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Table 4 Hydraulic results as optimal dimensionless inner pipe ratio over different Standard Dimension Ratios (\({\text{SDR}}\)) and different cases

From: Net-exergetic, hydraulic and thermal optimization of coaxial heat exchangers using fixed flow conditions instead of fixed flow rates

Mat. \({r_a}\) \({\text{SDR}}\)
6 7.4 9 11 13.6 17 21 26 33 41
   Laminar
- - 0.6321 0.6121 0.5977 0.5862 0.5767 0.5690 0.5632 0.5586 0.5546 0.5517
   Turbulent
Plastic \(r_{min}\) 0.7111 0.6901 0.6749 0.6627 0.6524 0.6440 0.6378 0.6327 0.6283 0.6252
\(r_{m}\) 0.7110 0.6901 0.6749 0.6626 0.6524 0.6440 0.6377 0.6327 0.6283 0.6251
\(r_{max}\) 0.7109 0.6900 0.6748 0.6626 0.6523 0.6439 0.6377 0.6327 0.6283 0.6251
Steel \(r_{min}\) 0.7134 0.6923 0.6769 0.6645 0.6542 0.6456 0.6393 0.6342 0.6297 0.6265
\(r_{m}\) 0.7149 0.6938 0.6784 0.6659 0.6556 0.6470 0.6407 0.6355 0.6311 0.6278
\(r_{max}\) 0.7161 0.6948 0.6794 0.6669 0.6565 0.6479 0.6415 0.6364 0.6319 0.6287
Stand. \(r_{min}\) 0.6651 0.6441 0.6289 0.6167 0.6066 0.5983 0.5921 0.5872 0.5828 0.5797
\(r_{m}\) 0.6779 0.6570 0.6419 0.6297 0.6196 0.6113 0.6052 0.6002 0.5959 0.5928
\(r_{max}\) 0.6946 0.6739 0.6588 0.6467 0.6366 0.6283 0.6221 0.6172 0.6128 0.6097
Switch \(r_{min}\) 0.7303 0.7097 0.6946 0.6824 0.6723 0.6639 0.6576 0.6526 0.6481 0.6450
\(r_{m}\) 0.7291 0.7083 0.6931 0.6809 0.6706 0.6622 0.6559 0.6508 0.6464 0.6432
\(r_{max}\) 0.7256 0.7045 0.6892 0.6767 0.6664 0.6578 0.6514 0.6463 0.6418 0.6386
   Turbulent rough regime
Plastic \(r_{min}\) 0.7223 0.7012 0.6858 0.6733 0.6629 0.6543 0.6480 0.6428 0.6383 0.6351
\(r_{m}\) 0.7226 0.7014 0.6860 0.6736 0.6632 0.6546 0.6482 0.6431 0.6386 0.6354
\(r_{max}\) 0.7230 0.7019 0.6865 0.6740 0.6636 0.6550 0.6487 0.6435 0.6390 0.6358
Steel \(r_{min}\) 0.7137 0.6926 0.6773 0.6649 0.6545 0.6460 0.6397 0.6346 0.6301 0.6269
\(r_{m}\) 0.7156 0.6944 0.6791 0.6666 0.6563 0.6477 0.6414 0.6363 0.6318 0.6286
\(r_{max}\) 0.7178 0.6967 0.6813 0.6688 0.6585 0.6499 0.6436 0.6384 0.6339 0.6307
Stand. \(r_{min}\) 0.6330 0.6100 0.5936 0.5805 0.5696 0.5607 0.5542 0.5489 0.5443 0.5410
\(r_{m}\) 0.6413 0.6184 0.6020 0.5888 0.5780 0.5691 0.5625 0.5572 0.5526 0.5493
\(r_{max}\) 0.6529 0.6301 0.6137 0.6005 0.5897 0.5808 0.5742 0.5689 0.5642 0.5609
Switch \(r_{min}\) 0.7312 0.7106 0.6956 0.6835 0.6734 0.6650 0.6588 0.6538 0.6494 0.6462
\(r_{m}\) 0.7307 0.7100 0.6950 0.6828 0.6727 0.6643 0.6581 0.6530 0.6486 0.6455
\(r_{max}\) 0.7300 0.7093 0.6942 0.6820 0.6718 0.6634 0.6571 0.6521 0.6477 0.6445