8.3-1 - Thermal Conductivity of Monatomic Gases at Low Density

The MATLAB function ktcalc is used to calculate thermal conductivity of monatomic gases at low density using the Chapman-Engsok formula:

Here, the s and W are the Lennard-Jones parameters which can be found in start301 data or in Appendix B, Table B.2 of Bird, Steward, and Lightfoot. The units are as follows:

T [=] K

k [=] cal cm^-1 sec^-1 K^-1

s [=] Angstrom

function KT = ktcalc (T,index)

% Chapman-Enskog formula for thermal conductivity of monatomic gas at low
%   density
%
% function K = ktcalc(T,index)
%
% Argument List:
%   T     [=] temperature in the units of Tdeg
%   index [=] index of compounds in cnms whose coefficients are to be found
%              (If this argument is omitted, all coefficients will be found.)
% Returns:
%   K     [=] heat transfer coefficient in units of W/m/K
%
% Ex:  stationnm% start301a     to set compound names & data file
%      >> start402b             to load the data file
%      >> kt = ktcalc(298, 1)
%      kt =
%          0.0197                                Created 3/21/95-2 Jim Lee

global mw
lj = checklj;
T=at(T);
if nargin==1
  [mu omega_k D] = omegacalc(T./lj(:,2));
  KT = 1.9891e-4 * sqrt(T./mw) ./ (lj(:,1).^2.*omega_k) * 418.3925;
else
  [mu omega_k D] = omegacalc(T./lj(index,2));
  KT = 1.9891e-4 * sqrt(T./mw(index)) ./ (lj(index,1).^2.*omega_k) * 418.3925;
end

% This file was created by m2html.

Example 8.3-1

Compute the thermal conductivity of neon at 1 atm and 373.2 K.

>> ktcalc(373.2)  

ans =

    0.0562

Notice that the units of this answer are W/m/K. Using convu:

 0.5620000E-01W/(m*K) = 0.1343236E-03cal/(cm*s*K)

This agrees with the measured value of 1.35x10^-4 cal cm^-1 sec^-1 K^-1 and BS&L's value of 1.338x10^-4 cal cm^-1 sec^-1 K^-1.