Annaratone D. Handbook for Heat Exchangers and Tube Banks design

52 Appendix A Corrective Factors for Design Computation

BC

Fig. A.7

Table A.7 – Heat exchangers – B and C type – 4 passages of external ﬂuid Corrective factor χ

c

0.08 0.12 0.16 0.20 0.24 0.28 0.32 0.36 0.40 0.44

0.10 0.823 0.894 0.927 0.947 0.960 0.969 0.976 0.981 0.985 0.988

0.15 0.676 0.820 0.881 0.914 0.936 0.951 0.962 0.970 0.976 0.982

0.20 ........ 0.722 0.823 0.876 0.909 0.931 0.946 0.958 0.967 0.974

0.25 ........ 0.582 0.751 0.830 0.877 0.908 0.929 0.945 0.957 0.967

0.30 ........ ........ 0.654 0.774 0.839 0.881 0.910 0.931 0.946 0.958

0.35 ........ ........ 0.520 0.702 0.795 0.851 0.888 0.915 0.934 0.949

0.40 ........ ........ ........ 0.607 0.740 0.815 0.863 0.897 0.921 0.940

0.45 ........ ........ ........ 0.481 0.670 0.772 0.834 0.877 0.907 0.929

0.50 ........ ........ ........ ........ 0.578 0.719 0.801 0.853 0.890 0.917

0.60 ........ ........ ........ ........ 0.349 0.566 0.711 0.796 0.851 0.889

0.70 ........ ........ ........ ........ ........ 0.351 0.570 0.714 0.799 0.855

0.80 ........ ........ ........ ........ ........ ........ 0.364 0.589 0.728 0.810

0.90 ........ ........ ........ ........ ........ ........ ........ 0.395 0.621 0.750

1.00 ........ ........ ........ ........ ........ ........ ........ ........ 0.449 0.663

1.10 ........ ........ ........ ........ ........ ........ ........ ........ 0.294 0.526

1.20 ........ ........ ........ ........ ........ ........ ........ ........ ........ 0.347

If β >1.2 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 53

Table A.7 – (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 0.980 0.984 0.988

0.3 0.968 0.975 0.981 0.985 0.989

0.4 0.954 0.964 0.973 0.980 0.985 0.989

0.5 0.937 0.952 0.964 0.973 0.980 0.986 0.990

0.6 0.917 0.938 0.954 0.966 0.975 0.982 0.987

0.7 0.894 0.921 0.942 0.958 0.969 0.978 0.985 0.990

0.8 0.864 0.902 0.928 0.948 0.963 0.974 0.982 0.988

0.9 0.827 0.878 0.912 0.937 0.956 0.969 0.979 0.986

1.0 0.778 0.848 0.894 0.925 0.948 0.964 0.976 0.984 0.990

1.1 0.711 0.810 0.871 0.911 0.939 0.958 0.972 0.982 0.989

1.2

0.610 0.760 0.843 0.894 0.928 0.952 0.968 0.979 0.987

1.3

0.449 0.690 0.807 0.874 0.916 0.944 0.964 0.977 0.986

1.4

0.301 0.582 0.759 0.849 0.902 0.936 0.959 0.974 0.984

1.5

.......

0.416 0.693 0.818 0.886 0.927 0.954 0.971 0.983

1.6

.......

0.288 0.593 0.778 0.866 0.917 0.948 0.968 0.981 0.989

1.7

.......

0.435 0.724 0.842 0.905 0.942 0.964 0.979 0.988

1.8

.......

0.301 0.644 0.812 0.890 0.934 0.961 0.977 0.987

1.9

.......

0.233 0.517 0.773 0.874 0.926 0.957 0.975 0.986

2.0

.......

0.357 0.719 0.853 0.917 0.952 0.973 0.986

2.1

.......

0.265 0.641 0.828 0.906 0.947 0.971 0.985

2.2

.......

0.515 0.796 0.894 0.942 0.968 0.983

2.3

.......

0.359 0.754 0.880 0.936 0.965 0.982

2.4

.......

0.269 0.696 0.862 0.929 0.963 0.981

2.5

.......

0.215 0.607 0.841 0.921 0.959 0.980

2.6

.......

0.465 0.815 0.913 0.956 0.978

2.7

.......

0.328 0.781 0.903 0.952 0.977 0.989

2.8

.......

0.255 0.736 0.891 0.948 0.975 0.989

2.9

.......

0.205 0.671 0.878 0.944 0.973 0.988

3.0

.......

....... .......

.......

0.568 0.861 0.939 0.972 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

54 Appendix A Corrective Factors for Design Computation

AB

Fig. A.8

Table A.8 – Heat exchangers – A and B type – 5 passages of external ﬂuid Corrective factor χ

c

(valid also for I and L type with 5 passages of external ﬂuid)

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 0.778 0.910 0.946 0.963 0.972 0.979 0.984 0.987

0.10 0.776 0.876 0.918 0.941 0.956 0.966 0.974 0.979 0.984 0.987

0.15

.......

0.781 0.862 0.903 0.929 0.946 0.958 0.967 0.974 0.980

0.20

.......

0.612 0.790 0.858 0.897 0.923 0.941 0.954 0.964 0.972

0.25

.......

0.685 0.802 0.860 0.897 0.922 0.940 0.953 0.964

0.30

.......

0.726 0.815 0.866 0.900 0.924 0.941 0.954

0.35

.......

0.608 0.758 0.830 0.875 0.906 0.928 0.945.

0.40

.......

0.681 0.786 0.846 0.885 0.913 0.934

0.45

.......

0.547 0.730 0.811 0.862 0.897 0.922

0.50

.......

....... .......

0.653 0.769 0.835 0.878 0.908

0.60 0.643

0.764 0.832 0.877

0.70 0.651 0.769 0.837

0.80 0.673 0.784

0.90 0.705

1.00 0.560

If β >1.0 no solution is possible in this ﬁeld

Values in italics : 2<γ <4 ; Value in bold type : 4<γ <6

A.2 Heat Exchangers 55

Table A.8 – (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 0.978 0.983 0.987

0.3 0.965 0.973 0.979 0.984 0.988

0.4 0.949 0.961 0.970 0.978 0.984 0.988

0.5 0.931 0.948 0.961 0.971 0.978 0.984 0.989

0.6 0.909 0.932 0.950 0.963 0.973 0.980 0.986

0.7 0.882 0.914 0.936 0.954 0.966 0.976 0.983 0.989

0.8 0.848 0.891 0.921 0.943 0.959 0.971 0.980 0.987

0.9 0.804 0.864 0.904 0.932 0.952 0.966 0.977 0.985

1.0 0.743 0.829 0.882 0.918 0.943 0.961 0.973 0.983 0.989

1.1 0.648 0.783 0.856 0.902 0.933 0.954 0.969 0.980 0.988

1.2

.......

....... .......

.......

....... .......

.......

....... .......

.......

0.718 0.823 0.883 0.921 0.947 0.965 0.978 0.986

1.3 0.610 0.770 0.860 0.908 0.939 0.960 0.975 0.985

1.4 0.717 0.831 0.892 0.930 0.955 0.972 0.983

1.5 0.614 0.793 0.874 0.920 0.950 0.969 0.981 0.989

1.6 0.741 0.851 0.908 0.943 0.965 0.979 0.989

1.7 0.663 0.822 0.895 0.936 0.961 0.977 0.988

1.8

0.470 0.785 0.878 0.928 0.957 0.975 0.986

1.9 0.733 0.859 0.919 0.953 0.973 0.986

2.0 0.652 0.835 0.908 0.948 0.971 0.984

2.1 0.804 0.896 0.942 0.968 0.983

2.2 0.763 0.882 0.936 0.965 0.982

2.3 0.705 0.865 0.929 0.962 0.981

2.4 0.603 0.845 0.922 0.959 0.979

2.5 0.819 0.913 0.956 0.978 0.990

2.6 0.786 0.903 0.952 0.976 0.989

2.7 0.741 0.892 0.948 0.975 0.989

2.8 0.671 0.878 0.943 0.973 0.988

2.9 0.512 0.862 0.938 0.971 0.987

3.0

–

....... ....... ....... ....... ....... ....... ....... .......

0.843 0.933 0.969 0.986

....... ....... ....... ....... ....... .......

....... ....... ....... ....... .......

....... ....... ....... .......

....... ....... .......

....... .......

.......

If β<0.2 or ψ > 0.88 use the mean logarithmic temperature difference for counter ﬂow

Value in italics : 2<γ <4

56 Appendix A Corrective Factors for Design Computation

CD

Fig. A.9

Table A.9 – Heat exchangers – C and D type – 5 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 0.814 0.890 0.925 0.946 0.959 0.969 0.975 0.981 0.985 0.988

0.15

0.648 0.813 0.877 0.912 0.935 0.950 0.961 0.970 0.976 0.981

0.20

.......

0.706 0.817 0.872 0.906 0.929 0.945 0.958 0.967 0.974

0.25

.......

0.538 0.739 0.824 0.873 0.905 0.928 0.944 0.957 0.966

0.30

.......

0.631 0,765 0.835 0.878 0.908 0.929 0.945 0.958

0.35

.......

0.464 0.687 0.788 0.847 0.885 0.913 0.933 0.948

0.40

.......

0.578 0.729 0.809 0.859 0.894 0.919 0.938

0.45

.......

0.418 0.652 0.764 0.830 0.874 0.904 0.927

0.50

.......

0.545 0.707 0.794 0.849 0.888 0.915

0.60

.......

0.531 0.699 0.789 0.847 0.887

0.70

.......

0.537 0.703 0.793 0.851

0.80

.......

0.296 0.561 0.718 0.805

0.90

.......

0.326 0.599 0.741

1.00

.......

0.386 0.647

1.10

.......

0.483

1.20 .......

.......

0.280

If β>1.2 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 57

Table A.9 – (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 0.980 0.984 0.988 ……. ……. ……. ……. ……. ……. ……. …….

0.3 0.967 0.975 0.980 0.985 0.989 ……. ……. ……. ……. ……. …….

0.4 0.953 0.964 0.972 0.979 0.985 0.989 ……. ……. ……. ……. …….

0.5 0.936 0.951 0.963 0.973 0.980 0.985 0.990 ……. ……. ……. …….

0.6 0.915 0.937 0.953 0.965 0.975 0.982 0.987 ……. ……. ……. …….

0.7 0.891 0.920 0.941 0.957 0.969 0.978 0.985 0.990 ……. ……. …….

0.8 0.861 0.899 0.927 0.947 0.962 0.973 0.982 0.988 ……. ……. …….

0.9 0.822 0.875 0.911 0.936 0.955 0.968 0.978 0.986 ……. ……. …….

1.0 0.771 0.844 0.891 0.924 0.947 0.963 0.975 0.984 0.990 ……. …….

1.1 0.699 0.805 0.868 0.909 0.937 0.957 0.971 0.981 0.988 ……. …….

1.2 0.586 0.752 0.838 0.892 0.927 0.951 0.967 0.979 0.987 ……. …….

1.3 0.385 0.676 0.801 0.871 0.914 0.943 0.963 0.976 0.986 ……. …….

1.4 0.241 0.552 0.751 0.845 0.900 0.935 0.958 0.974 0.984 ……. …….

1.5 ........ 0.347 0.680 0.813 0.883 0.926 0.953 0.971 0.982 ……. …….

1.6 ........ 0.230 0.565 0.771 0.863 0.915 0.947 0.967 0.981 0.989 …….

1.7 ........ ........ 0.367 0.712 0.838 0.902 0.940 0.964 0.979 0.988 …….

1.8 ........ ........ 0.241 0.624 0.806 0.888 0.933 0.960 0.977 0.987 …….

1.9 ........ ........ ........ 0.468 0.765 0.871 0.925 0.956 0.975 0.986 …….

2.0 ........ ........ ........ 0.288 0.707 0.849 0.915 0.951 0.973 0.985 …….

2.1 ........ ........ ........ 0.212 0.619 0.823 0.904 0.946 0.970 0.984 …….

2.2 ........ ........ ........ ........ 0.463 0.790 0.892 0.941 0.968 0.983 …….

2.3 ........ ........ ........ ........ 0.290 0.745 0.877 0.934 0.965 0.982 …….

2.4 ........ ........ ........ ........ 0.215 0.681 0.859 0.927 0.962 0.981 …….

2.5 ........ ........ ........ ........ ........ 0.577 0.837 0.920 0.958 0.979 …….

2.6 ........ ........ ........ ........ ........ 0.396 0.809 0.911 0.955 0.978 0.990

2.7 ........ ........ ........ ........ ........ 0.263 0.774 0.900 0.951 0.976 0.989

2.8 ........ ........ ........ ........ ........ 0.204 0.725 0.888 0.947 0.975 0.989

2.9 ........ ........ ........ ........ ........ ........ 0.651 0.874 0.942 0.973 0.988

3.0 ........ ........ ........ ........ ........ ........ 0.526 0.858 0.937 0.971 0.987

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

58 Appendix A Corrective Factors for Design Computation

A.2.2 Heat Exchangers with 3 Passages of Internal Fluid (Fig. 2.6)

EF

Fig. A.10

Table A.10 – Heat exchangers – E and F type – 2 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 0.723 0.901 0.941 0.960 0.971 0.978 0.983 0.987 0.989 ……. …….

0.10 ........ 0.736 0.864 0.911 0.937 0.953 0.964 0.972 0.978 0.983 0.986

0.15 ........ ........ 0.750 0.849 0.896 0.924 0.942 0.956 0.965 0.973 0.979

0.20 ........ ........ ........ 0.765 0.846 0.890 0.918 0.937 0.952 0.962 0.970

0.25 ........ ........ ........ 0.616 0.781 0.849 0.889 0.917 0.936 0.950 0.962

0.30 ........ ........ ........ ........ 0.686 0.798 0.856 0.893 0.919 0.938 0.952

0.35 ........ ........ ........ ........ ........ 0.730 0.815 0.866 0.899 0.923 0.941

0.40 ........ ........ ........ ........ ........ 0.624 0.765 0.833 0.877 0.908 0.930

0.45 ........ ........ ........ ........ ........ ........ 0.696 0.795 0.851 0.890 0.917

0.50 ........ ........ ........ ........ ........ ........ 0.582 0.746 0.821 0.869 0.903

0.60 ........ ........ ........ ........ ........ ........ ........ 0.569 0.740 0.819 0.869

0.70 ........ ........ ........ ........ ........ ........ ........ ........ 0.586 0.747 0.825

0.80 ........ ........ ........ ........ ........ ........ ........ ........ ........ 0.623 0.764

0.90 ........ ........ ........ ........ ........ ........ ........ ........ ........ ........ 0.668

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 59

Table A.10 – (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 0.977 0.982 0.986 0.989 ……. ……. ……. ……. ……. ……. …….

0.3 0.963 0.971 0.978 0.983 0.987 ……. ……. ……. ……. ……. …….

0.4 0.946 0.959 0.969 0.976 0.983 0.987 ……. ……. ……. ……. …….

0.5 0.927 0.945 0.958 0.969 0.977 0.984 0.988 ……. ……. ……. …….

0.6 0.903 0.928 0.947 0.961 0.971 0.979 0.986 ……. ……. ……. …….

0.7 0.874 0.908 0.933 0.951 0.965 0.975 0.983 0.988 ……. ……. …….

0.8 0.837 0.884 0.917 0.940 0.957 0.970 0.979 0.986 ……. ……. …….

0.9 0.788 0.854 0.898 0.928 0.949 0.964 0.976 0.984 0.990 ……. …….

1.0 0.716 0.816 0.874 0.913 0.940 0.958 0.972 0.982 0.988 ……. …….

1.1 0.583 0.764 0.846 0.896 0.929 0.952 0.968 0.979 0.987 ……. …….

1.2 ........ 0.685 0.809 0.875 0.916 0.944 0.963 0.976 0.986 ……. …….

1.3 ........ 0.489 0.758 0.849 0.902 0.936 0.958 0.973 0.984 ……. …….

1.4 ........ ........ 0.683 0.817 0.885 0.926 0.953 0.970 0.982 0.990 …….

1.5 ........ ........ 0.499 0.774 0.865 0.915 0.946 0.967 0.980 0.989 …….

1.6 ........ ........ ........ 0.713 0.839 0.902 0.940 0.963 0.978 0.988 …….

1.7 ........ ........ ........ 0.604 0.807 0.888 0.932 0.959 0.976 0.987 …….

1.8 ........ ........ ........ ........ 0.764 0.870 0.924 0.955 0.974 0.986 …….

1.9 ........ ........ ........ ........ 0.701 0.848 0.914 0.950 0.972 0.985 …….

2.0 ........ ........ ........ ........ 0.583 0.821 0.902 0.945 0.969 0.984 …….

2.1 ........ ........ ........ ........ ........ 0.786 0.889 0.939 0.966 0.982 …….

2.2 ........ ........ ........ ........ ........ 0.738 0.874 0.932 0.963 0.981 …….

2.3 ........ ........ ........ ........ ........ 0.662 0.855 0.925 0.960 0.980 …….

2.4 ........ ........ ........ ........ ........ ........ 0.833 0.917 0.957 0.978 0.990

2.5 ........ ........ ........ ........ ........ ........ 0.804 0.908 0.953 0.976 0.989

2.6 ........ ........ ........ ........ ........ ........ 0.765 0.897 0.949 0.975 0.989

2.7 ........ ........ ........ ........ ........ ........ 0.709 0.884 0.945 0.973 0.988

2.8 ........ ........ ........ ........ ........ ........ 0.607 0.870 0.940 0.971 0.987

2.9 ........ ........ ........ ........ ........ ........ ........ 0.852 0.934 0.969 0.987

3.0 ........ ........ ........ ........ ........ ........ ........ 0.830 0.928 0.967 0.986

If ψ> 0.88 use the mean logarithmic temperature difference for counter ﬂow

Values in italics : 2<γ <4

60 Appendix A Corrective Factors for Design Computation

GH

Fig. A.11

Table A.11 – Heat exchangers – G and H type – 2 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

0.10 0.640 0.840 0.901 0.932 0.950 0.962 0.971 0.977 0.982 0.986 0.989

0.15 ........ 0.720 0.835 0.888 0.919 0.939 0.954 0.964 0.972 0.977 0.982

0.20 ........ 0.562 0.751 0.836 0.884 0.914 0.934 0.949 0.960 0.969 0.975

0.25 ........ ........ 0.643 0.773 0.842 0.884 0.912 0.933 0.948 0.959 0.968

0.30 ........ ........ 0.513 0.693 0.792 0.850 0.888 0.915 0.934 0.949 0.960

0.35 ........ ........ ........ 0.593 0.730 0.809 0.859 0.894 0.919 0.938 0.952

0.40 ........ ........ ........ 0.481 0.654 0.761 0.827 0.871 0.902 0.925 0.942

0.50 ........ ........ ........ ........ 0.461 0.630 0.742 0.813 0.862 0.896 0.921

0.60 ........ ........ ........ ........ ........ 0.452 0.619 0.735 0.808 0.859 0.895

0.70 ........ ........ ........ ........ ........ ........ 0.453 0.621 0.737 0.812 0.863

0.80 ........ ........ ........ ........ ........ ........ ........ 0.465 0.634 0.749 0.822

0.90 ........ ........ ........ ........ ........ ........ ........ 0.340 0.491 0.660 0.768

1.00 ........ ........ ........ ........ ........ ........ ........ ........ 0.361 0.533 0.694

1.10 ........ ........ ........ ........ ........ ........ ........ ........ ........ 0.395 0.588

1.20 ........ ........ ........ ........ ........ ........ ........ ........ ........ 0.306 0.451

1.30 ........ ........ ........ ........ ........ ........ ........ ........ ........ ........ 0.344

If β > 1.3 no solution is possible in this ﬁeld

Values in italics : 2<γ <4 ; Values in bold type : 4<γ <6

A.2 Heat Exchangers 61

Table A.11 – (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 0.976 0.982 0.986 0.989 ……. ……. ……. ……. ……. …….

0.4 0.956 0.966 0.974 0.980 0.985 0.989 ……. ……. ……. ……. …….

0.5 0.940 0.954 0.965 0.974 0.981 0.986 ……. ……. ……. ……. …….

0.6 0.921 0.941 0.956 0.967 0.976 0.983 0.988 ……. ……. ……. …….

0.7 0.899 0.925 0.945 0.959 0.970 0.979 0.985 ……. ……. ……. …….

0.8 0.871 0.906 0.932 0.950 0.964 0.975 0.983 0.988 ……. ……. …….

0.9 0.837 0.884 0.917 0.940 0.958 0.970 0.980 0.986 ……. ……. …….

1.0 0.793 0.856 0.899 0.929 0.950 0.965 0.976 0.984 ……. ……. …….

1.1 0.734 0.821 0.877 0.915 0.941 0.960 0.973 0.982 0.989 ……. …….

1.2 0.651 0.776 0.851 0.899 0.931 0.954 0.969 0.980 0.988 ……. …….

1.3 0.534 0.716 0.819 0.880 0.920 0.947 0.965 0.978 0.986 ……. …….

1.4 0.406 0.631 0.776 0.858 0.907 0.939 0.961 0.975 0.985 ……. …….

1.5 0.319 0.512 0.720 0.829 0.892 0.931 0.956 0.972 0.983 ……. …….

1.6 ........ 0.392 0.640 0.793 0.874 0.921 0.950 0.969 0.982 0.990 …….

1.7 ........ 0.314 0.528 0.745 0.851 0.909 0.944 0.966 0.980 0.989 …….

1.8 ........ ........ 0.409 0.680 0.824 0.896 0.937 0.963 0.978 0.988 …….

1.9 ........ ........ 0.327 0.588 0.789 0.880 0.929 0.958 0.976 0.987 …….

2.0 ........ ........ 0.271 0.469 0.743 0.862 0.921 0.954 0.974 0.986 …….

2.1 ........ ........ ........ 0.369 0.679 0.839 0.911 0.950 0.972 0.985 …….

2.2 ........ ........ ........ 0.304 0.589 0.810 0.899 0.944 0.969 0.984 …….

2.3 ........ ........ ........ ........ 0.473 0.773 0.886 0.939 0.967 0.983 …….

2.4 ........ ........ ........ ........ 0.376 0.724 0.870 0.932 0.964 0.982 …….

2.5 ........ ........ ........ ........ 0.310 0.656 0.851 0.925 0.961 0.980 …….

2.6 ........ ........ ........ ........ 0.258 0.558 0.827 0.917 0.958 0.979 …….

2.7 ........ ........ ........ ........ ........ 0.446 0.798 0.908 0.954 0.978 …….

2.8 ........ ........ ........ ........ ........ 0.360 0.759 0.897 0.950 0.976 0.989

2.9 ........ ........ ........ ........ ........ 0.301 0.706 0.884 0.946 0.975 0.989

3.0 ........ ........ ........ ........ ........ 0.268 0.632 0.870 0.942 0.973 0.988

If β<0.2orψ> 0.88 use the mean logarithmic temperature difference for counter ﬂow

Values in italics : 2<γ <4 ; Values in bold type : 4<γ <6

Annaratone D. Handbook for Heat Exchangers and Tube Banks design

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