# How can the thermal conductivity of a binary gas mixture be estimated?

Recently, I am seeking for a simple but relatively accurate method to estimate the thermal conductivity of a binary gas mixture, say ethanol vapor + nitrogen. I assume the mixture as ideal gas.

The molar fraction and thermal conductivities of the components are known. The parameters for a try are: mole fraction of ethanol vapor: $x_A=0.2$, thermal conductivity of ethanol vapor and nitrogen are $k_A=0.016\ \mathrm{W/(m\,K)}$, $k_B=0.026\ \mathrm{W/(m\,K)}$, temperature of the mixture gas $T=330\ \mathrm{K}$, and the bulk pressure is $101\ \mathrm{kPa}$.

I really hope someone could give me a hint or point me to a classical reference. Thank you in advance!

I'm thinking you could use the Fourier equation for heat flux

$$\phi =K \frac{S\theta}{e} \,\, ,$$ where

• $\phi$ = Heat flux
• $K$ = Termal conductivity coeficient in units of $kcal s^{-1}\ m^{-2}\ K^{-1} /m^{-1}$
• $S$ = Area of the section you're dealing $m^{2}$
• $θ$ = Difference of temperature $K$
• $e$ = Thickness in $m$.

And use for the resulting thermal conductivity the fraction

$$K_{r}=\frac{\sum K_{i}J_{i}(M_{i})^{1/3}}{\sum J_{i}(M_{i})^{1/3}} \,\, ,$$ where:

• $K_{r}$ = Resulting termal conductivity of the moisture;
• $K_{i}$ = Termal conductivity of each gas;
• $j_{i}$ = Molar fraction of each gas;
• $M_{i}$ = molar mass of each gas.

I think it'll work with some 2% of standard deviation. If you're able to read in portuguese, here is the link of my reference:

Reference

And here is the link of the Book cited by @Chester Miller.

I hope I hope I was Helpfull!

See also Section 9.3 Theory of Thermal Conductivity of Gases at Low Density in Transport Phenomena by Bird, Stewart, and Lightfoot.

• Hi @ Chester Miller, thank for your answer, but I can not find this reference in the library database... Could you please share me your soft copy? Many thank! Commented Nov 30, 2015 at 15:01
• I don't understand. This is a very well known book. It has been in use for over 50 years, and has stood the test of time. A new edition came out in around 2000. Here is the reference again: Bird, R.B., Stewart, W.E., and Lightfoot, E. N., Transport Phenomena, John Wiley, New York, 2nd Edition, 2002. Commented Nov 30, 2015 at 17:45
• Unfortunately I may have to disagree that this answers the question. Could you include some of the relevant parts of the book here? Commented Nov 30, 2015 at 21:02
• Isn't mentioning Section 9.3 good enough? I'm uncomfortable with the IP implications of copying some of the text. If you want, I can try to paraphrase some of it. Commented Nov 30, 2015 at 22:43
• @ChesterMiller, I think I have misunderstood your citation. The title of the book is Transport Phenomena, which is indeed a wonderful book! Commented Dec 1, 2015 at 0:43