,"Inches"];