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EXPERIMENTAL STUDIES ON NATURAL AND FORCED. CONVECTION AROUND SPHERICAL AND MUSHROOM. SHAPED PARTICLES. A Thesis.
EXPERIMENTAL STUDIES ON NATURAL AND FORCED CONVECTION AROUND SPHERICAL AND MUSHROOM SHAPED PARTICLES. A Thesis

Presented in Partial Fulfillment of the Requirements for the degree Master of Science in the Graduate School of The Ohio State University by Abdullah M. Alhaxsdan

* * * * * The Ohio State University 1989

Master's Examination Committeet Dr. Sudhir Sastry Dr. Harold Keener Dr. Santi Bhowmik

Approved by

' Adviser Department of Agricultural Engineering

ACKNOWLEDGEMENTS

I would like to acknowledge the guidence and support of Dr. Sudhir Sastry, advisor, and my thesis committee, Dr. Santi Bhowmik, and Dr. Harold Keener in guiding me for the research of this thesis.

In addition, I appreciate my

previous advisor Professor John Blaisdell, who is now retired, in supporting and

helping me start this thesis.

Thanks also to Mr. Dusty Bauman and Mr. Brian Heskitt for their help in lab work. A special thanks to my wife , Jwaher, in supporting me and her patience with me.

My daughter, Rehab, also is a

great delight during the work in this thesis.

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THESIS ABSTRACT THE OHIO STATE UNIVERSITY GRADUATE SCHOOL

NAME: ALHAMDAN, ABDULLAH M.

QUARTER/YEAR: SUMMER/1989

DEPARTMENT: AGRICULTURAL ENGINEERING ADVISOR«S NAME:

DEGREE: M.S.

SASTRY, SUDHIR K.

TITLE OP THESIS: EXPERIMENTAL STUDIES ON NATURAL AND FORCED CONVECTION AROUND SPHERICAL AND MUSHROOM SHAPED PARTICLES.

Heat transfer coefficients (h) between fluids and particles were determined for three situations: the first two involving natural convection of a mushroom-shaped particle immersed in Newtonian and non-Newtonian liquids, and the third involving continuous flow of a sphere within liquid in a tube. For natural convection studies, h was much higher for heating than for cooling, and decreased with time as equilibration occurred. For the continuous flow studies, h was found to increase with flow rate.

Advisor's Signature

VITA

February 1962

. . .

1984

Born - Riyadh, Saudi Arabia B.S. in Agricultural Engineering, King Saud University, Riyadh, Saudi Arabia

3 984-1985

T.A. In Agricultural Engineering at King Saud University

Publications Alhamdan,

A.,

Sastry,

S.,

and

Blaisdell,

J.

1988.

Experimental Determination of Free Convective Heat Transfer From a Mushroom-Shape Particle Immersed in Water. No. 88-6595, Am. Soc. Agric. Eng., St. Joseph, Mich.

FIELDS OF STUDY Major Field: Agricultural Engineering, Studies in Food Processing Engineering.

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Paper

TABLE OF CONTENTS

ACKNOWLEDGEMENTS

ii

VITA

iii

LIST OF TABLES

vi

LIST OF FIGURES

viii

SYMBOLS

x

INTRODUCTION

1

CHAPTER

PAGE

I. LITERATURE REVIEW

4

II. THE OBJECTIVES

12

III. ANALYSIS

13

IV. PHASE 1: NATURAL CONVECTION BETWEEN A WATER AND A MUSHROOM SHAPE PARTICLE

16

Materials and methodology

16

Results and discussion

21

V. PHASE 2: NATURAL CONVECTION BETWEEN A CMC SOLUTION AND A MUSHROOM-SHAPE PARTICLE .

31

Materials and methodology

31

Results and discussion

33

VI. PHASE 3: FORCED CONVECTION OF SPHERE.

IV

.

42

Materials and methodolgy Results and discussion.

43 ......

VII. CONCLUSION

49 37

APPENDICES Appendix A: Material properties Appendix B: Sample of calculation. LIST OF REFERENCES

61 ...

62 71

LIST OF TABLES

TABLE

PAGE

1. Average heat transfer coefficients (h), w/m K, for variable temperature differences for heating and cooling of still mushroom-shape particle immersed in still water

22

2. A summary of average Biot number, and heat parameters f and j values for mushroom-shape particle immersed in still water

22

3. Average fluid velocities (m/s) around the particle during cooling and heating the particle for different CMC solutions

35

4. Average heat transfer coefficients (h) for variable temperature differences and concentration for heating and cooling of still mushroom-shape particle immersed in still CMC solution.

...

35

5. A summary of average Biot number (Bi), and heat parameter (f) values for mushroom-shape particle immersed in still CMC solution

vi

36

6. Viscosity data (consistency coefficient "m" and flow behavior index "n" ) of CMC concentrations .5, .8, and 1.2 % at temperatures 20, 40, and 80°C.

36

7. A summary of heat transfer coefficients for moving sphere immersed in water flowing in a tube at different flow rates 1.26x10"*, 2.52x10'* , 4.42x10"*, 6.31x10"* m3/s and their slopes correlation coefficients "R"

50

8. A summary of average Biot number, and heat parameters f and j values for sphere particle flowing within fluid in holding tube at flow 1.26x10"*, 2.52x10"*, 4.42x10"*, and 6.31x10"* mVs

50

9. A comparison between the particle and the fluid velocities

56

vxi

LIST OF FIGURES

FIGURE

PAGE

1. Sketch of the mushroom particle ,

17

2. Typical plot of temperature difference versus time and their f and j heating parameters . . . 20 3. Plot of Nusselt number versus Rayleigh number for heating and cooling of mushroom-shape particle immersed in still water

23

4. Plot of Nusselt number versus Fourier number for heating and cooling of mushroom-shape particle immersed in still water

24

5. Plot of Rayleigh number versus Fourier number for heating and cooling of mushroom-shape particle immersed in still water

25

6. Plot of Nusselt number versus Rayleigh number for heating and cooling of mushroom-shape particle immersed in still CMC solution.

. . . 37

7. Plot of Nusselt number versus Fourier number for heating and cooling of mushroom-shape

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particle immersed in still CMC solution.

...

38

8. Sketch of experimental system for phase 3 . . .

44

9. Heat transfer coefficient versus flow rate for sphere flows within water

54

10. Nusselt number versus Reynolds number for sphere flows within water

55

SYMBOLSI

A = Surface area of the particle, m2. Cp = Specific heat of the particle, J/(Kg K ) . d = Equivalent particle diameter, m.Ta = Temperature of water stream in the tube, degree C. D = Tube diameter, m. g = gravitational acceleration, m/s2. h = Heat transfer coefficient, w/m2K. K = Thermal conductivity, w/mK. m = Mass of the particle, Kg. t = time, seconds. Tobj = Temperature of particle center during process, degree C. Ti = Initial temperature of the particle, degree C. u = water velocity in the tube, m/s. v = medium velocity around the particle due to free convection, m/s. V = Particle volume, m3.

Greek Letters: a = Thermal diffusivity, m2/s. 6 = Volumetric thermal expansion coefficient, K , n = viscosity of the liquid., Poscal.sec. p = mass density, Kg/m3. r = Shear stress, N/m2. u = Kinematic viscosity, m2/s. 7 = Shear rate for non-Newtonian liquids,s'1.

Dimensionless Parameters: Re = Reynolds Number= Pr = Prandtl Number = Cp/*/Kf Nu = Nusselt Number = hd/Kf Ra = Rayleigh Number = gB (Tobj-Te)