Iowa State University Capstones, Theses and Retrospective Theses and Dissertations Dissertations 1987 Interferometric study of natural convection heat transfer from a vertical flat plate with transverse roughness elements Sushil Hiroo Bhavnani Iowa State University Follow this and additional works at: https://lib.dr.iastate.edu/rtd Part of the Mechanical Engineering Commons Recommended Citation Bhavnani, Sushil Hiroo, "Interferometric study of natural convection heat transfer from a vertical flat plate with transverse roughness elements " (1987). Retrospective Theses and Dissertations. 11669. https://lib.dr.iastate.edu/rtd/11669 This Dissertation is brought to you for free and open access by the Iowa State University Capstones, Theses and Dissertations at Iowa State University Digital Repository. It has been accepted for inclusion in Retrospective Theses and Dissertations by an authorized administrator of Iowa State University Digital Repository. 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Other University iVIicrofilms international Interferometric study of natural convection heat transfer from a vertical flat plate with transverse roughness elements by Sushil Hiroo Bhavnani A Dissertation Submitted to the Graduate Faculty in Partial Fulfillment of the Requirements for the Degree of DOCTOR OF PHILOSOPHY Major: Mechanical Engineering Approved; Signature was redacted for privacy. Signature was redacted for privacy. For the Major Department Signature was redacted for privacy. Iowa State University Ames, Iowa 1987 ii TABLE OF CONTENTS PAGE LIST OF SYMBOLS viii DEDICATION xi I. INTRODUCTION 1 A. General 1 B. Literature Review 2 1. Free convection 2 2. Natural convection in enclosures 7 3. Forced convection 11 C. Objectives 12 II. EXPERIMENTAL APPARATUS 15 A. Introduction 15 B. Experimental Apparatus 18 1. Interferometer 18 2. Test section details 22 3. Associated instrumentation 31 III. EXPERIMENTAL PROCEDURE 32 A. Test Section Alignment 32 B. Data Collection Procedure 33 C. Data Reduction Procedure 34 IV. RESULTS AND DISCUSSION 39 A. Plane Plate 39 B. Ribbed Surfaces 43 1. High thermal conductivity ribs 43 2. Low thermal conductivity ribs 45 C. Stepped Surfaces 52 1. Vertical orientation 52 2. Inclined surfaces 57 D. Sinusoidal Surfaces 61 1. Surface at leading edge facing upwards 61 iii 2. Surface at leading edge facing downwards (reversed orientation) 67 E. Discussion of Results Reported in Literature 73 V. CONCLUSIONS AND RECOMMENDATIONS 75 A. Conclusions 75 B. Recommendations 77 VI. REFERENCES 79 VII. ACKNOWLEDGEMENTS 83 VIII. APPENDIX A. INTERFEROGRAM ANALYSIS 84 IX. APPENDIX B. POLYNOMIALS FOR REFRACTIVE INDEX CALCULATIONS . 88 X. APPENDIX C. SAMPLE CALCULATIONS 89 A. Overall Results 89 B. Interferoraetric Results 94 XI. APPENDIX D. ERROR ANALYSIS 102 XII. APPENDIX E. TABULATION OF INTERFEROMETRIC DATA 109 iv LIST OF FIGURES page Figure 1. Composite of data reported in literature on rough surfaces in free convection 5 Figure 2. Schematic of a basic Mach Zehnder Interferometer 19 Figure 3. Plan view of the ISU Mach-Zehnder Interferometer 20 Figure 4. The ISU Mach-Zehnder Interferometer 23 Figure 5. Schematic of test geometry (a) ribbed and (b) stepped 26 Figure 6. Schematic of a sinusoidal test section 27 Figure 7. Photograph of the sinusoidal test section with amplitude-to-wavelength ratio = 0.3 28 Figure 8. Cross sectional view of a ribbed test section showing fabrication details 30 Figure 9. Composite interferogram of a typical ribbed test section 35 Figure 10. Composite interferogram of a typical stepped test section 36 Figure 11. Composite interferogram of a typical sinusoidal test section 37 Figure 12. Local heat transfer coefficient for a plane vertical isothermal flat plate 40 Figure 13. Local Nusselt number for a plane vertical isothermal flat plate 41 Figure 14. Local heat transfer coefficient for ribbed plate with p/s =8:1 and p/q =8:1 (high conductivity ribs) 44 Figure 15. Local heat transfer coefficient for ribbed plate with p/s = 16:5 and p/q = 4:1 (high conductivity ribs) .... 46 Figure 16. Local heat transfer coefficient for ribbed plate with p/s =8:1 and p/q =8:1 (low conductivity ribs) 48 Figure 17. Composite interferogram of a ribbed plate with p/s = 8:1 and p/q = 8:1 (low conductivity ribs) 49 V Figure 18. Local heat transfer coefficient for ribbed plate with p/s = 16:1 and p/q = 16:1 (low conductivity ribs) .... 51 Figure 19. Local heat transfer coefficient for stepped plate with p/q = 8:1 53 Figure 20. Local heat transfer coefficient for stepped plate with p/q = 16:1 54 Figure 21. Local heat transfer coefficient for stepped plate with p/q = 32:1 55 Figure 22. Local heat transfer coefficient for stepped plate with p/q = 8:1, inclined at an angle of 7.1 degrees 58 Figure 23. Local heat transfer coefficient for stepped plate with p/q = 16:1, inclined at an angle of 3.6 degrees 59 Figure 24. Local heat transfer coefficient for stepped plate with p/q = 32:1, inclined at an angle of 1.9 degrees 60 Figure 25. Local heat transfer coefficient for sinusoidal plate with amplitude to wavelength ratio = 0.05 62 Figure 26. Local heat transfer coefficient for sinusoidal plate with amplitude to wavelength ratio = 0.1 63 Figure 27. Local heat transfer coefficient for sinusoidal plate with amplitude to wavelength ratio = 0.3 64 Figure 28. Local heat transfer coefficient for sinusoidal plate with amplitude to wavelength ratio = 0.05 and reversed orientation 68 Figure 29. Local heat transfer coefficient for sinusoidal plate with amplitude to wavelength ratio = 0.1 and reversed orientation 69 Figure 30. Local heat transfer coefficient for sinusoidal plate with amplitude to wavelength ratio = 0.3 and reversed orientation 70 Figure Cl. Typical set of raw data (run number 67) 95 Figure C2. Data reduction flow chart 96 vi LIST OF TABLES page Table 1. Summary of experimental results 72 Table El. Data for the plane flat plate (reference plot) 109 Table E2. Data for the ribbed surface with p/s =8:1 and p/q =8:1 (high conductivity ribs) Ill Table E3. Data for the ribbed surface with p/s = 16:5 and p/q =4:1 (high conductivity ribs) 113 Table E4. Data for the ribbed surface with p/s =8:1 and p/q = 8:1 (low conductivity ribs) 116 Table E5. Data for the ribbed surface with p/s = 16:1 and p/q = 16:1 (low conductivity ribs) 118 Table E6. Data for the stepped surface with p/q = 8:1 (vertical orientation) 120 Table E7. Data for the stepped surface with p/q = 16:1 (vertical orientation) 123 Table E8. Data for the stepped surface with p/q = 32:1 (vertical orientation) 125 Table E9. Data for the stepped surface with p/q = 8:1 (inclined at an angle of 7.1 degrees) 128 Table ElO. Data for the stepped surface with p/q =16:1 (inclined at an angle of 3.6 degrees) 130 Table Ell. Data for the stepped surface with p/q = 32:1 (inclined at an angle of 1.9 degrees) 132 Table E12. Data for the sinusoidal surface with a/w = 0.05 134 Table E13. Data for the sinusoidal surface with a/w = 0.1 136 Table E14. Data for the sinusoidal surface with a/w = 0.3 138 Table E15. Data for the sinusoidal surface with a/w = 0.05 (reverse orientation) 140 Table E16.