DRYENG RATES AND HEAT TRANSFER COEFFICIENTS ON A EéEATEDs SURFACE FOR THE DRYING OE SAND Thesis for “we Degree of M. 5. WCHEGRE‘E STATE UREVEESETY David Thomas Retford 1957 ThEbis This is to certify that the thesis entitled DRYING RATES AND HEAT TRANSFER COEFFICIENTS ON A HEATED SURFACE FOR THE DRYING OF SAND presented by David Thomas Retford has been accepted towards fulfillment of the requirements for degree in MASTER OF SCIENCE WWW Major professor Date May 214, 1957 0-169 DRYING RATES AND HEAT TRANSFER COEFFICIENTS ON A HEATED SURFACE FOR THE DRYING OF SAND By DAVID THOMAS RETFORD A THESIS Submitted to the College of'Engineering of Michigan State University of Agriculture and Applied Science in partial fulfillment of the requirements for the degree of MASTER OF SCIENCE Department of Chemical Engineering 1957 I" , z" I 'l'. 7 ." o- k ‘7 (/’ 1/ / é-/5?/5 TABLE OF CONTENTS PAGE ABSTRACT ACTOIOJLEDGTOTJT INTRODUCTION ....................... ...... .............. 1 RISTORI ........ ........ ................................ h APPARATUS AND PROCEDURE 9 DATA 0.......QQQOOOOOOOOOOOOOOOOO 00000 OOOOOOOOOOOOOOOOOO 18 PRESENTATION OP DATA ................................... 35 FulfiBUle ...................00.......0...’............... 56 CGJCHISIOIIS .. O O O O O O O O O I O O O O O C O O .. O O O C C 0 O. . O C 0 O .0 C O O. O O . 62 APPENDHA SM‘TIE CALCULATIOIG .OOOOOOOOOOOOOOOOOOOOOOOOOOOOOO. 63 APPENDIXB NOIVEIJCIATWE 0.0...OOOOOOOOOOOOOOOOOOOOO000......O. 65 RWEIICE OOOOOOOOOOOOOOOOOOO0.0000000000000COOO0...... 66 ACKNOJLEDGMENTS The author expresses his sincere thanks and good wishes to Dr. R. W. Ludt for his excellent guidance and willing assistance in the preparation of this work. Thanks are also due to Dr. C. F. Gurnham for his assistance in procuring equipment and Mr.'w. B. Clippinger in setting up the apparatus. ABSTRACT Drying rates and heat transfer coefficients were correlated for sand dried on a heated surface. Drying was done on a steam heated plate held at a constant surface temperature of 220°F. Three thicknesses of sand; 1-1/2 inch, 1 inch, and 1/2 inch were dried. Moisture content, heat transferred, and sand bed temper- atures were taken as primary data. Heat transfer coefficients and drying rates were calculated from this data. Heat transfer coefficient correlation with drying rate was obtained between 10% and 2% moisture content. The change in heat transfer coefficient appeared to be controlled by the area of wetted surface between 101 and 2 :Z moisture content. Maximum drying rates and heat transfer coefficients were Obtained at a sand thickness of 1/2 inch. / APproved: W7/{fl (149% INTRODUCTION INTRODUCTION Drying is a process that occurs constantly in the world around us. It is a very important process in our everyday life and plays a major role in.most industries. The usual case of drying in.nature is that called air drying (Diagram.l). During air drying, heated air flows across the face of the wet material and supplies heat for vaporization through the air interface. Meisture vapor leaves the bed counter current to the flow of heat. A second type of drying is hot surface drying (Diagram 2). In this case, heat to vaporize the liquid is supplied by the hot surface. Heat and vapor transmission take place in the same direction. Vaporization takes place both at the air interface and hot surface. This type of drying is used extensively in industry since the rate of drying is usually higher than that of air drying. Only recently has much work been performed to determine the mechanism of hot surface drying, although the mechanism of air drying has been quite thoroughly explained. Previous work indicates that hot surface drying gives the same type of drying curves as does air drying. However, care must be exercised in attempting to apply the theories of air drying to hot surface drying because of fundamental differences in heat and mass transfer. Heat and mass flow are counter current during air drying but in the same direction during Heat ‘ Vapor oist Sand Bed 2% Pi T27 8r ' [ :‘l \\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\ Air Drying of a Sand Bed “9°” ' Hoist Sand Bed \\\\\N _ T N\\\\\\ Diagram 2 Hot Surface Drying of a Sand Bed hot surface drying. In these tests sand was selected as the material to be dried so as to lower the number of uncontrolled variables. One advantage is that it is possible to get a relatively constant sand particle size by classification. Another important property is that no moisture is absorbed by the sand particles. The moisture in the sand bed is held only around the particles and in pore spaces between the particles. This type of moisture is called free moisture since it is not chemically or otherwise bound to the material being dried. Purpose and Scope of this Investigation The purpose of this study was to provide information which might be used with other recent work to further explain the mechanism of hot surface drying. It was hoped that the relationship between heat transfer coefficients and drying rates would aid in this explanation. Three sand bed thicknesses; 1-1/2 inch, 1 inch and, 1/2 inch were dried. The hot surface temperature was held at 220‘F during all tests. Moisture content, total heat transferred, and sand bed temperatures were taken as primary data. The data obtained were for the range of 17%'to 2% (dry basis) moisture content. HISTORY HISTORY There was very little data in the literature pertaining to hot surface drying. However, a description of work done on air drying may show relationships which.might be used to explain some part of the mechanism of hot surface drying. Air Drzigg ‘During the early work on air drying one major point of contro- versy arose. This was whether moisture moved through material by diffusion or by some other mechanism. Ceaglske and Hougen (2) showed that moisture flow in granular non-hydroscopic solids such as sand was due mainly to capillary forces. They showed data which indicated movement of moisture from an area of low concentration to an area of high concentration. This movement was not possible considering only diffusion forces. They also cited the work of Haines (S) and his discussion on moisture movement in solids. Haines explanation started with a dry bed of soil or sand. To this was added a small amount of water so that the points of contact of the particles held a small volume of moisture. This was called the pendular stage. Next, more water was added until each particle had a complete film.of moisture around it and the film was continuous through the sand bed. This was called the funicular stage. Finally water was added until all the pore spaces between the particles were filled. This was called the h capillary stage. Ceaglske and Hougen showed that during air drying , these three stages appeared in reverse order as more and more water was vaporized. Ceaglske and Hougen also used the method of Haines to determine suction potential of the sand bed as a function of sand saturation. Suction potential was explained by considering a column of water in a capillary tube. The water would resist movement down the tube until a certain pressure differential existed between the top and the bottom of the tube. The pressure differential necessary to overcome this resistance was called suction potential. Pearse, Oliver and Newitt (ll) gave a general discussion of air drying granular materials and concurred with Ceaglske and Hougen that moisture movement depended mainly on gravitational, capillary, and frictional forces. From this work a general description of air drying was derived: The sand bed.was made up of small particles with void spaces between them. These void spaces connected in a random way to form psuedo capillary tubes extending from the air surface to the bottom of the bed. As moisture was vaporized from the surface of the satur- ated sand bed, the top film in the capillaries started to increase their concavity. As more water was vaporized the surface film in the larger capillaries was broken and air moved in. The water in the large capillaries flowed to the bottom.of the bed due to capillarity. The water then flowed up to the surface through the small capillaries to keep all the particles at the surface wet. Constant rate drying occurred during this time and continued until there was not enough moisture in the capillaries to completely wet the particles at the surface. The first falling rate period commenced at the point called the critical moisture content where the capillaries could not maintain a completely wetted surface. Upon beginning the first falling rate period, vaporization continued to take place at the surface but at a slower rate. Toward the end of this period vaporization started within the sand bed. 'When liquid in the pore spaces and a continuous film of moisture no longer existed vaporization was completely within the bed and the second falling rate period started. This was the pendular stage of drying and lasted to complete dryness. Hot Surface Drying Drying of Prussian blue on heated shelves under vacuum was done by'Ernst, Arden, Schmied and Tiller (3). Ernst, Ridgway and Tiller (b) also dried Sil-O—Cel in the same manner. They found the normal constant rate drying period followed by one of falling rate. They also show that in shelf drying heat is supplied at both the bottom and top of the bed. Other investigators show the same type of curves with limited data. King and Newitt (7) found that when drying glass beads on a A hot surface in a stream of hot air, they had a psuedo constant rate followed by a falling rate period. The psuedo constant rate period had a very gradual constant rate of change. McCready (9) dried paper pulp on a hot surface and reported a constant rate period followed by a first and second falling rate period. Hougen, McCauley and iarshall (6) also worked on drying on a heated surface and introduced another method of moisture movement in a sand.bed, that of vapor condensation. Ludt (8) performed a number of experiments on drying sand of constant size on an electrically heated surface. He found that the usual constant rate period occurred, followed by'a variable rate period. Suction data by Ludt indicated that the large capillaries were emptied between 23% and 11%:moisture, where suction potential was relatively constant. Between 10% and 3% moisture, suction potential increased rapidly. This indicated emptying of the small capillaries. 'When comparing drying rates to these suction potential data Ludt found constant rate drying between 23% and 10% with falling rate commencing between DD% and 6% moisture. The lower plate temperatures gave falling rates starting at 10% moisture content. The higher plate temperatures had a critical moisture content of 6%. Moisture distribution curves showed a constant layer of moisture at the plate surface during constant rate drying. The value of this constant layer moisture was high for low plate temperatures and low for high plate temperatures. He concluded that the high vaporization rate at the high temperatures the vapor probably filled all the large capillaries and permitted liquid to reach the hot surface only through the small capillaries. Frictional forces and vapor flow in these small capillaries restricted the flow of liquid to the hot surface and may have controlled the vaporization rate. Temperature gradients were shown through the sand bed. This along with moisture distribution data showed that vapor was condensing to heat the sand bed. This condensed liquid flowed back to the plate surface as shown by Tambling (12). By using salt solutions Tambling found highest salt concentrations at the hot surface and somewhat lower concentrations at the upper surface. The concentration of salt through the body of the bed was a low value. This indicated that most of the vaporization took place at the hot surface with some vaporization at the air interface. The major part of the water flowed to these points. Bohl (1) commenced the work leading to this study and helped design the equipment. APPARATUS AND PROCEDU RE APPARATUS AND PROCEDURE Apparatus Drying was carried out on a 3/h inch thick by 12-1/2 inch diameter steel plate (Diagram 3). On the underside of this plate a funnel'with upper diameter of 7-1/2 inches was welded. This plate was then welded to a circular steam chest. A pipe was welded to the lower end of the funnel and extended through the bottom of the steam chest. A needle valve was placed on the end of this pipe. The condensate pipe and valve were both well insulated. The interior of the funnel was completely isolated from the rest of the steam chest except for eight L shaped l/h inch steam entry tubes. The tubes were welded to the side of the funnel in such a manner that the portions of the tube on either side of the funnel pointed down. This permitted steam to pass freely through the tube but condensate would not pass from one chamber to the next. The upper surface of the plate had three 1/8 inch deep by l/h inch wide grooves cut in it. These grooves ran radially from the periphery toward the center of the plate (Diagram.h). One groove extended to the center, one to within 2 inches of the center and one to within h inches of the center. No. 20 Copper-Constantan glass served thermocouple wires were placed in these grooves and the hot Junction soldered to the plate at the inner end of the groove. The centers of the hot junctions were approximately 0.05 inch below the surface of the plate. The rest of the thermocouple wire was held in 9 P e Surf ce Thermopguple Drying X Groove Ring \\ r :5: r V I R 7 Inlet Tube :/ Aik é Valve / , Ch ml é ‘ Insulati I F : A / Ill/[[f/v / ' r9 Valve ‘ Funnel . Chest Condensa e 00nd eeeee Legs \\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\ Diagram 3 Schematic Diagram of Steam Heated Drying Plate ‘ § LFJ\)"i '4— Diagran h Surface of Drying Plate ' Thermocouple‘Wire at Plate Surface place in the groove by cured epoxy resin. The lead ends of the thermocouple wires were connected to a switch box and thence to a Leeds and Northrup Portable Precision Potentiometer provided with an ice bath cold junction. Steam was admitted to the well insulated chest from a 15 psig supply line through a needle valve. Steam.pressure in the chest was indicated by a laboratory pressure gauge. Excess steam and chest condensate was drawn out through a pipe connected to the bottom of the chest. This also passed through a needle valve to a condensor. Metal rings of 10-1/2 inch diameter were used on the plate surface to hold the sand in place. Glass tubes of 1.5 cm.diameter were used as sample tubes. The tubes were open on each end. The tubes and rings were the height of the sand bed being investigated. Air tight weighing bottles were used to hold the sample tubes after they were removed from the sand bed. Sand bed temperatures were also indicated by No. 20 Copper- Constantan glass served thermocouples running through the sand bed. The thermocouples were held in place by two parallel strips of micarta (Diagram 5). The thermocouple junctions extended 3/h inch beyond the micarta strip. The wires ran 2 inches through the sand between the strips and then out of the sand bed to the switch box and potentiometer. Procedure Prior to each run the barometric pressure and wet and dry bulb temperature were taken. This data.is not shown.since temperature and humidity of the air seemed to be ineffective. This was also reported by Ludt (8). L 7\ E'ass Rod —+* Micarta Strips 2” in I, f 2 ‘>‘ % 3/11 Thermocouplesvfi *4. «I I R M Top View I ” 34 v...— 4 -—— O “(3‘ 4! II \ l 0 V) .f at]: /Z c l AA l o 4 Front View Diagram 5 Sand Bed Thermocouple Holder 1h The surface of the drying plate was cleaned each time with coarse and then fine emery cloth. The bottom of the 10-1/2 inch sand retainer ring was also cleaned to get a smooth fit. The retainer ring was placed on the plate surface with approx- imately ten sample tubes. These tubes were placed with 2 inches distance between them and at least 1 inch from the retainer ring. Dry Ottawa sand of 140-60 U.S. Standard mesh size with a settled density of 102.6 pounds/ft.3 was then poured carefully in and around the sample tubes so that it was completely level within the ring. The bed was leveled smoothly with a straight edge to the height of the ring. The steam chest was heated by opening the inlet and blow down valves wide. All air trapped in the chest was expelled in this manner. The inlet valve was closed and the steam pressure in the chest allowed to fall to 2 psig. The blow down valve was closed. The sand was thoroughly wetted by carefully pouring distilled water on the sand which had been covered with eight layers of cheese cloth to prevent erosion. The excess water was allowed to drain off and the cheese cloth removed. The steam inlet valve was again opened and the blow down valve cracked slightly. The temperature of the plate surface was checked and the inlet and blow down valves manipulated until the desired surface temperature of 220°F was reached. It was necessary to keep a constant check on the surface temperature during the run and regulate the inlet and'blow down valves accordingly. A record of chest pressure was kept during the run. 15 After the plate surface temperature reached 220°F, accumulated condensate in the funnel was drained off and a timed run started. A sample tube was taken at the beginning of the run end at timed intervals thereafter. Samples were taken by carefully extracting the tube from the bed.with laboratory tongs. The sample tube and sand were immediately placed in a numbered weighing bottle and sealed. Condensate samples were taken at the same time as moisture samples. The condensate was collected by inserting the portion of the pipe extending past the needle valve into a graduated cylinder. The needle valve was then quickly cracked and condensate from the 'funnel collected until steam started to come through. The valve was closed and the level of the liquid in the graduate read. Sand.bed temperatures were taken during separate tests. The plate surface was prepared as before. In addition to the sample tubes, the micarta thermocouple holder and thermocouples were placed on the surface and held in place with a weight. The height above the place to each thermocouple junction was measured and recorded. Sand was added as before, covering the tubes and thermocouples completely. The weight was removed from the thermocouple holder and the sand bed leveled. 'Water was added and a timed run started. No funnel condensate was collected during these runs. Sand.bed temperatures and moisture samples were taken at the end of the same timed interval while holding the plate surface temperature constant. Temperatures for the several runs were correlated by moisture content. The moisture content was determined by use of the sample tubes. 16 The weighing bottles containing the tubes and the sand were weighed wet, and then dried at 105°C for twenty-four hours. Dry weight and tare weight were taken after drying. Moisture content was calculated on dry basis. Apparatus and Procedure Limitations The condensate funnel was designed so as to collect condensate from a 7-1/2 inch diameter area. As the sand bed was centered on the plate during drying this left a l-l/2 inch overlap of the sand on all sides. This was provided so that the condensate collected would represent only heat supplied to the control Surface area of the sand bed. The 3/h inch thick plate used for drying held an appreciable amount of sensible heat. At the critical moisture content the steam pressure in the Chest was lowered to maintain the constant plate surface temperature. The steam side temperature of the plate then fell. This meant that heat left the plate and entered the sand bed. Therefore the amount of condensate collected at the critical.moisture content may not have represented all the heat transferred to the sand bed. This could be eliminated in future work by using a thin plate for the drying surface. As condensate from the funnel was collected there may have been some vaporization of liquid due to the pressure drop through the needle valve. Opposing this was the condensation of live steam at the end of the liquid flow. Both the vaporization and condensation were small. The collection was accomplished quickly and the liquid level immediately read. 17 Temperature measurement was made with an excellent instrument. All the thermocouples ran horizonally or at the same temperature level for several inches through the sand and plate surface. This prevented loss of heat from the hot junction by conduction. All temperatures were recorded to the nearest degree. The tubes for moisture samples were open on both ends. This let the moisture in the tube vaporize as did the whole sand bed. The wet sand stayed inside the tube and left a clean plate surface when withdrawn until only about 2% average moisture was left in the sand. As soon as the weighing bottle was sealed, dry sand was poured back in the hole left by the tube. As the area of each tube was only 0.3L6% of the total sand bed area this caused little variation. Some heat was conducted up the wall of the tube from the plate surface. This may have vaporized a small amount of moisture from the tube. However, glass was used as the material of construction of the tube since it is a relatively poor conductor of heat and made this error small. Run.#l.- 1/2" bed Time- Minutes 0 l CDKIO‘UlC'UJ Run #2 - 1/2n bed O‘U‘LE’U Q Steam Pressure-psig 11.0 9.0 8.0 7.5 5.0 5.0 h.5 h.0 h-0 13.0 12.5 13.0 10.5 8.0 h.5 b.5 h.5 h.0 ml Condensate per Interval 27.8 22.8 19.8 18.5 10.0 h.5 22.8 21.5 18.5 17.5 13.5 3.0 #Water #Dry'sahd 0.1991 0.09h6 0.10ho 0.0958 0.0553 0.0bh3 0.0735 0.0216 0.0535 0.1718 0.1703 0.1532 0.0917 0 .0 512 0.0350 0.0358 0.0199 18 Run #3 - 1/2" bed Time- Minutes 0 1 cos) 0‘U‘LE‘UJ Run.#h - 1/2n bed O\U'l 57' W .Q Steam Pressure-psig 13.0 13.0 13.0 7.0 6.5 6.0 h.5 h.5 b.5 13.5 13.5 11.0 10.0 7.0 6.0 h.5 h.5 3.5 ml Condensate per Interval 2h.5 22.5 18.5 17.5 8.8 3.5 2h.0 20.3 18.7 18.7 13.0 7.5 #Nater #Dry Sand 0.1925 0.1611 0.13h1 0.0681 0.0565 0.0522 0.0396 0.0220 0.0 337 0.1817 0.1719 0.1207 0.1118 0.0805 0.0h01 0.0291 0.0301 0.02h0 l9 Run #5 - 1/2n bed Time- Minutes 0 l CDNO‘UIE‘W Steam Pressure-psig 1h.0 1h.5 15.0 13.0 10.0 7.0 h.5 h.5 h.5 ml Condensate per Interval 28.5 25.2 22.8 18.0 1h.0 7.0 h.0 2.5 20 #Water %Dry Sand 0.161h 0.1h01 0.1387 0.0917 0.0803 0.0h19 . 0.0280 0.01h0 0.0207 21 SH 03 000 000 :00 tom 930.0 0.m m 00m 00m 03 03 0am 08 88.0 0.0 m 08 0G 08 08 08 0E 8S0 0.3 N 08 08 one. 0.8 08 03 003.0 mas H Rn M00 08 08 08 08 03H. 0 0. ma 0 U00. =N\H I Em gm 0: SH 02 Ra RH 09.. 008. 0 0. a 0 m3 :3 03 000 00,0. 00m 300. 0 0.m 0 was 000 000 000 000 a on 030.0 0.0 s 80. 08 08 08 08 03. $8.0 0.0 m s00 0.0m 9m on“ 0.8 03 80.10 0.d N «00 00m 03 03 03 03 some. 0 0.0a a $3.0 gem .0 $3.0 $0.0 320 .000 mean Dam mend seesaw: madam scam ooeopmwa no¢o3% omwmwmmm noeaa m. snowshoesoe son an} .. on use Run #8 - 1“ bed Minutes Run #9 - 1" bed Time- 0 3 6 9 12 15 19 21 2h \OOWO 12 15 18 Steam Pressure-psig 12.0 12.0 10.0 9.0 8.0 7.5 5.0 h.0 h.0 12.0 11.5 10.0 7.0 b.5 b.5 L.0 m1 Condensate per Interval 53.0 38.2 31.5 36.1 27.5 11.0 2.7 h.2 57.8 h7.5 37.8 25.1 7.0 6.5 #Water #Dry'Sand 0.2052 0.1773 0.117177 0.0895 0.0629 0.0h7h 0.027h 0.0277 0.0137 0.1739 0.1201 0.0777 0.0388 0.0275 0.0120 0.0068 22 Run #10 - 1" bed Time- Steam ml Condensate #Water Minutes Pressure-psig per Interval m 0 12.0 0.1317 2 12.0 36.8 0.1025 1. 12.0 317.0 0.0796 6 12.0 317.0 ' 0.0702 8 10.0 31.5 0.01123 9 7.0 0.0308 10 6.5 17.8 0.02147 11 6.0 0.0226 12 5.0 7.1 0.0200 1b 17.5 17.9 0.0180 16 1.. 5 3.2 0.0161 18 14.5 5.1 0.0117 20 h.5 3.9 0.0079 Run #11 - 1" bed 0 11.0 0.2253 2 12.0 1.1.0 0.1601 b 11.0 37.8 0.1156 6 11.0 314.9 0.1098 8 9.0 30.5 0.0831 10 7.5 20.8 0.01491. 12 5.5 21.0 0.0516 11. 5.0 7.8 0.0281; Run #12 - 1” bed Time- Minutes 0 COO\.L_‘I\) 10 12 16 18 20 Run #13 - 1" bed Steam Pressure-psig 11.0 11.0 11.0 11.0 10.8 8.0 5.0 h.5 h.0 h.0 h.0 13.0 13.0 13.0 12.5 12.5 12.5 12.5 7.0 7.0 6.5 ml Condensate per Interval b3.5 h1.6 39.9 35.8 33.5 1h.9 13.7 11.5 3.0 2.9 150 5 #Water RDry Sand 0.226h 0.1628 0.1280 0.0951 0.0865 0.0391 0.0396 0.0178 0.0170 0.0120 0.0119 0.1703 0.157h 0.1330 0.0773 0.0915 0.1169 0.0hh7 0.0685 0.0331 0.0h05 2h Run #111 - 1“ bed Time- Steam ml Condensate #Water Minutes Pressure-psig per Interval W 0 13.0 0.1707 1 13.0 0.1763 2 12.5 39.5 0.1201: 3 12.5 0.1290 h 12.0 35.7 0.1090 5 12.0 0.0881: 6 12.0 3M: 0.0801: 7 11.5 0.0959 8 11.0 33.1 0.07le 9 9.0 0.0515 10 6. 5 22.8 0.0160 Run #15 - 1" bed 0 13.5 0.1886 1 12.5 0.1795 2 12.0 170.8 0.1583 3 12.0 0.1317 b 11.0 38.0 0.0931. 5 11.0 0.0983 6 11.0 35.9 0.1255 7 10.5 0.1016 8 7.0 32.7 0.0568 9 6.0 0.0993 10 6.0 27.8 0.0600 26 a .2. a: mma RH $0” an o.m 3 Ra m? 03 SH 00H 0: m .0 fl oma 08” SH HS 0: SH 0; .04 one e: SH HS and 000 o. 0H 0H 0: a: and 000 00.0. 08 $00. 0 0. we 0 RH and 08 08 03 03 H80. 0 o. S 0 HS. 000 08 03 03 08 mood 0 0. we .1 a: one 08 03 03 02. omme. 0 0.3 N 03 m: one son 08 08 some. 0 0.: o sod . o coo. 0 e8. 0 eam . 0 :90 .30. 0 was... soon mend mosses: opoam o>onm pnmfiom nopwz% omwwmmnm toeae he chopmnomEoe 609 :H I ©H% :sm 27 0mH Noe woe one see one m.: 4H see she mes one med and m.: me man one 50H mes now 000 o.m 0H one 00H ewe now won 00m dmso.0 . m.m 0 one see 000 000 won 0am mH0H.0 m.m o and How odd 0H0 0HN 0H0 soeo.o 0.HH e mes man 000 0am 0am 0H0 omma.o m.Ha N ems ems Asa 00H one 0H0 os0H.0 0.0H 0 eos.o e00.0 eao.0 eHm.o emm.0 =n0.0 meow meow when mosses: opmam o>ono powwow n0903% emwwmmnm loses mo onspmnomeoe pop :H I wa cam Run.#18 - 1 1/2" bed Time- Minutes 0 3 6 9 12 15 18 21 2h 27 30 Run.#19 - 1 1/2" bed 0 3 6 9 12 15 18 21 2h 27 30 Steam Pressure-psig 8.0 8.0 7.5 7.5 7.5 7.5 7.0 5.0 b.0 h.0 h.0 11.0 12.0 13.0 13.0 13.0 10.0 7.0 5.5 5.5 5.5 5.5 ml Condensate per Interval b9.h 55.0 50.9 b9.5 h8.9 35.9 19.0 7.5 5.5 h.9 51.6 h9.7 h8.7 h6.0 31.3 12.8 6.1 2.8 2.8 3.8 #Nater 0.19h5 0.22h9 0.1532 0.1507 0.081h 0.0677 0.0600 0.0305 0.02h5 0.0231 0.0221 0.2121 0.11752 0.1109 0.0673 0.0809 0.0359 0.02h9 0.0h59 0.021h 0.019h 0.0290 28 #Dry Sand Run #20 1 1/2" bed Time- Minutes 0 3 6 9 12 15 18 21 2h 27 Run #21 - 1 1/2" bed 0 1 CURIOU'LE‘W Steam Pressure-psig 11.0 10.0 10.0 10.0 9.0 9.0 9.0 6.0 8.5 h.0 7.5 7.5 7.0 7.0 6.5 6.5 6.5 6.5 6.5 m1 Condensate per Interval 61.0 5h.2 52.5 50.8 h9.5 39.5 25.5 10.0 7.2 62.5 56.0 37.6 #Water 29 #Dry Sand 0.1996 0.1702 0.1503 0.1392 0.090h 0.0701 0.0h09 0.0320 0.0186 0.0171 0.1711 0.2003 0.1680 0.1801 0.1529 0.1819 0.1391 0.1362 Run #22 - 1 1/2" bed Time- Minutes Run #23 - 1 1/2" bed Steam Pressure-psig 10.0 9.0 7.0 6.5 6.5 6.5 6.5 6.5 6.5 ‘ 6.5 10.0 8.0 6.5 6.5 6.5 6.0 6.0 6.0 6.0 6.0 6.0 m1 Condensate per Interval 56.8 h9.2 h5.5 h5.5 37.8 3808 35.5 35.8 #Water #Dry Sand 0.191h 0.2003 0.1717 0.180h 0.1601 0.1b97 0.1b18 0.1311 0.1088 0.1222 0.1995 0.1881 0.1811 0.17hh 0.1758 0.1660 0.1h62 0.1770 0.1391 0.1282 0.1091 30 31 00H 00H 0% 000 000 03 0000. 0 m . 4 mm 02 02 000 SN 08 08 080. 0 0.m 00 02 N? m 00 000 08 08 0000.0 0.m S E 02 08 0H... 08 03 0000. 0 m .m 00 00H 08 08 08 03 03 0S 0. 0 m .0 5 RH 08 08 08 03 90 0000.0 0.5 fl RH 08 0.8 00.... 03 03 8010 0.0 2 03 9N 03 08 08 0: 08a. 0 m é 0 SH 03 03 08 08 08 . 0&1 0 m g m 02 08 08 . 0: 08 08 002.0 m; m 00H «3 08 08 03 05 0mg. 0 m g H .544 :0H.H zmw.o .590 zmmoo ..©0.0 mcmm 55 m mama mmpdcflz 00.me m>op< pnmflmm 592$ 93000.5 I053 80000 mo 35.0.090qu9 000 000.... Nina u 0% Sm 32 03 03 0: SH SH 000 030.0 0.: mm 02 m: 00H RH 000 0.8. 0000.0 0.4 mm «3 :3 RH mom 000 08 080.0 m3 00 42. 03 H00 80 08 03. 0000.0 m5 .3 HS 02 000 000 08 03 090. 0 m .0 S 0: mom 03 08 08 03 030.0 m . 0 0H 00H 03 03 03 08 08 0000.0 0.m ma HS 0H... 08 08 03 08 0&0. 0 m .0 NH 03 03 03 08 03 08 0000.0 mg. m 00H 08 08 03 03 08 0210 m; 0 02 08 03 03 03 03 23.0 m; 0 SH 08 03. 03 08 03. RSO m; N m5 :3 08 . 03 03 08 015. 0 0.0 0 :00; :24 30.0 30.0 :20 _ ..00.0 050 in; 01.80 03:00.1 mpmam m>on< psmamm ump03% mnsmmmum Imsaa. 5.30 he mRSpwthEwe 000 003.” {HA .. m 91* gm Run #26 - Thin Sand Layer - 1/8 inch Water Layer Time- Minutes 0 1 CD -a O\ 01 3? \u \0 10 ll 12 13 Steam Pressure-psig 10.5 10.5 10.0 10.0 10.0 10.0 10.0 10.0 10.0 10.0 10.0 10.0 10.0 10.0 10.0 ml Condensate per Interval 31.5 30.0 29.5 29.5 29.5 29.5 29.5 33 Run #27 - 1/8 inch Water Layer Time- Minutes 10 11 12 13 1b Steam m1 Condensate Pressure-psig per Interval 9.5 9.5 9.5 30.5 10.0 9.5 27.5 9.5 9.0 27.0 9.0 9.0 27.5 9.0 9.0 27.5 9.0 9.0 27.5 9.0 9.0 27-5 Run.#28 - 1/2 inch Saturated Sand 10.5 10.5 10.5 Layer - Plate Temperature 217°F 31 31 31 3h PRESENTA TI 0N OF DATA PRESENTATION OF DATA Five to seven drying tests were used for each sand bed thickness. . The data from each test were plotted on a moisture-time graph.’ The straight line portion of the graph was drawn by determining the slope by the method of least squares. Plots for each bed thickness were then correlated to obtain similar moisture content at zero time. The correlated experimental data for each test were then plotted on a common moisture-time graph for each thickness (Graphs No. 1, 7 and 13). The method of least squares was again used to determine the 810pe of the straight line portion of the graph. The curved portion of the graph was drawn by averaging the points and drawing a smooth curve. A broken line was drawn at the high moisture end of the graph to show an estimated deviation from a straight line representation. The drying rate for each bed thickness was Obtained from the slope of the moisture-time curve. Rates were plotted against moisture content for each thickness ( Graphs No. 2, 8 and 1h). A broken line showed the rate calculated from the estimated portion of the moisture-time curve. Heat transfer coefficients for each run were calculated. They were plotted against moisture content on a common graph for each thickness (Graphs No. 3, 9 and 15). A smooth curve was drawn through the points. The heat necessary for vaporization was calculated by using the rate curve. An estimated heat for vaporization was also calculated 35 36 from the estimated portion of the rate curve. Total heat transferred was calculated from the smooth curve drawn through the heat transfer coefficient plot. These two heat terms were plotted against moisture content for each thickness (Graphs No. b, 10 and 16). Two to four tests were made to determine sand bed temperatures. Bed temperature data were plotted against moisture content (Graphs No. 5, 11 and 17). A second plot of temperature against height above the plate was made for each sand bed thickness from the temperature-moisture graphs (Graphs No. 6, 12 and 18). One plot of the data of Ludt (8) showing layer moisture plotted against height above the plate at 213“F was also shown (Graph No. 19). Heistnre Percentage - Dry Basia Graph No. 1 1/2 inch Sand Bed Moisture Content vs. Time Plate Temperature 220°F 0 L 1 1 1 1, 1 1 1 1 1 I l I 1 I 'F 0 1 2 3 h S 6 7 8 9 10 Time-Minutes 37 Graph No. 2 1/2 inch Sand Bed Drying Rate vs. Moisture Content Plate Temperature 220'F no -- / Estimated 7 T" ea c o 040 c o— Calculated Drying Rate - #Water/Hr.-Ft.2 v1 1 I Q -41- q- 1 1 11 1 _1_ I I I I O 2 h 6 8 10 12 1h 16 18 - 20 Moisture Percentage - Dry Basis and .— —-11— de- Heat Transfer Coefficient - Btu./tir.-I~'t.‘-°F Graph N00 3 1/2 inch Sand Bed 1,100 firs 1,000 db 800.aa. 600 -1. 900 ~~ 1100 -1*- ZOO-— Heat Transfer Coefficient vs. Moisture Content Plate Temperature 220'F I l L J l l l 39 111111 1168101211: Moisture Percentage - Dry Basis 1 16 1 1 18 '41- 1.10 Graph N0. 11 1/2 inch Sand Bed Rest Transferred vs. Moisture Content Plate Temperature 220'F 10,000 -——. 99000 *‘1— / 8,000 _..... / / Heat for Vaporization /0 Estimated Heat Transferred - Btu./Hr.-Ft.‘ .T’ 8 o I 1 o 8 C‘ .7 5,000 ____ 5’ § 1 1 3,000 .1- 2,000 ._... +,‘1‘otal Heat Transferred + ’9/ a / Mo— Heat for Vaporization Calculated ‘— J I l I l I l V i I I 2 h 6 8 10 12 Moisture Percentage - Dr Sand Bed Temperature - degree F L11 Graph N00 5 1/2 inch Sand Bed Sand.Temperature vs. Moisture Content Plate Temperature 220'F 210 --~ // e e\:—-(1) (2) (3) (b) "L“ // . <51 0 ./ \ ' 200 ____(l) (6) ._(2)/0 19o —— - -1... EB ' 180 —e ( 6) Di t Ab Plat m r... < 81:10.32: ° (2) 0.20" -—1 (3) 0025" " (1.) 0.28" (5) 0.36" 160 .1. (6) O-W fir- 159 1 1 1 1 1 1 1 1 1 1 1 0.28681012114161820 Moisture Percentage - Dry Basis Sand Bed Temperature - degree F 112 Graph No. 6 1/2 inch Sand Bed Temperature vs. Height Above Plate Plate Temperature 220'F 210 ....... _ _. 0 0 0 "““‘“-o .‘—“‘~“1}~(2) _..1: 0\ \ (1) 200 --11-— s ‘0) —1_.. 180.... ‘.P' Moisture Content \\3 8 ‘9 170.... (3) 6% (h) 2% 160 .1. 15° 1111111111 0 0.1 0.2 003 00h 0.5 Height Above Plate - Inches h3 Graph No. 7 1 inch Sand Bed Moisture Content vs. Time Plate Temperature 220°F K3 E; 1 1 Moisture Percentage - Dry Basis E3 1 1 L l 1 1 1 1 1 1 1 h 6 8 10 12 lb 16 18 20 Time-Midhtes 10 fl 0‘ Drying Rate - #Water/Hr.qFt.2 =- \n w Graph NOe 8 1 inch Sand Bed Drying Rate vs. Moisture Content Plate Temperature 220'F 1111 ‘1‘ Estimated e’ / e-ik— / ._1_. / / .1- e e e/ a a a 0- Calculated / l l L l l 1 1 1 1 r 1 ‘r 1 1L 1 0 2 h 6 8 10 12 1h 16 18 20 Moisture Percentage - Dry Basis _ ‘. ncav 1‘ «150.364 UWJ‘JULUIIU - DUUO/ ru‘0—r ”0 Graph No. 9 1 inch Send Bed Heat Transfer Coefficient vs. Moisture Content Plate Temperature 220°F 1,000 900 _1. 0 700 __ 600 1100 200.. 100 L l I 1 l l l I l 1" I I 71 I 1 1 1 I la 6 8 10 12 111 16 18 20 Moisture Percentage - Dry Basis 115 Graph No. 10 1 inch Sand Bed Heat Transferred vs. Moisture Content Plate Temperature 220'? b6 10,000 __ 9 000 __ , / Total Heat Transferred 6 8,000 + Q/ N / 337,000 L /° / Heat for Vaporization é " /° /+ Estimated \ ___..—--° /+/ 369000 .._.. /: + +-—-—'-’:/ + +—-Heat for Vaporization 11:1 / Calculated 1°35 ’000 01 + 1. 8 01,000 ____ / 5 . 1. 5.. 1.33.000 -1. :1: 2,000 __ 1,000 __J ~ ‘ O 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1L 0 2 h 6 8 10 12 111 16 18 20 Moisture Percentage - Dry Basis Graph No. 11 1 inch Sand Bed Sand Temperature vs. Moisture Content Plate Temperature 220°F h? 210_ o c 5) 6) F" / 0 \o\ :h) ( .1 (5)8 0 Q 3 200 1.. \0 ( ) 1n '3— 151) 8190 .1“ 1' ° O\o ; .1... (111’ g e 13 .6180 + 0 3(2) 9' l 5 (3) Height Above Plate 2 .1. (1) 0.90" a (2) 0.80" ”170 {o (131; 8.8110" G’\( ) . " 1 51 1" (2 (5) 0.25" o (6) 0.05" n/ 160 + fi— 19) 1 L J 1 J 1 l 1 1 1 1 1 1 1‘ 1 1 o 2 h 8 10 12 111 16 18 20 Moisture Percentage - Dry Basis Sand Bed Temperature - degree F Graph No. 12 1 inch Sand Bed Sand Temperature vs. Height Above Plate Plate Temperature 220°F 210_ fig /1 o O1 C) 200 e 190* \ (2) (3) 180+ 0‘ ( ) l 170., ___ Moisture Content \~(h) (1) 111% (2) 10$ 160—1. (3) 61 (h) 2% —-1— 150 i 1 1 1 1 1 1 1 1 1 1 1 T I I I I T T 1 l 0 ll .2 .3 .h .5 .6 .7 .8 .9 .10 Height Above Plate - Inches Graph No. 13 1-1/2 inch Sand Bed Mbisture Content vs. Time Plate Temperature 220'F h9 Time-Minutes Q E111..- >0 Eli.“ '.. 0 1110.1- g 8 g -1. 0 . §s__ 11' f: 11.1- 8.1- .0 I 1 ' 1 1 1 1L 1 1 1 1 1 1 1 f 7 I I T I I I I I I I I 02116810121111618 20 22 21126 10 Drying Rate - #Water/Hr.qFt.2 to :r 01 c» -0 1'0 Graph No. 1h 1-1/2 inch Sand Bed Drying Rate vs. Moisture Content Plate Temperature 220’F Mbisture Percentage - Dry Basis ...1_ 1,09 $0059“ ‘* 0 / -H // 0&3‘1’6 / 03‘ --1—- 0—0 9 fl .3 o 0— 0 -—e .4- J l 1 1 1 1 1 1 1 1 1 1 o 2 h 6 8 10 12 ll; 16 18 20 Heat Transfer Coefficient - Btu./Hr.-r"t."- .1- (Graph No. 15 l-1/2 inch Sand Bed Heat Transfer Coefficient vs. Moisture Content Plate Temperature 220'F 1,000 -"—' 900 -+— ////9, 800 /° —r_ o /o °C> <3’ 0 0 700 ~1— 0 0% 8—————-8"'””13 o 0 e 900 -- hOO Jr- 0 300 ~P- o 200 1" 100-00 ‘gp 9 O 1 1 1 1 1 1 1 1 1 1 I I I I I I I 1 I I 0 2 h 6 8 10 12 1h 16 18 2O Moisture Percentage - Dry Basis Heat Transxerrea - ncu./nr.-ru. . 52 Graph N00 16 1-1/2 inch Sand Bed Heat Transferred vs. Moisture Content Plate Temperature 220°F 9,000..- Total Heat Transferred 0’ 8,000—»_ / 0 ,Heat for Vaporization /+ Estimated 7 000—- o / : 0/ /+ 6,000-—- /L + " +1 + + +"‘ Heat for Vaporizetion / Calculated /i 5,0001” / h,ooo..._ " 3,000.... 0 2,000.“, 1,000....» f 0 1 I I Al I I I I I I o 2 h 6 g 10 12 1h 16 18 20 Moisture Percentage - Dry Basis Sand Bed Temperature - degree F 53 Graph No. 17 l-l/2 inch Sand Bed Sand Temperature vs. Moisture Content Plate Temperature 220'F 0 0 @— 2,3,IJ,5,6 ‘”-e 0 180-1» 0 \l I e 2 IQF‘ Height Above Plate 1 " 10133" 2 - 1.1 " 1m -b‘ 3 " 0.87" h - 0.70“ 5 - 0.37” qi— 6 - 0005" 160-41‘ 0 I ‘___ l 13) 1 1 1 1 1 1 1 1 di— 1 I I I I I I I O 2 h g 8 10 12 1b 16 18 20 Mbisture Percentage - Dry Basis ' Sand Bed Temperature - Degrees F Graph No. 18 1-1/2 inch Sand Bed Sand Temperature vs. Height Above Plate Plate Temperature 220°F I 1 \> a?” 3» 210'w—0 “s‘\\\\\\9 0 so ox\\\\\\\\\ (9 200 L— ...1._ O 2 e 190 «.— 1 8;} 1_. 180-+- o "L' ‘lbiature Content 1 db; 2 ~10 170-1I- a- 6g -25 ..1& ~1— 0 -" \h 13) l 1 l 1 J 1 1 1 I 1 t l 1 1 I r I l IT I 1 .5 .6 .7 .8 .9 1.0 1.1 1.21.3 1.11 1.5 Height Above Plate - Inches “b ‘— ‘- r-I— Layer Moisture Percentage - Dry Basis Graph NO- 19 55 3/h inch Sand Bed Layer Moisture vs. Height Above Plate Plate Temperature 213‘F Data of Ludt ( 8) 20--‘r-— 18‘“. I / +1 \ + + + \ 16—--+/ / \+ +\*17% 11‘ + I“ /\+\+\ *lSi /////// +\«1373 12""/7I‘ +\ «11% +— / +1. 10.1: ,+ / +/ {9% \ ‘+ / *7! \ ‘ \ + + 8-;\ ‘I'\ +\ + +/ ‘41- \ + / 6.n_. -+-———*"" *Composite Moisture Percentage h—«a— 2-1— 0 1 l l l l I l I J I I I I V I I I I I 0 0.1 0.2 0.3 ~0.I1 0.5 0.6 0.7 0.8 0.9 1.0 -— Height Above Plate - Inches RESULTS RESULTS Drying Rates The. drying rate of the 1/2 inch thick sand bed was the highest of the three sand beds tested. The rate dropped from 6.9 #Water/Hr.- ft.2 to 6.2 #Water/Hr.-ft.2 when increasing the thickness to 1 inch. No drop in rate occurred when increasing the thickness to 1-1/2 inch. The reason for the maximum rate at 1/2 inch thickness of sand cannot be completely explained. A partial explanation of the increase in rate can be given as follows: Considering Diagram No. 2, heat added at any time under the bed was called q. Heat remaining in the bed as sensible heat was qo. Heat leaving as latent heat in the vapor was called L. Heat leaving the sand surface as losses was called ql. At the center of the sand bed lateral heat losses were negligible and by a heat balance q ' q0 + ql + L. The highest value of L would result in the highest drying rate and L ' q - qO - ql. Theoretically if the temperatures of the sand bed were equal to that of the vapor passing through no more heat would be needed to heat the beds and q0 would equal zero. The heat loss at the sand surfaces would be equal because of equal surface temperatures. Therefore for a sand bed heated to the temperature of the vapor or 210°F, the drying rate would depend only on the heat transferred at the hot surface. The 1/2 inch sand bed had a higher amount of heat transferred 56 . 57 at its hot surface and its drying rate was higher than the 1 inch sand bed. Data presented in Graph No. b of the 1/2 inch sand bed at 10% moisture content showed q - 7900 Btu./Hr.-ft.2 and L = 6750 Btu./Hr.—ft2. Data from Graph No. 10 for the 1 inch sand bed at 10% moisture content showed q- 6900 Btu./Hr.-ft2 and L = 6050 Btu./Hr.-ft2. However more complications entered in the comparison since the value of ql or heat loss at the air surface was greater for the 1/2 inch bed. The surface temperature of the 1/2 inch and 1 inch sand beds at 10;;moisture were 209°F and 192°F respectively from Graphs No. S and 11. The mass of the 1 inch sand bed was twice that of the 1/2 inch sand bed and the value of qO for the 1 inch bed may have reached a value of twice that of the 1/2 inch sand bed. The exact value of these heat terms could not be determined. Therefore a complete explanation of the increased drying rate of the 1/2 inch sand bed was not possible. The initial portion of the moisture-time graphs showed deviation from constant rate drying and a smooth curve represented by a broken line was estimated and drawn through the points. This curve indicated that there may have been an initial drying rate in the sand bed which was higher than the constant rate value. Graph No. 19 showed high moisture content at the surface initially, and a decrease in moisture content later. A large amount of moisture was initially available for vaporization. Additional moisture was being supplied by the capillaries. A high vaporization rate would result in a decrease in hot surface moisture content and was shown by the data. Later as moisture for vaporization was supplied only by the capillaries the vaporization rate slowed to a constant value, as shown by the data. Therefore the initial rate of vaporization may have been higher than 58 the later constant rate value. A critical moisture content of 6% was shown for all three sand beds. It was difficult to pin point this value but the data showed a definite rate change near this point. Sand Bed Temperatures The sand bed temperatures were shown in Graphs No. S, 6, ll, 12, 17 and 18. To determine heat transfer coefficients it was necessary to determine the temperature of the sand at the hot surface. These temperatures were determined by extrapolating the temperature-height above plate graphs to zero height. This showed that the temperature of the sand at the plate surface was 210°F for all bed thicknesses during constant and higher rate drying. At very low moisture content the temperature was zoh‘F for the 1/2 inch bed while still 210°F for the other two. Interesting data was obtained from the thermocouple nearest the sand surface. Since the sand was initiallycooled when water was added to saturate the bed it was necessary for the bed to heat up again. The upper thermocouple showed that the temperature of the sand surface rose up to a peak value and remained constant for a short period. The temperature started to fall off sharply at the critical moisture content. This led to a description of the sand bed temperature cycle as follows: The sand.bed was heated by condensing vapor and the temperature increased until one of two situations occurred; either the sand reached the temperature of the condensing vapor or vapor flow started to fall 59 off. ‘When the vapor flow did start to fall the bed temperature fell since heat losses were greater than heat being supplied by the vapor. The 1/2 inch sand bed temperature approached the temperature of the condensing vapor while the 1-1/2 inch sand bed showed a gradual increase in temperature until the critical moisture content was reached. At the critical moisture content the temperature of all three sand beds started to fall. Heat Transfer Coefficients The shapes of the heat transfer coefficient curves for all three beds were similar. The curves also looked like the drying rate curves between 10% and 2% moisture content. A theoretical explanation of the change of the value of the heat transfer coefficient was possible between 10% and 2%:moisture. At 33%.moisture the value of the heat transfer coefficient had reached a relatively constant value. A constant area of wetted hot surface had been reached and no other changes were occurring. The liquid being vaporized from the surface was supplied by the capillaries. At the critical moisture content there was not enough liquid left in the sand bed to maintain the constant liquid flow in the capillaries. The moisture content at the hot surface started to decrease and the wetted area decreased. The heat transfer coefficient started to decrease also. This indicated that the heat transfer coefficient depended on the wetted area. As the liquid flow in the capillaries came to a stop, the moisture content at the plate surface reached zero and the wetted area disappeared. Heat transfer occurred only to the sand particles and air at the hot surface. A low constant value of the heat transfer coefficient at low moisture content could be expected. The data showed that the heat transfer coefficient changed as described. After a high initial value followed by a gradual decrease, a constant value was reached near l0%.moisture. The heat transfer coefficient fell off sharply at the critical moisture content. The data did not show a final constant value since it was not possible to get data at low moisture content. The change in the heat transfer coefficient at higher moisture content cannot be fully explained. That the heat transfer coefficient was not a function of moisture content or wetted area alone was shown by Run 28. Run 28 consisted of a 1/2 inch sand bed kept saturated with water. A heat transfer coefficient was calculated as 870 Btu./Hr.- ft.2-°F. An.extrapolation of Graph 3 to high moisture content gave a value higher than this. This indicated other factors controlling the value of the coefficient between saturation and 10fiimoisture content. One such factor may have been the turbulence at the plate surface at high moisture content. It was seen during a qualitative test of drying in a glass beaker that small caverns were fermed at the drying surface during the early stage of drying. These caverns remained until drying was near completion. As these caverns were formed much moist sand and liquid was swirled around on the glass surface. This turbulence may have reduced the film resistance to heat transfer to such an extent that the high values of the heat transfer coefficients resulted. The time at which these factors no longer controlled the value of the heat transfer coefficient was five minutes after 61 commencing drying for all three sand beds. Quanitative values of the heat transfer coefficientsshowed that the highest initial value was obtained with the 1/2 inch sand bed. The heat transfer coefficients in the other two beds changed in the same manner as did those of the 1/2 inch sand bed but were lower in actual value. Two other special tests, Runs 26 and 27 were made. Run 26 consisted of a saturated 1/8 inch sand layer. Run 2? consisted of a 1/8 inch layer of pure water. Condensate samples were taken as data. Heat transfer coefficients of 580 and ShO Btu./Hr.-ft.2—°F respectively were calculated for the 1/8 inch sand layer and water. The value of the coefficient on a 1/2 inch saturated sand bed was 870 Btu./Hr.- ft.2-°F as shown in Run 28. This showed that the sand increased the heat transfer coefficient in some manner. This phenomena merits further investigation to determine the cause of this increase. The total amount of heat transferred compared to the heat necessary for vaporization in the three thicknesses of sand showed that each bed had about the same efficiency between 10% and 2% moisture content. Comparative values of the efficiencies are as follows: Efficiency Moisture Content 1-1/2 inch bed L inch bed 1/2 inch bed 15% 80%. ' 71% 66% 10% 95% 87% 85% 6% 98% 92% 97% This shows more heat losses with the 1/2 inch sand bed even though its drying rate was higher. CONCLUSIONS l. 2. 3. CONCLUSIONS The heat transfer coefficients correlated very well with the drying rates between 10% and 2% moisture content. The heat transfer coefficients appeared to be controlled by the area of wetted hot surface between 10 z and 2% moisture content. The greatest heat transfer coefficient near 1/2 inch sand thickness. The greatest drying rate was obtained near 1/2 inch sand bed thicknes s . 62 APPENDIX APPENDIX A SAMPLE CALCULATIONS l. Drying Rate The drying rate is expressed as pounds of water evaporated per square foot per hour. It is calculated by multiplying the slope per minute of the moisture content line by 60 and a weight per area factor: R - m.60'Wa For a slope of 0.00812 for the 1-1/2 inch sand bed: R - 0.00812 1/min. (60) min./hr. (12.8262) #Water/Sq.ft. - 6.25 #Water/sthwhr. 2. Heat Transfer Coefficient The heat transfer coefficient is expressed as Btu.'s per hour per square foot per degree Fahrenheit. It is calculated by first calculating the heat transferred per square foot of area by use of the m1 of condensate. The temperature drop is determined by sub- tracting the surface temperature of the sand from the plate surface temperature. The plate temperature is constant at 220°F and the sand temperature at the surface is determined by extrapolating the plot of bed temperatures (Graph 6) to zero height above the plate surface. 03- ml/Q p'H'v Af-l 60 88- (28.5) ml/min. (0.00211) #/me. (9h5.9) Btu./# (60) min./hr. (1/0.306so) 1/ft.2 Qa= 11,13h Btu./'Hr.-rt.2 63 6b This heat all passes through the plate to the sand bed. Q'HAAtorQa-HAt 11,1311 Btu./hr.-ft.2 1/10 degree F - H - 1113.1 Btu./hr.-ft.2- degree F ‘Wa Qa Ml/e APPENDIX B NOMENCLATURE Rate of Vaporization (#Water/ft.2-hr.) Slope of Drying Curve (1/minute) weight Water per square foot of Dry Sand (water/rt?) Amount of Heat Transferred per square foot (Btu./hr.-ft.2) Militers of Condensate per time Interval (ml/minute) Density of water at 212’}? (#water/me) Heat of Vaporization of Steam (Btu./#Water) Area of Condensate Funnel under Plate (ft.2) Film Heat Transfer Coefficient (Btu./hr.-ft.2- degree F) Temperature Drop from Plate to Sand (degree F) Time Interval between Condensate and Moisture Samples 65 REFERENCES REFERENCES l. Bohl, R. W}, M.S. unpublished thesis, Chem. Engr., Mich. State U. (1956). 2. Ceaglske, N. H. and Hougen, O. A., Trans. Am. Inst. Chem. Engrs., 33, 283 (1937). 3. Ernst. R. C., Ardern, D. 13., Schmied, 0. K. and Tiller, F. M., Ind. Eng. Chem., 30, 1119 (1938). 11. Ernst, R. 0., Ridgway, J. 11., and Tiller, F. M., Ind. Eng. Chem., 30, 1122 (1938). S. Haines, W. B., J. Agric. Science, 17, 2611 (1927); 20, 97 (1930). 6. Hougen, O. A., IxIcCauley, H. J., and Marshall, w. R. Jr., Trans. Am. Inst. Chem. Engrs., 36, 183 (19110). 7. King, A. R. and Newitt, D. 11., Trans. Instn. Chem. Engrs., 33, 6h (1955). 8. Ludt, R. W., AIChE Journal, 1957, (to be published). 9. McCreedy, D. W., Paper Trade Journal, 101, 66, September (1935). 10. Oliver, T. R. and Newitt, D. 81., Trans. Instn. Chem. Engrs., 27, 9 (l9h9). ll. Pearse, J. F., Oliver, T. R. and Newitt, D. M. Trans. Instn. Chem. Engrs., 27, l (1989). 12. Tambling, To No, MOS. theSiS, Chemo Engro, MiChe State U. (1953). 66 Date Due 1 ,,-¢‘ . '. . ..‘\.':.§ 11"”‘1 I??? I T‘I 8 ML "1“ | h a.) It? I! Demco-293 T gflfliflmflfir” ”'Tfit'liu‘ljflmflfll’flhfiliimnitfimfin 03142