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Determination of Thermal Conductivity, Specific Heat and Thermal Biosystems Engineering (2002) 82 (2), 169–176 doi:10.1006/bioe.2002.0066, available online at http://www.idealibrary.com on PH}Postharvest Technology Determination of Thermal Conductivity, Specific Heat and Thermal Diffusivity of Borage Seeds W. Yang1; S. Sokhansanj2; J. Tang3; P. Winter4 1 Department of Food Science, University of Arkansas, 2650 N. Young Ave., Fayetteville, AR 72704, USA; e-mail of corresponding author: [email protected] 2 Oak Ridge National Lab, Bioenergy Feedstock Development Program, Oak Ridge, TN 37831-6422, USA; e-mail: [email protected] 3 Food Engineering Program, Department of Biological Systems Engineering, Washington State University, Pullman, WA 99164-6120, USA; e-mail: [email protected] 4 Hinz Automation, Inc., 410 Jessop Ave., Saskatoon, SK, Canada S7N 2S5; e-mail: [email protected] (Received 16 March 1999; accepted in revised form 15 February 2002; published online 11 June 2002) Thermal conductivity, specific heat capacity and thermal diffusivity of borage (Borago officinalis) seeds were determined at temperatures ranging from 6 to 208C and moisture contents from 1Á2to30Á3% w.b. The thermal conductivity was measured by the transient technique using a line heat source. The maximum slope method was used to analyse the line source heating data for thermal conductivity determination. The specific heat capacity was measured by different scanning calorimetry and ranged from 0Á77 to 1Á99 kJ kgÀ1KÀ1. The thermal conductivity of borage seeds ranged from 0Á11 to 0Á28 W mÀ1 KÀ1 and increased with moisture content in the range of 1Á2–30Á3% w.b. The thermal diffusivity ranged from 2Á32 Â 10À7 to 3Á18 Â 10À7 m2 sÀ1. Bulk density of borage seeds followed a parabolic relationship with moisture content. Uncertainty analysis revealed that variation in the thermal conductivity contributed mostly to the accuracy of the thermal diffusivity. # 2002 Silsoe Research Institute. Published by Elsevier Science Ltd. All rights reserved 1. Introduction well-established methods (Mohsenin, 1980; Dickerson, 1965), but measuring any two of them would lead to the Borage is a speciality oilseed with a high content of third through the relationship crude oil (33%) and crude protein (28%). It is especially k high in gamma linolenic acid which is currently in great a ¼ ð1Þ c demand for pharmaceutical and health-care applica- r p tions. Thermal conductivity, thermal diffusivity and where a is the thermal diffusivity, k is the thermal specific heat capacity are three important engineering conductivity, r is the bulk density and cp is the specific properties of a material related to heat transfer heat. characteristics. These parameters are essential in study- Methods for measuring thermal conductivity can be ing heating, drying and cooling processes for borage classified into two broad categories: steady- and seeds. Thermal properties of many agricultural and food transient-state heat transfer methods (Mohsenin, products have been reported in the literature, and most 1980). The tests using steady-state methods often require of these data are compiled by Polley et al. (1980) and a long time to complete and moisture migration may ASAE (2001) for engineering research and design introduce significant measurement errors (Mohsenin, purposes. The thermal property data of many novelty 1980; Kazarian & Hall, 1965; Dutta et al., 1988). The crops are not, however, available in the literature. For latter methods are more suitable for biological materials borage seeds, no other thermal property data than the that are generally heterogeneous and often contain high specific heat capacity as reported by Yang et al. (1997) moisture content. The line source method is the most can be found in the literature. widely used transient-state method. This method uses Thermal conductivity, thermal diffusivity and specific either a bare wire or a thermal conductivity probe as a heat capacity each can be measured by several heating source, and estimates the thermal conductivity 1537-5110/02/$35.00 169 # 2002 Silsoe Research Institute. Published by Elsevier Science Ltd. All rights reserved 170 W. YANG ET AL. Notation terms: q T À T0 ¼ ½A À lnðrnÞ ð7Þ A Constant 2pk À1 À1 cp specific heat, kJ kg K or F a function I electric current, A qA q 1 À1=2 q T À T0 ¼ À ln ra þ lnðtÞð8Þ k thermal conductivity, W mÀ1 KÀ1 2pk 2pk 2 4pk M moisture content, per cent wet basis Equation (8) shows a linear relationship between n an intermediate variable (T À T ) and lnðtÞ with the slope S ¼ q=ð4pkÞ. The q heat transfer rate, W 0 r radial axis, m slope S can be obtained from the experimental data of R electric resistance per unit length, O mÀ1 (T À T0) versus lnðtÞ by linear regression, and the r2 coefficient of determination thermal conductivity can then be calculated from the S Slope linear slope S: t time, s I 2R T temperature, 8C k ¼ ð9Þ 4pS T0 initial temperature, 8C a thermal diffusivity, m2 sÀ1 Owing to non-ideal conditions in reality, such as non- r average bulk density, kg mÀ3 zero mass and volume of the hot wire, heterogeneous oa uncertainty in thermal diffusivity and anisotropic properties of biological materials, finite ok uncertainty in thermal conductivity sample size and axial heat flow (Mohsenin, 1980; Suter oc uncertainty in specific heat et al., 1975; Wang & Hayakawa, 1993), temperature rise or uncertainty in bulk density (T À T0) versus lnðtÞ does not always follow a linear relationship. This calls for correction during data reduction. The most used early method for data based on the relationship between the sample core correction was the time-correction factor method (Van temperature and the heating time. In principle, the heat der Held & Van Drunen, 1949), which minimized the is generated in a hot wire at a rate q in W: non-linearity of the (T À T0) versus lnðtÞ curve by q ¼ I 2R ð2Þ subtracting a factor from the time elapsed. Murakami where I is the electric current in A and R is the electric and Okos (1988) proposed a method using the 2 resistance in O mÀ1. For a long cylindrical sample, where maximum coefficient of determination (R ) for the the end effects and the mass of the hot wire can be correction, which searched for a maximum linear neglected and when the sample is homogeneous and portion of the curve by successive linear regression 2 isotropic, heat conduction in the sample is governed by using R values as a criteria for the maximum linearity. the following equation (in cylindrical coordinates), Wang and Hayakawa (1993) verified, theoretically and assuming that k remains constant: experimentally, the maximum slope method that was first used by Asher et al. (1986). This method calculates @T @2T 1@T ¼ a þ ð3Þ the thermal conductivity using the maximum slope @t @r2 r @r around a plateau of the local slope versus ln(t) plot. The where T is the sample temperature anywhere in the study of Wang and Hayakawa (1993) showed that cylinder in 8C, t is the time in s, r is the radial axis in m, the thermal conductivities determined using the max- and a is the thermal diffusivity in m2 sÀ1. The solution to imum slope method are comparable or more accurate Eqn (3) is (Hooper & Lepper, 1950) than the time-correction method and the maximum R2 q method. T À T ¼ FðrnÞð4Þ 0 2pk Among the published methods for specific heat measurement, differential scanning calorimetry (DSC) where T is the initial sample temperature, n is an 0 has so far been the most accurate and rapid method. intermediate variable and Tang et al. (1991) reviewed the literature on the ðrnÞ2 ðrnÞ4 FðrnÞ¼A À lnðrnÞþ À þÁÁ ð5Þ measurement of specific heat for agricultural products, 2 8 and provided analyses on the key factors that can affect the specific heat measurement using the DSC method. n ¼ 1ðatÞÀ1=2 ð6Þ 2 Yang et al. (1997) described DSC procedures for where A is a constant. If the product of r and n is very measuring the specific heat of borage seeds, and small, namely, a negligibly small value for r and a large developed a model to correlate the specific heat with value for t, Eqn (5) can be approximated by the first two temperature and moisture content. They also studied the THERMAL PROPERTIES OF BORAGE SEEDS 171 factors that influenced the values for the specific heat of borage seeds. The objective of this study is to determine the thermal conductivity, specific heat capacity and thermal diffu- sivity of borage seeds as a function of seed moisture content and temperature. 2. Materials and methods 2.1. Sample preparation Borage (Boragoofficinalis) seeds at 6Á7% initial moisture content on a wet basis (w.b.) were obtained from a seed cleaning facility. The seeds were conditioned to nine different moisture contents ranging from 1Á2to 30Á3% w.b. The samples at the moisture contents below Fig. 1. Schematic of the apparatus for thermal conductivity 6Á7% w.b. were prepared by drying 1 kg borage seeds in measurement; A, bare-wire apparatus; B, air duct; C, air a convection air oven at 758C. The samples at the plenum; D, DC power supply; E, heater wire; F, thermocouple moisture contents above 6Á7% w.b. were obtained by for core temperature measurement; G, thermocouple for surface temperature measurement spraying pre-determined amounts of distilled water on borage seeds followed by periodic tumbling of the samples in sealed containers. The samples were then stored at 48C before testing. ductivity. A major disadvantage of using a water bath is the necessity of sealing the sample holding tube, which 2.2. Thermal conductivity measurement may be very time consuming and cumbersome, and there exists the possibility of water leakage into sample Thermal conductivity measurements were conducted during the tests.
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