Thermal Conductivity, Heat Capacity and Moisture ...

Thermal Conductivity,

Heat Capacity and Moisture Isotherm

of Ocean Perch at Different

Moisture Levels and Temperatures

Murat O. Balaban

George M. Pigott

ABSTRACT. Thermal conductivity (W 1m K) of ocean perch (Sebastes Marinus) was measured by the heated thermocouple method (moisture M 47%-76% wet basis (wb), temperature T 20-80°C). The equa tion k = 0.268 + 1.97 10-0 3 T + 3.41 10-0 3 M was fitted to the data. Heat capacity (J/kg K) was measured by direct water immer sion (M range 21 % -77% wb, T range 23 - 80°C). The fitted equa tion was Cp = 2128.7 - 13.6 T + 23.7 M. Moisture isotherm was measured with a relative humidity probe (M range 14% - 77% wb, T range 28 - 39°C). The fitted equation WIIS: lu(a w) = [l1M 2 9.501 10-5] 1[-4.6291 10- 3 - 1.3101 10"4 T]. These equations could be used as estimations of the above properties for Jean fish in these moisture and temperature ranges.

INTRODUCTION

Quantitative analysis of heating and cooling in seafood process ing operations requires an accurate knowledge of the therrnophysical properties such as thermal conductivity (k) and heat capacity (Cp). Murat O. Balaban, Assoc. Professor of Food Engineering. Food Science and Human Nutrition Department, FSHN 341. University of Florida, Gainesville, FL 32611. George M. Pigott. Professor, and Director of the Institute for Food Science and Technology. HF-IO. University of Washington, Seattle. WA 98195. Partial financial support for this study was provided by O.E.C.D. and by the Egtvedt fund. Journal of Aquatic Food Product Technology. Vol. 1(2) 1992 © 1992 by The Haworth Press, Inc. All rights reserved.

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JOURNAL OF AQUATIC FOOD PRODUCT TECHNOLOGY

Moisture isotherms are important in many mass transfer operations such as drying and smoking. Thermal conductivity can be measured by either a steady state, or a non-steady state method (Annama and Rao, 1974). Extensive analy sis, advantages and disadvantages of both methods can be found in the book by Mohsenin (1980). The advantage of the non-steady state measurement is its speed (10 sec per experiment) and simplicity (ex perimental conditions such as constant heat flux, constant temper ature, etc. are not needed). Sweat and Haugh (1974), and Sweat (1975) discussed the manufacture and use of the thermal conductivity probe. Annama and Rao (1974) studied the thermal conductivity and diffusivity of fresh and dry fish. Dickerson (1977) discussed the rela tionship between water content and enthalpy, specific heat and ther mal conductivity of foods. Jason and Long (1955) reported the thermal conductivity of fish. Thermal conductivity data in the lit erature are generally reported as either a function of temperature (T), or as a function of moisture content (M). Data including both variables are rare in the seafood area. Experimental methods for the measurement of heat capacity of foods are extensively discussed by Mohsenin (1980). Heat capacity of fish is reported by Jason and Long (1955). Hwang and Hayakawa (1979) described a specific heat calorimeter for foods. Specific heat is also generally reported either as a function of T, or that of M, but not both in the case of seafood. There are a number of studies on the measurement and analysis of food moisture isotherms in the literature. Boquet et aI. (1978), Chirife and Iglesias (1977, 1978), Iglesias (1977), and Iglesias and Chirife (1976, 1982) reported various moisture isotherm equations that could apply to foods. They studied two, three and four parameter models. The dependence of aw on T is not reflected in the majority of isotherm equations. In food processing operations such as cooking and drying, both M and T change simultaneously. Therefore, k, Cp and aw should be determined as functions of both M and T for a better prediction of operations by mathematical models that use them. No date could be found relating these properties to both M and T for ocean perch. The objective of this study was to determine: (l) Thermal conducti vity, heat capacity, and aw-moisutre content relation of ocean perch

Peer Reviewed Papers

59

(Sebastes Marinus) as a function of T and M (2) to find empirical equations and fit parameters to these by using experimental data.

MATERIALS AND METHODS Ocean perch was purchased from a local commercial outlet and was kept on ice for two days after catching. Upon arrival to the laboratory, fish were filleted, skinned, and placed in a - 30°C room after being individually vacuum packed.

Thermal Conductivity Measurement The thermal conductivity probe used in this study incorporated both a heating element and a thermocouple inserted into a hypoder mic needle. The probe was obtained from Dr. Vince Sweat of Texas A&M University, and calibrated by glycerol. The calibration factor was used to correct for the final thermal conductivity values. The heating element was connected to a constant voltage DC circuit in cluding a variable resistor and an ammeter. These allowed for the current and voltage to be monitored during the experiment. The probe would be inserted into the sample at a constant initial temperature, and the heating circuit would be turned on for 10 sec. The heat generated would be dissipated depending on the magnitude of ther mal conductivity of the sample. The chromel-constantan thermo couple having one end in the reference temperature (Dewar flask with ice-water slush) would measure the temperature increase with time. Experimental set-up is given by Balaban (1984), and shown in Figure 1. The signal from the chromel-constantan thermocouple was amplified with a Sigma Omni I thermocouple amplifier (Sigma, Stamford, CT), and fed to a strip-chart recorder. Ln(time) vs. T of probe was plotted for each sample. Straight lines were fitted to the data, and slopes of the resulting lines were used in the calculation of k, as given by Stalhane and Pyk (1931): (1)

k

0

C

FIGURE 1. Experimental set up for the thermal conductivity measurement by the heated thermocouple method : Signal lines; -.-.-.- : Thermocouple lines; - - - - : Heating circuitry lines . ..............

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E Q)

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LU

i i : ii c.&-!

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Ammeter

F'rCltJ"


61

All terms and their units are given in the Nomenclature. Twelve fish samples were taken from the - 30°C room and equilibrated to 25°C in jars. Initial moisture contents were deter mined by the oven method (AOAC, 14.084, 1980). Samples were separated into 4 batches of 3 samples. Each batch was dried to a given moisture content by monitoring sample weights, placed in jars, and equilibrated to 25, 40, 60 and 75°C in different ovens. The thermal conductivity probe was inserted into the geometrical center of each sample while still in the jar. Initial T was recorded, and the probe was heated for approximately 10 sec. The temperature rise in the probe was recorded vs. time (t). After all the samples in a batch were processed, they were moved to another oven and the experiment repeated at a different T. Ninety six sets of data were collected. For the 60 and 75°C experiments and samples with moisture levels above 66% w.b., there was drip loss due to high T. The drip was quantitatively collected for each sample and oven dried to calculate the solids and water lost from the sample by drip. Moisture contents of these samples were corrected accordingly.

Heat Capacity Measurement Mohsenin (1980) discusses methods of heat capacity measurement by using equipment such as comparison calorimeter, adiabatic agricultural calorimeter, and differential scanning calorimeter. Direct water immersion method, also called the method of mixtures by Mohsenin (1980), was chosen because of its simplicity and speed. This method assumes negligible heat loss to the surroundings during the experiment, and negligible heat of solution of the food in water. The first assumption was confirmed by preliminary experiments by monitoring the temperature of water placed in the Dewar flask for a 3 hr period. The initial temperatures of this water were chosen as the extremes of the temperature range used in the study. The max imum change in temperature was less than 0.3°C. All the experiments were concluded within this time period. The second approximation is valid for muscle tissue. A sample of known weight M, and of known initial temperature T, was immersed in water of weight M, in a Dewar flask (Fisher,

62


Pittsburgh, PA). The flask and the water were initially at temperature T i- The final temperature of the system after the sample was add ed was T r. Heat capacity Cp of the sample was calculated as:

Mil' 4186.8

+ (M

u,

CP)calorime,,,

(2)

The value of (M Cp)calorimctcr was found from another experiment. The calorimeter was equilibrated to an initial temperature Te • A known amount M, of water at temperature T w was added to the calorimeter and allowed to equilibrate. The final temperature T, of the system was recorded. From the heat balance, one can calculate (M CP)ealori,neter as:

(3)

The apparatus for the experimental measurement of heat capacity was the same set-up described above for thermal conductivity, but without the heating loop. Details of the experimental procedure are given by Balaban (1984). Fifteen fish samples were taken from the - 30°C room. Their moisture content was determined by the oven method (AOAC, 14.084, 1980). They were dried to different final moisture levels ranging from 77 % to 21 % wb. Final weights were recorded. Samples were equilibrated in jars placed in different ovens to four different temperatures: 20,40,60 and 80°C. The calorimeter was equilibrated with a measured amount of water for 20 min (time required for the temperature vs. time curve to become completely horizontal). The thermocouple was inserted into the sample, and the initial T recorded. The sample with the thermocouple was immersed in the water in the calorimeter. Thermal equilibration was allowed. The final temperature T, was recorded.

Isotherm Measurement Water activity was measured with a relative humidity instrument from YSI (Yellow Springs, OH) consisting of a probe, a thermistor


63

to measure experimental temperature, and associated circuitry. Equilibration time of the probe was given in the manual as 30 min. The instrument was calibrated and equilibration time confirmed with the following saturated salt solutions at 2°C: LiCI, MgCI 2 , K2C03 , NaN03, NaCzH30Z.3HzO, (NH4)zS04' KZS04. The a w values of the saturated salt solutions were taken from Kaymont Corp. (P.O. Box 348, Huntington Sta., N.Y. 11746). Five fish samples of approx imately the same size (ca. 5 g) were taken from the -30°C room, allowed to thaw and weighed. Except for the first sample, all were dried to different final moisture contents ranging from 77 to 14% wb, and placed in jars. Circular holes were cut into lids of jars, and rubber stoppers were fitted to the holes. The wires of the probe and the thermistor were passed through the rubber stopper. The outer opening of that hole was sealed with silicone jelly to stop gas ex change. All five jars were placed in ovens at 28, 36 or 39°C, and the a, and T measurements were obtained for that temperature, the jars were moved to another oven at a different temperature. Equilibra tion was allowed for 6 hr for thermal and moisture equilibrium. The same procedure was applied. After all the a, measurements were recorded, the moisture content of each sample was measured with the oven method (AOAC, 14.084, 1980).

RESULTS AND DISCUSSION The proximate composition of ocean perch is given by Considine and Considine (1982) as: 78% water, 19% protein, 1.5% fat, 1.1 % ash.

Thermal Conductivity Measurement The T vs. t data, slopes and intercepts of fitted lines to T vs. In(t), and calculated k values for all 96 sets of experiments are not given here due to space restrictions. Experimental k values were plotted against initial T values, with M as parameter (Figure 2). The inter cepts of these lines were plotted against M ranges of the data. A linear relation was observed. Based on this, an empirical equation for k as a linear function of M and T was proposed. Multiple linear

0

~

FIGURE 2. Measured thermal conductivity values at different temperatures and moisture contents.

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65

regression was used to fit the date to the equation (Table I). The inclusion of both T and M into the regression resulted in a closer agreement between experimental and calculated k values. The final equation is:

k

= 0.268 +

1.97 10-3 T

+ 3.41

10-3 M

(4)

The average difference between thermal conductivities predicted by this equation and the experimental values was 0.9 %, with a range of 3% to 0.005%. It is reported that above freezing temperatures, k increases with M and T (Mohsenin, 1980). This is in agreement with the results of the present study. In the absence of any experimen tal data, the equation above would be a good starting point for the estimation of the thermal conductivity oflean fish (fat content around I %) in the experimental temperature and moisture content ranges given. For example, Jason and Long (1955) give the k value of cod (fat content 1.2%) at 1°C as 0.545 watts/m-v'K. Assuming 80% moisture content, Equation 4 estimates the thermal conductivity as 0.543 watts/m - "K. If the temperature is lower, but above freezing, the equation could still be used to estimate k. However, freezing will drastically increase thermal conductivity, and Equation 5 should not be used in this case.

Heat Capacity Measurement Based on the immersion experiment data, the Cp values of ocean perch at different T and M values were calculated (Table 2). Multiple linear regression analysis was applied to data (Table 3). The inclusion of both T and M into the regression resulted in a closer agreement of experimental and calculated Cp values. The data were fitted to the empirical equation: Cp = 2128.7 - 13.6 T

+ 23.7

M

(5)

The Cp of fresh ocean perch is given as 3516.91 J/kg K at 80% moisture (Mohsenin, 1980). Using eqn. 5, the calculated Cp of ocean perch at 80% moisture and at 35°C is 3549.4 J/kg K. The temperature effect on Cp is negative in the equation. This

0.. 0..

TABLE 1. Statistical analysis for thermal conductivity as a function oftemperature and moisture content.

Multiple Regression Analysis

Constant T °c M

Estimate

95% Confidence Limits Lower Upper

Standard Error

t Value

Value

0.26819 0.00197 0.00341

0.25416 0.00187 0.00322

0.007 5 5.1 109.5 10-5

37.9 38.6 35.9

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---

15 20 Wet basis moisture, % (c)

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25

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25


73

BIBLIOGRAPHY Annama, T., and Rao, C. V. N. 1974. Studies on thermal diffusivity and conduc tivity of fresh and dry fish. Fishery Tech. 11(1):28. Association of Official Analytical Chemists (AOAC). IORO. Official Methods of Analysis. Washington, D.C. Balaban, M. 1984. Mathematical model of air drying applied to fish. Ph.D. Disser tation. University of Washington. Seattle. Boquet, R. t Chirife, J. and Iglesias, H. A. 1978. Equation for fitting water sorp tion isotherms of foods. II. Evaluation of various two-parameter models. Food Techn. 13:319. Chirife, J. and Iglesias, H. A. 1977. Some characteristics of the heat of water vapor sorption in dried foodstuffs. Food Techn. 12(6):605 Chirife, J. and Iglesias, H.A. 1978. Equations for fitting water sorption isotherms of foods: Part I.: A review. Food Techn. 13:159. Considine, n.M. and Considine, G.D. 1982. Food and food production en cyclopedia. Van Nostrand Reinhold Co. New York. Dickerson, R. W. Jr. 1977. Relationships between water content, enthalpy, specific heat and thermal conductivity of foods. ASHRAE Transactions. 83(1):525. Hwang, M.P. and Hayakawa, K.I. 1979. A specific heat calorimeter for foods. J. Food Sci. 44(2):435. Iglesias, H.A. 1977. Effect of fat content on the vapor sorption isotherm of air dried, minced bccf. Lebensmittel Wissenschaft and Technologie. 10(3): 151. Iglesias, H.A. and Chirife, J. 1976. Prediction of the effect of temperature on water sorption isotherms of food materials. Food Techn. II: 109. Iglesias, H.A. and Chirife, J. 1982. Handbook offood isotherms: Water sorption parameters for food and food components. Academic Press. New York. Jason, A.C. and Long, R. A. K. 1955. The specific heat and thermal conductivity of fish muscle. Proc. 9th II/t. Confer. Refrig, 1:2160. Mohsenin, N. N. 1980. Thermal properties of foods ami agricultural materials. Gordon and Breach Science Publishers. New York. Short, B.E. and Staph, H.E. 1951. The energy content of foods. Ice and Refrig. 121(11):23. Stalhanc, B., and Pyk, S. 1931. New methods for determining the coefficient of thermal conductivity. Tek- Tidskr. 61 :328. Sweat, V.E. and Haugh, C.C. 1974. A thermal conductivity probe for small food samples. Transactions of the ASAE. 17(1):56. Sweat, V. E. 1975. Modeling the thcnnal conductivity of meals. Transactions of the ASAE. 18(3): 564.

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APPENDIX

NOMENCLATURE A,B,C empirical parameters a,b,c empirical parameters Cp heat capacity, J/kg K I

electrical current intensity, amp. 0.2 amps in this study.

k

thermal conductivity, W/m K

M percent wet basis moisture content (M Cp)c.lorlmeter : product of weight and heat capacity of the calorimeter,

J/K

Mp sample weight, kg Mw weight of water, kg

Q heat input per foot of the line heat source, W/m R electrical resistance, ohms/m. 214.9 ohms/m in this study, given by the manufacturer of the probe. PI

3.14159, dimensionless.

T

temperature, C

TI

initial temperature, C

T2 final temperature, C Tc

temperature of calorimeter, C

Tf

final temperature of mixture, C

Tp

initial temperature of the sample, C

Tw temperature of water, C

t

time, sec

tl

initial time, sec

t 2 final time, sec