Request to Clarify Equations for Thermal Conductivity 2

[KimWonGun]

Seeking guidance on building a simple rig to measure thermal conductivity for insulating materials, I came across a paper which includes the attached figure and equations. This is a modified version of Lee's disk method.

But when analyzing the equations dimensionally, units did not drop out to just leave W / m / K standing. The paper did not include a derivation for the equations, and I have not been successful yet to find helpful references.

The "a" variables refer to the exposed surfaces of the copper specimens and d refers to the sample thickness. I think all other variables are straightforward.

What am I missing?

 

[ione]

e is expressed as J/(m2*s*°C)

H = e*Aa*Ta + e*Ab*Tb + e*Ac*Tc + e*As*(Ta+Tb)/2 + e*Ah*(Tb+Tc)/2


Where Ts = (Ta+Tb)/2 is the temperature of the specimen

H = VI (power = tension*current)

VI = e*Aa*Ta + e*Ab*Tb + e*Ac*Tc + e*As*(Ta+Tb)/2 + e*Ah*(Tb+Tc)/2

Solve for e

e = VI/[Aa*Ta + Ab*Tb + Ac*Tc + As*(Ta+Tb)/2 + Ah (Tb+Tc)/2]

and not e=VI*[Aa*Ta + Ab*Tb + Ac*Tc + As*(Ta+Tb)/2 + Ah (Tb+Tc)/2]

and then……..

 

[IRstuff]

The approach in the excerpt seems complicated. I've seen other references to this concept using a "with" and "without" measurement to eliminate most of the parasitics in the structure. In that case, the difference in delta temperature can almost completely be attributed to the disk under test and heat flow/(deltaT_corrected*area/thickness) --> W/m-K

TTFN
faq731-376