Example 8.2-1 Effect of Pressure on Thermal Conductivity of Gases

The thermal conductivity of gases generally increase with pressure as shown in Figure 1. (Bird, Stewart, Lightfoot) Data on thermal conductivity of gases in the high pressure and low pressure range is usually more difficult to obtain. Figure 1 displays a correlation between the reduced thermal conductivity and the reduced pressure. Reduced conductivity is given by k/k⁰ and the reduced pressure is given by p/p_c.

Figure 2 shows generalized correlation values in the low pressure range. The values are compiled using Bromley's Method to find k⁰ (thermal conductivity at low pressure).

Bromley Method Equations: 1) For monoatomic gases 2)For linear molecules 3)Nonlinear molecules

Figure 1 is only based on data obtained from N₂, CH₄, Ar, He, H₂, C₂H₄, and CO₂. Therefore, the applicability of Figure 1 to estimate thermal conductivities of polar or more complex molecules is questionable. Shown below is a comparision of the reduced thermal conductivity in a generalized correlation diagram to data obtained with ethane:

 PROBLEM:

Estimate the thermal conductivity of ethane at 153^oF and 191.9 atm from the atmospheric value. k⁰ = 0.0159 BTU hr^-1 ft^{-1 o}F^-1 at this temperature.

 SOLUTION:

1) Compute T_r & P_r (T_r=T/T_c , P_r=P/P_c)

2) Refer to Figure 1

3) k = k^#k⁰=4.7 * 0.0159=0.075 Btu/hr/ft/F

1) Bird, Stewart and Lightfoot, Transport Phenomena, ; John Wiley & Sons, 1960

2) Reid, Robert, Properties of Gases & Liquids; Mc-Graw Hill book Company, 1958