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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