Annaratone D. Handbook for Heat Exchangers and Tube Banks design
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142 Appendix B Factor ψ or Corrective Factors for Verification Computation
Table B.14 – (continued)
β
γ
1.2 1.4 1.6 1.8 2.0 2.3 2.6 2.9 3.2 3.6 4.0
0.1 0.327 0.277 0.237 0.204 0.177 0.146 0.124 0.108 0.097 0.087 0.080
0.2 0.352 0.306 0.270 0.240 0.217 0.190 0.172 0.159 0.150 0.142 0.139
0.3 0.376 0.334 0.301 0.275 0.255 0.232 0.216 0.206 0.199 0.195 0.193
0.4 0.399 0.361 0.331 0.308 0.290 0.271 0.259 0.251 0.246
0.243
0.243
0.5 0.420 0.386 0.360 0.340 0.324 0.308 0.298 0.292 0.289
0.288
0.290
0.6 0.441 0.410 0.387 0.369 0.356 0.343 0.335 0.331
0.330
0.330 0.333
0.7 0.461 0.433 0.413 0.397 0.386 0.376 0.370
0.367
0.367 0.369 0.372
0.8 0.481 0.455 0.437 0.424 0.415 0.406 0.402
0.401
0.401 0.404 0.408
0.9 0.499 0.476 0.460 0.449 0.441 0.435
0.432 0.432 0.433 0.437 0.441
1.0 0.516 0.496 0.482 0.473 0.466 0.462
0.460 0.461 0.463 0.466 0.471
1.1 0.533 0.515 0.503 0.495 0.490
0.486 0.486 0.487 0.490 0.494 0.498
1.2 0.549 0.533 0.522 0.516 0.512
0.510 0.510 0.512 0.515 0.519 0.523
1.3 0.564 0.550 0.541 0.536 0.533
0.531 0.532 0.535 0.537 0.542 0.546
1.4 0.578 0.566 0.558 0.554 0.552
0.551 0.553 0.555 0.558 0.563 0.566
1.5 0.592 0.581 0.575 0.571
0.570 0.570 0.572 0.575 0.578 0.582 0.585
1.6 0.605 0.596 0.590 0.588
0.587 0.588 0.590 0.593 0.596 0.600 0.603
1.7 0.618 0.610 0.605
0.603 0.603 0.604 0.607 0.609 0.612 0.616 0.619
1.8 0.630 0.623 0.619
0.618 0.618 0.619 0.622 0.625 0.628 0.631 0.634
1.9 0.641 0.635 0.632
0.631 0.632 0.634 0.636 0.639 0.642 0.645 0.647
2.0 0.652 0.647 0.645
0.644 0.645 0.647 0.650 0.652 0.655 0.658 0.660
2.1 0.663 0.658
0.656 0.656 0.657 0.659 0.662 0.665 0.667 0.670 0.672
2.2 0.672 0.669
0.667 0.668 0.669 0.671 0.674 0.676 0.678 0.681 0.683
2.3 0.682 0.679
0.678 0.678 0.680 0.682 0.684 0.687 0.689 0.691 0.693
2.4 0.691
0.688 0.688 0.689 0.690 0.692 0.695 0.697 0.699 0.701 0.703
2.5 0.699
0.697 0.697 0.698 0.699 0.702 0.704 0.706 0.708 0.710 0.712
2.6 0.708
0.706 0.706 0.707 0.709 0.711 0.713 0.715 0.717 0.719 -----
2.7 0.716
0.714 0.715 0.716 0.717 0.719 0.722 0.723 0.725 0.727 -----
2.8 0.723
0.722 0.723 0.724 0.725 0.727 0.730 0.731 0.733 ----- -----
2.9
0.730 0.730 0.730 0.732 0.733 0.735 0.737 0.739 0.740 ----- -----
3.0
0.737 0.737 0.738 0.739 0.740 0.742 0.744 0.746 0.747 ----- -----
Minimum values of ψ are in bold type
B.3 Heat Exchangers 143
Table B.15 – Heat exchangers – G type – 3 passages of external fluid – Fig. A.13 – 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 0.558 0.509 0.463 0.423 0.386
0.2 0.951 0.906 0.822 0.747 0.681 0.621 0.568 0.520 0.477 0.439 0.404
0.3 0.952 0.906 0.824 0.750 0.686 0.628 0.577 0.531 0.491 0.454 0.422
0.4 0.952 0.907 0.825 0.754 0.691 0.635 0.586 0.543 0.504 0.469 0.439
0.5 0.952 0.907 0.827 0.757 0.696 0.642 0.595 0.553 0.517 0.484 0.455
0.6 0.952 0.907 0.828 0.760 0.700 0.649 0.604 0.564 0.529 0.498 0.471
0.7 0.952 0.908 0.830 0.763 0.705 0.655 0.612 0.574 0.541 0.512 0.486
0.8 0.952 0.908 0.831 0.766 0.710 0.662 0.620 0.584 0.553 0.525 0.501
0.9 0.952 0.909 0.833 0.768 0.714 0.668 0.628 0.594 0.564 0.538 0.516
1.0 0.952 0.909 0.834 0.771 0.719 0.674 0.636 0.603 0.575 0.551 0.530
1.1 0.953 0.910 0.836 0.774 0.723 0.680 0.643 0.612 0.586 0.563 0.543
1.2 0.953 0.910 0.837 0.777 0.727 0.686 0.651 0.621 0.596 0.575 0.556
1.3 0.953 0.910 0.838 0.780 0.731 0.691 0.658 0.630 0.606 0.586 0.569
1.4 0.953 0.911 0.840 0.782 0.735 0.697 0.665 0.638 0.616 0.597 0.581
1.5 0.953 0.911 0.841 0.785 0.739 0.702 0.672 0.646 0.625 0.607 0.592
1.6 0.953 0.912 0.842 0.787 0.743 0.708 0.678 0.654 0.634 0.618 0.604
1.7 0.953 0.912 0.844 0.790 0.747 0.713 0.685 0.662 0.643 0.627 0.614
1.8 0.953 0.913 0.845 0.793 0.751 0.718 0.691 0.669 0.652 0.637 0.625
1.9 0.953 0.913 0.846 0.795 0.755 0.723 0.697 0.677 0.660 0.646 0.635
2.0 0.954 0.913 0.848 0.797 0.758 0.728 0.703 0.684 0.668 0.655 0.644
2.1 0.954 0.914 0.849 0.800 0.762 0.732 0.709 0.690 0.675 0.663 0.654
2.2 0.954 0.914 0.850 0.802 0.765 0.737 0.715 0.697 0.683 0.672 0.663
2.3 0.954 0.914 0.852 0.805 0.769 0.741 0.720 0.703 0.690 0.680 0.671
2.4 0.954 0.915 0.853 0.807 0.772 0.746 0.725 0.710 0.697 0.687 0.679
2.5 0.954 0.915 0.854 0.809 0.775 0.750 0.731 0.716 0.704 0.695 0.687
2.6 0.954 0.916 0.855 0.811 0.779 0.754 0.736 0.721 0.710 0.702 0.695
2.7 0.954 0.916 0.857 0.813 0.782 0.758 0.741 0.727 0.717 0.709 0.702
2.8 0.954 0.916 0.858 0.816 0.785 0.762 0.745 0.733 0.723 0.715 0.709
2.9 0.955 0.917 0.859 0.818 0.788 0.766 0.750 0.738 0.729 0.722 0.716
3.0 0.955 0.917 0.860 0.820 0.791 0.770 0.755 0.743 0.734 0.728 0.722
144 Appendix B Factor ψ or Corrective Factors for Verification Computation
Table B.15 – (continued)
β
γ
1.2 1.4 1.6 1.8 2.0 2.3 2.6 2.9 3.2 3.6 4.0
0.1 0.323 0.272 0.230 0.195 0.167 0.134 0.109 0.090 0.076 0.062 0.052
0.2 0.345 0.297 0.257 0.225 0.199 0.167 0.143 0.125 0.111 0.097 0.086
0.3 0.366 0.321 0.284 0.254 0.230 0.200 0.178 0.161 0.147 0.133 0.122
0.4 0.386 0.344 0.310 0.282 0.260 0.233 0.212 0.195 0.182 0.169 0.157
0.5 0.406 0.367 0.336 0.310 0.289 0.264 0.245 0.229 0.217 0.204 0.193
0.6 0.425 0.389 0.360 0.336 0.317 0.294 0.276 0.262 0.251 0.238 0.227
0.7 0.444 0.410 0.383 0.362 0.344 0.323 0.307 0.294 0.283 0.271 0.260
0.8 0.462 0.431 0.406 0.386 0.370 0.351 0.336 0.324 0.314 0.302 0.292
0.9 0.479 0.450 0.428 0.410 0.395 0.377 0.364 0.353 0.343 0.332 0.322
1.0 0.495 0.469 0.448 0.432 0.419 0.403 0.390 0.380 0.371 0.360 0.351
1.1 0.511 0.487 0.468 0.453 0.441 0.426 0.415 0.405 0.397 0.387 0.378
1.2 0.527 0.504 0.487 0.473 0.462 0.449 0.438 0.429 0.422 0.412 0.403
1.3 0.541 0.521 0.505 0.493 0.482 0.470 0.461 0.452 0.445 0.436 0.427
1.4 0.555 0.537 0.522 0.511 0.502 0.490 0.481 0.474 0.467 0.458 0.450
1.5 0.569 0.552 0.538 0.528 0.520 0.509 0.501 0.494 0.487 0.479 0.471
1.6 0.582 0.566 0.554 0.544 0.537 0.527 0.519 0.513 0.506 0.499 0.491
1.7 0.594 0.580 0.569 0.560 0.553 0.544 0.537 0.530 0.524 0.517 0.510
1.8 0.606 0.593 0.583 0.575 0.568 0.560 0.553 0.547 0.542 0.535 0.528
1.9 0.618 0.605 0.596 0.589 0.583 0.575 0.569 0.563 0.558 0.551 0.545
2.0 0.628 0.617 0.608 0.602 0.596 0.589 0.583 0.578 0.573 0.567 0.561
2.1 0.639 0.628 0.620 0.614 0.609 0.603 0.597 0.592 0.587 0.581 0.576
2.2 0.649 0.639 0.632 0.626 0.621 0.615 0.610 0.605 0.601 0.595 0.590
2.3 0.658 0.649 0.643 0.637 0.633 0.627 0.622 0.618 0.613 0.608 0.604
2.4 0.668 0.659 0.653 0.648 0.644 0.638 0.634 0.629 0.626 0.621 0.617
2.5 0.676 0.669 0.663 0.658 0.654 0.649 0.645 0.641 0.637 0.633 0.629
2.6 0.685 0.678 0.672 0.668 0.664 0.659 0.655 0.651 0.648 0.644 0.640
2.7 0.693 0.686 0.681 0.677 0.674 0.669 0.665 0.661 0.658 0.654 0.651
2.8 0.700 0.684 0.690 0.686 0.683 0.678 0.674 0.671 0.668 0.665 0.661
2.9 0.708 0.702 0.698 0.694 0.691 0.687 0.683 0.680 0.677 0.674 0.671
3.0 0.715 0.710 0.705 0.702 0.699 0.695 0.692 0.689 0.686 0.683 0.681
B.3 Heat Exchangers 145
Table B.16 – Heat exchangers – E and F type – 4 passages of external fluid – Fig. A.14 – 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 0.509 0.465 0.424 0.388
0.2 0.951 0.906 0.822 0.747 0.681 0.622 0.569 0.522 0.480 0.442 0.408
0.3 0.952 0.906 0.824 0.751 0.686 0.629 0.579 0.534 0.494 0.458 0.427
0.4 0.952 0.907 0.825 0.754 0.691 0.637 0.588 0.546 0.508 0.475 0.445
0.5 0.952 0,907 0.827 0.757 0.697 0.644 0.597 0.557 0.521 0.490 0.463
0.6 0.952 0.908 0.828 0.760 0.701 0.651 0.606 0.568 0.534 0.505 0.480
0.7 0.952 0.908 0.830 0.763 0.706 0.657 0.615 0.579 0.547 0.520 0.496
0.8 0.952 0.908 0.831 0.766 0.711 0.664 0.624 0.589 0.559 0.534 0.512
0.9 0.952 0.909 0.833 0.769 0.716 0.670 0.632 0.599 0.571 0.547 0.527
1.0 0.952 0.909 0.834 0.772 0.720 0.677 0.640 0.609 0.583 0.560 0.541
1.1 0.953 0.910 0.836 0.775 0.725 0.683 0.648 0.618 0.594 0.573 0.555
1.2 0.953 0.910 0.837 0.778 0.729 0.689 0.655 0.627 0.604 0.585 0.569
1.3 0.953 0.911 0.839 0.781 0.733 0.694 0.663 0.636 0.615 0.597 0.582
1.4 0.953 0.911 0.840 0.783 0.737 0.700 0.670 0.645 0.625 0.608 0.594
1.5 0.953 0.911 0.842 0.786 0.741 0.706 0.677 0.653 0.634 0.619 0.606
1.6 0.953 0.912 0.843 0.789 0.745 0.711 0.683 0.661 0.643 0.629 0.618
1.7 0.953 0.912 0.844 0.791 0.749 0.716 0.690 0.669 0.652 0.639 0.629
1.8 0.953 0.913 0.846 0.794 0.753 0.721 0.696 0.677 0.661 0.649 0.639
1.9 0.953 0.913 0.847 0.796 0.757 0.727 0.703 0.684 0.669 0.658 0.649
2.0 0.954 0.913 0.848 0.799 0.761 0.731 0.709 0.691 0.678 0.667 0.659
2.1 0.954 0.914 0.850 0.801 0.764 0.736 0.715 0.698 0.685 0.676 0.668
2.2 0.954 0.914 0.851 0.804 0.768 0.741 0.720 0.705 0.693 0.684 0.677
2.3 0.954 0.915 0.852 0.806 0.771 0.745 0.726 0.711 0.700 0.692 0.686
2.4 0.954 0.915 0.853 0.808 0.775 0.750 0.731 0.717 0.707 0.700 0.694
2.5 0.954 0.915 0.855 0.810 0.778 0.754 0.737 0.723 0.714 0.707 0.702
2.6 0.954 0.916 0.856 0.813 0.781 0.758 0.742 0.729 0.720 0.714 0.710
2.7 0.954 0.916 0.857 0.815 0.785 0.763 0.747 0.735 0.727 0.721 0.717
2.8 0.954 0.917 0.858 0.817 0.788 0.767 0.751 0.741 0.733 0.728 0.724
2.9 0.955 0.917 0.859 0.819 0.791 0.770 0.756 0.746 0.739 0.734 0.731
3.0 0.955 0.917 0.861 0.821 0.794 0.774 0.761 0.751 0.745 0.740 0.737
146 Appendix B Factor ψ or Corrective Factors for Verification Computation
Table B.16 – (continued)
β
γ
1.2 1.4 1.6 1.8 2.0 2.3 2.6 2.9 3.2 3.6 4.0
0.1 0.326 0.276 0.235 0.202 0.174 0.143 0.120 0.103 0.091 0.079 0.072
0.2 0.350 0.304 0.267 0.236 0.212 0.184 0.164 0.149 0.139 0.130 0.124
0.3 0.373 0.331 0.297 0.270 0.248 0.224 0.206 0.194 0.186 0.178 0.174
0.4 0.396 0.357 0.326 0.302 0.283 0.262 0.247 0.237 0.230 0.225 0.222
0.5 0.417 0.382 0.354 0.333 0.316 0.298 0.286 0.278 0.273 0.269 0.268
0.6 0.438 0.406 0.381 0.362 0.348 0.332 0.322 0.316 0.313 0.311 0.311
0.7 0.457 0.428 0.406 0.390 0.377 0.365 0.357 0.353
0.350 0.350 0.351
0.8 0.476 0.450 0.431 0.416 0.406 0.395 0.389
0.386
0.386 0.386 0.388
0.9 0.494 0.471 0.454 0.441 0.432 0.424 0.420
0.418
0.418 0.420 0.423
1.0 0.512 0.491 0.475 0.465 0.458 0.451
0.448
0.448 0.449 0.451 0.454
1.1 0.528 0.509 0.496 0.487 0.481 0.476
0.475
0.475 0.477 0.480 0.483
1.2 0.544 0.527 0.516 0.508 0.504 0.500
0.499
0.500 0.502 0.506 0.509
1.3 0.559 0.544 0.535 0.528 0.525
0.522
0.522 0.524 0.526 0.530 0.534
1.4 0.574 0.561 0.552 0.547 0.544
0.543
0.544 0.546 0.548 0.552 0.556
1.5 0.588 0.576 0.569 0.565 0.563
0.562
0.564 0.566 0.569 0.572 0.576
1.6 0.601 0.591 0.585 0.581
0.580
0.580 0.582 0.585 0.587 0.591 0.594
1.7 0.614 0.605 0.600 0.597
0.596
0.597 0.599 0.602 0.605 0.608 0.611
1.8 0.626 0.618 0.614
0.612
0.612 0.613 0.615 0.618 0.621 0.624 0.627
1.9 0.637 0.630 0.627
0.626
0.626 0.628 0.630 0.633 0.635 0.639 0.642
2.0 0.648 0.642 0.640
0.639
0.639 0.641 0.644 0.647 0.649 0.652 0.655
2.1 0.659 0.654 0.652
0.651 0.652 0.654 0.657 0.659 0.662 0.665 0.667
2.2 0.669 0.665
0.663
0.663 0.664 0.666 0.669 0.671 0.674 0.676 0.679
2.3 0.678 0.675
0.674
0.674 0.675 0.677 0.680 0.683 0.685 0.687 0.689
2.4 0.687 0.685
0.684
0.684 0.686 0.688 0.691 0.693 0.695 0.697 0.699
2.5 0.696 0.694
0.693 0.694 0.696 0.698 0.700 0.703 0.705 0.707 0.709
2.6 0.704
0.703 0.703 0.703 0.705 0.707 0.710 0.712 0.714 0.716 0.720
2.7 0.712
0.711 0.711 0.712 0.714 0.716 0.718 0.720 0.722 0.724 -----
2.8 0.720
0.719 0.719 0.721 0.722 0.724 0.727 0.729 0.730 0.732 -----
2.9
0.727 0.727 0.727 0.728 0.730 0.732 0.734 0.736 0.738 ----- -----
3.0
0.734 0.734 0.735 0.736 0.737 0.740 0.742 0.743 0.745 ----- -----
Minimum values of ψ are in bold type
B.3 Heat Exchangers 147
Table B.17 – Heat exchangers – G and H type – 4 passages of external fluid – Fig. A.15 – 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 0.509 0.464 0.423 0.387
0.2 0.951 0.906 0.822 0.747 0.681 0.621 0.568 0.521 0.478 0.440 0.405
0.3 0.952 0.906 0.824 0.751 0.686 0.629 0.578 0.532 0.492 0.456 0.423
0.4 0.952 0.907 0.825 0.754 0.691 0.636 0.587 0.544 0.505 0.471 0.441
0.5 0.952 0.907 0.827 0.757 0.696 0.643 0.596 0.555 0.518 0.486 0.458
0.6 0.952 0.907 0.828 0.760 0.701 0.649 0.604 0.565 0.531 0.501 0.474
0.7 0.952 0.908 0.830 0.763 0.705 0.656 0.613 0.576 0.543 0.515 0.490
0.8 0.952 0.908 0.831 0.766 0.710 0.662 0.621 0.586 0.555 0.528 0.505
0.9 0.952 0.909 0.833 0.769 0.715 0.669 0.629 0.595 0.566 0.541 0.520
1.0 0.952 0.909 0.834 0.772 0.719 0.675 0.637 0.605 0.577 0.554 0.534
1.1 0.953 0.910 0.836 0.774 0.723 0.681 0.645 0.614 0.588 0.566 0.547
1.2 0.953 0.910 0.837 0.777 0.728 0.687 0.652 0.623 0.599 0.578 0.560
1.3 0.953 0.910 0.838 0.780 0.732 0.692 0.659 0.632 0.609 0.589 0.573
1.4 0.953 0.911 0.840 0.783 0.736 0.698 0.666 0.640 0.619 0.600 0.585
1.5 0.953 0.911 0.841 0.785 0.740 0.703 0.673 0.648 0.628 0.611 0.597
1.6 0.953 0.912 0.843 0.788 0.744 0.709 0.680 0.656 0.637 0.621 0.608
1.7 0.953 0.912 0.844 0.790 0.748 0.714 0.686 0.664 0.646 0.631 0.619
1.8 0.953 0.913 0.845 0.793 0.752 0.719 0.693 0.672 0.655 0.641 0.629
1.9 0.953 0.913 0.847 0.795 0.755 0.724 0.699 0.679 0.663 0.650 0.639
2.0 0.954 0.913 0.848 0.798 0.759 0.729 0.705 0.686 0.671 0.659 0.649
2.1 0.954 0.914 0.849 0.800 0.763 0.733 0.711 0.693 0.678 0.667 0.658
2.2 0.954 0.914 0.851 0.803 0.766 0.738 0.716 0.699 0.686 0.675 0.667
2.3 0.954 0.915 0.852 0.805 0.770 0.743 0.722 0.706 0.693 0.683 0.675
2.4 0.954 0.915 0.853 0.807 0.773 0.747 0.727 0.712 0.700 0.691 0.683
2.5 0.954 0.915 0.854 0.809 0.776 0.751 0.732 0.718 0.707 0.698 0.691
2.6 0.954 0.916 0.855 0.812 0.779 0.755 0.737 0.724 0.713 0.705 0.699
2.7 0.954 0.916 0.857 0.814 0.783 0.760 0.742 0.729 0.720 0.712 0.706
2.8 0.954 0.916 0.858 0.816 0.786 0.764 0.747 0.735 0.726 0.718 0.713
2.9 0.955 0.917 0.859 0.818 0.789 0.767 0.752 0.740 0.731 0.725 0.720
3.0 0.955 0.917 0.860 0.820 0.792 0.771 0.756 0.745 0.737 0.731 0.726
148 Appendix B Factor ψ or Corrective Factors for Verification Computation
Table B.17 – (continued)
β
γ
1.2 1.4 1.6 1.8 2.0 2.3 2.6 2.9 3.2 3.6 4.0
0.1 0.324 0.273 0.232 0.198 0.170 0.137 0.114 0.096 0.082 0.070 0.061
0.2 0.347 0.299 0.261 0.229 0.204 0.174 0.152 0.136 0.124 0.113 0.105
0.3 0.369 0.324 0.289 0.260 0.237 0.210 0.190 0.176 0.165 0.155 0.148
0.4 0.390 0.349 0.316 0.290 0.269 0.244 0.227 0.214 0.204 0.195 0.189
0.5 0.410 0.372 0.342 0.319 0.299 0.278 0.262 0.250 0.242 0.234 0.228
0.6 0.430 0.395 0.368 0.346 0.329 0.309 0.295 0.285 0.278 0.271 0.265
0.7 0.449 0.417 0.392 0.372 0.357 0.339 0.327 0.318 0.311 0.305 0.300
0.8 0.467 0.437 0.415 0.397 0.383 0.368 0.357 0.349 0.343 0.337 0.332
0.9 0.484 0.457 0.437 0.421 0.409 0.395 0.385 0.378 0.372 0.367 0.362
1.0 0.501 0.476 0.458 0.444 0.433 0.420 0.412 0.405 0.400 0.394 0.390
1.1 0.517 0.495 0.478 0.465 0.455 0.444 0.436 0.430 0.425 0.420 0.415
1.2 0.532 0.512 0.497 0.485 0.476 0.467 0.459 0.454 0.449 0.444 0.439
1.3 0.547 0.529 0.515 0.504 0.496 0.488 0.481 0.476 0.471 0.466 0.461
1.4 0.561 0.544 0.532 0.522 0.515 0.507 0.501 0.496 0.492 0.486 0.481
1.5 0.575 0.559 0.548 0.540 0.533 0.526 0.520 0.515 0.511 0.505 0.500
1.6 0.588 0.574 0.563 0.556 0.550 0.543 0.538 0.533 0.529 0.523 0.518
1.7 0.600 0.587 0.578 0.571 0.566 0.559 0.554 0.550 0.545 0.540 0.535
1.8 0.612 0.600 0.592 0.585 0.580 0.575 0.570 0.565 0.561 0.556 0.550
1.9 0.623 0.613 0.605 0.599 0.594 0.589 0.584 0.580 0.576 0.570 0.565
2.0 0.634 0.624 0.617 0.612 0.608 0.602 0.598 0.594 0.590 0.584 0.579
2.1 0.645 0.635 0.629 0.624 0.620 0.615 0.611 0.607 0.603 0.597 0.592
2.2 0.654 0.646 0.640 0.635 0.632 0.627 0.623 0.619 0.615 0.610 0.605
2.3 0.664 0.656 0.651 0.646 0.643 0.638 0.634 0.630 0.626 0.622 0.617
2.4 0.673 0.666 0.661 0.657 0.653 0.649 0.645 0.641 0.638 0.633 0.628
2.5 0.681 0.675 0.670 0.666 0.663 0.659 0.655 0.652 0.648 0.643 0.639
2.6 0.690 0.684 0.679 0.676 0.673 0.669 0.665 0.661 0.658 0.654 -----
2.7 0.698 0.692 0.688 0.685 0.682 0.678 0.674 0.671 0.667 0.663 -----
2.8 0.705 0.700 0.696 0.693 0.690 0.686 0.683 0.680 0.676 ----- -----
2.9 0.712 0.708 0.704 0.701 0.698 0.695 0.691 0.688 0.685 ----- -----
3.0 0.719 0.715 0.711 0.709 0.706 0.702 0.699 0.696 0.693 ----- -----
B.3 Heat Exchangers 149
Table B.18 – Heat exchangers – E type – 5 passages of external fluid – Fig. A.16 – 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 0.509 0.465 0.425 0.388
0.2 0.951 0.906 0.822 0.748 0.681 0.622 0.569 0.522 0.480 0.442 0.408
0.3 0.952 0.906 0.824 0.751 0.686 0.629 0.579 0.534 0.494 0.459 0.427
0.4 0.952 0.907 0.825 0.754 0.692 0.637 0.588 0.546 0.508 0.475 0.446
0.5 0.952 0.907 0.827 0.757 0.697 0.644 0.598 0.557 0.522 0.491 0.464
0.6 0.952 0.908 0.828 0.760 0.702 0.651 0.607 0.568 0.535 0.506 0.481
0.7 0.952 0.908 0.830 0.763 0.706 0.658 0.615 0.579 0.548 0.521 0.497
0.8 0.952 0.908 0.831 0.766 0.711 0.664 0.624 0.590 0.560 0.535 0.513
0.9 0.952 0.909 0.833 0.769 0.716 0.671 0.632 0.600 0.572 0.548 0.528
1.0 0.952 0.909 0.834 0.772 0.720 0.677 0.640 0.609 0.583 0.561 0.543
1.1 0.953 0.910 0.836 0.775 0.725 0.683 0.648 0.619 0.595 0.574 0.557
1.2 0.953 0.910 0.837 0.778 0.729 0.689 0.656 0.628 0.605 0.586 0.570
1.3 0.953 0.911 0.839 0.781 0.733 0.695 0.663 0.637 0.616 0.598 0.583
1.4 0.953 0.911 0.840 0.783 0.738 0.701 0.670 0.646 0.626 0.609 0.596
1.5 0.953 0.911 0.842 0.786 0.742 0.706 0.677 0.654 0.635 0.620 0.608
1.6 0.953 0.912 0.843 0.789 0.746 0.711 0.684 0.662 0.644 0.630 0.619
1.7 0.953 0.912 0.844 0.791 0.750 0.717 0.691 0.670 0.653 0.640 0.630
1.8 0.953 0.913 0.846 0.794 0.754 0.722 0.697 0.678 0.662 0.650 0.641
1.9 0.953 0.913 0.847 0.796 0.757 0.727 0.703 0.685 0.670 0.659 0.651
2.0 0.954 0.913 0.848 0.799 0.761 0.732 0.709 0.692 0.679 0.668 0.660
2.1 0.954 0.914 0.850 0.801 0.765 0.737 0.715 0.699 0.686 0.677 0.670
2.2 0.954 0.914 0.851 0.804 0.768 0.741 0.721 0.706 0.694 0.685 0.679
2.3 0.954 0.915 0.852 0.806 0.772 0.746 0.727 0.712 0.701 0.693 0.687
2.4 0.954 0.915 0.853 0.808 0.775 0.750 0.732 0.718 0.708 0.701 0.695
2.5 0.954 0.915 0.855 0.811 0.778 0.755 0.737 0.724 0.715 0.708 0.703
2.6 0.954 0.916 0.856 0.813 0.782 0.759 0.742 0.730 0.721 0.715 0.711
2.7 0.954 0.916 0.857 0.815 0.785 0.763 0.747 0.736 0.728 0.722 0.718
2.8 0.954 0.917 0.858 0.817 0.788 0.767 0.752 0.741 0.734 0.729 0.725
2.9 0.955 0.917 0.860 0.819 0.791 0.771 0.757 0.747 0.740 0.735 0.732
3.0 0.955 0.917 0.861 0.821 0.794 0.775 0.761 0.752 0.745 0.741 0.738
150 Appendix B Factor ψ or Corrective Factors for Verification Computation
Table B.18 – (continued)
β
γ
1.2 1.4 1.6 1.8 2.0 2.3 2.6 2.9 3.2 3.6 4.0
0.1 0.327 0.276 0.235 0.202 0.175 0.144 0.122 0.105 0.093 0.082 0.075
0.2 0.351 0.305 0.268 0.238 0.214 0.187 0.167 0.153 0.143 0.134 0.129
0.3 0.374 0.332 0.299 0.272 0.251 0.227 0.210 0.199 0.191 0.185 0.182
0.4 0.397 0.358 0.328 0.305 0.286 0.266 0.252 0.242 0.237 0.232 0.231
0.5 0.418 0.384 0.356 0.336 0.319 0.302 0.291 0.284 0.280
0.277 0.277
0.6 0.439 0.408 0.383 0.365 0.351 0.337 0.328 0.322 0.320
0.319 0.320
0.7 0.459 0.430 0.409 0.393 0.381 0.369 0.362 0.359
0.358 0.358 0.360
0.8 0.478 0.452 0.433 0.419 0.410 0.400 0.395
0.393 0.393 0.394 0.397
0.9 0.496 0.473 0.456 0.445 0.436 0.429 0.425
0.424 0.425 0.428 0.431
1.0 0.514 0.493 0.478 0.468 0.461 0.456
0.454 0.454 0.455 0.458 0.462
1.1 0.530 0.512 0.499 0.491 0.485 0.481
0.480 0.481 0.483 0.486 0.490
1.2 0.546 0.530 0.519 0.512 0.507 0.505
0.504 0.506 0.508 0.512 0.516
1.3 0.561 0.547 0.537 0.532 0.528
0.527 0.527 0.529 0.532 0.536 0.540
1.4 0.576 0.563 0.555 0.550 0.548
0.547 0.548 0.551 0.553 0.557 0.561
1.5 0.590 0.578 0.572 0.568
0.566 0.566 0.568 0.570 0.573 0.577 0.581
1.6 0.603 0.593 0.587 0.584
0.583 0.584 0.586 0.589 0.592 0.596 0.599
1.7 0.616 0.607 0.602
0.600 0.600 0.601 0.603 0.606 0.609 0.612 0.616
1.8 0.628 0.620 0.616
0.615 0.615 0.616 0.619 0.622 0.624 0.628 0.631
1.9 0.639 0.633 0.630
0.629 0.629 0.631 0.633 0.636 0.639 0.642 0.645
2.0 0.650 0.645
0.642 0.642 0.642 0.644 0.647 0.650 0.652 0.655 0.658
2.1 0.660 0.656
0.654 0.654 0.655 0.657 0.660 0.662 0.665 0.668 0.670
2.2 0.670 0.667
0.665 0.665 0.666 0.669 0.671 0.674 0.676 0.679 0.681
2.3 0.680 0.677
0.676
0.676 0.677 0.680 0.683 0.685 0.687 0.690 0.691
2.4 0.689 0.686
0.686
0.687 0.688 0.690 0.693 0.695 0.697 0.699 0.701
2.5 0.698 0.696
0.695
0.696 0.698 0.700 0.703 0.705 0.707 0.709 0.710
2.6 0.706
0.704 0.704 0.705 0.707 0.709 0.712 0.714 0.716 0.717 -----
2.7 0.714
0.713
0.713 0.714 0.716 0.718 0.720 0.722 0.724 0.726 -----
2.8 0.722
0.721
0.721 0.722 0.724 0.726 0.728 0.730 0.732 ----- -----
2.9 0.729
0.728
0.729 0.730 0.732 0.734 0.736 0.738 0.739 ----- -----
3.0 0.736
0.735
0.736 0.738 0.739 0.741 0.743 0.745 ----- ----- -----
Minimum values of ψ are in bold type
B.3 Heat Exchangers 151
Table B.19 – Heat exchangers – G type – 5 passages of external fluid – Fig. A.17 – 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 0.509 0.464 0.423 0.387
0.2 0.951 0.906 0.822 0.747 0.681 0.621 0.568 0.521 0.478 0.439 0.405
0.3 0.952 0.906 0.824 0.751 0.686 0.628 0.577 0.532 0.491 0.455 0.423
0.4 0.952 0.907 0.825 0.754 0.691 0.635 0.587 0.543 0.505 0.470 0.440
0.5 0.952 0.907 0.827 0.757 0.696 0.642 0.595 0.554 0.518 0.485 0.457
0.6 0.952 0.907 0.828 0.760 0.701 0.649 0.604 0.565 0.530 0.500 0.473
0.7 0.952 0.908 0.830 0.763 0.705 0.656 0.613 0.575 0.542 0.514 0.488
0.8 0.952 0.908 0.831 0.766 0.710 0.662 0.621 0.585 0.554 0.527 0.503
0.9 0.952 0.909 0.833 0.769 0.714 0.668 0.629 0.595 0.565 0.540 0.518
1.0 0.952 0.909 0.834 0.771 0.719 0.674 0.636 0.604 0.577 0.553 0.532
1.1 0.953 0.910 0.836 0.774 0.723 0.680 0.644 0.613 0.587 0.565 0.546
1.2 0.953 0.910 0.837 0.777 0.727 0.686 0.652 0.622 0.598 0.577 0.559
1.3 0.953 0.910 0.838 0.780 0.732 0.692 0.659 0.631 0.608 0.588 0.571
1.4 0.953 0.911 0.840 0.782 0.736 0.697 0.666 0.639 0.617 0.599 0.583
1.5 0.953 0.911 0.841 0.785 0.740 0.703 0.673 0.648 0.627 0.610 0.595
1.6 0.953 0.912 0.843 0.788 0.744 0.708 0.679 0.656 0.636 0.620 0.606
1.7 0.953 0.912 0.844 0.790 0.748 0.713 0.686 0.663 0.645 0.630 0.617
1.8 0.953 0.913 0.845 0.793 0.751 0.718 0.692 0.671 0.653 0.639 0.628
1.9 0.953 0.913 0.847 0.795 0.755 0.723 0.698 0.678 0.662 0.648 0.637
2.0 0.954 0.913 0.848 0.798 0.759 0.728 0.704 0.685 0.670 0.657 0.647
2.1 0.954 0.914 0.849 0.800 0.762 0.733 0.710 0.692 0.677 0.666 0.656
2.2 0.954 0.914 0.850 0.802 0.766 0.738 0.716 0.698 0.685 0.674 0.665
2.3 0.954 0.915 0.852 0.805 0.769 0.742 0.721 0.705 0.692 0.682 0.674
2.4 0.954 0.915 0.853 0.807 0.773 0.746 0.726 0.711 0.699 0.689 0.682
2.5 0.954 0.915 0.854 0.809 0.776 0.751 0.732 0.717 0.706 0.697 0.690
2.6 0.954 0.916 0.855 0.812 0.779 0.755 0.737 0.723 0.712 0.704 0.697
2.7 0.954 0.916 0.857 0.814 0.782 0.759 0.742 0.728 0.718 0.711 0.705
2.8 0.954 0.916 0.858 0.816 0.785 0.763 0.746 0.734 0.724 0.717 0.711
2.9 0.955 0.917 0.859 0.818 0.788 0.767 0.751 0.739 0.730 0.724 0.718
3.0 0.955 0.917 0.860 0.820 0.791 0.771 0.756 0.744 0.736 0.730 0.725