Biblid: 1450-5029 (2009) 13; 3; p.274-279 UDK: 591.133.1:544.032.4 Original scientific paper Originalni naučni rad THERMAL CONDUCTIVITY AND THERMAL DIFFUSIVITY VALUES OF FOODS VREDNOSTI KOEFICIJENATA PROVOĐENJA TOPLOTE I TEMPERATURNE PROVODNOSTI HRANE Dr. Monika BOŽIKOVÁ University of Agriculture in Nitra, Faculty of Engineering, Department of Physics, Tr. A. Hlinku 2, 949 76, Nitra, Slovakia, e-mail: Monika.Bozikova@uniag.sk ABSTRACT For food industry it is very important to preserve high quality during processing from biological materials to final food products. Processing and manipulation with biological materials have significant influence on their physical characteristics. The values of physical parameters and development of physical characteristics can determine the condition of biological materials. Food industry engineers need to know mainly mechanical and thermophysical parameters because these are changed continuously during processing and manipulation. This paper deals with some thermophysical parameters of different biological materials (raw food materials and final food materials). There were measured thermal conductivity and thermal diffusivity of granular materials, selected vegetables and fruits and also liquids and suspension materials. This paper reports the thermal conductivity - temperature and thermal diffusivity temperature relationships and for granular materials moisture content relations. Two temperature ranges were measured according to experimental materials. Two types of thermophysical characteristics progresses were found (linear or polynomic). It strongly depends on structure and character of measured material. All results are summarised in tables and graphs. Key words: food, biological material, thermal conductivity, thermal diffusivity, temperature. INTRODUCTION There are many methods and techniques of thermophysical parameters measurements (Tye, 1991 Ginzburg, 1985). Researches of materials and rapid industrial development have created a demand for experimental methods that would give reliable data of the thermophysical properties of materials in a short time. A great number of experimental techniques have appeared in literature so far. The methods differ in basic principles of measurement; in number of thermophysical properties they allow to estimate simultaneously; they differ in suitability to test different materials and under various experimental conditions. But in national standards transient methods are usually used. Transient methods represent a large group of techniques where measuring probes, i.e. the heat source and the thermometer, are placed inside the specimen (Krempaský, 1999). This experimental arrangement suppresses the sample surface influence on the measuring process. The temperature of the specimen is stabilized and uniformed. Then the dynamic heat flow in the form of a pulse or step-wise function is generated inside the specimen. From the temperature response to this small disturbance, the thermophysical parameters of the sample can be calculated. Biological materials have a complicated structure. This complicated structure is a reason for great variability of their chemical, biological and physical properties (Blahovec, 1993). During processing of biological materials they are heated, cooled, dried, moistened, or mechanically manipulated. It is necessary to know thermophysical properties of biological materials to choose the optimal technological procedure. Nowadays, there are many methods of measurement, apparatus and instruments for thermophysical measurements. For the measurements in this research, Isomet was used. It is used for quick and exact thermophysical parameters measurement of various materials like liquid, solid and bulk materials. Isomet can be used for measurement of thermophysical parameters as temperature, thermal conductivity, thermal diffusivity etc. In the experiment, Isomet was used for measurements of thermal conductivity and thermal diffusivity of some food products. We made dependencies of thermal conductivity λ, thermal diffusivity a on the temperature, and for selected food products dependencies of thermophysical parameters on the moisture content were also measured. METHODS Thermal conductivity λ is numerically equal to the amount of heat that has penetrated in time isothermal area unit divided by temperature gradient unit. Thermal conductivity is related to pressure, temperature and moisture content, as dispersed materials are related to size of fragments, porosity and bulk density. Thermal conductivity characterizes ability of material to transport heat. Biological materials with different structure have different mechanism of heat transfer (Childers, 1990). Heat transfer is characterized by the Fourier law (1). r q = λ grad T (1) where is: q heat flow, λ - thermal conductivity, grad T gradient of temperature. Thermal diffusivity a is characterized as velocity equalisation of temperature in various points of temperature field. These thermophysical parameters we can be acquired from the equation (2). λ a = (2) cρ where is: c specific heat, ρ - bulk density. Thermophysical parameters were measured by the instrument Isomet version 104 and the last measurement was made by a new version of instrument Isomet 2104 made by the firm Applied Precision (Božikova, 2008). It is used for quick and exact measurement of thermophysical parameters of various materials. Measurements were performed with a spike probe and also for biological materials with compact, suspension and bulk structure was used a surface probe with significant measurement range for different kinds of measured samples. A spike probe was inserted into the analysed material and surface probe was located on the sample. For measurement with a surface probe the measured samples had cylindrical shape with diameter of 63 mm. This diameter is the same as the one of a surface probe. The theoretical description was published in literature (Božiková, 2006). A probe generates heat. Time process of temperature that is related by thermophysical parameters of sample is analysed. The process of temperature t in a spike probe is defined by equation T ( t) = Aln ( t) + B, where A, B are constants which depend on 274 PTEP 13(2009) 3
parameters of sample and its thermal characteristics. Thermophysical parameters can be calculated from the time-temperature characteristics. Bulk density ρ S is defined as the ratio of total mass m and total volume V of granular material (3) ρ m S = V (3) where is: m total mass, V total volume of material Moisture content ω (wet basis) is defined as mass of water contained in biological material divided by mass of wet biological material (4) m1 m2 ω = 100% (4) m1 where is: ω - moisture content, m 1 mass of wet sample, m 2 mass of dry substance of sample. We measured moisture content with instrument HE 50 Pfeuffer and we also used standard ISO - STN 126000 Basic concepts of food dehydration for control measured values. RESULTS The measured samples was stored in storage boxes at the temperature from 2 C to 3 C and 90% of the air moisture content during 24 hours before measurement and dependencies of thermophysical parameters on the temperature were measured during temperature stabilization of samples. All measurements were made in laboratory conditions. Different moisture content 0.17 was made by natural drying of samples in laboratory conditions. Different temperatures were obtained during temperature stabilization from cool box temperature to the room temperature. A special laboratory heater was used for heating of the samples. All samples were stabilized at the room temperature 23 C during 24 hours before measurements. We measured dependencies of thermal conductivity λ and thermal diffusivity a on the moisture content for corn and wheat flour in range (2 18) % of the moisture content. Sample 1 corn flour had bulk density 510 kg.m -3. Thermal conductivity was in range (0.098 0.153) W.m -1.K -1 and thermal diffusivity in range (15.1 15.7).10-8 m 2.s -1. Sample 2 wheat flour had bulk density 530 kg.m -3. Thermal conductivity was in range (0.124 0.169) W.m -1.K -1 and thermal diffusivity in range (23.28 24.01).10-8 m 2.s -1. Results for samples of corn and wheat flour are presented on figures 1-3. Dependences of thermal conductivity and thermal diffusivity on moisture content had linear increasing progress for corn and wheat flour. Thermal conductivity and thermal diffusivity has polynomic progress for all the measured samples of flour. The relation between thermal conductivity, diffusivity and bulk density were also measured, and they had polynomical decreasing progress for flour samples. Thermal conductivity λ and thermal diffusivity a have different values for different sort of flour. 0.16 0.165 0.15 0.16 0.14 0.155 0.15 0.145 0.14 0.135 0.13 0.12 0.11 0.10 0.13 0.125 0.09 0.12 24.2 0.08 Fig. 1 Influence of moisture content ω on thermal conductivity λ, a- corn flour, b wheat flour Sl. 1. Uticaj vlažnosti ω na koeficijent provođenja toplote λ, a - kukuruzno brašno, b - pšenično brašno 15.8 24.1 24.0 E-8 15.7 15.6 E-8 23.9 thermal diffusivity [m2/s] 23.8 23.7 23.6 thermal diffusivity [m2 /s] 15.5 15.4 15.3 23.5 15.2 23.4 23.3 15.1 23.2 15.0 Fig. 2 Influence of moisture content ω on thermal diffusivity a, a) - corn flour, b) - wheat flour Sl. 2. Uticaj vlažnosti ω na temperaturnu provodnost a, a) - kukuruzno brašno, b) - pšenično brašno PTEP 13(2009) 3 275
0.1350 0.170 0.1325 0.165 thermal conductivityť [W/m.K] 0.1300 0.1275 0.1250 0.1225 0.1200 thermal diffusivity x E-6 [m2/s] 0.160 0.155 0.150 0.145 0.140 0.1175 0.135 0.1150 12 14 16 18 20 22 24 26 28 0.130 12 14 16 18 20 22 24 26 28 Fig. 3. Influence of temperature on thermal conductivity and thermal diffusivity of wheat flour Sl. 3. Uticaj temperature na koeficijent provođenja toplote i temperaturnu provodnost pšeničnog brašna Results for selected fruits and vegetables There were measured trermophysical parameters for fruits and vegetables during temperature stabilisation and especially for apples after processing into grated apple, dried apple and apple juice. All obtained values are in great agreement with values 0.132 presented in literature (Ginzburg at al, 1985). We obtained values of thermal conductivity (Tab. 1) and thermal diffusivity (Tab. 2) for samples - fresh apple, grated apple, dried apple and apple juice in temperature range (6-28) C. Selected graphic relations are shoved on figures 4 5. 0.424 0.128 0.124 0.120 0.420 0.416 0.412 0.408 0.116 0.404 Fig. 4. Influence of temperature on thermal conductivity during its stabilization for a) dried apple, b) fresh apple Sl. 4. Uticaj temperature na koeficijent provođenja toplote tokom stabilizacije za a) - sušene jabuke, b) - sveže jabuke Table 1. Thermal conductivity and diffusivity of dried apple, grated apple and apple juice during temperature stabilization in temperature range 6 28ºC Tabela 1. Vrednost koeficijenta provođenja toplote i temperaturne provodnosti sušenih jabuka, kaše od jabuke i soka od jabuke tokom stabilizacije temperature u temperaturnom opsegu od 6-28ºC Sample/Uzorak Temperature range/temperaturni opseg Thermal conductivity/koeficijent provođenja toplote [W.m -1. K -1 ] Thermal diffusivity/temperaturna provodnost [ x 10-8 m 2.s -1 ] dried apple/sušena jabuka 0.118 0.132 2.26-2.48 grated apple/kaša od jabuke 6 28ºC 0.553 0.575 12.80-13.81 apple juice/sok od jabuke 0.660-0.642 14.25-14.67 276 PTEP 13(2009) 3
2.50 12 thermal diffusivity x10e-8 [m2/s] 2.45 2.40 2.35 2.30 thermal diffusivity x10e-8 [m2/s] 11 10 9 2.25 8 Fig. 5. Influence of temperature on thermal diffusivity during its stabilization for a) dried apple, b) fresh apple Sl. 5. Uticaj temperature na temperaturnu provodnost tokom stabilizacije za a) - sušene jabuke, b) - sveže jabuke Table 2. Thermal conductivity and diffusivity of selected fruits and vegetables during temperature stabilization in temperature range 6-28ºC Tabela 2. Vrednost koeficijenta provođenja toplote i temperaturne provodnosti odabranog voća i povrća tokom stabilizacije temperature u temperaturnom rangu od 6-28ºC Sample/Uzorak Temperature range/temperatur ni opseg Thermal conductivity/koeficijent provođenja toplote [W.m -1. K -1 ] Thermal diffusivity/temperaturna provodnost [ x 10-8 m 2.s -1 ] Apples - variety Gala/Jabuke-sorta Gala 0.492 0.525 14.5 14.8 Apples variety Jonagold/Jabukesorta Jonagold 0,514 0,529 15.5 15.8 Pears I. variety/kruške-i. sorta 0.462 0.470 13.4 13.6 Pears II. variety/kruške-ii. sorta (6 28)ºC 0.510 0.524 13.6 13.8 Potatoes I. variety/krompir-i sorta 0.629 0.631 14.4 14.7 Potatoes II. variety/krompir-ii. sorta 0.640 0.652 14.5 14.8 Carrots/Mrkva 0.602 0.611 15.2 15.1 The study of the relationships between thermal conductivity, thermal diffusivity and temperature, the results of which are showed on figures 4-5 and tables 1, 2 demonstrate linear increasing relations between thermophysical parameters and temperature during temperature stabilization for samples fresh apple, grated apple, dried apple and apple juice. For data reliability protection there were realized series of measurements for every point in graphics characteristics with number of hundred measurements and results were obtained as valued averages. Results for selected liquids and suspensoid materials Thermal conductivity and thermal diffusivity were measured for different types of liquids like: beer, wine, juice, lemonade, milk and suspension products like acidophilus milk and processed cheese. The 1st series of measurements provided the values of thermal conductivity and thermal diffusivity of milk with different fat content during temperature stabilization. Relations have linear increasing progress and from the characteristics it is evident that temperature and fat content have significant influence on thermophysical parameters. If fat content increases, then thermal conductivity decreases and thermal diffusivity increases. All relations were measured also for Acidophilus milk which has thermal diffusivity of 18.5x10-8 m 2.s -1 and thermal conductivity of 0.51 W.m -1.K -1, for processed cheese thermal diffusivity was 16.5x10-8 m 2.s -1 and thermal conductivity 0.71 W.m -1.K -1. PTEP 13(2009) 3 277
milk 0.5% - mlieko 0.5% 14.5 milk 0.5% - mlieko 0.5% 0.60 milk 1.5% - mlieko 1.5% 14.0 milk 1.5% - mlieko 1.5% Thermal conductivity [W/m.K] 0.56 milk 3.5% - mlieko 3.5% Thermal diffusivity [xe-8 m2/s] 13.5 13.0 milk 3.5% - mlieko 3.5% 0.52 12.5 5 10 15 20 25 Temperature [ C] 12.0 5 10 15 20 25 Temperature [ C] Fig. 6. Influence of temperature on thermal conductivity and diffusivity for milk with different relative fat content Sl. 6. Uticaj temperature na koeficijent provođenja toplote i temperaturnu provodnost mleka sa različitim sadržajem masti 0.64 0.22 0.62 0.21 Thermal conductivity (W/m.K) 0.60 0.58 0.56 0.54 0.52 Thermal diffusivity x E-6 (m2/s) 0.20 0.19 0.18 0.17 0.16 0.50 0.15 0.48 10 12 14 16 18 20 Temperature( C) 0.14 10 12 14 16 18 20 Temperature ( C) Fig. 7. Influence of temperature on thermal conductivity and thermal diffusivity for beer during the temperature stabilization Sl. 7. Uticaj temperature na koeficijent provođenja toplote i temperaturnu provodnost piva tokom stabilizacije temperature Table 3 Thermal conductivity and diffusivity of selected liquids during temperature stabilization in temperature range 5 25ºC Tabela 3. Vrednost koeficijenta provođenja toplote i temperaturne provodnosti odabranih tečnosti tokom stabilizacije temperature u temperaturnom rangu od 5-25ºC Sample/Uzorak Temperature range/temperat urni opseg Thermal conductivity range [W/m.K]/Opseg vrednosti koeficijenta provođenja toplote [W/m.K] Thermal diffusivity range x 10-6 [m 2 /s]/opseg vrednosti temperaturne provodnosti x 10-6 [m 2 /s] Functional progress/oblik funkcije alcohol- liquor/alkohol 0397 0.484 0.452 0.568 linear/linearna linear/linearna orange juice/sok od 0.432 0.574 0.130 0.179 linear/linearna polynomical (5-25) C narandže wine/vino 0.491 0.626 0.457 0.627 linear/linearna linear/linearna beer/pivo 0.481 0.636 0.147 0.203 linear/linearna linear/linearna λ a 278 PTEP 13(2009) 3
CONCLUSION The summary presentation of the measurement results refers to variability of thermophysical parameters during the changes of moisture content and temperature stabilization. Samples with liquid structure were measured by a spike probe, suspension and granular materials were measured by a spike and a surface probe and for measurements of materials with compact structure a surface probe was used. All results were obtained during the natural temperature stabilization process, because of practical reasons. In food processing and storage food materials are exposed to premeditated or casual temperature changes. From the obtained values it is evident, that high water content and high content of fresh fruit ingredient are causes of non stability of biological materials. Results for granular materials are showed on fig. 1-3, ones characteristic for thermal conductivity have linear increasing progress while ones characteristic for thermal diffusivity have polynomic progress and during the measurement an important relation between size of fragments and thermophysical parameters was also found. Based on the presented results, it is necessary to have knowledge about the dependencies of thermophysical parameters of biological materials if we want to preserve their quality during the manipulation, processing and storage. ACKNOWLEDGEMENTS: This work was supported by grant projects VEGA 1/4400/07, VEGA 1/0643/09 and VEGA 1/0708/09, GA SPU I-08-000-11. REFERENCES [1] Blahovec, J: Agricultural materials (in Czech), CUA, Prague, 1993, p.186. [2] Božiková, Monika: Thermal characteristics of milk products. PTEP - Journal on processing and energy in agriculture, 12(2008)3, p. 107-109. [3] Božiková, Monika: Some chosen thermophysical parameters of apples and applesauce. Acta technologica agriculturae, Nitra: SPU Nitra, ročník 8, č. 4, 2006, ISSN 1335-2555, p. 89-92. [4] Tye, R. P: Measurement of Thermal Conductivity and Releted Properties: a Half Century of Radical Change. High Temp. High Press, 1991, p.1-11. [5] Ginzburg, A. S: Thermophysical properties of food substance (in Czech). CUA, Prague, 1985. p.269-271. [6] Childers, J: Physics, Radisson Wesley Publishing Company, Inc. USA, 1990, ISBN 0-201-11951-X. [7] Krempaský, J. 1999. Meranie termofyzikálnych veličín. Veda, Bratislava, p. 335. [8] ISO - STN 126 000 Basic concepts of food dehydration, 1998. Received: 16.04.2009. Accepted: 12.09.2009. PTEP 13(2009) 3 279