Bbtechnol. ROQ. IQQI, 7, 267-271
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NOTES Measurement of Heat Transfer Coefficients in Rotating Liquid/ Particulate Systemst Nikolaos G. Stoforod and Richard L. Merson' Department of Food Science and Technology and Department of Agricultural Engineering, University of California, Davis, California 95616
A new method, involving the use of liquid crystals as temperature sensors, was developed t o measure surface temperatures on moving particles. The method involves coating the monitored particles with aqueous solutions of encapsulated liquid crystals and recording the color changes on the particle surface as a function of temperature. Experimentally measured particle surface and liquid temperatures were used t o calculate heat transfer coefficients for water-heated, axially rotating, cylindrical acrylic vessels containing liquid and solid spherical particles. The theoretical analysis associated with calculating the heat transfer coefficients from the experimental data is presented. The method is illustrated by measuring overall (heating medium/container wall/internal liquid) and liquid-particle film heat transfer Coefficients for Teflon spheres in deionized water and aluminum spheres in 1.5 cSt silicone fluid.
Introduction Modeling heat sterilization of canned foods containing liquid/ particulate mixtures in continuousrotary sterilizers (Lenz and Lund, 1978; Lekwauwa and Hayakawa, 1986) requires knowledge of the overall heat transfer coefficient, Uo,between the external heating medium and the internal rotating liquid, and also the liquid-particle film heat transfer coefficient, h,, between the rotating liquid and the particles. Traditionally,for heat transfer coefficient calculations, the temperatures of the internal liquid and the particle surface must both be known. In the past, particle surface temperatures have been measured with thermocouples, for example,by inserting an axially rotating thermocouple diametrically through one of the particles to the opposite surface (Hassan, 1984; Deniston et al., 1987). Questions arise regarding exact thermocouple placement and motion restriction of the monitored particle. Lenz and Lund (1978) used lead spheres to measure particle temperatures, thereby obviating the problem of measuring surface temperatures, since for their system Bi < 0.1. To overcome errors due to particle surface temperature measurements, Stoforos and Merson (1990) presented a method for estimating heat transfer coefficients using experimental data for only internal liquid temperature. A detailed literature review concerning heat transfer coefficient calculations is given by Stoforos (1988). The objective of this work was to develop a method for the determination of the overall and the liquid-particle heat transfer coefficients encountered during thermal processing of liquid/particulate systems. The approach was to obtain particle surface temperatures by using liquid crystals as temperature sensors. Such an approach does ~
~~~~~
Presented in part at the National Meeting of the American Institute of Chemical Engineers, Minneapolis, MN, August 16-19, 1987. 8 Present address: National Food Processors Association, 6363 Clark Ave., Dublin, CA 94568. f
875&7938/91/3007-0267$02.50/0
not impose movement restrictions on the monitored particles. This paper describes the experimental methodology and the theoretical approach to the interpretation of the data in detail and demonstrates the use of the method by calculating heat transfer coefficients for two cases: Teflon spheres in deionized water and aluminum spheres in silicone fluid. Liquid Crystals. Liquid crystals are cholesteric compounds that exhibit the flow properties of a fluid and the optical properties of a crystal. Heating such a compound near ita phase transition temperature causes the crystalline solid to enter an intermediate phase called "mesophase" or "liquid-crystal". It is in this phase that the compound scatters available white light into spectral components. During heating of a black surface coated with liquid crystal material, different colors are reflected at different temperatures. The surface color changes from black to red, yellow, green, blue, violet, and finally back to black. Upon cooling the surface, this order of colors is reversed. Above or below the phase transition temperature, the liquid crystal layer is transparent and only the black background is seen. Phase transitions can occur between -20 and 225 "C depending on the particular liquid crystal. The temperature for color changes can be selected by mixing different liquid crystals (Hallcrest Products, 1987a,b). Liquid crystals readily available commercially are in two forms: raw (or "neat") liquid crystals and encapsulated material for use in water suspensions. For encapsulated liquid crystals, the color changes can take place at temperatures as low as -10 "C and as high as 50 "C. Raw materials can respond at higher temperatures, to about 85 O C . Liquid crystals can pass through the entire visible spectrum in a temperature range as narrow as 1 "C or as broad as 50 "C. The color responses to temperature changes are almost instantaneous; they are visible on surfaces as small as 0.65 mm2, and they can detect temperature differences as small as 0.1 "C. Theory. The system under investigation is a cylindrical
0 1991 American Chemical Society and American Institute of Chemical Engineers
268
Biotechnol. Prog., 1991, Vol. 7,
acrylic container filled with a liquid with dispersed spherical particles, axially rotated in the horizontal position, and suddenly immersed in a constant-temperature heating water bath. In this section, energy balance equations are used to express the heat transfer coefficients as functions of experimentally determined data. Assuming that the interior fluid temperature is uniform, neglecting the energy accumulated in the container walls, and using a lumped parameter approach, an overall energy balance on the container yields
By integrating eq 1with constant physical and thermal properties and uniform initial temperatures for both liquid and particles and by allowing time to approach infinity (( T,(m)) = Tf(a) = Tmu), we obtain
No. 3
In this work an iterative procedure was followed to account for average particle temperatures at t = tf,. For constant heating medium temperature and equal initial fluid and particle temperatures, fluid and particle temperature histories have been presented by Stoforos and Merson (1990). From those equations, expressions for the particle surface temperature, Tps,and for the volume averaged particle temperature, ( T,),were obtained. By use of a one-term approximation to the resulting series solution, an expression for ( T,)as a function of Tpscan be obtained (Stoforos, 1988). At time equal to tf,, this approximation is given by
where
Ah
is the kth root of
(C,+ C, - A2)A cos (A)
+ ((C, - A2)Bi(C,+ C, - A,) sin (A) = 0 (8)
and CIand C2 are defined by
where V, is the volume of the container occupied by both fluid and particles and c is the volume fraction occupied by the particles. If fluid temperatures are accurately measured up to time tf, the only uncertainty associated with eq 2 is due to estimating the term
Apt is the total surface area of the particles and Tpsthe particle surface temperature. For uniform diameter spherical particles, Apt = 3cVc,/Rp, eq 5 integrates to
From eq 7, ( T,(tf,)) can be calculated if Bi is known. An initial estimate of h, (and hence Bi) can be obtained from eq 6 for t = tf,, assuming ( Tp(tfp))= Tps(tfp).By use of this value for h,, a first approximation for ( Tp(tfp))can be obtained from eq 7. This value for the average particle temperature is substituted back into eq 6 to find an improved value for h,. By use of this scheme iteratively, the true value for h, can be obtained. One or two iterations are usually enough for convergence. A caution is necessary concerning the validity of eq 7, the one-term approximation to the series solution. The eigenvalues, Ak, are obtained by solving eq 8. For all but one eigenvalue, the difference between two subsequent eigenvalues approaches ?r. In the region of (C,+ C Z ) ~ / ~ lies an additional eigenvalue. For high thermal diffusivity materials (e.g., aluminum), the value of (C,+ C Z ) ' /is~ close to zero, and the "additional" eigenvalue is the second one. Furthermore, its value is very close to that of the first eigenvalue. For these cases, a two-term approximation to the series solution is needed; the one-term approximation is not valid. Therefore, the proposed procedure for h, calculation is limited to low a, materials. For high a, spheres, h, can be calculated directly from eq 6 for t = tf,, assuming ( Tp(tfp)) = Tps(tfP)which is a good assumption for high a,.
Note that eq 5 defines instantaneous h, values, while for a specific time, t, eq 6 gives an h, value that satisfies the energy balance equations up to that time. The h, values reported in this work are mean values between zero time and t = tf,, the final time for which particle surface temperature data were obtained. Note that, based on the coated liquid crystal layer with the highest temperature sensing range, the heating medium temperature was selected such that Tmu- Tps(tfp)= 2 "C. Average particle temperature data required in eq 6 usually are not available. Hassan (1984) assumed ( T,) = Tpsat the end of heating.
Materials and Methods Liquid Crystals. Aqueous suspensions of encapsulated liquid crystals (Hallcrest Products, Glenview, IL) responding to temperatures between 26 and 50 "Ca t selected temperature ranges of 2 "C were coated onto 2.54-cm Teflon or aluminum spheres as follows. The spheres were spray painted black (400gloss black heat resistance paint, Ace Hardware Corp., Oak Brook, IL), dried, brushed with primer (Tycote, Hallcrest Products, Glenview, IL), dried, brushed with a uniform layer of liquid crystal, dried, and coated with a layer of a different liquid crystal suspension, capable of changing color in a temperature range different from the first layer. As the last step, a film of transparent varnish (Man O'War Gloss Spar Marine Varnish, McClos-
This term can be evaluated by exponentially extrapolating experimental temperature data using a "long time" approximation for t > tf (Stoforos and Merson, 1990) (3) to give
The liquid-particle heat transfer coefficient can be obtained from an energy balance on the particles (5)
Bbtechnol. Rog., 1991, Vol. 7, No. 3
key Varnish Co., Los Angeles, CA) was sprayed over the dry layers to prevent dissolution of the liquid crystals and to minimize breakage of the fragile liquid crystal layers during the heating experiments. Eight temperature ranges were used, with at least two spheres in each range. To calibrate the liquid crystals, the coated spheres were allowed to equilibrate in a water bath and the surface color was compared with standard colors from the Munsell Book of Color (Munsell Color, 1976). Five colors were identified: red, 7.5R 3/8; green, 7.5GY 5/10; blue, 7.5B 2/6; violet, 2.5PB 2/6; and black, 1OY 2/2. The most reliable color, due to its clarity, distinctiveness, and short duration, was the green (7.5GY 5/10). This color had an error of less than f0.3 "C. Red (7.5R 3/8) was the next most reliable color. The average temperatures a t which the spheres were colored red and green for each liquid crystal temperature range are reported by Stoforos (1988). Processing Apparatus. To observe particle color changes, the processing apparatus was constructed of transparent acrylic. The cylindrical container (7.720 cm inside diameter, 10.836 cm inside height) was equivalent to a 303 X 406 metal can in terms of inside dimensions, with 0.8 mm wall and end piece thickness. The ends of the container were specially constructed with flanges to accommodate O-ring seals and a drive belt to rotate the container. Container rotational speed (0-150 rpm) was controlled by a solid-state speed controller (Model 455530, Cole-Parmer, Chicago, IL). A support frame held the rotating container in the horizontal position and submerged in an acrylic heating chamber (33.5 X 33.5 X 67 cm). Well-mixed 50 "C distilled water was circulated to the chamber from a thermostatically controlled heating tank. A 24-gauge Teflon-coated copper-constantan thermocouple was used to monitor the heating medium temperature. Liquid temperature inside the rotating cylinder was measured with a 2.7-cm insulated thermocouple (0. F. Ecklund, Inc., Cape Coral, FL) mounted on the rotational axis through a S-28 rotary contacter (Model OFE, 0. F. Ecklund, Inc.). A data acquisition system (Model 27024, Molytek, Inc., Pittsburgh, PA) was interfaced with a LSI-11 microcomputer (Digital Equipment Corp., Maynard, MA) to store the heating medium and internal liquid temperature data for further analysis. Experimental Procedure. Spheres in the container were covered with deaerated liquid to 0.65 cm vertical headspace, weighed, and equilibrated in a separate water bath to uniform initial temperature of about 20 "C. While the container was in the cold water bath, the axial rotation at the selected rpm was started so that steady-state motion was approached before the container entered the heating chamber. During heating, liquid crystal color changes were observed visually and videotaped (Model DXC-1640, Sony Corp., Japan) for further review. Liquid temperatures were registered at 2-s intervals. The processing time was long enough to approach temperature equilibrium between the rotating fluid and the heating medium (-20 min). Preliminary Experiments. Two preliminary experiments were performed to check the main assumptions in eq 1. First, the uniformity of the fluid and particle surface temperatures was checked for a case where rotation was expected to provide good mixing of the container contents. One hundred thirty five, 1.27 cm diameter, Teflon spheres were processed in deionized water at 100 rpm. Thirty five of these spheres were coated with liquid crystals sensing a t 26-28,30-35,40-42, and 46-48 "C temperature ranges. One coated sphere was fixed at the center of the container. The method of coating these spheres was the same as
209
Table I. Experimental Conditions and Thermal and Physical Properties of the Processed Materials Teflon spheres aluminum spheres in deionized water in 1.5 cSt silicone fluid 994.4 836 1729 4175 2126 2743 1046 896 204.26 0.251 1.13x 10-7 83.1 X 104 0.01286 0.01285 0.3730 0.3175 0.2072 0.2678 0.206 0.204 47.26 X lo4 47.74 x 104 102.2 15.9 ~
described earlier except that four ranges of liquid crystals were applied instead of two, and they were applied in a single layer rather than separately. This was accomplished by mixing equal amounts of the four liquid crystals and then immersing the spheres in the mixture. Since each liquid crystal in the layer was diluted, the resulting colors were not very intense and this technique was not adopted for the principal experiments. The second preliminary experiment tested whether the accumulation of energy in the container walls was negligible. A 1 cm wide stripe of liquid crystal mixture of the four temperature ranges (26-28,30-35,40-42, and 46-48 "C)was painted on both the external and internal container surfaces. The arithmetic average, ( T,), of inner and outer wall temperatures was used to calculate the energy accumulation
for m, = 0.0357 kg being the mass of the container walls and C, = 1464.4J/(kg K)the specificheat of acrylic (Gross, 1969). For this experiment the container was filled with 11 2.54 cm diameter Teflon spheres and deionized water and was processed a t T, = 48.8 "C and 110 rpm. Principal Experiments. Particle surface temperatures were measured for two cases: Teflon spheres (poly(tetrafluorethylene), McMaster-Carr Supply Co., Los Angeles, CA) processed in deionized water and aluminum spheres (Small Parts, Inc., Miami, FL) in silicone fluid (Dow Corning 200 fluid, Dow Corning Corp., Midland, MI) of 1.5 cSt kinematic viscosity at 25 "C. Eleven spheres were processed each time. The experimental conditions, together with the physical and thermal properties of the liquids and particles, are summarized in Table I. Fluid properties (pf, C,f) were evaluated at 34 "C, the average of the initial and final bulk fluid temperatures. Properties for deionized water were obtained from Heldman and Singh (19811, while values for silicone fluid properties were those suggested by the supplier (Dow). Values of specific heat, Cpp,and thermal conductivity, k,, of liquid crystal coated particles were assumed to be the literature values given by Hassan (1984) for the same, but uncoated, particles. The density of the coated particles (p,) was obtained by measuring the volume of water displaced by weighed spheres. Thermal diffusivity values were calculated as a, = kp/ppCpp. Weighing fluid and particles allowed calculation of e and V,. An average value for the radius (R,) of the liquid crystal coated particles was obtained with a micrometer.
Results and Discussion Preliminary Experiments. In the preliminary experiment using the 1.27 cm diameter Teflon spheres in
Biotechnol. h g , , 1991, Vol. 7, No. 3
270 50
..... ....... ........... wA.0
m.4
.........................
.............................
I*.. &...fi...I*
% .
m -0
. A 0
-
Fluid. 8xp8rlmantai Fluid, thooretlcsl Particles, theoralical Container wail, experimental
Heating medium Outalde Well Inalde wall Internal lluld
. . . . . . . . . . . . . . . . . . . . . . 0
200
400
600
800
1000
0
200
400
TIME (sac)
Figure 1. Experimental time-temperature profiles for the outside and inside container wall, heating medium, and fluid for Teflon spheres in deionized water at 110 rpm.
water, the same color was observed on the surfaces of all particles except those touching the container walls. The latter changed color sooner than the spheres away from the wall, corresponding to approximately 1"C higher temperature. Temperature uniformity of particle surfaces was also observed in the principal experiments with fewer larger particles. This supports the assumption that the rotating fluid temperature can be uniform and that all particles can be at the same-temperature. However, this result should not be extrapolated to different conditions without experimental verification. Results referring to the second preliminary experiment are presented in Figure 1,where temperatures of heating medium, outside and inside container wall, and inside fluid are plotted as functions of time. The outside wall temperature rapidly equilibrated with the heating medium temperature, while the inside fluid temperature (on the axis of rotation) lagged behind the interior wall temperature. By use of the temperature data in Figure 1,the energy accumulated in the walls of the container and in the fluid were calculated as a function of time from expression 11 and the first term of the right-hand side of eq 1, respectively. Derivatives appearing in these expressions were numerically evaluated a t the mean time of adjacent temperature data. Experimental energy accumulation rates for the inside fluid and the container walls are presented in Figure 2 along with energy accumulation rates for the fluid and for the Teflon spheres calculated from theoretical temperature data. The analytical solutions presented by Stoforos and Merson (1990) were used to predict fluid and average particle temperatures. These equations were used with Tmu= 48.8 "C, Tfi = Tpi = 20.5 "C,and valuesof the heat transfer coefficients (U, = 197.0 W/(m2 K) and Bi = 119.2) obtained from experimental results for Teflon spheres in deionized water presented later in this section (Table 11). Vertical scattering of the experimental energy accumulation rates for the fluid reflects theO.l "Cresolution of the fluid temperature data. Figure 2 shows that the energy received by the container walls is negligible compared to the accumulation of energy in the fluid and the particles. Hence, eq 1, widely used for metal cans, also holds for the acrylic container used in these experiments. Heat Transfer Coefficients, Experimental temperature data for aluminum spheres in silicone fluid are presented in Figure 3. These data were used in eqs 2 and 6 with ( Tp(tfp) ) = Tpr(tfp) to calculate overall and liquidparticle film heat transfer coefficients (Table 11). As described above, data for Teflon spheres and deionized
800
600
1000
TIME (sec)
Figure 2. Accumulation of energy in the container walls and the processed fluid and particles for Teflon spheres in deionized water at 100 rpm.
' f 20
W I-
A
15
-
I
0
.
.
'
I
200
"
'
, . . . 400
I
"
'
600
I
800
"
'
,
1000
TIME (sec)
Figure 3. Experimental time-temperature profilesfor aluminum spheres in 1.5 cSt silicone fluid at 15.9 rpm.
water were used iteratively in eq 6 to yield the h, values in Table 11 for that system. With an alternative approach, heat transfer coefficients can also be calculated from the experimental temperature data by minimizing the error sum of squares of the differences between predicted and experimental fluid and particle temperature data
Values in Table I1were obtained by systematically varying U, and Bi in the calculation of predicted data, and the (U,, Bi) pair resulting in the minimum SSE was selected as the pair best fitting the experimental data. Predicted values were obtained from the analytical solutions given by Stoforos and Merson (1990). The parameter w appearing in eq 12 is a weighting factor defined as w = ( N ,- l)/(Np- 1)
(13)
which gives equal importance to the two series in eq 12, with Nf and Npbeing the total number of experimental fluid and particle surface temperature data, respectively, used with eq 12. Heat transfer coefficients obtained by using eqs 2 and 6 are in good agreement with those from eq 12. Minor differences are attributed to assumptions in deriving the analytical solutions, evaluation of the integral in eq 6 from limited TpBdata, or possible temperature effects on h,.
27 1
Bbtechml. Rog., 1991, Vol. 7, No. 3
Table 11. Heat Transfer Coefficients for Teflon Spheres in Deionized Water at 102.2 rpm and Aluminum Spheres in 1.5 cSt Silicone Fluid at 16.9 rpm aluminum spheres in Teflon spheres in calcudeionized water 1.5 cSt silicone fluid lation U,,W/ hp,W/ uo,WJ h,, WJ method ( m Z K ) Bi (mZK) ( m 2 K ) Bi (mZK) eqs 2 197.0 119.2 2326.2 115.1 0.0160 254.0 and 6 eq 12
187.4
138.0
2693.3
108.6
0.0184
292.5
Summary and Conclusions By use of experimental fluid and particle surface temperature data, overall and liquid-particle film heat transfer coefficients were calculated for a water-heated, axially rotating, thin-walled acrylic cylindrical vessel containing liquid and solid particles. Experimental particle surface temperatures were obtained by using liquid crystals as temperature sensors. Calculations of heat transfer coefficients from experimental data can require average particle temperatures at the end of heating. These data are not usually available. A method for obtaining these data for low thermal diffusivity particles was presented. Two cases were illustrated: Teflon spheres in deionized water processed at 102.2 rpm and aluminum spheres in silicone fluid (1.5 cSt) at 15.9 rpm. For Teflon spheres in water, the overall heat transfer coefficient, Uo (water/ plastic/water), was 197.0 W/(m2 K) while the liquidparticle film heat transfer coefficient, h,, was 2326.2 W/(m2 K). For aluminum in silicone fluid, U, and h, were 115.1 and 254.0 W/ (m2 K), respectively. The experimentally obtained heat transfer coefficients were based on fluid temperature at the centerline of the container. The use of liquid crystals to measure temperature histories on moving surfaces seems very promising. Further experiments are suggested to observe the effects of thermophysical properties and processing conditions on the heat transfer coefficients in rotating liquid/particulate food systems.
Notation total inside can surface area, m2 total particle surface area, m2 regression coefficients from eq 3, dimensionless Biot number, Bi = hpRp/kp,dimensionless specific heat of container, J/(kg K) specific heat of liquid, J/(kg K) specific heat of particle, J/(kg K) coefficients given by eqs 9 and 10, dimensionless liquid-particle f i i heat transfer coefficient,W / (m2
K) thermal conductivity of particle, W/(m K) mass of container, kg mass of fluid, kg mass of particles, kg can rotational speed, revolutions per minute number of experimental fluid temperature data used in eq 13,dimensionless number of experimental particle surface temperature data used in eq 13,dimensionless particle radius, m error sum of squares of the difference between predicted and experimental values average container wall temperature, OC fluid temperature, OC initial fluid temperature, "C heating medium temperature, "C
ultimate heating medium temperature, after the come-up time, "C average particle temperature, O C initial particle temperature, O C particle surface temperature, O C heating time, s time at the end of heating, s final time at which experimental particle surface temperature data are obtained, s overall (heating medium/container wall/internal liquid) heat transfer coefficient, W/(m*K) effective can volume, m3 weighting factor appearing in eq 12,defined by eq 13, dimensionless Greek Letters thermal diffusivity of particle, ap= kp/ppCpp,m2/s aP t volume fraction occupied by the particles, dimensionless e heating time, 8 = apt/Rp2,dimensionless kth eigenvalue, given by eq 8, dimensionless xk Pf fluid density, kg/m3 PP particle density, kg/m3
Acknowledgment We thank Professor J. W. Baughn for suggesting liquid crystals and A. Wilson, G. Anderson, D. Lewis, M. Cummings, W. Felver, and L. Rasser for technical assistance.
Literature Cited Deniston, M. F.;Hassan, B. H.; Merson, R. L. Heat transfer coefficients to liquids with food particles in axially rotating cans. J. Food Sci. 1987, 52 (4), 962. Gross, S., Ed. 1969-1970 Modern Plastics Encyclopedia; McGraw-Hill, Inc.: New York, 1969;Vol. 46,No. 10A. Hallcrest Products. Welcome t o the world of liquid crystals, Glenview, IL, 1987a. Hallcrest Products. Thermochromic liquid crystals, Glenview, IL, 198713. Hassan,B. H. Heat Transfer CoefficientsforParticles inLipuid in Axially Rotating Cans. Ph.D. Thesis, University of California, Davis, CA, 1984. Heldman,D. R.; Singh, R. P. Food ProcessEngineering, 2nd ed.; AVI Publishing Co., Inc.: Westport, CT, 1981. Lekwauwa, A. N.; Hayakawa, K. Computerized model for the prediction of thermal responses of packaged solid-liquidfood mixture undergoing thermal processes. J.Food Sci. 1986,51 (4), 1042.
Lenz, M. K.; Lund, D. B. The lethality-Fourier number method. Heating rate variations and lethality confidence intervals for forced-convectionheated foods in containers. J.Food Process Eng. 1978, 2, 227. Munsell Color Munsell Book of Color; Macbeth Division of Kollmorgen Corp.: Baltimore, MD, 1976. Stoforos,N. G. Heat Transferin Axially RotatingCanned Liquid/ Particulate Food Systems. Ph.D. Thesis, University of California, Davis, CA, 1988. Stoforos,N. G.; Merson,R. L. Estimatingheat transfercoefficients in liquid/particulate canned foods using only liquid temperature data. J. Food Sci. 1990,55 (2),478. Accepted April 15, 1991.
