Annaratone D. Handbook for Heat Exchangers and Tube Banks design
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112 Appendix B Factor ψ or Corrective Factors for Verification Computation
B.1 Fluids in Parallel Flow or Counter Flow
Table B.1 – Factor ψ for fluids in parallel flow
β
γ
0.05 0.10 0.15 0.20 0.25 0.30 0.35 0.40 0.45 0.50 0.55
0.1 0.951 0.905 0.862 0.820 0.781 0.744 0.710 0.676 0.645 0.615 0.587
0.2 0.951 0.906 0.863 0.822 0.784 0.748 0.714 0.682 0.652 0.624 0.597
0.3 0.952 0.906 0.864 0.824 0.787 0.752 0.719 0.688 0.659 0.632 0.607
0.4 0.952 0.907 0.865 0.826 0.789 0.755 0.723 0.694 0.666 0.640 0.616
0.5 0.952 0.907 0.866 0.827 0.792 0.758 0.728 0.699 0.673 0.648 0.625
0.6 0.952 0.908 0.867 0.829 0.794 0.762 0.732 0.705 0.679 0.656 0.634
0.7 0.952 0.908 0.868 0.830 0.796 0.765 0.736 0.710 0.685 0.663 0.643
0.8 0.952 0.908 0.869 0.832 0.799 0.768 0.740 0.715 0.692 0.670 0.651
0.9 0.952 0.909 0.869 0.834 0.801 0.771 0.744 0.720 0.698 0.677 0.659
1.0 0.952 0.909 0.870 0.835 0.803 0.774 0.748 0.725 0.703 0.684 0.666
1.1 0.953 0.910 0.871 0.837 0.806 0.777 0.752 0.729 0.709 0.690 0.674
1.2 0.953 0.910 0.872 0.838 0.808 0.780 0.756 0.734 0.714 0.697 0.681
1.3 0.953 0.911 0.873 0.840 0.810 0.783 0.760 0.738 0.720 0.703 0.688
1.4 0.953 0.911 0.874 0.841 0.812 0.786 0.763 0.743 0.725 0.709 0.695
1.5 0.953 0.912 0.875 0.843 0.814 0.789 0.767 0.747 0.730 0.715 0.701
1.6 0.953 0.912 0.876 0.844 0.816 0.792 0.770 0.751 0.735 0.720 0.707
1.7 0.953 0.912 0.877 0.845 0.818 0.794 0.774 0.755 0.740 0.726 0.714
1.8 0.953 0.913 0.878 0.847 0.820 0.797 0.777 0.759 0.744 0.731 0.719
1.9 0.953 0.913 0.878 0.848 0.822 0.800 0.780 0.763 0.749 0.736 0.725
2.0 0.954 0.914 0.879 0.850 0.824 0.802 0.783 0.767 0.753 0.741 0.731
2.1 0.954 0.914 0.880 0.851 0.826 0.805 0.786 0.771 0.757 0.746 0.736
2.2 0.954 0.914 0.881 0.852 0.828 0.807 0.789 0.774 0.762 0.751 0.741
2.3 0.954 0.915 0.882 0.854 0.830 0.810 0.792 0.778 0.766 0.755 0.746
2.4 0.954 0.915 0.882 0.855 0.832 0.812 0.795 0.781 0.770 0.760 0.751
2.5 0.954 0.916 0.883 0.856 0.833 0.814 0.798 0.785 0.773 0.764 0.756
2.6 0.954 0.916 0.884 0.857 0.835 0.817 0.801 0.788 0.777 0.768 0.761
2.7 0.954 0.916 0.885 0.859 0.837 0.819 0.804 0.791 0.781 0.772 0.765
2.8 0.954 0.917 0.886 0.860 0.839 0.821 0.806 0.794 0.784 0.776 0.769
2.9 0.955 0.917 0.886 0.861 0.840 0.823 0.809 0.797 0.788 0.780 0.774
3.0 0.955 0.918 0.887 0.862 0.842 0.825 0.812 0.800 0.791 0.784 0.778
B.1 Fluids in Parallel Flow or Counter Flow 113
Table B.1 – (continued)
β
γ
0.60 0.70 0.80 0.90 1.00 1.10 1.20 1.30 1.40 1.50 1.60
0.1 0.561 0.512 0.468 0.429 0.394 0.362 0.334 0.308 0.286 0.265 0.247
0.2 0.572 0.526 0.486 0.450 0.418 0.389 0.364 0.342 0.322 0.304 0.289
0.3 0.583 0.540 0.503 0.470 0.440 0.415 0.392 0.373 0.355 0.340 0.327
0.4 0.594 0.554 0.519 0.488 0.462 0.439 0.419 0.401 0.386 0.373 0.362
0.5 0.604 0.567 0.534 0.506 0.482 0.461 0.444 0.428 0.415 0.404 0.394
0.6 0.614 0.579 0.549 0.523 0.501 0.483 0.467 0.453 0.442 0.432 0.423
0.7 0.624 0.591 0.563 0.539 0.519 0.502 0.488 0.467 0.466 0.458 0.451
0.8 0.633 0.602 0.576 0.554 0.536 0.521 0.509 0.498 0.489 0.482 0.476
0.9 0.642 0.613 0.589 0.569 0.552 0.539 0.528 0.518 0.510 0.504 0.499
1.0 0.651 0.623 0.601 0.583 0.568 0.555 0.545 0.537 0.530 0.525 0.520
1.1 0.659 0.633 0.613 0.596 0.582 0.571 0.562 0.555 0.549 0.544 0.540
1.2 0.667 0.643 0.624 0.608 0.596 0.586 0.578 0.571 0.566 0.562 0.559
1.3 0.675 0.652 0.634 0.620 0.609 0.600 0.593 0.587 0.583 0.579 0.576
1.4 0.682 0.661 0.644 0.631 0.621 0.613 0.607 0.602 0.598 0.595 0.592
1.5 0.689 0.670 0.654 0.642 0.633 0.626 0.620 0.616 0.612 0.609 0.607
1.6 0.696 0.678 0.663 0.652 0.644 0.637 0.632 0.628 0.625 0.623 0.621
1.7 0.703 0.686 0.672 0.662 0.655 0.649 0.644 0.641 0.638 0.636 0.635
1.8 0.709 0.693 0.681 0.672 0.665 0.659 0.655 0.652 0.650 0.648 0.647
1.9 0.716 0.700 0.689 0.681 0.674 0.669 0.666 0.663 0.661 0.660 0.659
2.0 0.722 0.707 0.697 0.689 0.683 0.679 0.676 0.673 0.672 0.670 0.669
2.1 0.728 0.714 0.704 0.697 0.692 0.688 0.685 0.683 0.682 0.681 0.680
2.2 0.733 0.721 0.712 0.705 0.700 0.697 0.694 0.692 0.691 0.690 0.689
2.3 0.739 0.727 0.719 0.713 0.708 0.705 0.703 0.701 0.700 0.699 0.699
2.4 0.744 0.733 0.725 0.720 0.716 0.713 0.711 0.709 0.708 0.708 0.707
2.5 0.749 0.739 0.732 0.727 0.723 0.720 0.719 0.717 0.716 0.716 0.715
2.6 0.754 0.745 0.738 0.733 0.730 0.728 0.726 0.725 0.724 0.723 0.723
2.7 0.759 0.750 0.744 0.739 0.736 0.734 0.733 0.732 0.731 0.731 0.730
2.8 0.764 0.755 0.749 0.745 0.743 0.741 0.740 0.739 0.738 0.738 0.737
2.9 0.768 0.760 0.755 0.751 0.749 0.747 0.746 0.745 0.745 0.744 0.744
3.0 0.773 0.765 0.760 0.757 0.755 0.753 0.752 0.751 0.751 0.751 0.750
114 Appendix B Factor ψ or Corrective Factors for Verification Computation
Table B.1 – (continued)
β
γ
1.7 1.9 2.1 2.3 2.5 2.8 3.1 3.4 3.7 4.0
0.1 0.231 0.203 0.181 0.163 0.149 0.133 0.121 0.113 0.106 0.102
0.2 0.275 0.252 0.234 0.219 0.208 0.196 0.187 0.181 0.176 0.174
0.3 0.315 0.296 0.281 0.269 0.261 0.251 0.244 0.240 0.237 0.235
0.4 0.352 0.336 0.323 0.314 0.307 0.300 0.295 0.292 0.290 0.288
0.5 0.385 0.372 0.362 0.354 0.349 0.343 0.340 0.337 0.336 0.335
0.6 0.416 0.405 0.397 0.391 0.386 0.382 0.379 0.378 0.377 0.376
0.7 0.444 0.435 0.428 0.424 0.420 0.417 0.415 0.414 0.413 0.412
0.8 0.470 0.463 0.457 0.453 0.451 0.448 0.447 0.446 0.445 0.445
0.9 0.495 0.488 0.483 0.480 0.478 0.476 0.475 0.475 0.474 0.474
1.0 0.517 0.511 0.507 0.505 0.503 0.502 0.501 0.501 0.500 0.500
1.1 0.537 0.533 0.530 0.528 0.526 0.525 0.525 0.524 0.524 0.524
1.2 0.556 0.552 0.550 0.548 0.547 0.546 0.546 0.546 0.546 0.546
1.3 0.574 0.571 0.569 0.567 0.567 0.566 0.566 0.565 0.565 0.565
1.4 0.590 0.588 0.586 0.585 0.584 0.584 0.584 0.583 0.583 0.583
1.5 0.606 0.603 0.602 0.601 0.601 0.600 0.600 0.600 0.600 0.600
1.6 0.620 0.618 0.617 0.616 0.616 0.616 0.616 0.615 0.615 0.615
1.7 0.633 0.632 0.631 -------------------------- 0.630 ------------------------------
1.8 0.646 0.645 0.644 -------------------------- 0.643 ------------------------------
1.9 0.658 0.657 0.656 0.656 ----------------- 0.655 ------------------------------
2.0 0.669 0.668 ------------------------------------- 0.667 ------------------------------
2.1 0.679 ------------ 0.678 -------------- ------------------ 0.677 -----------------
2.2 0.689 ------------------------------------- 0.688 --------------------------------------
2.3 0.698 0.698 --------------------------- 0.697 ---------------------------------------
2.4 0.707 ------------------------------------ 0.706 ---------------------------------------
2.5 0.715 0.715 --------------------------- 0.714 ---------------------------------------
2.6 0.723 0.723 --------------------------- 0.722 ---------------------------------------
2.7 ---------------------------------------------- 0.730 ---------------------------------------
2.8 ---------------------------------------------- 0.737 ---------------------------------------
2.9 ---------------------------------------------- 0.744 ---------------------------------------
3.0 ---------------------------------------------- 0.750 ---------------------------------------
B.1 Fluids in Parallel Flow or Counter Flow 115
Table B.2 – Factor ψ for fluids in counter flow
β
γ
0.05 0.10 0.15 0.20 0.25 0.30 0.35 0.40 0.45 0.50 0.55
0.1 0.951 0.905 0.862 0.820 0.781 0.744 0.709 0.675 0.643 0.613 0.584
0.2 0.951 0.906 0.863 0.822 0.783 0.747 0.712 0.680 0.649 0.619 0.591
0.3 0.952 0.906 0.863 0.823 0.785 0.750 0.716 0.684 0.654 0.626 0.598
0.4 0.952 0.907 0.864 0.825 0.788 0.753 0.720 0.689 0.659 0.632 0.605
0.5 0.952 0.907 0.865 0.826 0.790 0.755 0.723 0.693 0.665 0.638 0.612
0.6 0.952 0.907 0.866 0.828 0.792 0.758 0.727 0.697 0.670 0.644 0.619
0.7 0.952 0.908 0.867 0.829 0.794 0.761 0.730 0.702 0.675 0.650 0.626
0.8 0.952 0.908 0.868 0.831 0.796 0.764 0.734 0.706 0.680 0.655 0.632
0.9 0.952 0.909 0.869 0.832 0.798 0.767 0.737 0.710 0.685 0.661 0.639
1.0 0.952 0.909 0.870 0.833 0.800 0.769 0.741 0.714 0.690 0.667 0.645
1.1 0.952 0.910 0.870 0.835 0.802 0.772 0.744 0.718 0.694 0.672 0.651
1.2 0.953 0.910 0.871 0.836 0.804 0.774 0.747 0.722 0.699 0.678 0.658
1.3 0.953 0.910 0.872 0.837 0.806 0.777 0.751 0.726 0.704 0.683 0.664
1.4 0.953 0.911 0.873 0.839 0.808 0.780 0.754 0.730 0.708 0.688 0.669
1.5 0.953 0.911 0.874 0.840 0.810 0.782 0.757 0.734 0.713 0.693 0.675
1.6 0.953 0.912 0.875 0.841 0.812 0.785 0.760 0.738 0.717 0.698 0.681
1.7 0.953 0.912 0.875 0.843 0.813 0.787 0.763 0.741 0.721 0.703 0.687
1.8 0.953 0.912 0.876 0.844 0.815 0.789 0.766 0.745 0.726 0.708 0.692
1.9 0.953 0.913 0.877 0.845 0.817 0.792 0.769 0.749 0.730 0.713 0.697
2.0 0.953 0.913 0.878 0.847 0.819 0.794 0.772 0.752 0.734 0.718 0.703
2.1 0.954 0.913 0.879 0.848 0.821 0.796 0.775 0.756 0.738 0.722 0.708
2.2 0.954 0.914 0.879 0.849 0.822 0.799 0.778 0.759 0.742 0.727 0.713
2.3 0.954 0.914 0.880 0.850 0.824 0.801 0.781 0.762 0.746 0.731 0.718
2.4 0.954 0.915 0.881 0.851 0.826 0.803 0.783 0.766 0.750 0.736 0.723
2.5 0.954 0.915 0.882 0.853 0.827 0.805 0.786 0.769 0.753 0.740 0.728
2.6 0.954 0.915 0.882 0.854 0.829 0.808 0.789 0.772 0.757 0.744 0.732
2.7 0.954 0.916 0.883 0.855 0.831 0.810 0.791 0.775 0.761 0.748 0.737
2.8 0.954 0.916 0.884 0.856 0.832 0.812 0.794 0.778 0.764 0.752 0.741
2.9 0.954 0.917 0.885 0.857 0.834 0.814 0.796 0.781 0.768 0.756 0.746
3.0 0.955 0.917 0.885 0.858 0.836 0.816 0.799 0.784 0.771 0.760 0.750
116 Appendix B Factor ψ or Corrective Factors for Verification Computation
Table B.2 – (continued)
β
γ
0.6 0.7 0.8 0.9 1.0 1.1 1.2 1.3 1.4 1.5 1.6
0.1 0.557 0.506 0.460 0.419 0.381 0.347 0.316 0.288 0.263 0.240 0.218
0.2 0.565 0.516 0.472 0.431 0.395 0.362 0.332 0.304 0.279 0.256 0.236
0.3 0.573 0.525 0.483 0.444 0.408 0.376 0.347 0.320 0.296 0.274 0.253
0.4 0.581 0.535 0.493 0.456 0.422 0.391 0.363 0.337 0.313 0.291 0.271
0.5 0.588 0.544 0.504 0.468 0.435 0.405 0.378 0.353 0.330 0.309 0.290
0.6 0.596 0.553 0.515 0.480 0.449 0.420 0.394 0.370 0.348 0.327 0.309
0.7 0.603 0.562 0.525 0.492 0.462 0.434 0.409 0.386 0.365 0.345 0.327
0.8 0.611 0.571 0.535 0.504 0.475 0.448 0.424 0.402 0.382 0.364 0.347
0.9 0.618 0.580 0.546 0.515 0.487 0.462 0.440 0.419 0.400 0.382 0.366
1.0 0.625 0.588 0.556 0.526 0.500 0.476 0.455 0.435 0.417 0.400 0.385
1.1 0.632 0.597 0.565 0.537 0.512 0.490 0.469 0.451 0.434 0.418 0.403
1.2 0.639 0.605 0.575 0.548 0.525 0.503 0.484 0.466 0.450 0.436 0.422
1.3 0.646 0.613 0.584 0.559 0.536 0.516 0.498 0.482 0.467 0.453 0.440
1.4 0.652 0.621 0.594 0.570 0.548 0.529 0.512 0.497 0.483 0.470 0.458
1.5 0.659 0.629 0.603 0.580 0.560 0.542 0.526 0.511 0.498 0.487 0.476
1.6 0.665 0.636 0.611 0.590 0.571 0.554 0.539 0.526 0.514 0.503 0.493
1.7 0.671 0.644 0.620 0.600 0.582 0.566 0.552 0.540 0.528 0.518 0.510
1.8 0.677 0.651 0.629 0.609 0.592 0.578 0.565 0.553 0.543 0.534 0.526
1.9 0.683 0.658 0.637 0.618 0.603 0.589 0.577 0.566 0.557 0.549 0.541
2.0 0.689 0.665 0.645 0.628 0.613 0.600 0.589 0.579 0.570 0.563 0.556
2.1 0.695 0.672 0.653 0.636 0.622 0.610 0.600 0.591 0.583 0.577 0.571
2.2 0.700 0.679 0.660 0.645 0.632 0.621 0.611 0.603 0.596 0.590 0.584
2.3 0.706 0.685 0.668 0.653 0.641 0.631 0.622 0.615 0.608 0.602 0.598
2.4 0.711 0.691 0.675 0.662 0.650 0.641 0.632 0.626 0.620 0.615 0.610
2.5 0.717 0.698 0.682 0.669 0.659 0.650 0.642 0.636 0.631 0.626 0.623
2.6 0.722 0.704 0.689 0.677 0.667 0.659 0.652 0.646 0.642 0.638 0.634
2.7 0.727 0.710 0.696 0.685 0.675 0.668 0.661 0.656 0.652 0.648 0.645
2.8 0.732 0.715 0.702 0.692 0.683 0.676 0.670 0.666 0.662 0.659 0.656
2.9 0.736 0.721 0.709 0.699 0.691 0.684 0.679 0.675 0.671 0.669 0.666
3.0 0.741 0.726 0.715 0.706 0.698 0.692 0.687 0.684 0.680 0.678 0.676
B.1 Fluids in Parallel Flow or Counter Flow 117
Table B.2 – (continued)
β
γ
1.7 1.9 2.1 2.3 2.5 2.8 3.1 3.4 3.7 4.0
0.1 0.199 0.166 0.138 0.115 0.096 0.073 0.056 0.042 0.032 0.025
0.2 0.216 0.183 0.155 0.131 0.111 0.087 0.068 0.053 0.042 0.033
0.3 0.234 0.201 0.173 0.149 0.128 0.103 0.083 0.067 0.054 0.043
0.4 0.253 0.220 0.192 0.168 0.147 0.121 0.100 0.082 0.068 0.056
0.5 0.272 0.240 0.212 0.188 0.167 0.141 0.119 0.101 0.085 0.073
0.6 0.291 0.260 0.233 0.210 0.189 0.162 0.140 0.121 0.105 0.092
0.7 0.311 0.281 0.255 0.232 0.212 0.186 0.164 0.145 0.129 0.114
0.8 0.331 0.302 0.277 0.255 0.236 0.210 0.189 0.170 0.154 0.140
0.9 0.351 0.323 0.300 0.279 0.260 0.236 0.216 0.198 0.183 0.169
1.0 0.370 0.345 0.323 0.303 0.286 0.263 0.244 0.227 0.213 0.200
1.1 0.390 0.366 0.346 0.327 0.311 0.291 0.273 0.258 0.244 0.233
1.2 0.410 0.387 0.368 0.352 0.337 0.318 0.302 0.288 0.277 0.266
1.3 0.429 0.408 0.391 0.376 0.362 0.346 0.331 0.319 0.309 0.300
1.4 0.448 0.429 0.413 0.399 0.388 0.373 0.360 0.350 0.341 0.334
1.5 0.466 0.449 0.435 0.423 0.412 0.399 0.388 0.380 0.372 0.366
1.6 0.484 0.469 0.456 0.445 0.436 0.424 0.415 0.408 0.402 0.398
1.7 0.502 0.488 0.476 0.467 0.459 0.449 0.441 0.435 0.431 0.427
1.8 0.518 0.506 0.496 0.487 0.481 0.472 0.466 0.461 0.458 0.455
1.9 0.535 0.524 0.515 0.507 0.502 0.495 0.490 0.486 0.483 0.481
2.0 0.550 0.540 0.533 0.526 0.521 0.516 0.512 0.508 0.506 0.505
2.1 0.565 0.557 0.550 0.544 0.540 0.536 0.532 0.530 0.528 0.527
2.2 0.580 0.572 0.566 0.562 0.558 0.554 0.552 0.550 0.548 0.548
2.3 0.594 0.587 0.582 0.578 0.575 0.572 0.570 0.568 0.567 0.567
2.4 0.607 0.601 0.596 0.593 0.591 0.588 0.587 0.585 0.585 0.584
2.5 0.619 0.614 0.610 0.608 0.606 0.604 0.602 -------- 0.601 --------
2.6 0.631 0.627 0.624 0.621 0.620 0.618 0.617 -------- 0.616 --------
2.7 0.643 0.639 0.636 0.634 0.633 0.632 0.631 -------- 0.630 --------
2.8 0.654 0.650 0.648 0.647 0.645 0.644 0.644 -------- 0.643 --------
2.9 0.664 0.661 0.659 0.658 0.657 -------- 0.656 -------- 0.655 0.655
3.0 0.674 0.672 0.670 0.669 0.668 ----------------- 0.667 ------------------
118 Appendix B Factor ψ or Corrective Factors for Verification Computation
B.2 Fluids in Cross Flow
Table B.3 – Factor ψ for fluids in cross flow
β
γ
0.05 0.10 0.15 0.20 0.25 0.30 0.35 0.40 0.45 0.50 0.55
0.1 0.951 0.905 0.862 0.820 0.781 0.744 0.709 0.676 0.644 0.614 0.586
0.2 0.951 0.906 0.863 0.822 0.784 0.747 0.713 0.681 0.650 0.621 0.594
0.3 0.952 0.906 0.864 0.824 0.786 0.751 0.717 0.686 0.656 0.628 0.602
0.4 0.952 0.907 0.865 0.825 0.788 0.754 0.721 0.691 0.662 0.635 0.610
0.5 0.952 0.907 0.865 0.827 0.791 0.757 0.725 0.696 0.668 0.642 0.618
0.6 0.952 0.908 0.866 0.828 0.793 0.760 0.729 0.701 0.674 0.649 0.625
0.7 0.952 0.908 0.867 0.830 0.795 0.763 0.733 0.705 0.679 0.655 0.633
0.8 0.952 0.908 0.868 0.831 0.797 0.766 0.737 0.710 0.685 0.662 0.640
0.9 0.952 0.909 0.869 0.833 0.799 0.769 0.740 0.714 0.690 0.668 0.647
1.0 0.952 0.909 0.870 0.834 0.801 0.771 0.744 0.719 0.695 0.674 0.654
1.1 0.953 0.910 0.871 0.836 0.804 0.774 0.748 0.723 0.700 0.680 0.660
1.2 0.953 0.910 0.872 0.837 0.806 0.777 0.751 0.727 0.705 0.685 0.667
1.3 0.953 0.910 0.873 0.838 0.808 0.780 0.754 0.731 0.710 0.691 0.673
1.4 0.953 0.911 0.873 0.840 0.810 0.782 0.758 0.735 0.715 0.696 0.679
1.5 0.953 0.911 0.874 0.841 0.812 0.785 0.761 0.739 0.720 0.702 0.685
1.6 0.953 0.912 0.875 0.843 0.814 0.788 0.764 0.743 0.724 0.707 0.691
1.7 0.953 0.912 0.876 0.844 0.815 0.790 0.767 0.747 0.728 0.712 0.697
1.8 0.953 0.913 0.877 0.845 0.817 0.793 0.770 0.751 0.733 0.717 0.702
1.9 0.953 0.913 0.878 0.847 0.819 0.795 0.774 0.754 0.737 0.722 0.708
2.0 0.954 0.913 0.878 0.848 0.821 0.797 0.777 0.758 0.741 0.726 0.713
2.1 0.954 0.914 0.879 0.849 0.823 0.800 0.779 0.761 0.745 0.731 0.718
2.2 0.954 0.914 0.880 0.850 0.825 0.802 0.782 0.765 0.749 0.735 0.723
2.3 0.954 0.915 0.881 0.852 0.826 0.804 0.785 0.768 0.753 0.740 0.728
2.4 0.954 0.915 0.882 0.853 0.828 0.807 0.788 0.771 0.757 0.744 0.733
2.5 0.954 0.915 0.882 0.854 0.830 0.809 0.791 0.775 0.761 0.748 0.737
2.6 0.954 0.916 0.883 0.855 0.832 0.811 0.793 0.778 0.764 0.752 0.742
2.7 0.954 0.916 0.884 0.857 0.833 0.813 0.796 0.781 0.768 0.756 0.746
2.8 0.954 0.916 0.885 0.858 0.835 0.815 0.799 0.784 0.771 0.760 0.750
2.9 0.955 0.917 0.885 0.859 0.837 0.817 0.801 0.787 0.775 0.764 0.755
3.0 0.955 0.917 0.886 0.860 0.838 0.820 0.804 0.790 0.778 0.768 0.759
B.2 Fluids in Cross Flow 119
Table B.3 – (continued)
β
γ
0.6 0.7 0.8 0.9 1.0 1.1 1.2 1.3 1.4 1.5 1.6
0.1 0.559 0.509 0.463 0.423 0.386 0.353 0.323 0.295 0.270 0.248 0.227
0.2 0.568 0.520 0.477 0.438 0.403 0.372 0.343 0.317 0.294 0.272 0.252
0.3 0.577 0.531 0.490 0.454 0.420 0.390 0.363 0.338 0.316 0.295 0.277
0.4 0.586 0.542 0.503 0.468 0.437 0.408 0.382 0.359 0.338 0.318 0.300
0.5 0.595 0.553 0.516 0.482 0.453 0.426 0.401 0.379 0.359 0.340 0.323
0.6 0.603 0.563 0.528 0.496 0.468 0.442 0.419 0.398 0.379 0.362 0.346
0.7 0.612 0.573 0.539 0.509 0.483 0.458 0.437 0.417 0.399 0.382 0.367
0.8 0.620 0.583 0.551 0.522 0.497 0.474 0.453 0.435 0.418 0.402 0.388
0.9 0.627 0.592 0.562 0.535 0.510 0.489 0.469 0.452 0.436 0.421 0.408
1.0 0.635 0.602 0.572 0.547 0.524 0.503 0.485 0.469 0.454 0.440 0.427
1.1 0.642 0.610 0.583 0.558 0.537 0.517 0.500 0.485 0.471 0.458 0.446
1.2 0.650 0.619 0.593 0.569 0.549 0.531 0.515 0.500 0.487 0.475 0.464
1.3 0.657 0.627 0.602 0.580 0.561 0.544 0.529 0.515 0.503 0.491 0.481
1.4 0.663 0.635 0.612 0.591 0.572 0.556 0.542 0.529 0.518 0.507 0.498
1.5 0.670 0.643 0.621 0.601 0.584 0.568 0.555 0.543 0.532 0.522 0.514
1.6 0.676 0.651 0.629 0.611 0.594 0.580 0.568 0.556 0.546 0.537 0.529
1.7 0.683 0.658 0.638 0.620 0.605 0.591 0.580 0.569 0.560 0.551 0.544
1.8 0.689 0.666 0.646 0.629 0.615 0.602 0.591 0.581 0.573 0.565 0.558
1.9 0.695 0.673 0.654 0.638 0.624 0.613 0.602 0.593 0.585 0.578 0.571
2.0 0.701 0.679 0.662 0.647 0.634 0.623 0.613 0.604 0.597 0.590 0.584
2.1 0.706 0.686 0.669 0.655 0.643 0.632 0.623 0.615 0.608 0.602 0.597
2.2 0.712 0.692 0.676 0.663 0.652 0.642 0.633 0.626 0.619 0.614 0.608
2.3 0.717 0.699 0.683 0.671 0.660 0.651 0.643 0.636 0.630 0.625 0.620
2.4 0.722 0.705 0.690 0.678 0.668 0.659 0.652 0.646 0.640 0.635 0.631
2.5 0.727 0.710 0.697 0.685 0.676 0.668 0.661 0.655 0.650 0.645 0.641
2.6 0.732 0.716 0.703 0.692 0.693 0.676 0.669 0.664 0.659 0.655 0.651
2.7 0.737 0.722 0.709 0.699 0.691 0.684 0.678 0.673 0.668 0.664 0.661
2.8 0.742 0.727 0.715 0.706 0.698 0.691 0.686 0.681 0.677 0.673 0.670
2.9 0.746 0.732 0.721 0.712 0.705 0.699 0.693 0.689 0.685 0.682 0.679
3.0 0.751 0.737 0.727 0.718 0.711 0.706 0.701 0.697 0.693 0.690 0.687
120 Appendix B Factor ψ or Corrective Factors for Verification Computation
Table B.3 – (continued)
β
γ
1.7 1.9 2.1 2.3 2.5 2.8 3.1 3.4 3.7 4.0
0.1 0.209 0.176 0.150 0.127 0.108 0.085 0.068 0.054 0.043 0.035
0.2 0.234 0.203 0.177 0.154 0.135 0.111 0.093 0.077 0.065 0.055
0.3 0.260 0.229 0.203 0.181 0.162 0.138 0.119 0.103 0.089 0.078
0.4 0.284 0.255 0.230 0.208 0.190 0.166 0.146 0.129 0.115 0.103
0.5 0.308 0.280 0.256 0.235 0.217 0.194 0.174 0.157 0.143 0.130
0.6 0.331 0.304 0.282 0.262 0.244 0.222 0.202 0.186 0.171 0.159
0.7 0.353 0.328 0.307 0.288 0.271 0.249 0.231 0.215 0.201 0.188
0.8 0.375 0.351 0.331 0.313 0.297 0.277 0.259 0.244 0.230 0.218
0.9 0.396 0.373 0.354 0.338 0.323 0.303 0.287 0.272 0.259 0.248
1.0 0.416 0.395 0.377 0.361 0.348 0.329 0.314 0.300 0.288 0.278
1.1 0.435 0.416 0.399 0.384 0.372 0.355 0.340 0.328 0.317 0.307
1.2 0.454 0.436 0.420 0.407 0.395 0.379 0.366 0.354 0.344 0.335
1.3 0.472 0.455 0.441 0.428 0.417 0.403 0.391 0.380 0.371 0.363
1.4 0.489 0.473 0.460 0.449 0.439 0.425 0.414 0.405 0.396 0.389
1.5 0.505 0.491 0.479 0.468 0.459 0.447 0.437 0.429 0.421 0.415
1.6 0.521 0.508 0.497 0.487 0.479 0.468 0.459 0.451 0.445 0.439
1.7 0.537 0.524 0.514 0.505 0.498 0.488 0.480 0.473 0.467 0.462
1.8 0.551 0.540 0.531 0.523 0.516 0.507 0.500 0.494 0.488 0.484
1.9 0.565 0.555 0.546 0.539 0.533 0.525 0.518 0.513 0.509 0.505
2.0 0.579 0.569 0.561 0.555 0.549 0.542 0.536 0.532 0.528 0.524
2.1 0.592 0.583 0.576 0.570 0.565 0.558 0.553 0.549 0.546 0.543
2.2 0.604 0.596 0.589 0.584 0.580 0.574 0.570 0.566 0.563 0.561
2.3 0.616 0.608 0.603 0.598 0.594 0.589 0.585 0.582 0.579 0.577
2.4 0.627 0.620 0.615 0.611 0.607 0.603 0.599 0.597 0.594 0.593
2.5 0.638 0.632 0.627 0.623 0.620 0.616 0.613 0.611 0.609 0.607
2.6 0.648 0.643 0.638 0.635 0.632 0.629 0.626 0.624 0.622 0.621
2.7 0.658 0.653 0.649 0.646 0.643 0.640 0.638 0.636 0.635 0.634
2.8 0.667 0.663 0.659 0.657 0.654 0.652 0.650 0.648 0.647 0.646
2.9 0.677 0.672 0.669 0.667 0.665 0.663 0.661 0.660 0.659 0.658
3.0 0.685 0.682 0.679 0.677 0.675 0.673 0.671 0.670 0.669 0.669
B.3 Heat Exchangers 121
B.3 Heat Exchangers
B.3.1 Heat Exchangers with Two Passages of Internal Fluid
(Fig. 2.5)
Table B.4 – Heat exchangers – A and D type – 2 passages of external fluid – Fig. A.2 – Factor ψ
β
γ
0.05 0.10 0.20 0.30 0.40 0.50 0.60 0.70 0.80 0.90 1.00
0.1 0.951 0.905 0.820 0.744 0.676 0.614 0.559 0.510 0.465 0.425 0.389
0.2 0.951 0.906 0.822 0.748 0.681 0.622 0.569 0.522 0.480 0.443 0.409
0.3 0.952 0.906 0.824 0.751 0.687 0.630 0.579 0.535 0.495 0.460 0.428
0.4 0.952 0.907 0.825 0.754 0.692 0.637 0.589 0.546 0.509 0.476 0.447
0.5 0.952 0.907 0.827 0.757 0.697 0.644 0.598 0.558 0.523 0.492 0.465
0.6 0.952 0.908 0.828 0.760 0.702 0.651 0.607 0.569 0.536 0.507 0.482
0.7 0.952 0.908 0.830 0.763 0.707 0.658 0.616 0.580 0.549 0.522 0.499
0.8 0.952 0.908 0.831 0.766 0.711 0.665 0.625 0.590 0.561 0.536 0.515
0.9 0.952 0.909 0.833 0.769 0.716 0.671 0.633 0.601 0.573 0.550 0.530
1.0 0.952 0.909 0.834 0.772 0.721 0.677 0.641 0.610 0.585 0.563 0.545
1.1 0.953 0.910 0.836 0.775 0.725 0.683 0.649 0.620 0.596 0.576 0.559
1.2 0.953 0.910 0.837 0.778 0.729 0.689 0.656 0.629 0.607 0.588 0.572
1.3 0.953 0.911 0.839 0.781 0.734 0.695 0.664 0.638 0.617 0.600 0.585
1.4 0.953 0.911 0.840 0.784 0.738 0.701 0.671 0.647 0.627 0.611 0.598
1.5 0.953 0.911 0.842 0.786 0.742 0.707 0.678 0.655 0.637 0.622 0.610
1.6 0.953 0.912 0.843 0.789 0.746 0.712 0.685 0.663 0.646 0.632 0.621
1.7 0.953 0.912 0.844 0.792 0.750 0.717 0.691 0.671 0.655 0.642 0.632
1.8 0.953 0.913 0.846 0.794 0.754 0.722 0.698 0.679 0.664 0.652 0.643
1.9 0.953 0.913 0.847 0.797 0.758 0.728 0.704 0.686 0.672 0.661 0.653
2.0 0.954 0.913 0.848 0.799 0.761 0.732 0.710 0.693 0.680 0.670 0.663
2.1 0.954 0.914 0.850 0.802 0.765 0.737 0.716 0.700 0.688 0.679 0.672
2.2 0.954 0.914 0.851 0.804 0.769 0.742 0.722 0.707 0.696 0.687 0.681
2.3 0.954 0.915 0.852 0.806 0.772 0.747 0.727 0.713 0.703 0.695 0.690
2.4 0.954 0.915 0.854 0.809 0.775 0.751 0.733 0.720 0.710 0.703 0.698
2.5 0.954 0.915 0.855 0.811 0.779 0.755 0.738 0.726 0.717 0.710 0.706
2.6 0.954 0.916 0.856 0.813 0.782 0.760 0.743 0.732 0.723 0.717 0.714
2.7 0.954 0.916 0.857 0.815 0.785 0.764 0.748 0.737 0.730 0.724 0.721
2.8 0.954 0.917 0.858 0.817 0.788 0.768 0.753 0.743 0.736 0.731 0.728
2.9 0.955 0.917 0.860 0.820 0.791 0.772 0.758 0.748 0.742 0.737 0.735
3.0 0.955 0.917 0.861 0.822 0.794 0.776 0.762 0.753 0.747 0.743 0.741