Ann: VHD Technology - Thermal Performance Breakthrough, page-55

Thank you @Spatula for your post. Based on specific heat capacity of 720 J/kg and 2000 kg/m density, you show a down-grade in thermal conductivity.

Searching for a relationship between specific heat capacity and density for VHD graphite, Chat GTP served a table suggesting a value of 1020J/kg for 2000 kg/m3 density graphite and higher specific heat values for lower densities.

Using the Chat GTP information, below a summary of my digging deeper.

Summary conclusion: (not advice, DYOR)
Based on thermal diffusivity of 288 mm²/sand a thermal conductivity of 617 W/mk , the implied graphite block density corresponding to this result is estimated to exceed 1900 kg/m3. This is in line with densities reported for the pilot plant commissioning tests and surpasses industry standards for nuclear graphite (1,700–1,900 kg/m³) and electrode graphite (1,550–1,800 kg/m³)

For those who want to get into the nitty gritty leading me to this conclusion, keep on reading:

Thermal diffusivity, thermal conductivity, density, and specific heat capacity are all related so that any one of these can be calculated if the others are known.

α=kρcp\alpha = \frac{k}{\rho c_p}α=ρcpk

where:

• α\alphaα = thermal diffusivity (in mm²/s or m²/s),
• kkk = thermal conductivity (in W/m·K),
• ρ\rhoρ = density (in g/cm³ or kg/m³),
• cpc_pcp = specific heat capacity (in J/kg·K).

Values reported included:

Densityup to 2050 kg/m3

Thermal diffusivity 288 mm²/s

Thermal conductivity617W/m.k

Specific heat capacity??

I may have missed any reference to specific heat capacity, if it was reported by GCM. , but there is a relationship between specific heat capacity and density of VDH graphite.

ChatGPT said:

For very high-density (VHD) graphite, the specific heatcapacity (cpc_pcp)and density (ρ\rhoρ) are typically inversely correlated but within a relatively narrow range.

Here is the estimated correlation between density and specific heat capacity for block graphite:

	Density (kg/m³)	Specific Heat Capacity (J/kg·K)
1	1600	1500
2	1700	1380
3	1800	1260
4	1900	1140
5	2000	1020
6	2100	900

This follows a general trend where higher density leadsto lower specific heat capacity, due to reduced phonon scattering and fewer voids in the material.

General Trend

• As density increases, graphite has fewer voids and less porosity, leading to a slight decrease in specific heat capacity per unit mass.
• This is because denser graphite has fewer low-energy vibration modes (phonon scattering effects decrease), reducing its ability to store thermal energy per unit mass. However, the change is not dramatic, as graphite's bonding structure remains similar across different densities.

Based on the reported thermal diffusivity of 288 mm2/s, the thermal conductivity can be calculated for the various densities and corresponding specific heat capacitvalues of and the tabled relationship of density and corresponding specific heat capacities tabled.

ChatGPT said:

Here’s how thermal conductivity (kkk) varies with density and specific heat capacity, assuming a constant thermal diffusivity of 288 mm²/s:

	Density (kg/m³)	Specific Heat Capacity (J/kg·K)	Thermal Conductivity (W/m·K)
1	1600	1500	691.2
2	1700	1380	675.6
3	1800	1260	653.2
4	1900	1140	623.8
5	2000	1020	587.5
6	2100	900	544.3

My takeaway

Based on the table above, the reported thermal conductivity of 617 W/mk corresponds to a density in excess of 1900 kg/m3, in line with densities reported for the pilot plant commissioning tests and surpassing industry standards for nuclear graphite (1,700–1,900 kg/m³) 1 and electrode graphite (1,550–1,800 kg/m³)