An Alternative Method of Determining the Effect of Pressure on Thermal Conductivity

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The following correlation may be used to estimate the thermal conductivities of various substances in lue of Figure 8.2-2 in BSL.

 

 

 T_r=1. 03:

0.6 < P_r < 0.8 -- ---------- k# = P_r + 0.65

0.8 < P_r < 1.0 ------------- k# = 2P_r - 0.15

1.0 < P_r < 1.3 ------------- k#= 7.24P_r - 5.398

1.3 < P_r < 7.0 --------------k# = 2.6378Ln(P_r) + 3.3704

T_r = 1. 05:

0.6 < P_r < 0.8 ------------- k# = 0.6P_r + 0.87

0.8 < P_r < 1.0 ------------- k# = 1.75P_r - 0.05

1.0 < P_r < 1.3 ------------- k# = 2.6667P_r - 1

1.3 < P_r < 1.5 ------------- k# = 4.6154P_r - 3.3846

1.5 < P_r < 7.0 ------------- k# = 2.8525Ln(P_r ) + 2.3665

T_r = 1. 10:

0.6 < P_r < 0.8 ------------- k# = 0.1P_r + 1.14

0.8 < P_r < 1.2 ------------- k# = 0.95P_rx+ 0.46

1.2 < P_r < 7.0 ------------- k# = 2.1814P_r - 0.9966

T_r = 1. 15:

0.6 < P_r < 1.0 ------------- k# = 0.225P_r + 1.0467

1.0 < P_r < 1.5 ------------- k# = 0.9237P_r+ 0.34

1.5 < P_r < 2.0 ------------- k# = 1.4873P_r - 0.4699

2.0 < P_r < 7.0 ------------- k# = 0.6599P_r + 1.3446

T_r = 1. 20:

0.6 < P_r < 1.0 ------------ k# = 0.1P_r + 1.1167

1.0 < P_r < 1.5 ------------ k# = 0.56 P_r + 0.66

1.5 < P_r < 2.0 ------------ k#= P_r

2.0 < P_r < 7.0 ------------ k#= 0.6008P_r+ 0.9951

T_r = 1. 30:

1.0 < P_r < 1.5 ------------ k# = 0.2568P_r + 0.9347

1.5 < P_r < 2.0 ------------ k# = 0.72P_r + 0.24

2.0 < P_r < 7.0 ------------ k# = 0.4441P_r + 0.9056

T_r = 1. 40:

0.6 < P_r < 1.0 ------------ k#= 0.125P_r + 1.03

1.0 < P_r < 1.5 ------------ k#= 0.24P_r + 0.92

1.5 < P_r < 7.0 ------------ k#= 0.4017P_r + 0.7008

T_r = 1. 60:

1.0 < P_r < 1.5 ------------ k#= 0.1P_r + 1.03

1.5 < P_r < 2.0 ------------ k#= 0.24P_r + 0.82

2.0 < P_r < 7.0 ------------ k#= 0.2623P_r + 0.7991

T_r = 1. 80:

1.0 < P_r < 1.5 ------------ k#= 0.04P_r+ 1.08

1.5 < P_r < 2.0 ------------ k#= 0.16P_r+ 0.9

2.0 < P_r < 7.0 ------------ k#= 0.1782P_r + 0.8735

T_r = 2. 00:

1.0 < P_r < 1.5 ------------ k#= 0.04P_r + 1.07

1.5 < P_r < 2.0 ------------ k#= 0.16P_r+ 0.89

2.0 < P_r < 2.5 ------------ k#= 0.08P_r+ 1.05

2.5 < P_r < 7.0 ------------ k#= 0.1382P_r + 0.9014

T_r = 2. 50:

1.0 < P_r < 1.5 ------------ k#= 0.04P_r + 1.02

1.5 < P_r < 2.0 ------------ k#= 0.08P_r + 0.96

2.0 < P_r < 2.5 ------------ k#= 0.04P_r + 1.04

2.5 < P_r < 7.0 ------------ k#= 0.0765P_r+ 0.9427

T_r = 3. 00:

1.0 < P_r < 1.5 ------------ k#= 0.04P_r+ 1.01

1.5 < P_r < 2.0 ------------ k#= 0.06P_r + 0.98

2.0 < P_r < 6.0 ------------ k#= 0.0339P_r + 1.0346

6.0 < P_r < 7.0 ------------ k#= 0.07P_r + 0.82

 

Example 8.2-1. Effect of Pressure on Thermal Conductivity

PROBLEM: Estimate the thermal conductivity of ethane at 153 degrees F and 191.9 atm from the atmospheric value k0 = 0.0159 Btu/(hr ft F) at this temperature.

SOLUTION: Use the previous correlations. First compute the required parameters using critical properties from Table B.1 in BSL:

> restart;

> T[r]:=(153+460)/(1.8*305.4);

> P[r]:=191.9/48.2;

From the correlation for Tr = 1.10 we find that k# equals

> k[lb]:=2.1814*P[r]-0.9966;

We know that k = k0 * k#.

> k:=k0*k[lb];

> k0:=0.0159;

Thus, k approximately equals

> k*Btu/hr/ft/F;