Heat transfer from a vertical bundle of serrated finned tubes in an air fluidized bed by Daniel Wade Vanderhoof A thesis submitted in partial fulfillment of the requirements for the degree of MASTER OF SCIENCE in Chemical Engineering Montana State University © Copyright by Daniel Wade Vanderhoof (1978) Abstract: The objective of this investigation is to determine and present information on heat transfer from vertical bundles' of serrated fin tubes in an air fluidized bed. A cylindrical plexiglass column 14 inches in diameter and glass beads as the solid particles were used. The experimental variables were particle diameter (0.0076 inches to 0.0164 inches), air flow rate (63 pounds per hour to 564 pounds per hour), fin length. (0.125 inches to 0.344 inches), fin width (0.094 inches to 0.156 inches), number of rows per inch (6 to 10), number of fins per inch (86 to 250). The heat transfer coefficient increased with decreasing particle size and increasing flow rate. For some conditions a maximum heat transfer coefficient was observed with respect to flow rate. The heat transfer coefficient increased with increasing fin spacing and decreasing fin length. Gains as large as 74 percent, when compared to bare tubes, were obtained using the smallest particles and largest fin spacing.  STATEMENT OF PERMISSION TO COPY In presenting this thesis in partial fulfillment of the requirements for an advanced degree at Montana State University, I agree that the Library shall make it freely available for inspec­ tion. I further agree that permission for extensive copying of this thesis for scholarly purposes may be granted by my major professor, or in his absence, by the Director of Libraries. It is understood that any copying or publication of this thesis for financial gain shall not be allowed without my written permission. Signature Dat e )A STA IQlfl b ' HEAT TRANSFER FROM A VERTICAL BUNDLE OF SERRATED FINNED TUBES A thesis submitted in partial fulfillment of the requirements for the degree of MASTER OF SCIENCE in Chemical Engineering IN AN AIR FLUIDIZED BED by DANIEL WADE VANDERHOOF Approved: MONTANA STATE UNIVERSITY Bozeman, Montana May, 1978 iii ACKNOWLEDGMENT . The author wishes to thank the staff of the Chemical Engineering Department and his Graduate Committee for their time and effort. Special acknowledgement is given to William Genetti for his assistance throughout the project. The funding for this research was provided by the National Science Foundation. TABLE OF CONTENTS VITA ........................................................ ...... . ii ACKNOWLEDGEMENTS . . :........... :....... ............I...... .......... iii E M N O F P O A R E I N ..... ....... : ____ ....................... vi E M N O F P P M C T Y I N ........______________ ............................'___ vii A R N O Y A n O ........... ...... :.......... . . . i.... . .viii M p O Y F r T n O M F p ......... .;............. ;.......... ;;................... i THEORY AND PREVIOUS RELATED RESEARCH ..... . I...'........... .. . 3 Mechanisms of Fluidization for Heat Transfer .............. 3 Previous Related Research .... •....,......... '......... ...... 5 EXPERIMENTAL PROGRAM . . ................ ................ .............. 7 EXPERIMENTAL EQUIPMENT .:................................... 9 Fluidizing System ................................ 9 Heater and Finned Tube Assemblies . .......................... U Electrical System ........................................ 13 EXPERIMENTAL PROCEDURE ... ......................'___ ’.... ....... Minimum Fluidization Determination. .......................... Procedure for a Typical Run ............. :.............. .. . . 19 RESULTS AND DISCUSSION ............................ 2-L Determination of Heat Transfer Coefficients ................ 21 Effect of Mass Velocity on h ................................. 24 Effect of Particle Size on h ......... ;...........'......;. . . 27 Effect of Fin Spacing on h ............ .....'.............. . 27 •Page Effect of Pin Length' on h .............. .................... ; 28 Effect .of Pin Separation on h .............................. ' 28 Effect of Tube Location on h .............. .........,......... .29 V - . Page Performance of Finned Tubes ........... ...................... . 38 CONCLUSIONS ................. .......................................... 45 RECOMMENDATIONS .......................... ................ ............ 46 ERROR ANALYSIS ........................................................ . 47 CALCULATIONS ........................................ . .... ............ 48. Air ■ Mass' Velocity .................... . .................... 48 Tube Temperatures ............................................ 49 Bed Temperatures ......... ...... ........................ . 49 Heat Input to Each Tube ................................ -...... 49 Total Tube Area.^............... .............................. . 49 Air Thermal Conductivity ................... .................. 50 Air Viscosity ............................ ..................... 50 Heat Transfer Coefficient ..................... ;............. . 50 Particle Nusselt Number ...................................... 51 Particle Reynolds Number ................... .................. _ 51 NOMENCLATURE ..................................'........................ 52 BIBLIOGRAPHY 54 vi . " • • " LIST OF TABLES , ' . ' Table . Page I .Range of Experimental Variables . .............. '....... . 8 II Glass Bead Characteristics and Distribution. ^ ..... 9 III Finned Tube Dimensions .......•. ....... ....... ....... '........ 12 IV Minimum Fluidizing Velocities .'............. ...... 19 • LIST OF FIGURES Figure Page 1 Proposed Heat Transfer' Mechanism . ..........^..... .............. & 2 Schematic View of Equipment ................. . ................. .. 14 3 Top View of Finned Tubes ........ . ;.................. ............15 4 Side View of Fin Tube ......................... .................... 16 5 Details of Cartridge Heater ....................................... 17 6 h Versus Q/AT, #4 Tubes .... ...... ...................... ...... . 25 7 h Versus Q/AT, #5 Tubes ........................................... 26 8 h Versus Air Mass Velicity, #1 Tubes .;....................... 30 9 h Versus Air Mass Velocity, #2 Tubes ............................ 31 10 h Versus Air Mass Velocity, #3 Tubes .......................... 32 11 h Versus Air Mass Velocity, #4 Tubes ...... :...... . 33 12 h Versus Air Mass Velocity, #5 Tubes ............. 34 13 h Versus Air Mass Velocity, Small Particles ...... . ............. 35 14 h Versus Air Mass Velocity, Medium Particles .................... 36 15 h Versus Air Mass' Velocity, Large Particles ........ ■....... . 37 16 p- Versus Air Mass Velocity, #1 Tubes ............................. 40 17 p Versus Air Mass Velocity, .#2 Tubes ........ 41 18 p Versus Air Mass Velocity, #3 Tubes ....................... 42 19 p Versus Air Mass Velocity,. #4 Tubes ........ 43 20 p Versus Air Mass Velocity, #5 Tubes ............... 44 vii viii ABSTRACT The objective of this investigation is to determine and present information on heat transfer from vertical'bundles' of serrated fin tubes' in an air fluidized b e d . . A cylindrical plexiglass column 14 inches in diameter and glass beads as the solid particles were used. The experi­ mental variables were particle diameter (0.0076 inches to 0.0164 inches), air flow rate (63 pounds per hour to 564 pounds per hour), fin length. (0.125 inches to 0.344 inches), fin width (0.094 inches to 0.156 inches), number of rows per inch (6 to 10), number of fins per inch (86 to 250). The heat transfer coefficient increased with decreasing particle size and increasing flow rate. For some conditions a maximum heat transfer coef­ ficient was observed with respect to flow rate. The heat transfer coef­ ficient increased with increasing fin spacing and decreasing fin length. Gains as large as 74 percent, when compared to bare tubes, were obtained using the smallest particles and largest fin spacing. INTRODUCTION Fluidized beds are used in a variety of industrial operations. Some of the applications are drying, calcining, mixing, coating and removal of fines from-bed particles. A fluidized bed consists of a column which contains solid parti­ cles that are supported by a porous distributor plate. A fluidizing mass, gas or liquid, flows upward through the distributor plate. At low mass velocities there is no movement of the. solid p a r t i c l e ' s As ■ the mass velocity is increased, the pressure drop across the bed of solid particles increases. When.the pressure drop equals the weight of the solid particles, the bed will begin to expand. The mass velocity which causes this initial expansion is called the minimum fluidization, velo­ city. The particles are separated and begin moving but there is no bubbling. Increasing the mass velocity increases the particle separa­ tion and movement and bubbles begin to rise up through the bed. As the bubbles rise.they expand and burst upon reaching the top surface of the bed. The bed of solid particles resembles a 'hoiling liquid" (I). The size and number of bubbles increase as the mass velocity in­ creases. The bubbles agitate the bed and increase the random motion of the particles. The condition of free bubbling is known as aggregative fluidization and is encountered in most industrial applications. As the mass velocity is increased, the bubble size will grow until slugging occurs. Some of the physical advantages of a fluidized bed are the uniform 2temperature distribution, good solid mixing, high heat transfer coeffi­ cients between the bed and an immersed surface, the ability for contin­ uous feed or recycle and good flexibility in the size and type of bed materials that can be used.. The simplistic design with few moving parts results in lower capital and maintenance costs. Some of the disadvantages of fluidized beds are erosion of column walls and immersed surfaces, solid particle degradation, difficulty in handling sticky materials and difficulty in accurately controlling resi­ dence time in continuous feed operations. There are many applications where heat is extracted or added to the fluidized bed. Originally this was accomplished by heat transfer through the walls of the column. Because of the increased surface area bare tubes were immersed in the fluidized bed to increase the amount of heat transfer.. A lot of work has been done to establish reliable de­ sign criteria for heat transfer from immersed surfaces. There has been some work done evaluating heat transfer from extended surfaces in flu­ idized beds. It has been possible to improve.heat transfer rates with the use of extended surfaces. The purpose of this investigation is to determine and present information on the heat transfer from a bundle of vertically oriented serrated fin tubes.1 THEORY AND PREVIOUSLY RELATED RESEARCH Mechanism of Fluidization for Heat Transfer The heat transfer coefficients from the bed to an appropriate sur­ face are considerably larger than coefficients from a surface to a gas or a surface to a fixed bed. Several models based on different control­ ling heat transfer resistances have been.developed to'explain the higher heat transfer coefficients. A "film" model developed by Levenspiel and Walton (2)describes a thin laminar film of fluidizing gas next to the surface which controls ' the rate of heat t r a n s f e r D u r i n g fluidization the "scouring" action of the particles reduces the thickness of the laminar film thereby in­ creasing the heat transfer rate. A."packet" model was developed by Mickley and Fairbanks (3). This model describes "packet's"..of particles'coming into contact withlthe: , . heat transfer surface for short periods of time. The unsteady state heat conduction into the packet of particles is the controlling resis­ tance. After staying near the surface for a short period of time the • "packet" returns to the bulk of the bed and dissipates its energy. The "particle" theory was developed by Ziegler, Koppel and Brazel- ton (4)and extended by Genetti and Knudsen (5). Assuming spherical par­ ticles of uniform diameter and that the physical properties of the sol­ ids and the fluids are constant, the theory proposes that particles from the bulk of the fluizided bed at the bulk medium temperature, T^, 4move next to the heat transfer surface at temperature Tg . Energy is ' transferred by convection from the surrounding fluid for a short time period, 0. The fluid temperature is assumed to be the arithmetic mean of the surface temperature and the bulk medium temperature. After a short time the particle returns to the bulk medium where it dissi­ pates its acquired energy. This mechanism is shown in Figure I. . The conduction heat transfer and radiation heat transfer from the surface to the particle are neglected. The following equation describes the heat transfer rate from an.immersed surface in a fluidized bed.- Nu. h’D 7.2 I T , 6 k S e I 2 (I) Nu P = Particle Nusselt Number, Dimensionless h = Heat Transfer Coefficient, Btu/hr-f-t^-°F D = Particle Diameter, ft P k .= Fluid Thermal Conductivity,, BtuZhf-Et-0F , 8 0 = Average Contact Time,"hr pg = Solid Particle Density, IbsZft^ Cp = Solid Particle Heat Capacity, BfuZlb-°F Genetti and Knudsen extended the "particle" theory by recommend- 5ing that 7.2 be substituted with 1 0 ( l - e ' ) ^ w h e r e (l-.e) is the particle volume fraction. . Kuhii and Levenspiel:' (6) have compared models and sug­ gested a"general model which includes' the different•theories . Previous Related Research Heat transfer from an immersed surface to the. solid particles has received a lot of attention in the past. Studies have been done to de­ termine the effect of particle diameter, particle shape, density, heat capacity, fluid thermal conductivity, viscosity, void fraction and- mass velocity. Chen and Withers (7,8) investigated heat transfer from verti­ cally oriented bare and finned tubes in a fluidized bed. They varied fin height and fin spacing. They reported gains as large as 190 percent, for heat transfer from helical copper fin tubes compared to plain tubes. Bartel and Genetti (9) investigated the heat, transfer from a hori­ zontal bundle of carbon steel bare tubes and finned tubes. They varied fin height, tube spacing, particle diameter and mass velocity. Gains up to 80 percent, compared to bare tubes were reported. Priehe and Genetti (10), investigated heat transfer.from horizontal serrated and Z spined tubes. For copper spines, gains as large as 60 percent were ob­ served. Kratovil (.11) investigated heat transfer from a horizontal bun­ dle of continuous, helical copper finned tubes. Gains up to 190 percent were observed compared to bare tubes . 6HEAT TRANSFER SURFACE T b HOT PARTICLE RETURNS TO BULK MEDIUM T b T s T s PARTICLE ABSORBS / ENERGY AT HOT ( T(r,0) PARTICLE FROM Tb BULK MEDIUM FIGURE I. PROPOSED HEAT TRANSFER MECHANISM EXPERIMENTAL PROGRAM The objective of this investigation was to determine the heat '■ ■ transfer coefficients of several bundles of serrated, or discontinuous, finned tubes oriented in the vertical position. The parameters that should affect the heat transfer coefficients are separated into three categories. First, the parameters of the fluidized bed. . These are the solid particle size, shape and composition, and the physical properties : of the fluidizing medium, the density, temperature, thermal conducti­ vity and air viscosity. Second are the operating, condition parameters. These are the fluidizing medium mass velocity and the static height, of ■ solid particles in the bed. Third are the parameters describing the geometry of the equipment. These are the size and shape of the column, and the dimensions and orientation of the finned tube bundles. The 6 experimental variables for this investigation were: particle diameter, air mass velocity, fin length, fin width, number of rows of fins per inch, and the number of fins per inch. Air was used as the fluidizing medium. The inlet air temperature was in the range of 100 F to 115 F, and the physical properties of the inlet air were considered constant. Spherical glass beads were used as. the solid particles. The density of the glass beads is approximately 3 155 lbs/ft . Electrical heaters were used as the heat source and 5 different tube bundles were investigated. Table-I gives the range.of experimental variables. - ' . ' 8TABLE I. RANGE OF EXPERIMENTAL VARIABLES Variable Range Particle Diameter 0.0076, 0.0109, 0.0164 Inch Diameter Air Mass Velocity 63 to 564 lbs/hr-ft^ Fin Length 0.125, 0.188, 0.344 Inches Fin Width 0.938, 0.156 Inches Numbers of Rows/Inch 6.0, 8.0, 10.0 Number of Fins/Inch 85.7, 88.3, 14.49, 193.7, 250.3 EXPERIMENTAL EQUIPMENT Fluidizing System The main parts of the fluidizing system are the column, glass beads, distributor plate, funnel and air blower. A schematic drawing of the experimental equipment is shown in Figure 2. Tlie column was cylindrical and constructed of clear plexiglass that was 0.25 inches thick. The column was 13.5 inches inside diameter and 59 inches in height. A 0.75 inch thick flange was connected to the top and bottom of the column. One acess port, 4 inches in diameter was located with its center 6 inches from the bottom of the column. The column was supported on a wooden frame which was bolted to the floor. Three sizes of glass beads were used in this investigation. Their sizes and distributions were determined by Everly (9) and are listed in Table II. TABLE II. GLASS BEADS CHARACTERISTICS AND DISTRIBUTION Avg. Diameter (Inch) Distribution (Inch) Small 0.0076 0.005 - 0.0098 Medium 0.0109 0.0098 - 0.016 Large 0.0164 >0.016 10 - The distributor plate consisted of two layers of a lightweight cotton cloth sandwiched between two layers of 100 mesh stainless steel wire cloth which was placed between two pieces of 0.03125 inch thick steel perforated plates. The perforations were 0.25 inches in diameter with a 0.5 inch center to center distance. The funnel was 13.5 inches in diameter at top and 2 inches in diameter at the bottom. It was 12 inches in height and constructed of 16 gauge galvanized steel. The spout of the funnel was 2 inches in diameter and 4 inches long. The - distributor plate, fitted with rubber gaskets, and-the funnel section ' were bolted to the bottom of the column using a 13-1/2 inch diameter wooden ring to reinforce the funnel. A I inch diameter drain pipe was fastened to the distributor plate and projected through the side of the funnel. The drain pipe was fitted with a gate valve. Two blowers were connected in parallel to .the fluidized bed. The first blower was a size 4L Sutorbxlt Blower driven by a 3 H.P. electrical motor. The blow­ er fed into a 2 inch, schedule 40 pipe which was connected to the funnel with a flexible rubber hose. The air flow rate was regulated by adjust­ ing a gate valve in a 2 inch bypass line. The air flow rate was mea­ sured by using a 1.5 inch orifice with vena contracta taps and a water filled manometer. The second blower was a Sutorbilt Blower driven by a 7.5 H.P. electrical motor. The second blower fed into a 2.5 inch sched­ ule 40 steel pipe before reaching the column. The pipes from the two blowers were connected directly below the funnel section. The air flow 11 rate was regulated by adjusting a gate valve in a 2 inch bypass line.. The air flow rate was measured using a 1.5 inch orifice with vena con- tracta taps and a water filled manometer,. Gate valves were installed - in the two air lines so the blowers could be operated independently. ' , Heater and Finned Tube Assemblies Watlow Firerod Cartridge Heaters were used as the heat source in this investigation. ■ As shown in Figure 5», each cartridge was 10 inches long, comprised of a heated section .6.5 inches long and two insulated ends. The finned tubes were 6.5 inches long and.outside diameter was . 0.625 inches. The heaters were inserted into.the finned tubes with the two insulated ends protruding and a set screw.in the wall of the tubes was tightened down so the heater could not slip. The bottom end of the heater was inserted into a copper pipe 9.125 inches long and 0.5 inch inside diameter. The other end of the heater, with the lead wires, was ■ inserted into a similar copper pipe 52 inches long. The opposite ends of the two copper pipes were inserted, into holes in the distributor plate and the top perforated plate holding.the tubes in a vertical posi­ tion. All the investigations were done with^bundles of 7 finned tubes. A bundle configuration with one tube in the center of the bed and the other 6 tubes equally spaced around the center tube was used... The cen­ ter distances between the outside tubes and the center tube, and between adjacent outer tubes was 2 inches. A total of 5 different sizes of 12 - finned tubes were investigated. The surface areas and various dimen­ sions are given in Table III. A top view and a side view of the fin tubes are shown in Figure 3 and Figure 4. TABLE III. FINNED TUBE DIMENSIONS (Fin length, width, thickness, (All areas in Ft^) spacing in inches) #1 Tubes #2 Tubes #3 Tubes #4 Tubes #5 Tubes Fin Length 0.188 0.188 0.188 0.344 0.125 Fin Width 0.094 0.094 0.094 0.156 0.156 Fin Thickness 0.031 0.031 0.031 0.025 0.0156 Fin Spacing 0.135 0.094 0.069 0.100 0.109 Rows/Inch 6.0 8.0 ' 10 .0 8.0 8.0 Total Area 0.395 0.498 0.618 0.571 0.260 Fin Area 0.326 0.436 0.563 0.497 0.181 Tube Area 0.069 0.062 0.055 0.007 0.079 Avg. N o . of Fins 942 1269 1627 557 574 Electrical System A single thermocouple was attached to the surface of each finned tube midway along the length.. The thermocouple wires and heater lead wires were threaded up inside the copper pipe, out of the column, and to their respective panels. One thermocouple was used to measure the bed temperature in three different locations. , The three thermowells • were located 11.5 inches above the distributor plate and were equally spaced around the circumference of the bed. The thermowells projected 3 inches into the bed. The lead wires from the 8 thermocouples were plugged into a panel board which was wired to a switch box. A Model 156X15-P Brown Potentiometer was used to.measure the temperature di­ rectly. The electrical heaters in each tube were connected to a Simpson Model 390 Wattmeter and then to the electrical power supply, The heat ers were connected in parallel and the wattmeter was connected so the wattage to the individual heaters could be measured by flipping the appropriate toggle switch. The power was supplied from a H O volt AC line through a Powerstat and a Fenwall Model 524 high limit controller I. Air Blower 2. Bypass valve, 3. Main Air Line Valve, 4. Manometer, 5. Orifice, 6. Power Source, 7. Powers tat, 8. Wattmeter, 9. High Temperature Limit Controller, 10. Plexiglass Column, 11. Potentiometer FIGURE 2. SCHEMATIC VIEW OF EQUIPMENT OFD Tubes #4, #5 Tubes //I, //2, //3 i e Oi I FIGURE 3. TOP VIEW OF FINNED TUBES K H6.5 M N I l l l ITT T K Fin Length 6 Rows/Inch FIGURE 4. SIDE VIEW OF FIN TUBE 4 --- M M— T Fin Spacing INSULATED SECTIONS HEATED SECTION \ M-04 6.5 3 " — H OUTSIDE DIAMETER 0.495" FIGURE 5. DETAILS OF CARTRIDGE HEATER EXPERIMENTAL PROCEDURE Minimum Fluidization Determination The first experimental work performed in this investigation was to determine the minimum fluidizing1 velocities for the three particle sizes The minimum velocities were determined- by visual observation of the bed. The particles of the desired diameter were poured into the top of the column until a static height of 18 inches above the distributor plate were attained. The number one b lower was used for the smallest parti- - cIes and the number two blower was used for the other two particle sizes. The appropriate blower was turned on and the.air flow rate was regulated until the.bed whs bubbling freely. . The heaters were turned on and the bed was operated for 2-3 hours before reaching normal operating temperature. Then the air flow rate was.regulated until the bed was just beginning to expand.• A water-filled micromanometer was used to measure the pressure drop across the orifice. The observations were re­ peated several times from the direction of increasing as well as den creasing flow rate. The experimental minimum fluidizing velocities for the three particle sizes are shown in Table IV. 19 TABLE IV. MINIMUM FLUIDIZING VELOCITIES Bead Size (Inches) Minimum Fluidizing Velocity Jibs /hr/ ft*) .0076 62.8 .0109 63.7 .0164 125.3 Procedure for a Typical Run l*he finned tubes to be investigated were chosen, the thermocouples were attached to each of the 7 tubes and a heater was inserted and fas­ tened to each tube. The copper pipes used to hold the tube assemblies were put into the bed. The heater lead wires and thermocouple wires were threaded into the upper copper pipe and connected to their respec­ tive panels. The ends of the heaters were inserted into the copper pipes and the end of the copper pipes were fastened down so they would not come loose during operation of the bed. One of the particle sizes was selected and the column was filled to a static height of 18 inches. The appropriate blower was turned on and the valve in the bypass line was adjusted to regulate the air flow rate to two times the minimum fluidiz­ ing velocity. The power to the heaters was turned on and adjusted to a level of 200 watts per heater. The column was allowed to operate for 4 hours to reach steady state operating conditions. The temperatures of 20 the tubes and bed, wattage, air inlet conditions and pressure drop /. across the orifice were recorded. . The column was allowed to operate for another hour and readings were taken again. For subsequent runs the valve in the bypass line was adjusted to get the desired flow rate and the column was operated for 2 hours to reach steady state. The tem­ peratures , wattage, air inlet conditions and pressure drop were record­ ed again. The column was operated for another hour before taking a sec­ ond set of readings. This procedure was repeated until all of the de­ sired flow rates had been investigated. - The column was shut down and the particles were drained out through the I inch drain pipe. The access port was opened and a vacuum cleaner was used to remove any remaining beads from the distributor plate and the walls of the column. The drain pipe and access port were closed and the next particle size was loaded into the column as described pre­ viously. After all 3 particle sizes were investigated, the finned tubes were replaced and the procedure was repeated until all 5 fin. tube • bundles had been.investigated. RESULTS AND DISCUSSION Determination of Heat Transfer Coefficients A-single thermocouple was attached to the surface of each tube in ■ the bundle. The.thermocouple was used to measure the temperature at the base of the fin. Since there will be a .temperature distribution along the length of the fin, this temperature can not be used to .determine the heat transfer coefficient. To determine the temperature distribution in the fin, an energy . balance was taken about a differential element. . The temperature - - across the width, and the thickness were assumed constant.. The fol­ lowing procedure was used to solve for the temperature distribution: I. The heat conducted into the element at x was set equal to the heat conducted out of the element at x + Ax plus the heat loss by convection from the surface. . (2)-k wv dT dx -k w v.dT dx . + h Wv(T-Tb )Ax x+Ax where k= Thermal conductivity of the fin, Btu/hr-ft-°F . w= Fin width, ft . v= Fin thickness, ft ' ' 2 o h= Average heat transfer coefficient, B'ttf/hr-ft - F substituting 0 for (T-Tb) and■rearranging , 22 d^9 - 2 (w+v) h 0 = O (3) , 2 . wv ' ■ k dx the boundary conditions are a) x = 0 0 =CT -T,) (4) x = L d0 = -h 0 dx k IL (5) For the #1, #2 and #3 finned tubes the second order differen­ tial equation was solved numerically to determine the tempera­ ture distribution in the fin. 2. Once the temperature distribution was determined the mean tem­ perature of the fin was calculated. The heat transfer coeffi­ cients were then determined using the following equation: (6) h = Heat transfer coefficient, B tu/hr-ft^-°F q = Heat input per tube, Btu/hr 2 = Bare tube area, ft 2 = Fin area, ft Tw^Tb = temperature minus bed temperature, °F '(T-Tj3') = Mean fin temperature minus bed temperature, °F MF 3. For the #4 and #5 finned tubes, the second order, differential equation was solved analytically. The solution was of the form: 0 = A sinh(Cx) + B cosh (Cx) (7) 23 where C = 2 (w+v) ti wv k (8) Applying the two boundary conditions to solve for the constants A and B gave the■following temperature ^ distribution:' 0 L a r g e P a r t i c l e s 70 - O 60 — C u O 0 a ► CM 4-1 «4-1 I U r C 50 © - C l S > ▻ _ ? 4-1 M J 3 a > 40 — 30 — _ _ _ _ _ _ _ _ _ I_ _ _ _ :_ _ _ _ _ _ _ I_ _ _ _ _ I I 100 200 300 400 500 600 Air Mass Velocity, lbs/hr-ft2 FIGURE 8. h VERSUS AIR MASS VELOCITY, //I TUBES B t u / h r - f t 31 - I ^ Small Particles 3 Medium Particles > Large Particles e Pu O I C M 0 B 30 ► ► ► ► B ► O I ____________ I_____________I_____________I_____________I_ 100 200 300 400 500 Air Mass Velocity, Ibs/hr-f FIGURE 9. h VERSUS AIR MASS VELOCITY, #2 TUBES 600 B t u / h r - f t 32 ' I I T ® Small Particles O a Medium Particles ► Large Particles 40 O O O O 30 - B B > > ► > ► > 20 O a _ _ _ I_ _ _ _ _ _ _ _ _ _ _ I_ _ _ _ _ i I 100 200 300 400 500 600 2 Air Mass Velocity , Ibs/hr-ft FIGURE 10. h VERSUS AIR MASS VELOCITY, #3 TUBES B t u / h r - f t 33 • Small Particles ► Large Particles Air Mass Velocity ,Ibs/hr-ft FIGURE 11. h VERSUS AIR MASS VELOCITY, #4 TUBES B t u / h r - f t 0 F . 34 - 100 90 80 70 60 50 r i i n <5 e Small Particles B Medium Particles ► Large Particles O O O © a ra a ► ► ► H a > — Q ■ > I _j_____________ 1_ 100 200 300 400 500 600 o Air Mass Velocity, Ibs/hr-ft FIGURE 12. h VERSUS AIR MASS VELOCITY, #5 TUBES B t u / h r - f t 35 O //I Tubes a #2 Tubes ► #3 Tubes O #4 Tubes X it5 Tubes Air Mass Velocity, lbs/hr-ft FIGURE 13. h VERSUS AIR MASS VELOCITY, SMALL PARTICLES B t u / h r - f t 36 Tubes Tubes Tubes Tubes Air Mass Velocity, Ibs/hr-ft FIGURE 14. h VERSUS AIR MASS VELOCITY,MEDIUM PARTICLES Bt u/ hr -f t 37 #1 Tubes > //2 Tubes a //3 Tubes X H Tubes O #5 Tubes & X fc I X O X - X © X ti X © S ► a Q O ► a I 100 200 300 400 500 Air Mass Velocity, lbs/hr-ft2 FIGURE 15. h VERSUS AIR MASS VELOCITY, LARGE PARTICLES 600 38 - Performance of Finned Tubes Since the reported heat transfer coefficients are based on the■ total area of the finned tubes, it is difficult to compare different tubes unless the areas are also presented. The most effective way is to compare the performance of the different tubes. The performance is calculated using Equation 13. „ _ CQ/AT) Fin Tube . n ox P (Q/AT) Bare Tube . . ■ p = Performance, dimensionless Q = Heat transferred, Btu/hr o AT = Temperature driving force F ■ The area of the bare tube, used to determine (Q/AT) bare tube, is I calculated using the 'overall fin diameter’, (OFD). The OFD is defined as the tube diameter across the fin tips (see Figure 3). Using the OFD to calculate A^, you are comparing the amount of heat transferred from the finned tube to the heat transferred from a bare tube occupying the same volume. The performance is the ratio of the heat transfer from an extended surface to a bare tube at the same temperature drop between the heat transfer surface and the bulk medium. The performances for each tube are shown in Figures 16, 17, 18, 19, and 20. The performance increased with increasing mass flow rate. The ■' . ■ — 39 — - - ■ ■ performance tends to increase with an increase in particle size. There is a larger difference in performance between the large particles and the medium particles than between the medium particles and the small particles. ; For all the tubes there were some operating conditions where the performance value was less than I. The low performance values were pri-. ' marily at the lower mass velocities. With the #4 tubes ( longest fins ) and the small particles, the per­ formance was never greater than I. The largest performance value of 1.74 occurred using the //I tubes and the large particles. The //I tubes have the largest fin spacing of the tubes. The #5 tubes also had a high . performance (1.72). These tubes had the shortest fins and a larger fin separation. • 40 - 1.8 1.6 1.4 1.2 1.0 0.8 I I \ ~ T ~ Small Particles a Medium Particles ► ► Large Particles ► > ▻ — ► ® ■ B O B e — O O a “ O I I I I 100 200 300 400 500 600 Air Mass Velocity, Ibs/hr-f FIGURE 16. P VERSUS AIR MASS VELOCITY, #1 TUBES — 41 — 1.6 - O I Small ~ T ~ Particles - - - - - - 1- - - - - - - - - - - 1- - - — □ Medium Particles > Large Particles ► ► 1.4 — 18 » » $► - 1.2 - B > - B 1.0 - O - a B » O O 0.8 ' 0.6 I I I I 100 200 300 400 500 600 Alr Mass Velocity, lbs/hr-ft~ FIGURE 17. p VERSUS AIR MASS VELOCITY, //2 TUBES 42 P 1.6 1.4 1.2 1.0 0.8 0.6 I r~ ~T ~T~ # Small Particles # Medium Particles ► Large Particles ► ► ► ► > & R » • ea ® Qe - e a m I__________ L_ _____ L ____I____ 100 200 300 400 500 600 Air Mass Velocity* Ibs/hr-f FIGURE 18. p VERSUS AIR MASS VELOCITY, #3 TUBES 43 - 1.5 ~ T ~ ~ T ~ T I > — ► > > > 1.3 - B — Q © Small Particles n Medium Particles 1.1 — > ► Large Particles 0.9 •©« ______ I_____ O & - © 0.7 - — 0.5 I L_ _L I 100 200 300 400 500 600 Air Mass Velocity, Ibs/hr-ft2 FIGURE 19. p VERSUS MASS FLOW RATE, #4 TUBES - 44 - 1.7 T ► 1.5 e Small Particles ■ Medium Particles ► Large Particles 1.3 * * 9 a fr e o 1.1 0.9 100 200 300 400 Air Mass Velocity, Ibs/hr-ft' 500 600 FIGURE 20. p VERSUS AI R MASS VELOCITY, #5 TUBES CONCLUSIONS From this investigation the following conclusions were drawn: I. Heat transfer coefficients increased with increasing air mass velocity. For some conditions a maximum .was reached. .2. Heat transfer coefficients decreased with increasing particle size. The effect was greater between the large and medium particles than between the medium and small particles. 3. Heat transfer coefficients increased with increasing fin spacing. 4. Heat transfer coefficients decreased with increasing fin length. 5. Heat transfer coefficients increase with increasing fin separation. 6. Tube location did not affect the h values. 7. Performance increased with increasing mass velocity, increasing fin spacing and, increasing fin separation. 8. Gains of up to 74% were obtained when compared to bare, tubes. RECOMMENDATIONS 1. A further investigation with serrated fin tubes should be con­ ducted with expanded experimental variables. 2. An investigation to determine the effect of fin separation on the heat transfer coefficients. ERROR ANALYSIS ■Assuming the experimental heat transfer is only affected by the measurements of q and (T^-T^),' the error analysis Is performed on equa­ tion 14. h = q ‘ ' (14) ' ' V W The wattmeter was assumed to be accurate within + 5 percent. The bed temperature is assumed to be measured within + 0.5°F and the tube wall temperature could be measured within + 1.5°F. The minimum (T -T1 ) ' — - . w b value in this investigation was 18.5°F. The maximum and minimum errors for h can be determined using the previous assumptions. This analysis is based on an h 'true' value of 1.0 Maximum tv h = .' 1.05 = 1.18 . (15) I - 2/18.5 Error = (1.18-1.0) x 100 = 18 percent Minimum h h = ■ .95 = .86 (16) I + 2/18.5 - ' Error = (.86-1.0) x 100 =-14 percent The experimental error range is +18 percent, -14 percent. The maxi­ mum deviations from the 'true' value should be + 18 percent. CALCULATIONS Air Mass Velocity For both blowers a 1.5 inch orifice with vena contracta taps and a water filled manometer were used to measure the air flow rates in the column. The following equation was used for the calculations (1): 0.5 G - 3600 C Y S o • c 2 g^ . (Pi-P,) Pi 1-04 (17) G = Air Mass Velocity, .lbs/hr-ft C = Orifice.Coefficient, Dimensionless 0 Y = Expansion Factor, Dimensionless 2 S = Cross Sectional Area of Orifice, ft c 2 .A^ = Cross Sectional Area of Column, ft ■ 2 gc = Gravitational Constant, ft-lb / sec -Ib^ 2 P^ = Pressure at Upstream Pressure Tap, Ib^/'ft P^ = Pressure at Downstream Pressure Tap, lb / ft^ 2 p = Density of Air at the Upstream Pressure, lb /'ft 1 m 0 = Ratio of Orifice Diameter to Inside Pipe Diameter Dimensionless For a square edged orifice, the expansion factor is given as fol­ lows: I - P1-P2 ( .41-.350 ) P1 Kr (18) K = C /C r p v / I — 49 — The orifice coefficient is a function of the Reynolds number. It was found to be nearly constant at 0.61 for both blowers for the range of air flow rates used. Tube Temperatures The tube temperatures were read directly using thermocouples con­ nected to a Brown Potentionmeter. . ■ ■ Bed Temperature The bed temperature, T^, was the average couple readings. Heat Input to Each Tube The power to each tube was measured with verted, to the appropriate units. q =■ (Watts) 3.4129 B'tu ■ ■ Watt-hr Total Tube Area The total fin area was found by multiplying the area per fin by the number of fins.. . The total tube area was calculated by adding the total fin area and the area of the unfinned portion of the tube. The average of the three bed thermo- a wattmeter and then con- (19) of the 7 tubes was used in the calculations. 50 Air Thermal Conductivity The air thermal conductivity, k , was determined by linear inter­ polation between the values listed in Kreith (10).. The evaluation tem­ perature was the bed temperature, T, . b Air Viscosity The air viscosity was calculated for each bed temperature from the following equation which was fit to experimental data (9) : U = (2.45 (Tb-32) + 1538.1) 2.688 x 10"5 ' (20) Pg = Air Viscosity,lb/hr-ft T^ = Bed Temperature, °F Heat Transfer Coefficient THe heat transfer coefficients were calculated using the equation: V V V ’ V 1- V m HF 2 h - Heat Transfer Coefficient, Btu/hr-ft -0F- q = Heat Input Per Tube, . Btu/hr 2 A^ = Unfinned Area of Tube, ft 2 A^ = Finned Area of Tube, ft T^ = Tube Wall Temperature, °F following (21) 51 = Bed Temperature, °F (T-T) = Mean Temperature Difference, °F D MF Particle Nusselt Number Nu = h D P ___ E ' k S Nu = Nusselt Number, Dimensionless “P 9 h = Heat Transfer Coefficient, Btii/hr-ft °F = Particle Diameter, ft 2 . k = Air Thermal Conductivity, Btu/hr-ft °F S Particle Reynolds Number Re = G D P P g Re ' = Particle Reynolds Number, Dimensionless P 9 G = Air Mass Velocity, Ibs/hr-ft 0^ = Particle Diameter, ft Pg = Air Viscosity,Ibs/hr-ft (22) (23) NOMENCLATURE h k k g L N OFD P q,Q R s c Definition Bare Tube Area Cross Sectional Area of Column Area of Fins Total Area Orifice Coefficient Heat Capacity of Solids Particle Diameter Air Mass Velocity Gravitational Constant Heat Transfer Coefficient Thermal Conductivity Thermal Conductivity of Fluidizing Mass Fin Length Number of Fins Particle Nusselt Number Overall Fin Diameter Performance Rate of Heat Transfer Particle Reynolds Number Cross Sectional Area of Orifice Bed Temperature Units Dimensionless BtuZlb-0F Inches Ibs/hr-ft^ ft-lbZhr2-Ib P BtuZhr-ft2-°F BtuZhr-ft-°F BtuZhr-ft-°F Inches Dimensionless Dimensionless Inches Dimensionless BtuZhr Dimensionless 53 - Definition Units T ,T S W Surface or Wall Temperature °F (T-T ) MF Mean Temperature Difference Between Fin and Bed °F V Fin Thickness ft W Fin Width ft Y Expansion Factor Dimensionless 6 Ratio of Orifice Diameter to Pipe Diameter Dimensionless I-E Particle Fraction Dimensionless 0 Average Contact Time hr P1 Density of Fluidizing Mass lb/ft3 Ps Density of Solids lb/ft3 Viscosity of Fluidizing Mass Ib/ft-hr BIBLIOGRAPHY 1. .Perry, R.H., Chemical Engineers' Handbook, 4th Edition, McGraw- . Hill Book Co., New York, 1973. 2. Levenspiel, 0., Chemical Reaction Engineering, John Wiley and Sons Inc., New York, 1963. 3. Mickley, H.S., and D.F. Fairbanks, A.I.Ch.E. Journal,' I, 374(1955) 4. Ziegler, E.N., L.B. Koppel, and W.T. Brazelton, Ind. Eng. Chem. Fundamentals, 3, 324(1964). 5. Genetti, W.E^, and J.G' Knudsen, I. Chem. Eng.. Symp. Series, 30, 147(1968) . , 6. Kunii, D., and 0. Levenspiel, Fluidization Engineering,. John Wiley and Sons, Inc., New York, 1969. 7. Chen, J.C. and J.G. Withers, "An Experimental Study of Heat Trans­ fer from Plain and Finned Tubes in Fluidized Beds", A.I.Ch.E. Paper No. 34, 15th National Heat Transfer Conference, San Francisco(1975). 8. Chen, J.C., "Heat Transfer, to Tubes in Fluidized Beds", A.S.M.E. Paper No. 76-HT-75, 16th National Heat Transfer Conference, St. Louis(1976) . 9. Everly, D.W., M.S. Thesis, Montana State University(1978) . 10. Kreith, F., Principles of Heat Transfer, Intext Press, Inc., New York, 1973.