Annaratone D. Handbook for Heat Exchangers and Tube Banks design
Подождите немного. Документ загружается.
122 Appendix B Factor ψ or Corrective Factors for Verification Computation
Table B.4 – (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 0.147 0.125 0.109 0.098 0.088 0.082
0.2 0.352 0.306 0.270 0.240 0.217 0.191 0.173 0.160 0.152 0.145 0.142
0.3 0.376 0.334 0.301 0.275 0.255
0.233 0.218 0.208 0.202
0.198 0.198
0.4 0.399 0.361 0.331 0.309 0.291
0.272 0.260 0.253 0.250
0.248 0.250
0.5 0.420 0.386 0.360 0.340 0.325
0.310 0.301 0.296
0.294 0.295 0.298
0.6 0.441 0.411 0.387 0.370 0.357
0.345 0.338
0.336 0.336 0.338 0.343
0.7 0.461 0.434 0.413 0.398 0.388
0.378 0.374
0.373 0.374 0.379 0.385
0.8 0.481 0.456 0.438 0.425 0.417
0.409
0.407 0.407 0.410 0.416 0.423
0.9 0.499 0.477 0.461 0.451 0.444
0.438 0.438 0.439 0.443 0.450 0.458
1.0 0.516 0.497 0.483 0.474 0.469
0.466 0.466 0.469 0.474 0.481 0.490
1.1 0.533 0.516 0.504 0.497 0.493
0.491 0.493 0.497 0.502 0.510 0.519
1.2 0.549 0.534 0.524 0.518 0.516
0.515 0.518 0.523 0.528 0.537 0.546
1.3 0.564 0.551 0.543 0.538
0.537 0.538 0.541 0.546 0.552 0.561 0.570
1.4 0.579 0.567 0.561 0.557
0.556 0.558 0.563 0.568 0.575 0.583 0.592
1.5 0.593 0.583 0.577
0.575 0.575 0.578 0.583 0.589 0.595 0.604 0.613
1.6 0.606 0.598 0.593
0.592 0.592 0.596 0.601 0.607 0.614 0.623 0.631
1.7 0.619 0.612
0.608 0.608 0.609 0.613 0.618 0.625 0.631 0.640 0.648
1.8 0.631 0.625
0.622 0.622 0.624 0.629 0.634 0.641 0.647 0.656 0.664
1.9 0.643 0.637
0.636 0.636 0.639 0.643 0.649 0.656 0.662 0.670 0.678
2.0 0.654 0.649
0.648 0.650 0.652 0.657 0.663 0.669 0.676 0.684 0.691
2.1 0.664 0.661
0.660 0.662 0.665 0.670 0.676 0.682 0.688 0.696 0.703
2.2 0.674
0.672 0.672 0.674 0.677 0.682 0.688 0.694 0.700 0.708 0.715
2.3 0.684
0.682 0.682 0.685 0.688 0.693 0.699 0.705 0.711 0.719 0.725
2.4 0.693
0.692 0.693 0.695 0.698 0.704 0.710 0.716 0.721 0.729 0.735
2.5 0.702
0.701 0.702 0.705 0.708 0.714 0.720 0.726 0.731 0.738 0.744
2.6
0.710 0.710 0.711 0.714 0.718 0.723 0.729 0.735 0.740 0.747 0.753
2.7
0.718 0.718 0.720 0.723 0.726 0.732 0.738 0.743 0.748 0.755 0.761
2.8
0.726 0.726 0.728 0.731 0.735 0.740 0.746 0.751 0.756 0.763 0.768
2.9
0.733 0.734 0.736 0.739 0.743 0.748 0.754 0.759 0.764 0.770 0.775
3.0
0.740 0.741 0.743 0.747 0.750 0.756 0.761 0.766 0.771 0.777 0.782
Minimum values of ψ are in bold type
B.3 Heat Exchangers 123
Table B.5 – Heat exchangers – B and C types – 2 passages of external fluid Fig. A.3 – 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 0.464 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 0.532 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 0.487
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 0.769 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 0.788 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 0.653
2.2 0.954 0.914 0.850 0.802 0.765 0.737 0.715 0.697 0.683 0.671 0.662
2.3 0.954 0.914 0.852 0.805 0.769 0.741 0.720 0.703 0.690 0.679 0.671
2.4 0.954 0.915 0.853 0.807 0.772 0.746 0.725 0.709 0.697 0.687 0.679
2.5 0.954 0.915 0.854 0.809 0.775 0.750 0.731 0.715 0.704 0.694 0.687
2.6 0.954 0.916 0.855 0.811 0.779 0.754 0.736 0.721 0.710 0.701 0.694
2.7 0.954 0.916 0.857 0.813 0.782 0.758 0.741 0.727 0.716 0.708 0.702
2.8 0.954 0.916 0.858 0.816 0.785 0.762 0.745 0.732 0.722 0.715 0.709
2.9 0.955 0.917 0.859 0.818 0.788 0.766 0.750 0.738 0.728 0.721 0.715
3.0 0.955 0.917 0.860 0.820 0.791 0.770 0.754 0.743 0.734 0.727 0.722
124 Appendix B Factor ψ or Corrective Factors for Verification Computation
Table B.5 – (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 0.108 0.089 0.075 0.060 0.050
0.2 0.345 0.297 0.257 0.225 0.198 0.167 0.143 0.124 0.110 0.095 0.084
0.3 0.366 0.321 0.284 0.254 0.229 0.200 0.177 0.159 0.145 0.130 0.119
0.4 0.386 0.344 0.310 0.282 0.259 0.232 0.210 0.193 0.180 0.165 0.154
0.5 0.406 0.367 0.335 0.310 0.288 0.263 0.243 0.227 0.214 0.200 0.189
0.6 0.425 0.389 0.360 0.336 0.316 0.293 0.274 0.260 0.247 0.234 0.223
0.7 0.444 0.410 0.383 0.361 0.343 0.322 0.305 0.291 0.279 0.267 0.256
0.8 0.462 0.430 0.406 0.385 0.369 0.349 0.334 0.321 0.310 0.298 0.288
0.9 0.479 0.450 0.427 0.409 0.394 0.375 0.361 0.349 0.339 0.328 0.318
1.0 0.495 0.469 0.448 0.431 0.417 0.400 0.387 0.376 0.367 0.357 0.347
1.1 0.511 0.487 0.467 0.452 0.439 0.424 0.412 0.402 0.393 0.383 0.375
1.2 0.526 0.504 0.486 0.472 0.460 0.447 0.435 0.426 0.418 0.409 0.401
1.3 0.541 0.520 0.504 0.491 0.481 0.468 0.458 0.449 0.441 0.433 0.425
1.4 0.555 0.536 0.521 0.509 0.500 0.488 0.478 0.470 0.464 0.455 0.448
1.5 0.569 0.551 0.537 0.526 0.518 0.507 0.498 0.491 0.484 0.477 0.470
1.6 0.581 0.565 0.553 0.543 0.535 0.525 0.517 0.510 0.504 0.497 0.491
1.7 0.594 0.579 0.567 0.558 0.551 0.542 0.534 0.528 0.522 0.516 0.510
1.8 0.606 0.592 0.581 0.573 0.566 0.558 0.551 0.545 0.540 0.533 0.528
1.9 0.617 0.604 0.594 0.587 0.580 0.573 0.566 0.561 0.556 0.550 0.545
2.0 0.628 0.616 0.607 0.600 0.594 0.587 0.581 0.576 0.571 0.566 0.562
2.1 0.638 0.627 0.619 0.612 0.607 0.600 0.595 0.590 0.586 0.581 0.577
2.2 0.648 0.638 0.630 0.624 0.619 0.613 0.608 0.604 0.600 0.595 0.591
2.3 0.658 0.648 0.641 0.636 0.631 0.625 0.620 0.616 0.613 0.608 0.605
2.4 0.667 0.658 0.652 0.646 0.642 0.637 0.632 0.628 0.625 0.621 0.618
2.5 0.675 0.667 0.661 0.657 0.653 0.648 0.643 0.640 0.637 0.633 0.630
2.6 0.684 0.676 0.671 0.666 0.663 0.658 0.654 0.651 0.648 0.644 0.642
2.7 0.692 0.685 0.680 0.676 0.672 0.668 0.664 0.661 0.658 0.655 0.652
2.8 0.699 0.693 0.688 0.684 0.681 0.677 0.673 0.671 0.668 0.665 0.663
2.9 0.707 0.701 0.696 0.693 0.690 0.686 0.683 0.680 0.677 0.675 0.673
3.0 0.714 0.708 0.704 0.701 0.698 0.694 0.691 0.689 0.686 0.684 0.682
B.3 Heat Exchangers 125
Table B.6 – Heat exchangers – A and B type – 3 passages of external fluid – Fig. A.4 – Factor ψ
(valid also for I and L type with 3 passages of external fluid)
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 0.479 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 0.636 0.588 0.545 0.508 0.474 0.445
0.5 0.952 0.907 0.827 0.757 0.696 0.644 0.597 0.557 0.521 0.490 0.462
0.6 0.952 0.908 0.828 0.760 0.701 0.650 0.606 0.568 0.534 0.505 0.479
0.7 0.952 0.908 0.830 0.763 0.706 0.657 0.615 0.578 0.547 0.519 0.495
0.8 0.952 0.908 0.831 0.766 0.711 0.664 0.623 0.589 0.559 0.533 0.511
0.9 0.952 0.909 0.833 0.769 0.716 0.670 0.632 0.599 0.571 0.547 0.526
1.0 0.952 0.909 0.834 0.772 0.720 0.676 0.640 0.608 0.582 0.560 0.541
1.1 0.953 0.910 0.836 0.775 0.724 0.682 0.647 0.618 0.593 0.572 0.555
1.2 0.953 0.910 0.837 0.778 0.729 0.688 0.655 0.627 0.604 0.584 0.568
1.3 0.953 0.911 0.839 0.781 0.733 0.694 0.662 0.636 0.614 0.596 0.581
1.4 0.953 0.911 0.840 0.783 0.737 0.700 0.669 0.644 0.624 0.607 0.593
1.5 0.953 0.911 0.841 0.786 0.741 0.705 0.676 0.653 0.634 0.618 0.605
1.6 0.953 0.912 0.843 0.789 0.745 0.711 0.683 0.661 0.643 0.628 0.617
1.7 0.953 0.912 0.844 0.791 0.749 0.716 0.690 0.669 0.652 0.638 0.628
1.8 0.953 0.913 0.846 0.794 0.753 0.721 0.696 0.676 0.660 0.648 0.638
1.9 0.953 0.913 0.847 0.796 0.757 0.726 0.702 0.683 0.669 0.657 0.648
2.0 0.954 0.913 0.848 0.799 0.761 0.731 0.708 0.691 0.677 0.666 0.658
2.1 0.954 0.914 0.850 0.801 0.764 0.736 0.714 0.697 0.685 0.675 0.667
2.2 0.954 0.914 0.851 0.803 0.768 0.741 0.720 0.704 0.692 0.683 0.676
2.3 0.954 0.915 0.852 0.806 0.771 0.745 0.725 0.711 0.699 0.691 0.685
2.4 0.954 0.915 0.853 0.808 0.775 0.750 0.731 0.717 0.706 0.699 0.693
2.5 0.954 0.915 0.855 0.810 0.778 0.754 0.736 0.723 0.713 0.706 0.701
2.6 0.954 0.916 0.856 0.813 0.781 0.758 0.741 0.729 0.720 0.713 0.709
2.7 0.954 0.916 0.857 0.815 0.784 0.762 0.746 0.734 0.726 0.720 0.716
2.8 0.954 0.917 0.858 0.817 0.787 0.766 0.751 0.740 0.732 0.727 0.723
2.9 0.955 0.917 0.859 0.819 0.791 0.770 0.756 0.745 0.738 0.733 0.730
3.0 0.955 0.917 0.861 0.821 0.794 0.774 0.760 0.751 0.744 0.739 0.736
126 Appendix B Factor ψ or Corrective Factors for Verification Computation
Table B.6 – (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 0.175 0.143 0.121 0.104 0.092 0.081 0.075
0.2 0.350 0.304 0.266 0.236 0.212 0.185 0.165 0.151 0.141 0.133 0.129
0.3 0.373 0.331 0.297 0.270 0.248 0.224 0.207 0.196 0.188 0.182 0.180
0.4 0.395 0.356 0.326 0.302 0.283 0.262 0.248 0.239 0.233 0.229 0.228
0.5 0.417 0.381 0.354 0.332 0.316 0.298 0.286 0.279 0.275
0.273 0.273
0.6 0.437 0.405 0.380 0.361 0.347 0.332 0.322 0.317
0.314 0.314 0.316
0.7 0.457 0.427 0.405 0.389 0.376 0.364 0.357 0.353
0.352 0.353 0.356
0.8 0.476 0.449 0.429 0.415 0.404 0.394 0.389
0.386 0.386 0.388 0.392
0.9 0.494 0.470 0.452 0.440 0.431 0.423 0.419
0.418 0.419 0.422 0.426
1.0 0.511 0.489 0.474 0.463 0.456 0.449
0.447 0.447 0.449 0.453 0.458
1.1 0.527 0.508 0.495 0.485 0.479 0.475
0.473 0.474 0.477 0.481 0.487
1.2 0.543 0.526 0.514 0.506 0.502
0.498 0.498 0.499 0.502 0.508 0.514
1.3 0.558 0.543 0.533 0.526 0.522
0.520 0.521 0.523 0.526 0.532 0.538
1.4 0.573 0.559 0.550 0.545 0.542
0.541 0.542 0.545 0.549 0.554 0.561
1.5 0.587 0.574 0.567 0.563 0.561
0.560 0.562 0.565 0.569 0.575 0.582
1.6 0.600 0.589 0.583 0.579
0.578 0.578 0.581 0.584 0.588 0.594 0.601
1.7 0.612 0.603 0.598 0.595
0.594 0.595 0.598 0.602 0.606 0.612 0.619
1.8 0.624 0.616 0.612
0.610 0.610 0.611 0.614 0.618 0.623 0.629 0.635
1.9 0.636 0.629 0.625
0.624 0.624 0.626 0.629 0.633 0.638 0.644 0.650
2.0 0.647 0.641 0.638
0.637 0.638 0.640 0.644 0.648 0.652 0.658 0.664
2.1 0.657 0.652 0.650
0.649 0.650 0.653 0.657 0.661 0.665 0.671 0.677
2.2 0.667 0.663
0.661 0.661 0.662 0.665 0.669 0.673 0.678 0.684 0.689
2.3 0.677 0.673
0.672 0.672 0.674 0.677 0.681 0.685 0.689 0.695 0.701
2.4 0.686 0.683
0.682 0.683 0.684 0.688 0.692 0.696 0.700 0.706 0.711
2.5 0.695
0.692 0.692 0.693 0.695 0.698 0.702 0.706 0.710 0.716 0.721
2.6 0.703
0.701 0.701 0.702 0.704 0.708 0.712 0.716 0.720 0.725 0.730
2.7 0.711
0.710 0.710 0.711 0.713 0.717 0.721 0.725 0.729 0.734 0.739
2.8 0.719
0.718 0.718 0.720 0.722 0.725 0.729 0.733 0.737 0.742 0.747
2.9 0.726
0.725 0.726 0.728 0.730 0.733 0.737 0.741 0.745 0.750 0.755
3.0
0.733 0.733 0.734 0.735 0.737 0.741 0.745 0.749 0.752 0.757 0.762
Minimum values of ψ are in bold type
B.3 Heat Exchangers 127
Table B.7 – Heat exchangers – C and D type – 3 passages of external fluid – Fig. A.5 – 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 0.406
0.3 0.952 0.906 0.824 0.751 0.686 0.629 0.578 0.532 0.492 0.456 0.424
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 0.605 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 0.596 0.567 0.542 0.520
1.0 0.952 0.909 0.834 0.772 0.719 0.675 0.637 0.605 0.578 0.554 0.534
1.1 0.953 0.910 0.836 0.774 0.724 0.681 0.645 0.614 0.589 0.566 0.548
1.2 0.953 0.910 0.837 0.777 0.728 0.687 0.652 0.623 0.599 0.578 0.561
1.3 0.953 0.910 0.838 0.780 0.732 0.692 0.660 0.632 0.609 0.590 0.573
1.4 0.953 0.911 0.840 0.783 0.736 0.698 0.667 0.641 0.619 0.601 0.585
1.5 0.953 0.911 0.841 0.785 0.740 0.703 0.673 0.649 0.628 0.611 0.597
1.6 0.953 0.912 0.843 0.788 0.744 0.709 0.680 0.657 0.637 0.622 0.608
1.7 0.953 0.912 0.844 0.790 0.748 0.714 0.687 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 0.630
1.9 0.953 0.913 0.847 0.795 0.756 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 0.734 0.711 0.693 0.679 0.667 0.658
2.2 0.954 0.914 0.851 0.803 0.766 0.738 0.717 0.700 0.686 0.676 0.667
2.3 0.954 0.915 0.852 0.805 0.770 0.743 0.722 0.706 0.693 0.684 0.676
2.4 0.954 0.915 0.853 0.807 0.773 0.747 0.727 0.712 0.700 0.691 0.684
2.5 0.954 0.915 0.854 0.810 0.776 0.751 0.733 0.718 0.707 0.698 0.692
2.6 0.954 0.916 0.856 0.812 0.780 0.756 0.738 0.724 0.714 0.706 0.699
2.7 0.954 0.916 0.857 0.814 0.783 0.760 0.743 0.730 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 0.719 0.713
2.9 0.955 0.917 0.859 0.818 0.789 0.768 0.752 0.740 0.732 0.725 0.720
3.0 0.955 0.917 0.860 0.820 0.792 0.771 0.757 0.746 0.737 0.731 0.727
128 Appendix B Factor ψ or Corrective Factors for Verification Computation
Table B.7 – (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 0.113 0.094 0.081 0.067 0.058
0.2 0.347 0.299 0.261 0.229 0.203 0.173 0.150 0.133 0.120 0.107 0.098
0.3 0.369 0.325 0.289 0.260 0.236 0.208 0.187 0.172 0.159 0.147 0.137
0.4 0.390 0.349 0.316 0.289 0.268 0.242 0.223 0.209 0.197 0.185 0.176
0.5 0.410 0.372 0.342 0.318 0.298 0.275 0.258 0.244 0.234 0.223 0.214
0.6 0.430 0.395 0.367 0.345 0.327 0.306 0.291 0.279 0.269 0.259 0.250
0.7 0.449 0.417 0.391 0.371 0.355 0.336 0.322 0.311 0.302 0.293 0.284
0.8 0.467 0.437 0.414 0.396 0.382 0.365 0.352 0.342 0.334 0.325 0.317
0.9 0.484 0.457 0.436 0.420 0.407 0.392 0.380 0.371 0.363 0.355 0.347
1.0 0.501 0.476 0.457 0.442 0.431 0.417 0.407 0.398 0.391 0.383 0.376
1.1 0.517 0.494 0.477 0.464 0.453 0.441 0.431 0.424 0.417 0.410 0.403
1.2 0.533 0.512 0.496 0.484 0.474 0.463 0.455 0.448 0.442 0.435 0.428
1.3 0.547 0.528 0.514 0.503 0.495 0.485 0.477 0.470 0.465 0.458 0.452
1.4 0.562 0.544 0.531 0.521 0.514 0.505 0.497 0.491 0.486 0.480 0.474
1.5 0.575 0.559 0.547 0.539 0.532 0.523 0.517 0.511 0.506 0.500 0.494
1.6 0.588 0.574 0.563 0.555 0.548 0.541 0.535 0.530 0.525 0.519 0.514
1.7 0.600 0.587 0.577 0.570 0.564 0.557 0.552 0.547 0.542 0.537 0.532
1.8 0.612 0.600 0.591 0.585 0.579 0.573 0.568 0.563 0.559 0.554 0.549
1.9 0.624 0.613 0.605 0.598 0.594 0.588 0.583 0.578 0.574 0.569 0.564
2.0 0.634 0.624 0.617 0.611 0.607 0.602 0.597 0.593 0.589 0.584 0.579
2.1 0.645 0.636 0.629 0.624 0.620 0.615 0.610 0.606 0.602 0.598 0.593
2.2 0.655 0.646 0.640 0.635 0.632 0.627 0.623 0.619 0.615 0.611 0.607
2.3 0.664 0.656 0.651 0.646 0.643 0.638 0.634 0.631 0.627 0.623 0.619
2.4 0.673 0.666 0.661 0.657 0.654 0.649 0.646 0.642 0.639 0.635 0.631
2.5 0.682 0.675 0.671 0.667 0.664 0.660 0.656 0.653 0.650 0.646 0.642
2.6 0.690 0.684 0.680 0.676 0.673 0.669 0.666 0.663 0.660 0.656 0.653
2.7 0.698 0.692 0.688 0.685 0.682 0.679 0.676 0.672 0.670 0.666 0.663
2.8 0.706 0.701 0.697 0.694 0.691 0.688 0.684 0.682 0.679 0.676 0.673
2.9 0.713 0.708 0.705 0.702 0.699 0.696 0.693 0.690 0.688 0.685 0.682
3.0 0.720 0.716 0.712 0.709 0.707 0.704 0.701 0.698 0.696 0.693 0.691
B.3 Heat Exchangers 129
Table B.8 – Heat exchangers – A and D type – 4 passages of external fluid – Fig. A.6 – Factor ψ
(valid also for I and N type with 4 passages of external fluid)
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 0.424 0.388
0.2 0.951 0.906 0.822 0.747 0.681 0.622 0.569 0.521 0.479 0.441 0.407
0.3 0.952 0.906 0.824 0.751 0.686 0.629 0.578 0.533 0.493 0.458 0.426
0.4 0.952 0.907 0.825 0.754 0.691 0.636 0.588 0.545 0.507 0.474 0.444
0.5 0.952 0.907 0.827 0.757 0.696 0.643 0.597 0.556 0.521 0.489 0.461
0.6 0.952 0.908 0.828 0.760 0.701 0.650 0.606 0.567 0.533 0.504 0.478
0.7 0.952 0.908 0.830 0.763 0.706 0.657 0.614 0.578 0.546 0.518 0.494
0.8 0.952 0.908 0.831 0.766 0.711 0.663 0.623 0.588 0.558 0.532 0.510
0.9 0.952 0.909 0.833 0.769 0.715 0.670 0.631 0.598 0.570 0.546 0.525
1.0 0.952 0.909 0.834 0.772 0.720 0.676 0.639 0.608 0.581 0.559 0.539
1.1 0.953 0.910 0.836 0.775 0.724 0.682 0.647 0.617 0.592 0.571 0.553
1.2 0.953 0.910 0.837 0.778 0.729 0.688 0.654 0.626 0.603 0.583 0.566
1.3 0.953 0.910 0.839 0.780 0.733 0.694 0.662 0.635 0.613 0.595 0.579
1.4 0.953 0.911 0.840 0.783 0.737 0.699 0.669 0.644 0.623 0.606 0.592
1.5 0.953 0.911 0.841 0.786 0.741 0.705 0.676 0.652 0.632 0.616 0.603
1.6 0.953 0.912 0.843 0.788 0.745 0.710 0.682 0.660 0.642 0.627 0.615
1.7 0.953 0.912 0.844 0.791 0.749 0.716 0.689 0.668 0.651 0.637 0.626
1.8 0.953 0.913 0.846 0.794 0.753 0.721 0.695 0.675 0.659 0.646 0.636
1.9 0.954 0.913 0.847 0.796 0.757 0.726 0.702 0.683 0.668 0.656 0.646
2.0 0.954 0.913 0.848 0.798 0.760 0.731 0.708 0.690 0.676 0.665 0.656
2.1 0.954 0.914 0.849 0.801 0.764 0.735 0.713 0.696 0.683 0.673 0.665
2.2 0.954 0.914 0.851 0.803 0.767 0.740 0.719 0.703 0.691 0.681 0.674
2.3 0.954 0.915 0.852 0.806 0.771 0.745 0.725 0.710 0.698 0.689 0.683
2.4 0.954 0.915 0.853 0.808 0.774 0.749 0.730 0.716 0.705 0.697 0.691
2.5 0.954 0.915 0.855 0.810 0.778 0.753 0.735 0.722 0.712 0.704 0.699
2.6 0.954 0.916 0.856 0.812 0.781 0.758 0.740 0.728 0.718 0.712 0.707
2.7 0.954 0.916 0.857 0.815 0.784 0.762 0.745 0.733 0.725 0.718 0.714
2.8 0.954 0.916 0.858 0.817 0.787 0.766 0.750 0.739 0.731 0.725 0.721
2.9 0.955 0.917 0.859 0.819 0.790 0.770 0.755 0.744 0.737 0.731 0.728
3.0 0.955 0.917 0.861 0.821 0.793 0.773 0.759 0.749 0.742 0,737 0.734
130 Appendix B Factor ψ or Corrective Factors for Verification Computation
Table B.8 – (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 0.275 0.234 0.201 0.174 0.142 0.119 0.102 0.090 0.078 0.071
0.2 0.349 0.303 0.265 0.235 0.210 0.182 0.162 0.147 0.137 0.128 0.122
0.3 0.372 0.329 0.295 0.268 0.246 0.221 0.203 0.191 0.182 0.175 0.171
0.4 0.394 0.355 0.324 0.299 0.280 0.258 0.243 0.232 0.226 0.220 0.218
0.5 0.415 0.379 0.351 0.329 0.312 0.293 0.280 0.272 0.267 0.263 0.262
0.6 0.436 0.403 0.377 0.358 0.343 0.326 0.316 0.309 0.305
0.303 0.303
0.7 0.455 0.425 0.402 0.385 0.372 0.358 0.349 0.344 0.342
0.341 0.342
0.8 0.474 0.447 0.426 0.411 0.400 0.388 0.381 0.377
0.376 0.376 0.378
0.9 0.492 0.467 0.449 0.436 0.426 0.416 0.411 0.408
0.407 0.409 0.411
1.0 0.509 0.487 0.470 0.459 0.451 0.443 0.439
0.437 0.437 0.439 0.442
1.1 0.525 0.505 0.491 0.481 0.474 0.468 0.465
0.464 0.465 0.467 0.471
1.2 0.541 0.523 0.510 0.502 0.496 0.491
0.489 0.489 0.490 0.493 0.497
1.3 0.556 0.540 0.529 0.521 0.517 0.513
0.512 0.512 0.514 0.518 0.522
1.4 0.570 0.556 0.546 0.540 0.536
0.533 0.533 0.534 0.536 0.540 0.544
1.5 0.584 0.571 0.563 0.558 0.555
0.553 0.553 0.554 0.557 0.561 0.565
1.6 0.597 0.586 0.579 0.574 0.572
0.571 0.571 0.573 0.576 0.580 0.585
1.7 0.610 0.600 0.593 0.590
0.588 0.588 0.589 0.591 0.594 0.598 0.602
1.8 0.622 0.613 0.607 0.605
0.603 0.603 0.605 0.607 0.610 0.614 0.619
1.9 0.633 0.625 0.621 0.619
0.618 0.618 0.620 0.623 0.626 0.630 0.635
2.0 0.644 0.637 0.633 0.632
0.631 0.632 0.634 0.637 0.640 0.644 0.649
2.1 0.655 0.649 0.645
0.644 0.644 0.645 0.647 0.650 0.653 0.658 0.662
2.2 0.665 0.659 0.657
0.656 0.656 0.658 0.660 0.663 0.666 0.670 0.675
2.3 0.674 0.670 0.668
0.667 0.667 0.669 0.672 0.674 0.678 0.682 0.686
2.4 0.683 0.679 0.678
0.677 0.678 0.680 0.683 0.685 0.689 0.693 0.697
2.5 0.692 0.689
0.687 0.687 0.688 0.690 0.693 0.696 0.699 0.703 0.707
2.6 0.700 0.698
0.697 0.697 0.698 0.700 0.703 0.706 0.709 0.713 0.717
2.7 0.708 0.706
0.705 0.706 0.707 0.709 0.712 0.715 0.718 0.722 0.726
2.8 0.716
0.714 0.714 0.714 0.715 0.718 0.720 0.723 0.726 0.730 0.734
2.9 0.723
0.722 0.722 0.722 0.724 0.726 0.729 0.732 0.735 0.738 0.742
3.0 0.730
0.729 0.729 0.730 0.731 0.734 0.736 0.739 0.742 0.746 0.750
Minimum values of ψ are in bold type
B.3 Heat Exchangers 131
Table B.9 – Heat exchangers – B and C type – 4 passages of external fluid – Fig. A.7 – 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 0.424 0.387
0.2 0.951 0.906 0.822 0.747 0.681 0.622 0.568 0.521 0.478 0.440 0.406
0.3 0.952 0.906 0.824 0.751 0.686 0.629 0.578 0.533 0.492 0.456 0.424
0.4 0.952 0.907 0.825 0.754 0.691 0.636 0.587 0.544 0.506 0.472 0.442
0.5 0.952 0.907 0.827 0.757 0.696 0.643 0.596 0.555 0.519 0.487 0.459
0.6 0.952 0.907 0.828 0.760 0.701 0.650 0.605 0.566 0.532 0.502 0.475
0.7 0.952 0.908 0.830 0.763 0.706 0.656 0.613 0.576 0.544 0.516 0.491
0.8 0.952 0.908 0.831 0.766 0.710 0.663 0.622 0.586 0.556 0.529 0.506
0.9 0.952 0.909 0.833 0.769 0.715 0.669 0.630 0.596 0.568 0.543 0.521
1.0 0.952 0.909 0.834 0.772 0.719 0.675 0.638 0.606 0.579 0.555 0.535
1.1 0.953 0.910 0.836 0.775 0.724 0.681 0.645 0.615 0.590 0.568 0.549
1.2 0.953 0.910 0.837 0.777 0.728 0.687 0.653 0.624 0.600 0.580 0.562
1.3 0.953 0.910 0.839 0.780 0.732 0.693 0.660 0.633 0.610 0.591 0.575
1.4 0.953 0.911 0.840 0.783 0.736 0.698 0.667 0.641 0.620 0.602 0.587
1.5 0.953 0.911 0.841 0.785 0.740 0.704 0.674 0.650 0.629 0.613 0.599
1.6 0.953 0.912 0.843 0.788 0.744 0.709 0.681 0.658 0.639 0.623 0.610
1.7 0.953 0.912 0.844 0.791 0.748 0.714 0.687 0.665 0.647 0.633 0.621
1.8 0.953 0.913 0.845 0.793 0.752 0.720 0.694 0.673 0.656 0.642 0.631
1.9 0.953 0.913 0.847 0.796 0.756 0.725 0.700 0.680 0.664 0.652 0.641
2.0 0.954 0.913 0.848 0.798 0.759 0.729 0.706 0.687 0.672 0.660 0.651
2.1 0.954 0.914 0.849 0.800 0.763 0.734 0.712 0.694 0.680 0.669 0.660
2.2 0.954 0.914 0.851 0.803 0.767 0.739 0.717 0.701 0.687 0.677 0.669
2.3 0.954 0.915 0.852 0.805 0.770 0.743 0.723 0.707 0.695 0.685 0.678
2.4 0.954 0.915 0.853 0.807 0.773 0.748 0.728 0.713 0.702 0.693 0.686
2.5 0.954 0.915 0.854 0.810 0.777 0.752 0.733 0.719 0.708 0.700 0.694
2.6 0.954 0.916 0.856 0.812 0.780 0.756 0.738 0.725 0.715 0.707 0.701
2.7 0.954 0.916 0.857 0.814 0.783 0.760 0.743 0.731 0.721 0.714 0.708
2.8 0.954 0.916 0.858 0.816 0.786 0.764 0.748 0.736 0.727 0.721 0.715
2.9 0.955 0.917 0.859 0.818 0.789 0.768 0.753 0.742 0.733 0.727 0.722
3.0 0.955 0.917 0.860 0.821 0.792 0.772 0.757 0.747 0.739 0.733 0.729