Annaratone D. Handbook for Heat Exchangers and Tube Banks design
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62 Appendix A Corrective Factors for Design Computation
E
Fig. A.12
Table A.12 – Heat exchangers – E type – 3 passages of external fluid Corrective factor χ
c
β
ψ
0.04 0.08 0.12 0.16 0.20 0.24 0.28 0.32 0.36 0.40 0.44
0.05 0.608 0.887 0.934 0.955 0.967 0.975 0.981 0.985 0.988 ……. …….
0.10 ........ 0.668 0.844 0.899 0.929 0.947 0.960 0.969 0.976 0.981 0.985
0.15 ........ ........ 0.696 0.827 0.882 0.914 0.936 0.950 0.962 0.970 0.976
0.20 ........ ........ ........ 0.720 0.823 0.875 0.908 0.930 0.946 0.958 0.967
0.25 ........ ........ ........ ........ 0.743 0.827 0.875 0.906 0.929 0.945 0.957
0.30 ........ ........ ........ ........ 0.602 0.765 0.836 0.879 0.909 0.930 0.946
0.35 ........ ........ ........ ........ ........ 0.676 0.788 0.848 0.887 0.914 0.934
0.40 ........ ........ ........ ........ ........ ........ 0.724 0.810 0.861 0.896 0.921
0.45 ........ ........ ........ ........ ........ ........ 0.627 0.763 0.831 0.876 0.907
0.50 …… ........ ........ ........ ........ ........ ........ 0.700 0.796 0.852 0.891
0.60 ........ ........ ........ ........ ........ ........ ........ ........ 0.693 0.793 0.852
0.70 ........ ........ ........ ........ ........ ........ ........ ........ ........ 0.703 0.800
0.80 ........ ........ ........ ........ ........ ........ ........ ........ ........ ........ 0.725
0.90 ........ ........ ........ ........ ........ ........ ........ ........ ........ ........ 0.584
If β> 0.9 no solution is possible in this field
Values in italics : 2<γ <4 ; Values in bold type : 4<γ <6
A.2 Heat Exchangers 63
Table A.12 – (continued)
β
ψ
0.48 0.52 0.56 0.60 0.64 0.68 0.72 0.76 0.80 0.84 0.88
0.1 0.988 ……. ……. ……. ……. ……. ……. ……. ……. ……. …….
0.2 0.974 0.980 0.985 0.988 ……. ……. ……. ……. ……. ……. …….
0.3 0.959 0.968 0.976 0.982 0.986 0.990 ……. ……. ……. ……. …….
0.4 0.940 0.954 0.965 0.974 0.981 0.986 ……. ……. ……. ……. …….
0.5 0.918 0.939 0.954 0.966 0.975 0.982 0.987 ……. ……. ……. …….
0.6 0.891 0.920 0.940 0.956 0.968 0.977 0.984 0.989 ……. ……. …….
0.7 0.858 0.897 0.925 0.946 0.961 0.972 0.981 0.987 ……. ……. …….
0.8 0.815 0.870 0.907 0.933 0.953 0.967 0.977 0.985 ……. ……. …….
0.9 0.755 0.835 0.885 0.919 0.943 0.960 0.973 0.982 0.989 ……. …….
1.0 0.661 0.789 0.858 0.902 0.933 0.954 0.969 0.980 0.987 ……. …….
1.1 ........ 0.725 0.825 0.883 0.921 0.946 0.964 0.977 0.986 ……. …….
1.2 ........ 0.614 0.781 0.859 0.906 0.938 0.959 0.974 0.984 ……. …….
1.3 ........ ........ 0.718 0.829 0.890 0.928 0.954 0.970 0.982 0.990 …….
1.4 ........ ........ 0.609 0.791 0.871 0.918 0.947 0.967 0.980 0.989 …….
1.5 ........ ........ ........ 0.738 0.847 0.905 0.940 0.963 0.978 0.988 …….
1.6 ........ ........ ........ 0.655 0.817 0.891 0.933 0.959 0.976 0.987 …….
1.7 ........ ........ ........ ........ 0.778 0.874 0.924 0.955 0.974 0.986 …….
1.8 ........ ........ ........ ........ 0.725 0.853 0.914 0.950 0.971 0.984 …….
1.9 ........ ........ ........ ........ 0.636 0.828 0.903 0.944 0.969 0.983 …….
2.0 ........ ........ ........ ........ ........ 0.796 0.891 0.938 0.966 0.982 …….
2.1 ........ ........ ........ ........ ........ 0.752 0.875 0.932 0.963 0.980 …….
2.2 ........ ........ ........ ........ ........ 0.689 0.858 0.924 0.959 0.979 …….
2.3 ........ ........ ........ ........ ........ 0.561 0.836 0.916 0.956 0.977 0.989
2.4 ........ ........ ........ ........ ........ ........ 0.809 0.907 0.952 0.976 0.989
2.5 ........ ........ ........ ........ ........ ........ 0.773 0.896 0.948 0.974 0.988
2.6 ........ ........ ........ ........ ........ ........ 0.724 0.884 0.943 0.972 0.987
2.7 ........ ........ ........ ........ ........ ........ 0.644 0.869 0.938 0.970 0.987
2.8 ........ ........ ........ ........ ........ ........ ........ 0.852 0.933 0.968 0.986
2.9 ........ ........ ........ ........ ........ ........ ........ 0.831 0.927 0.966 0.985
3.0 ........ ........ ........ ........ ........ ........ ........ 0.805 0.920 0.964 0.984
If ψ> 0.88 use the mean logarithmic temperature difference for counter flow
64 Appendix A Corrective Factors for Design Computation
G
Fig. A.13
Table A.13 – Heat exchangers – G type – 3 passages of external fluid Corrective factor χ
c
β
ψ
0.04 0.08 0.12 0.16 0.20 0.24 0.28 0.32 0.36 0.40 0.44
0.1 0.740 0.871 0.918 0.942 0.957 0.967 0.975 0.980 0.984 0.987 …….
0.2 ........ 0.677 0.802 0.865 0.902 0.926 0.943 0.956 0.966 0.973 0.979
0.3 ........ ........ 0.637 0.757 0.828 0.873 0.905 0.927 0.943 0.956 0.966
0.4 ........ ........ 0.469 0.609 0.726 0.803 0.855 0.890 0.916 0.935 0.950
0.5 ........ ........ ........ 0.461 0.590 0.707 0.788 0.843 0.882 0.911 0.932
0.6 ........ ........ ........ ........ 0.456 0.581 0.698 0.782 0.839 0.880 0.910
0.7 ........ ........ ........ ........ ........ 0.456 0.580 0.699 0.783 0.842 0.883
0.8 ........ ........ ........ ........ ........ ........ 0.460 0.589 0.708 0.792 0.850
0.9 ........ ........ ........ ........ ........ ........ ........ 0.472 0.607 0.726 0.807
1.0 ........ ........ ........ ........ ........ ........ ........ 0.387 0.493 0.636 0.750
1.1 ........ ........ ........ ........ ........ ........ ........ ........ 0.403 0.527 0.675
1.2 ........ ........ ........ ........ ........ ........ ........ ........ ........ 0.429 0.576
1.3 ........ ........ ........ ........ ........ ........ ........ ........ ........ 0.363 0.471
1.4 ........ ........ ........ ........ ........ ........ ........ ........ ........ ........ 0.392
1.5 ........ ........ ........ ........ ........ ........ ........ ........ ........ ........ 0.337
If β> 1.5 no solution is possible in this field
Values in italics : 2<γ <4; Values in bold type : 4<γ <6
A.2 Heat Exchangers 65
Table A.13 – (continued)
β
ψ
0.48 0.52 0.56 0.60 0.64 0.68 0.72 0.76 0.80 0.84
0.2 0.983 0.987 ……. ……. ……. ……. ……. ……. ……. …….
0.3 0.973 0.979 0.984 0.988 ……. … …. ……. ……. ……. …….
0.4 0.961 0.970 0.977 0.983 0.987 ……. ……. ……. ……. …….
0.5 0.948 0.960 0.970 0.977 0.983 0.988 ……. ……. ……. …….
0.6 0.932 0.949 0.962 0.971 0.979 0.985 0.989 ……. ……. …….
0.7 0.913 0.935 0.952 0.964 0.974 0.982 0.987 ……. ……. …….
0.8 0.890 0.919 0.941 0.957 0.969 0.978 0.985 ……. ……. …….
0.9 0.862 0.900 0.928 0.948 0.963 0.974 0.982 0.988 ……. …….
1.0 0.826 0.878 0.913 0.938 0.957 0.970 0.979 0.986 ……. …….
1.1 0.781 0.849 0.895 0.927 0.949 0.965 0.976 0.985 ……. …….
1.2 0.719 0.813 0.874 0.913 0.941 0.960 0.973 0.983 0.989 …….
1.3 0.638 0.767 0.847 0.897 0.931 0.954 0.970 0.981 0.988 …….
1.4 0.536 0.705 0.813 0.879 0.920 0.947 0.966 0.978 0.987 …….
1.5 0.440 0.623 0.770 0.856 0.907 0.940 0.961 0.976 0.985 …….
1.6 0.372 0.522 0.712 0.827 0.892 0.931 0.957 0.973 0.984 …….
1.7 ........ 0.432 0.635 0.790 0.874 0.922 0.951 0.970 0.983 …….
1.8 ........ 0.367 0.538 0.742 0.851 0.911 0.946 0.967 0.981 0.990
1.9 ........ ........ 0.446 0.677 0.824 0.898 0.939 0.964 0.979 0.989
2.0 ........ ........ 0.378 0.591 0.789 0.882 0.932 0.960 0.977 0.988
2.1 ........ ........ 0.325 0.494 0.742 0.864 0.923 0.956 0.975 0.987
2.2 ........ ........ ........ 0.414 0.679 0.841 0.914 0.952 0.973 0.986
2.3 ........ ........ ........ 0.354 0.596 0.812 0.903 0.947 0.971 0.985
2.4 ........ ........ ........ ........ 0.500 0.776 0.890 0.942 0.969 0.984
2.5 ........ ........ ........ ........ 0.419 0.727 0.874 0.935 0.966 0.983
2.6 ........ ........ ........ ........ 0.358 0.660 0.855 0.928 0.963 0.982
2.7 ........ ........ ........ ........ ........ 0.573 0.832 0.921 0.9 60 0.981
2.8 ........ ........ ........ ........ ........ 0.480 0.802 0.912 0.957 0.979
2.9 ........ ........ ........ ........ ........ 0.404 0.764 0.901 0.953 0.978
3.0 ........ ........ ........ ........ ........ 0.343 0.712 0.889 0.949 0.976
If β<0.2orψ> 0.84 use the mean logarithmic temperature difference
Values in italics : 2<γ <4 ; Values in bold type : 4<γ <6
66 Appendix A Corrective Factors for Design Computation
EF
Fig. A.14
Table A.14 – Heat exchangers – E and F type – 4 passages of external fluid Corrective factor χ
c
β
ψ
0.04 0.08 0.12 0.16 0.20 0.24 0.28 0.32 0.36 0.40 0.44
0.05 0.764 0.904 0.942 0.960 0.971 0.978 0.983 0.986 0.989 ……. …….
0.10 ........ 0.758 0.867 0.912 0.937 0.953 0.964 0.972 0.978 0.982 0.986
0.15 ........ ........ 0.761 0.851 0.896 0.923 0.942 0.955 0.965 0.973 0.978
0.20 ........ ........ 0.546 0.771 0.847 0.889 0.917 0.937 0.951 0.962 0.970
0.25 ........ ........ ........ 0.645 0.783 0.848 0.889 0.916 0.935 0.950 0.961
0.30 ........ ........ ........ ........ 0.694 0.798 0.855 0.892 0.918 0.937 0.951
0.35 ........ ........ ........ ........ 0.520 0.732 0.814 0.864 0.898 0.922 0.940
0.40 ........ ........ ........ ........ ........ 0.634 0.764 0.832 0.875 0.906 0.928
0.45 ........ ........ ........ ........ ........ ........ 0.696 0.792 0.849 0.888 0.915
0.50 ........ ........ ........ ........ ........ ........ 0.590 0.743 0.819 0.867 0.901
0.60 ........ ........ ........ ........ ........ ........ ........ 0.570 0.736 0.816 0.866
0.70 ........ ........ ........ ........ ........ ........ ........ ........ 0.579 0.742 0.821
0.80 ........ ........ ........ ........ ........ ........ ........ ........ ........ 0.612 0.758
0.90 ........ ........ ........ ........ ........ ........ ........ ........ ........
........ 0.657
If β> 0.9 no solution is possible in this field
Values in italics : 2<γ <4 ; Value in bold type : 4<γ <6
A.2 Heat Exchangers 67
Table A.14 – (continued)
β
ψ
0.48 0.52 0.56 0.60 0.64 0.68 0.72 0.76 0.80 0.84 0.88
0.1 0.989 ……. ……. ……. ……. ……. ……. ……. ……. ……. …….
0.2 0.976 0.982 0.986 0.989 ……. ……. ……. ……. ……. ……. …….
0.3 0.962 0.971 0.978 0.983 0.987 ……. ……. ……. ……. ……. …….
0.4 0.945 0.958 0.968 0.976 0.982 0.987 ……. ……. ……. ……. …….
0.5 0.925 0.944 0.958 0.969 0.977 0.983 0.988 ……. ……. ……. …….
0.6 0.901 0.927 0.946 0.960 0.971 0.979 0.985 ……. ……. ……. …….
0.7 0.871 0.906 0.931 0.950 0.964 0.974 0.982 0.988 ……. ……. …….
0.8 0.833 0.882 0.915 0.939 0.956 0.969 0.979 0.986 ……. ……. …….
0.9 0.782 0.851 0.895 0.926 0.948 0.964 0.975 0.984 0.990 ……. …….
1.0 0.707 0.811 0.871 0.911 0.938 0.958 0.971 0.981 0.988 ……. …….
1.1 0.557 0.757 0.842 0.893 0.927 0.951 0.967 0.979 0.987 ……. …….
1.2 ........ 0.672 0.803 0.872 0.915 0.943 0.963 0.976 0.985 ……. …….
1.3 ........ ........ 0.750 0.845 0.900 0.934 0.957 0.973 0.984 ……. …….
1.4 ........ ........ 0.668 0.812 0.882 0.924 0.952 0.970 0.982 0.990 …….
1.5 ........ ........ ........ 0.766 0.861 0.913 0.945 0.966 0.980 0.989 …….
1.6 ........ ........ ........ 0.700 0.835 0.900 0.938 0.962 0.978 0.988 …….
1.7 ........ ........ ........ 0.569 0.801 0.885 0.931 0.958 0.976 0.987 …….
1.8 ........ ........ ........ ........ 0.755 0.866 0.922 0.954 0.973 0.986 …….
1.9 ........ ........ ........ ........ 0.686 0.844 0.912 0.949 0.971 0.984 …….
2.0 ........ ........ ........ ........ 0.527 0.815 0.900 0.943 0.968 0.983 …….
2.1 ........ ........ ........ ........ ........ 0.778 0.886 0.937 0.966 0.982 …….
2.2 ........ ........ ........ ........ ........ 0.726 0.870 0.931 0.963 0.981 …….
2.3 ........ ........ ........ ........ ........ 0.638 0.851 0.923 0.959 0.979 …….
2.4 ........ ........ ........ ........ ........ ........ 0.827 0.915 0.956 0.978 0.990
2.5 ........ ........ ........ ........ ........ ........ 0.796 0.905 0.952 0.976 0.989
2.6 ........ ........ ........ ........ ........ ........ 0.754 0.894 0.948 0.974 0.988
2.7 ........ ........ ........ ........ ........ ........ 0.692 0.881 0.943 0.973 0.988
2.8 ........ ........ ........ ........ ........ ........ 0.556 0.865 0.938 0.971 0.987
2.9 ........ ........ ........ ........ ........ ........ ........ 0.847 0.933 0.969 0.986
3.0 ........ ........ ........ ........ ........ ........ ........ 0.824 0.926 0.967 0.986
If ψ> 0.88 use the mean logarithmic temperature difference for counter flow
Value in italics : 2<γ <4
68 Appendix A Corrective Factors for Design Computation
GH
Fig. A.15
Table A.15 – Heat exchangers – G and H type – 4 passages of external fluid Corrective factor χ
c
β
ψ
0.08 0.12 0.16 0.20 0.24 0. 28 0.32 0.36 0.40 0.44
0.10 0.826 0.898 0.930 0.950 0.962 0.971 0.977 0.982 0.986 0.988
0.15 0.665 0.825 0.886 0.918 0.940 0.954 0.964 0.972 0.978 0.983
0. 20 ... .. ... 0.725 0.830 0.882 0.913 0.9 34 0.95 0 0.9 61 0. 969 0.9 76
0. 25 ... .. ... 0.55 3 0.757 0. 837 0.883 0.9 13 0. 93 4 0.9 48 0. 960 0.9 69
0. 30 ... .. ... .. . ..... 0.6 54 0. 782 0.847 0.8 87 0.91 5 0.9 35 0. 950 0.9 61
0. 35 ... .. ... .. . ..... 0.471 0.710 0.804 0.8 58 0.89 4 0.9 20 0. 938 0.95 2
0. 40 ... .. ... .. . ..... . ...... . 0.606 0.750 0.823 0.870 0.902 0.926 0.943
0. 50 ... .. ... .. . ..... . ...... . ... ..... 0.578 0.731 0.81 1 0.8 61 0. 896 0.9 22
0. 60 ... .. ... .. . ..... . ...... . ... ..... . ..... .. 0.571 0.725 0.8 07 0. 859 0.8 96
0. 70 ... .. ... .. . ..... . ...... . ... ..... . ..... .. ..... . .. 0. 58 1 0.7 29 0. 811 0.8 63
0. 80 ... .. ... .. . ..... . ...... . ... ..... . ..... .. ..... . .. 0.340 0.606 0. 743 0.82 2
0. 90 ... .. ... .. . ..... . ...... . ... ..... . ..... .. ..... . .. ........ 0.392 0. 642 0.765
1. 00 ... .. ... .. . ..... . ...... . ... ..... . ..... .. ..... . .. ........ .. ... ... 0. 469 0.685
1. 10 ... .. ... .. . ..... . ...... . ... ..... . ..... .. ..... . .. ........ .. ... ... 0.309 0.556
1. 20 ... .. ... .. . ..... . ...... . ... ..... . ..... .. ..... . .. ........ .. ... ... ... ..... 0.378
1. 30 ... .. ... .. . ..... . ...... . ... ..... . ..... .. ..... . .. ........ .. ... ... ... ..... 0.28 7
If β>1.3 or ψ<0.08 no solution is possible in this field
Values in italics : 2<γ <4; Values in bold type : 4<γ <6
A.2 Heat Exchangers 69
Table A.15 – (continued)
β
ψ
0.48 0.52 0.56 0.60 0.64 0 .68 0.72 0.76 0.80 0.84 0. 88
0.2 0.981 0.985 0.988 ……. ……. ……. ……. ……. ……. ……. …….
0.3 0.969 0.977 0.982 0.986 0.990 ……. ……. ……. ……. ……. …….
0.4 0.956 0.967 0.975 0.981 0.986 0.989 ……. ……. ……. ……. …….
0.5 0.941 0.955 0.966 0.975 0.981 0.986 ……. ……. ……. ……. …….
0.6 0.922 0.942 0.956 0.968 0.976 0.983 0.988 ……. ……. ……. …….
0.7 0.900 0.926 0.946 0.960 0.971 0.979 0.986 ……. ……. ……. …….
0.8 0.872 0.908 0.933 0.951 0.965 0.975 0.983 0.988 ……. ……. …….
0.9 0.837 0.885 0.918 0.941 0.958 0.971 0.980 0.987 ……. ……. …….
1.0 0.792 0.857 0.900 0.930 0.951 0.966 0.977 0.985 ……. ……. …….
1.1 0.730 0.822 0.879 0.917 0.942 0.960 0.974 0.983 0.989 ……. …….
1.2 0.639 0.776 0.853 0.901 0.933 0.954 0.970 0.981 0.988 ……. …….
1.3 0.494 0.713 0.820 0.882 0.922 0.948 0.966 0.978 0.987 ……. …….
1.4 0.349 0.619 0.777 0.859 0.909 0.940 0.961 0.976 0.985 ……. …….
1.5 0.283 0.476 0.718 0.831 0.894 0.932 0.957 0.973 0.984 ……. …….
1.6 ........ 0.350 0.633 0.795 0.875 0.922 0.951 0.970 0.982 ……. …….
1.7 ........ 0.290 0.505 0.746 0.854 0.911 0.945 0.967 0.980 0.989 …….
1.8 ........ ........ 0.378 0.679 0.826 0.898 0.939 0.963 0.979 0.988 …….
1.9 ........ ........ 0.310 0.579 0.791 0.882 0.931 0.959 0.977 0.987 …….
2.0 ........ ........ 0.272 0.448 0.745 0.864 0.922 0.955 0.975 0.986 …….
2.1 ........ ........ ........ 0.354 0.680 0.841 0.913 0.951 0.972 0.985 …….
2.2 ........ ........ ........ 0.302 0.585 0.813 0.901 0.946 0.970 0.985 …….
2.3 ........ ........ ........ 0.274 0.463 0.777 0.888 0.940 0.968 0.983 …….
2.4 ........ ........ ........ ........ 0.370 0.727 0.873 0.934 0.965 0.982 …….
2.5 ........ ........ ........ ........ 0.315 0.658 0.854 0.927 0.962 0.981 …….
2.6 ........ ........ ........ ........ 0.294 0.559 0.830 0.919 0.959 0.979 …….
2.7 ........ ........ ........ ........ ........ 0.446 0.801 0.910 0.955 0.978 …….
2.8 ........ ........ ........ ........ ........ 0.366 0.763 0.899 0.951 0.976 0.990
2.9 ........ ........ ........ ........ ........ 0.316 0.711 0.887 0.947 0.975 0.989
3.0 ........ ........ ........ ........ ........ ........ 0.638 0.872 0.943 0.973 0.988
If β<0.2 or ψ> 0.88 use the mean logarithmic temperature difference for counter flow
Values in italics : 2<γ <4; Values in bold type : 4<.γ <6
70 Appendix A Corrective Factors for Design Computation
E
Fig. A.16
Table A.16 – Heat exchangers – E type – 5 passages of external fluid – Corrective factor χ
c
β
ψ
0.04 0.08 0.12 0.16 0.20 0.24 0.28 0.32 0.36 0.40 0.44
0.05 0.728 0.898 0.939 0.958 0.969 0.977 0.982 0.986 0.989 ……. …….
0.10 ........ 0.731 0.859 0.907 0.934 0.950 0.962 0.970 0.977 0.982 0.986
0.15 ........ ........ 0.740 0.842 0.891 0.920 0.940 0.953 0.964 0.971 0.977
0.20 ........ ........ ........ 0.753 0.838 0.884 0.914 0.934 0.949 0.960 0.969
0.25 ........ ........ ........ 0.592 0.769 0.840 0.883 0.912 0.933 0.948 0.959
0.30 ........ ........ ........ ........ 0.666 0.786 0.848 0.887 0.914 0.934 0.949
0.35 ........ ........ ........ ........ ........ 0.712 0.804 0.858 0.894 0.919 0.938
0.40 ........ ........ ........ ........ ........ 0.590 0.749 0.823 0.870 0.902 0.926
0.45 ........ ........ ........ ........ ........ ........ 0.672 0.781 0.842 0.883 0.912
0.50 ........ ........ ........ ........ ........ ........ 0.524 0.727 0.810 0.861 0.897
0.60 ........ ........ ........ ........ ........ ........ ........ 0.484 0.720 0.807 0.860
0.70 ........ ........ ........ ........ ........ ........ ........ ........ 0.514 0.726 0.812
0.80 ........ ........ ........ ........ ........ ........ ........ ........ ........ 0.571 0.745
0.90 ........ ........ ........ ........ ........ ........ ........ ........ ........ ........ 0.631
If β> 0.9 no solution is possible in this field
Values in italics : 2<γ <4 ; Value in bold type : 4<γ <6
A.2 Heat Exchangers 71
Table A.16 – (continued)
β
ψ
0.48 0.52 0.56 0.60 0.64 0.68 0.72 0.76 0.80 0.84 0 .88
0.1 0.989 ……. ……. ……. ……. ……. ……. ……. ……. ……. …….
0.2 0.976 0.981 0.985 0.989 ……. … …. ……. ……. ……. ……. …….
0.3 0.961 0.970 0.977 0.982 0.987 ……. ……. ……. ……. ……. …….
0.4 0.943 0.957 0.967 0.975 0.982 0.987 ……. ……. ……. ……. …….
0.5 0.922 0.942 0.956 0.967 0.976 0.983 0.988 ……. ……. ……. …….
0.6 0.897 0.924 0.943 0.958 0.970 0.978 0.985 0.990 ……. ……. …….
0.7 0.866 0.903 0.929 0.948 0.963 0.973 0.982 0.988 ……. ……. …….
0.8 0.826 0.877 0.912 0.937 0.955 0.968 0.978 0.986 ……. ……. …….
0.9 0.771 0.844 0.891 0.923 0.946 0.962 0.974 0.983 0.989 ……. …….
1.0 0.688 0.802 0.866 0.908 0.936 0.956 0.970 0.981 0.988 ……. …….
1.1 0.463 0.743 0.835 0.889 0.925 0.949 0.966 0.978 0.986 ……. …….
1.2 ........ 0.649 0.794 0.867 0.91 1 0.941 0.961 0.975 0.985 ……. …….
1.3 ........ ........ 0.737 0.839 0.896 0.932 0.956 0.972 0.983 ……. …….
1.4 ........ ........ 0.644 0.803 0.877 0.922 0.950 0.969 0.981 0.989 …….
1.5 ........ ........ ........ 0.754 0.855 0.910 0.943 0.965 0.979 0.988 …….
1.6 ........ ........ ........ 0.681 0.827 0.896 0.936 0.961 0.977 0.987 …….
1.7 ........ ........ ........ 0.499 0.792 0.880 0.928 0.957 0.975 0.986 …….
1.8 ........ ........ ........ ........ 0.742 0.861 0.919 0.952 0.972 0.985 …….
1.9 ........ ........ ........ ........ 0.665 0.837 0.908 0.947 0.970 0.984 …….
2.0 ........ ........ ........ ........ ........ 0.807 0.896 0.941 0.9 67 0.983 …….
2.1 ........ ........ ........ ........ ........ 0.767 0.882 0.935 0.9 64 0.981 …….
2.2 ........ ........ ........ ........ ........ 0.710 0.865 0.928 0.9 61 0.980 …….
2.3 ........ ........ ........ ........ ........ 0.608 0.844 0.920 0.9 58 0.978 0.990
2.4 ........ ........ ........ ........ ........ ........ 0.819 0.911 0.954 0.977 0.989
2.5 ........ ........ ........ ........ ........ ........ 0.786 0.901 0.950 0.975 0.989
2.6 ........ ........ ........ ........ ........ ........ 0.741 0.890 0.946 0.974 0.988
2.7 ........ ........ ........ ........ ........ ........ 0.671 0.876 0.941 0.972 0.987
2.8 ........ ........ ........ ........ ........ ........ ........ 0.86 0 0.936 0.970 0.987
2.9 ........ ........ ........ ........ ........ ........ ........ 0.84 0 0.930 0.968 0.986
3.0 ........ ........ ........ ........ ........ ........ ........ 0.81 6 0.924 0.965 0.985
If ψ> 0.88 use the mean logarithmic temperature difference for counter flow
Value in italics : 2<γ <4