**Related Resources: Heat Transfer**

### Heat Exchanger Optimization

Heat Transfer Engineering

Heat Exchanger Design and Engineering

Heat Exchanger Optimization

Copnrad P. Hedderich

Naval Post Graduate School

382 Pages

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Preface

A computer code was developed for the analysis of aircooled heat exchangers and was coupled with a constrained function minimization code to produce an automated air-cooled heat exchanger design and optimization program with many new capabilities.

A general iteration free approximation method was used for the analysis which calculates the mean overall heat transfer coefficient and the overall pressure drop for many flow arrangements, taking into account the variation of the heat transfer coefficients and the pressure drop with temperature and/or length of flow path.

The code is not limited to surfaces found in the literature, but will accommodate any triangular pitch bank of finned tubes in multiple-pass configurations.

TOC

I. INTRODUCTION 12

A. BACKGROUND 12

B. REVIEW 13

C. METHODOLOGY 17

D. OBJECTIVES 18

II. NUMERICAL OPTIMIZATION 19

A. BACKGROUND 19

B. CONSTRAINED FUNCTION MINIMIZATION (CONMIN) 20

C. CONTROL PROGRAM FOR ENGINEERING SYNTHESIS (COPES) 27

III. HEAT EXCHANGER ANALYSIS 30

A. INTRODUCTION 30

B. PROBLEM FORMULATION 30

C. PERFORMANCE CALCULATION PROCEDURE 33

1. Log Mean Temperature Difference 33

2. Determination of Reference Temperatures

3. Correction of Reference Temperatures for Given Arrangement

4. Uncorrected Tubeside Heat Transfer Coefficient 40

5. Calculation of Wall and Associated Resistances ^2

6. Calculation of Airside Heat Transfer Coefficients

7. Calculation of Fin and Surface Efficiencies

8. Correction of the Tubeside Heat Transfer Coefficient

9. Calculation of Air and Tubeside Pressure Drops 46

10. Objective and Constraint Functions 48

IV. RESULTS 52

A. BACKGROUND 52

B. CASE STUDIES 54

1. Case One 54

2. Case Two 60

V. CONCLUSIONS 65

VI. RECOMMENDATIONS 68

VII. FIGURES 70

Appendix A: USER'S MANUAL 89

Appendix B: SAMPLE USER'S INPUT 115

Appendix C: SAMPLE OUTPUT FROM COPES 126

Appendix D: ANALIZE PROGRAM LISTING 139

LIST OF REFERENCES 184

INITIAL DISTRIBUTION LIST 188

List of Figures:

Figure

1. Flowchart for ANALIZ 70

2. Numerical Optimization Techniques 71

3. Usable-Feasible Direction 72

4. One Dimensional Search 73

5. Two-Variable Design Space with Initial Design 74

6. Two-Variable Design Space with First Iteration — 7 5

7. Two-Variable Design Space with Second Iteration - 76

8. Two-Variable Design Space with Third Iteration — 77

9. Two-Variable Design Space with Fourth Iteration - 78

10. General Configuration of Air-Cooled Heat Exchanger 79

11. Thermal Conductivity of Dry Air at Atmospheric Pressure 80

12. Thermal Conductivity of Saturated Water 81

13. Viscosity of Dry Air at Atmospheric Pressure 8 2

14. Viscosity of Saturated Water 83

15. 4 Row, 2 Pass Arrangement 84

16. DRATIO Constraint 85

17. THETA Constraint 8 5

18. Design Optimum - Case Study One 8 6

19. Design Optimum - Case Study Two 87

20. Two-Variable Function Space 88

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