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Effect of moisture content and temperature on thermal conductivity of Psidium guajava L. by line heat source method (transient analysis)
International Journal of Heat and Mass Transfer 78 (2014) 354–359
Contents lists available at ScienceDirect
International Journal of Heat and Mass Transfer journal homepage: www.elsevier.com/locate/ijhmt
Effect of moisture content and temperature on thermal conductivity of Psidium guajava L. by line heat source method (transient analysis) Shiva Kumar Modi a,⇑, Durga Prasad B. b, Basavaraj M. c a
Department of Mechanical Engineering, RYM Engineering College, Bellary, Karnataka, India Department of Mechanical Engineering, JNTU College of Engineering, Anantapur, AP, India c Principal, Ballarpur Institute of Technology, Ballarpur, Maharastra, India b
a r t i c l e
i n f o
Article history: Received 13 February 2014 Received in revised form 25 May 2014 Accepted 27 June 2014
Keywords: Guava Moisture content Food processing Temperature Thermal conductivity Density
a b s t r a c t Thermal conductivity (K) of Psidium guajava L. (guava fruit) cultivar (Rayalaseema area, AP, India) is one of the fundamental importance to establish the design of process equipment. A study on effect of moisture content (MC) and temperature on thermal conductivity (K) of guava fruit are presented. The thermal conductivity is evaluated by transient technique using line heat source method for various MC ranging from 80% to 40% (wb) at two different densities. The analysis reveals that the thermal conductivity of guava fruit increased with increase in moisture content and temperature in the range of 0.1526 to 0.6037 W/m °C. The experimental values were compared with standard (Sweat and Anderson) models and were found in good agreement. Ó 2014 Elsevier Ltd. All rights reserved.
1. Introduction Guava (Psidium guajava L.) fruit is generally ovoid or pear shaped native to Mexico and it is available throughout South America, Europe, Africa and Asia. It also grows in all subtropical areas [1]. Guava is often marketed as ‘‘super-fruits’’ which has a considerable nutritional importance in terms of vitamins A and C with seeds that are rich in omega-3, omega-6 poly-unsaturated fatty acids and especially dietary fiber, riboflavin, as well as in proteins, and mineral salts. The vitamin C in guava makes absorption of vitamin E much more effective in reducing the oxidation of the LDL cholesterol and increasing the (good) HDL cholesterol. The fibers in guavas promote digestion and ease bowel movements. The high content of vitamin A in guava plays an important role in maintaining the quality and health of eye-sight, skin, teeth, bones and the mucus membranes [2]. The anti-oxidant virtue in guavas [3] is believed to help reduce the risk of cancers of the stomach, esophagus, larynx, oral cavity and pancreas. It has been generally recognized that Thermo-physical properties of biological materials such as food stuffs are dependent on temperature, moisture content and composition. Therefore variability in composition and physical characteristics resulting
⇑ Corresponding author. E-mail address: [email protected] (S.K. Modi). http://dx.doi.org/10.1016/j.ijheatmasstransfer.2014.06.076 0017-9310/Ó 2014 Elsevier Ltd. All rights reserved.
from variations in soil, climatic conditions, irrigation techniques and fertilizer used would manifest themselves in measured thermo-physical properties [4–6]. Fruits and vegetables at different stages of processing are subjected to thermal treatments in the food industry, understanding their behavior to these thermal processes requires good knowledge of thermal and physical properties. These properties are essential for designing and optimization of every process involving heat transfer at unsteady state such as cooking, frying, and drying and post-harvest heat treatments. Thermal conductivity is an intrinsic property which measures the ability of a substance to conduct heat. The importance of thermal conductivity is to predict or control the heat flux in food material during processing when energy transfer is involved. 2. Theory The calculation of heat transfer in foods begins with the identification of three major parameters in heat transfer processes: 1. Thermal properties of the food. 2. Geometry of the food. 3. Thermal Processing conditions. Methods of measuring thermal conductivity are classified into two categories:
S.K. Modi et al. / International Journal of Heat and Mass Transfer 78 (2014) 354–359
355
Nomenclature D1 D2 HDL I K Kw Ks LDL MC q r R
= = = = = = = = = = = =
density (911 Kg/m3) density (1062 kg/m3) High Density Lipoprotein Electric Current (AMP(A)) thermal conductivity (W/m °C) thermal conductivity of water (W/m °C) thermal conductivity of solid (W/m °C) low density lipoprotein moisture content (%) heat input (W/m) radial axis (m) electric resistance (X m1)
T T1 T2 t t0 t1 t2 wb
The steady state heat transfer methods often require a long time to complete and moisture migration may introduce significant measurement errors [7]. The transient methods are most suitable for biological materials that are generally heterogeneous and often contain high moisture content, where the line heat source method is one of the most widely used. Here a bare wire method is used as a heating source, and estimates the thermal conductivity based on relationship between the sample core temperature and the heating time. The rate of heat generated in the wire ‘q’ W/m:
ð1Þ
where I = electric current in amps (A), R = electric resistance in X m1. For a long cylindrical sample, where the end effects and the mass of hot wire can be neglected and when the sample is homogeneous and isotropic, heat conduction in the sample is governed by the equation (cylindrical coordinates)
@T @ 2 T 1 @T ¼a þ @t @r 2 r @r
sample temperature (°C) temperature (°C) at time ‘t1’(s) temperature (°C) at time ‘t2’ (s) time (s) time correction factor (s) time (s) corresponding to temperature (T1) time (s) corresponding to temperature (T2) wet bulb
Greek symbols a = thermal diffusivity (m2/s)
1. Steady state heat transfer method. 2. Unsteady state (transient) heat transfer method [6].
Q ¼ I2 R
= = = = = = = =
!
ð2Þ
where T = is the sample temperature anywhere in the cylinder ‘°C’, t = time in ‘s’, r = is the radial axis in ‘m’, a = thermal diffusivity in ‘m2/s’.
temperature and moisture content by Kostaropoulous [10], Sweat [11] and Dickerson and Read [12]. Not much data were found on fruits/vegetables especially for Exotic tropical fruits such as Guava fruit. Hence, this study was made to investigate the thermal conductivity of fresh and dried fruit in the moisture range of 40–80% (wb) grown in the local area (Rayalaseema, AP, India). 3. Materials 3.1. Sample preparation and moisture content Fresh, Desiree, ripened and well matured fruits of uniform shape size and color with no apparent damage were procured from the local orchard (Rayalaseema area, AP, India) are washed in clean potable water (the flesh of each fruit was observed to be pink and the central pulp contains seeds) and allowed to equilibrate with room temperature prior to testing. The moisture content of the fresh samples was found to be 80% (wb) as determined using a standard method AOAC (Association of Official Analysts and Chemists) [13] in a Vacuum oven at 70 °C for 24 h with 03 replicates. To obtain samples with a range of moisture contents 80% to 40% (wb), the samples were dried for various periods in an experimental hot air drier at 55, 60 and 65 °C. The partly dried samples were sealed in a polyethylene film and stored at a constant temperature for 24 h to ensure uniform moisture content throughout the sample. 4. Experimental setup and methodology 4.1. Experimental setup
The solution to the above equation, transient heat flow method developed by Hoopper and Lepper [8] with time correction factor was employed. Sreenarayanan and Chattopadhyay [9] have explained theoretical consideration of the equation used. The modified equation for calculating thermal conductivity incorporating the time correction values is shown in the Eq. (3):
K¼
q t2 t0 ln 4pðT 2 T 1 Þ ðt 1 t 0 Þ
ð3Þ
where K = thermal conductivity of the sample (W/m °C) q = heat input (W/m) T1 and T2 = temperatures in °C at time t1 and t2 (s) t0 = time correction factor (8.2 s). t1 and t2 = time in seconds corresponding to temp. T1 and T2. The data on thermal conductivity for the food products have been reported in the literature under different conditions of
Schematic representation of line heat source apparatus used for measuring K is shown in Fig. 1 [14]. The bare wire thermal conductivity apparatus consisted of an aluminum cylindrical sample tube of 104 mm length and 28.4 mm inner diameter, with a removable Teflon cover and with a fixed bottom base cover. A chromel resistance heating wire of 33 gauge and a length of 200 mm stretched between copper leads along the axis of cylindrical tube used as line heat source, of which the effective length of heating element inside the test cylinder is 104 mm and the remaining length (96 mm) is used to connect the leads on either sides outside the test cylinder. A constant DC Power supply was used for all the tests. A pre-calibrated T-type 28 gauge iron-constantan thermocouple was installed for measuring the core temperature of the sample in the cylinder. The power input to the line heat source was sufficient to give a measurable temperature difference between the time t1 and t2.
356
S.K. Modi et al. / International Journal of Heat and Mass Transfer 78 (2014) 354–359
where K = Thermal conductivity of unknown material, (W/m °C). Kw = Thermal conductivity of Water, 0.614 W/m °C. Ks = Thermal conductivity of Solids, 0.2597 W/m °C. M = Moisture content of material in decimal. 5. Results and discussion Experiments were conducted to determine the thermal conductivity of Guava fruit at different instant of time, temperature and density with the moisture content ranging from 40% to 80% (wb). 5.1. Assay of thermal conductivity of guava fruit Fig. 1. Schematic representation of the apparatus used for measuring thermal conductivity [14].
4.2. Methodology A known mass of defined moisture content is filled in the cylindrical sample tube. The open end of the tube was sealed off with a polyethylene foil before the Teflon top cover was placed in order to prevent the evaporation of moisture. The sample in the tube is allowed to equilibrate with the ambient temperature. When the sample attains the constant temperature with ambient temperature, the power and stop watch were switched ON simultaneously. The core temperature shown by the thermocouple was noted for every 30 s up to 20 min. The current was determined to an accuracy of 0.01 A by measuring at Regulated Power Supply. The thermal conductivity values are determined using Eq. (3). The moisture content of the sample were measured before and after the test and found to be no considerable changes. Predicted model: Sweat [15] and Anderson [16] models were used to compare thermal conductivity with the experimental values: Sweat model:
K ¼ 0:148 þ 0:00493 M
ð4Þ
where, M = moisture content of the material in% (wb). Anderson model:
K ¼ MK w þ ð1 MÞK s
ð5Þ
Variation of thermal conductivity at different instant of time in the range of 40% to 80% (wb) moisture content for densities of 911 kg/m3 (D1) and 1062 kg/m3 (D2) are depicted in Figs. 2 and 3. It is observed that at all moisture contents, thermal conductivity of guava fruit increases with increase in time. But at lower moisture levels Thermal conductivity is relatively low with higher moisture levels with increase in temperature or time. Because, as the moisture evaporates the sample shrinks and the rate of shrinkage in the initial stage of heating is more, leading to porosity i.e. entrapped air which is a bad conductor of heat, hence decrease in the thermal conductivity [17,18]. It is observed that thermal conductivity increases with increase in time at all moisture contents. The analysis shows that at higher moisture contents (70% and 80% (wb)), thermal conductivity values lie in the range of 0.3027 W/m °C to 0.5775 W/m °C and 0.3210 W/ m °C to 0.6037 W/m °C results in increased thermal conductivity. Similarly at lower level moisture contents (50% and 40% (wb)), the thermal conductivity values lie in the range of 0.265 W/m °C to 0.5019 W/m °C and 0.1526 W/m °C to 0.4595 W/m °C respectively. This is due to low density, void spaces present and nonhomogeneity in the sample structure apparently causes the reduction the thermal conductivity. The variation of thermal conductivity with respect to center temperature of guava fruit (at different instant of time) in the range of 40% to 80% (wb) moisture content for densities D1 and D2 are shown in Figs. 4 and 5 respectively. It is observed that thermal conductivity increases with increase in center temperature for all moisture content 40% to 80% (wb). This behavior suggests that the structural characteristics of fruit
Fig. 2. Variation of thermal conductivity v/s time for various moisture content (for density of 911 kg/m3).
S.K. Modi et al. / International Journal of Heat and Mass Transfer 78 (2014) 354–359
Fig. 3. Variation of thermal conductivity v/s time for various moisture content (for density of 1062 kg/m3).
Fig. 4. Variation of thermal conductivity v/s centre temperature for various moisture content (for density of 911 kg/m3).
Fig. 5. Variation of thermal conductivity v/s centre temperature for various moisture content (for density of 1062 kg/m3).
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S.K. Modi et al. / International Journal of Heat and Mass Transfer 78 (2014) 354–359
Fig. 6. Variation of thermal conductivity v/s moisture content at different time (for density of 911 kg/m3).
Fig. 7. Variation of thermal conductivity v/s moisture content at different time (for density of 1062 kg/m3).
permit rapid moisture migration in response to increase in temperature. In the initial stage of heating at all moisture contents the thermal conductivity increases more rapidly because of presence of more suspended water particles on the surface of the sample making it wet. The Thermal conductivity increases rapidly in the beginning and attain steady state until final stage. Effect of moisture content (40% to 80% (wb)) on thermal conductivity of guava fruit at different timings for densities D1 and D2 shown in Figs. 6 and 7. Thermal conductivity increases with the increase in moisture content because moisture contained in the sample leads to heat transfer by conduction hence increase in the thermal conductivity values with increase in time. It is also observed that, at higher moisture content (60–80% (wb)), thermal conductivity values lie in the range of 0.2908– 0.5438 W/m °C, and 0.3210–0.6037 W/m °C results in increase in thermal conductivity values. This is because high density and moisture content present in the sample has by far greater influence on the increase of thermal conductivity values [9]. Similarly at lower moisture content i.e. less than 60% moisture content thermal conductivity decreases due to surface
Fig. 8. Variation of thermal conductivity v/s time for different densities at 40% and 80% moisture content.
S.K. Modi et al. / International Journal of Heat and Mass Transfer 78 (2014) 354–359
moisture being evaporated causing the case hardening of the surface. At 40% (wb) the thermal conductivity lies in the range of 0.1526–0.4595 W/m °C. The variation of thermal conductivity with time for two densities (D1, D2) at 80% and 40% moisture content are shown in Fig. 8. It is observed that, at different bulk densities (D1 and D2) of 80% and 40% (wb) moisture content, thermal conductivity values increases with increase in time/temperature and corresponding increase in density. This indicates that thermal conductivity is not merely a function of physical properties like density, temperature and moisture content but also is a function of physical structure of food sample [10]. 6. Conclusion Experimental investigations have been carried out in order to investigate the effect of moisture content (MC) and temperature on thermal conductivity (K) of guava fruit. From the above discussion the following conclusion were made: 1. Significant variation in thermal conductivity was observed with changes in moisture content and temperature. 2. It is observed that, the thermal conductivity increases with increase in moisture content, caused mainly by conduction heat transfer of water particles of the sample. 3. The thermal conductivity also increases with increase in density, due to higher thermal contact between particle structures of the sample and also structure is nonporous with fewer voids (i.e. the volume of pores reduced, resulting in higher Thermal conductivity). 4. The variation of thermal conductivity may occur due to nonhomogeneity and positioning of temperature measurement within the sample. 5. The deviation of experimental results of thermal conductivity with the standard models is in the range of 10.15% to 18.38% (Sweat) and 12.08% to 14.29% (Anderson), and found to be in good agreement.
359
Conflict of interest None declared. References [1] R.M.P. Gutierre, S. Mitchell, R.V. Solis, Psidium guajava: a review of its traditional uses, phytochemistry and pharmacology, J. Ethnopharmacol. 117 (1) (2008) 1–27. [2] Dattatreya M. Kadam, Pratibha Kaushik, Ramesh Kumar, Evaluation of guava products quality, Int. J. Food Sci. Nutr. Eng. 2 (1) (2012) 7–11. [3] Y.Y. Lim, J. Murtijaya, Antioxidant properties of Phyllanthus amarus extracts as affected by different drying methods, Lwt-Food Sci. Technol. 40 (9) (2007) 1664–1669. [4] A.M. Ramos, A. Ibarz, Density of juice and fruit puree as a function of soluble solids content and temperature, J. Food Eng. 35 (1998) 57–63. [5] C. Osorio, J.G. Carriazo, H. Barbosa, Thermal and structural study of guava (Psidium guajava L) powders obtained by two dehydration methods, Quimica Nova 34 (4) (2011) U636–U684. [6] N.N. Mohsenin, Thermal Properties of Food and Agriculture Materials, Gordan and Breach Science Publishers, New York, 1980. [7] S.K. Dutta, V K Nema, R K Bharadwaj, Thermal properties of gram, J. Agric. Res. 39 (1988) 269–275. [8] F.C. Hooper, F.R. Lepper, Thermal heat flow apparatus for determination of thermal conductivities, Am. Soc. Heat Ventila Eng. ASHVE Trans. 56 (1950) 309–322. [9] V.V. Sreenarayanan, P.K. Chattopadhyay, Thermal conductivity and diffusivity of rice bran, J. Agric. Eng. Res. 34 (1986) 115–121. [10] A.E. Kostaropoulous, G.D. Sarvocos, Transport properties in processing of fruits and vegetables, J. Food Technol. 49 (9) (1995) 99–105. [11] V.E. Sweat, Experimental values of thermal conductivity of selected fruits and vegetables, J. Food Sci. 39 (1974). [12] R.W. Dickerson, B.R. Read Jr., Calculation and measurement of heat transfer in foods, Food Technol. 12 (1968) 37–48. [13] AOAC, Method of Analysis, 12th ed., Association of Official Analysis Chemists, Washington DC, 1925. [14] M. Basavaraj, G.P. Prabhu Kumar, B. Sathyanarayana Reddy, Studies on thermal conductivity of fig (Ficus carica L) fruit, J. Food Sci. Technol. 45 (1) (2008) 97–98. [15] V E. Sweat , Experimental measurement of yellow cake, in: Proceeding of the 13th International Conference on Thermal Conductivity, University of Missouri- Rolla, 1974, pp. 195–198. [16] S.A. Anderson, Automatic Refrigeration, MacLaren and Sons Ltd., Donfoss, Nordberg, Denmark, 1950. [17] VE. Sweat, in: M.A. Rao, S.S. Rizvi (Eds.), Thermal Properties of Foods in Engineering Properties of Foods, Marcel Dekker, New York, 1986, pp. 49–87. [18] GK. Vagenas, Marinos-kouris, Thermal properties of raisins, J. Food Eng. 11 (2) (1990) 147–158.
Contents lists available at ScienceDirect
International Journal of Heat and Mass Transfer journal homepage: www.elsevier.com/locate/ijhmt
Effect of moisture content and temperature on thermal conductivity of Psidium guajava L. by line heat source method (transient analysis) Shiva Kumar Modi a,⇑, Durga Prasad B. b, Basavaraj M. c a
Department of Mechanical Engineering, RYM Engineering College, Bellary, Karnataka, India Department of Mechanical Engineering, JNTU College of Engineering, Anantapur, AP, India c Principal, Ballarpur Institute of Technology, Ballarpur, Maharastra, India b
a r t i c l e
i n f o
Article history: Received 13 February 2014 Received in revised form 25 May 2014 Accepted 27 June 2014
Keywords: Guava Moisture content Food processing Temperature Thermal conductivity Density
a b s t r a c t Thermal conductivity (K) of Psidium guajava L. (guava fruit) cultivar (Rayalaseema area, AP, India) is one of the fundamental importance to establish the design of process equipment. A study on effect of moisture content (MC) and temperature on thermal conductivity (K) of guava fruit are presented. The thermal conductivity is evaluated by transient technique using line heat source method for various MC ranging from 80% to 40% (wb) at two different densities. The analysis reveals that the thermal conductivity of guava fruit increased with increase in moisture content and temperature in the range of 0.1526 to 0.6037 W/m °C. The experimental values were compared with standard (Sweat and Anderson) models and were found in good agreement. Ó 2014 Elsevier Ltd. All rights reserved.
1. Introduction Guava (Psidium guajava L.) fruit is generally ovoid or pear shaped native to Mexico and it is available throughout South America, Europe, Africa and Asia. It also grows in all subtropical areas [1]. Guava is often marketed as ‘‘super-fruits’’ which has a considerable nutritional importance in terms of vitamins A and C with seeds that are rich in omega-3, omega-6 poly-unsaturated fatty acids and especially dietary fiber, riboflavin, as well as in proteins, and mineral salts. The vitamin C in guava makes absorption of vitamin E much more effective in reducing the oxidation of the LDL cholesterol and increasing the (good) HDL cholesterol. The fibers in guavas promote digestion and ease bowel movements. The high content of vitamin A in guava plays an important role in maintaining the quality and health of eye-sight, skin, teeth, bones and the mucus membranes [2]. The anti-oxidant virtue in guavas [3] is believed to help reduce the risk of cancers of the stomach, esophagus, larynx, oral cavity and pancreas. It has been generally recognized that Thermo-physical properties of biological materials such as food stuffs are dependent on temperature, moisture content and composition. Therefore variability in composition and physical characteristics resulting
⇑ Corresponding author. E-mail address: [email protected] (S.K. Modi). http://dx.doi.org/10.1016/j.ijheatmasstransfer.2014.06.076 0017-9310/Ó 2014 Elsevier Ltd. All rights reserved.
from variations in soil, climatic conditions, irrigation techniques and fertilizer used would manifest themselves in measured thermo-physical properties [4–6]. Fruits and vegetables at different stages of processing are subjected to thermal treatments in the food industry, understanding their behavior to these thermal processes requires good knowledge of thermal and physical properties. These properties are essential for designing and optimization of every process involving heat transfer at unsteady state such as cooking, frying, and drying and post-harvest heat treatments. Thermal conductivity is an intrinsic property which measures the ability of a substance to conduct heat. The importance of thermal conductivity is to predict or control the heat flux in food material during processing when energy transfer is involved. 2. Theory The calculation of heat transfer in foods begins with the identification of three major parameters in heat transfer processes: 1. Thermal properties of the food. 2. Geometry of the food. 3. Thermal Processing conditions. Methods of measuring thermal conductivity are classified into two categories:
S.K. Modi et al. / International Journal of Heat and Mass Transfer 78 (2014) 354–359
355
Nomenclature D1 D2 HDL I K Kw Ks LDL MC q r R
= = = = = = = = = = = =
density (911 Kg/m3) density (1062 kg/m3) High Density Lipoprotein Electric Current (AMP(A)) thermal conductivity (W/m °C) thermal conductivity of water (W/m °C) thermal conductivity of solid (W/m °C) low density lipoprotein moisture content (%) heat input (W/m) radial axis (m) electric resistance (X m1)
T T1 T2 t t0 t1 t2 wb
The steady state heat transfer methods often require a long time to complete and moisture migration may introduce significant measurement errors [7]. The transient methods are most suitable for biological materials that are generally heterogeneous and often contain high moisture content, where the line heat source method is one of the most widely used. Here a bare wire method is used as a heating source, and estimates the thermal conductivity based on relationship between the sample core temperature and the heating time. The rate of heat generated in the wire ‘q’ W/m:
ð1Þ
where I = electric current in amps (A), R = electric resistance in X m1. For a long cylindrical sample, where the end effects and the mass of hot wire can be neglected and when the sample is homogeneous and isotropic, heat conduction in the sample is governed by the equation (cylindrical coordinates)
@T @ 2 T 1 @T ¼a þ @t @r 2 r @r
sample temperature (°C) temperature (°C) at time ‘t1’(s) temperature (°C) at time ‘t2’ (s) time (s) time correction factor (s) time (s) corresponding to temperature (T1) time (s) corresponding to temperature (T2) wet bulb
Greek symbols a = thermal diffusivity (m2/s)
1. Steady state heat transfer method. 2. Unsteady state (transient) heat transfer method [6].
Q ¼ I2 R
= = = = = = = =
!
ð2Þ
where T = is the sample temperature anywhere in the cylinder ‘°C’, t = time in ‘s’, r = is the radial axis in ‘m’, a = thermal diffusivity in ‘m2/s’.
temperature and moisture content by Kostaropoulous [10], Sweat [11] and Dickerson and Read [12]. Not much data were found on fruits/vegetables especially for Exotic tropical fruits such as Guava fruit. Hence, this study was made to investigate the thermal conductivity of fresh and dried fruit in the moisture range of 40–80% (wb) grown in the local area (Rayalaseema, AP, India). 3. Materials 3.1. Sample preparation and moisture content Fresh, Desiree, ripened and well matured fruits of uniform shape size and color with no apparent damage were procured from the local orchard (Rayalaseema area, AP, India) are washed in clean potable water (the flesh of each fruit was observed to be pink and the central pulp contains seeds) and allowed to equilibrate with room temperature prior to testing. The moisture content of the fresh samples was found to be 80% (wb) as determined using a standard method AOAC (Association of Official Analysts and Chemists) [13] in a Vacuum oven at 70 °C for 24 h with 03 replicates. To obtain samples with a range of moisture contents 80% to 40% (wb), the samples were dried for various periods in an experimental hot air drier at 55, 60 and 65 °C. The partly dried samples were sealed in a polyethylene film and stored at a constant temperature for 24 h to ensure uniform moisture content throughout the sample. 4. Experimental setup and methodology 4.1. Experimental setup
The solution to the above equation, transient heat flow method developed by Hoopper and Lepper [8] with time correction factor was employed. Sreenarayanan and Chattopadhyay [9] have explained theoretical consideration of the equation used. The modified equation for calculating thermal conductivity incorporating the time correction values is shown in the Eq. (3):
K¼
q t2 t0 ln 4pðT 2 T 1 Þ ðt 1 t 0 Þ
ð3Þ
where K = thermal conductivity of the sample (W/m °C) q = heat input (W/m) T1 and T2 = temperatures in °C at time t1 and t2 (s) t0 = time correction factor (8.2 s). t1 and t2 = time in seconds corresponding to temp. T1 and T2. The data on thermal conductivity for the food products have been reported in the literature under different conditions of
Schematic representation of line heat source apparatus used for measuring K is shown in Fig. 1 [14]. The bare wire thermal conductivity apparatus consisted of an aluminum cylindrical sample tube of 104 mm length and 28.4 mm inner diameter, with a removable Teflon cover and with a fixed bottom base cover. A chromel resistance heating wire of 33 gauge and a length of 200 mm stretched between copper leads along the axis of cylindrical tube used as line heat source, of which the effective length of heating element inside the test cylinder is 104 mm and the remaining length (96 mm) is used to connect the leads on either sides outside the test cylinder. A constant DC Power supply was used for all the tests. A pre-calibrated T-type 28 gauge iron-constantan thermocouple was installed for measuring the core temperature of the sample in the cylinder. The power input to the line heat source was sufficient to give a measurable temperature difference between the time t1 and t2.
356
S.K. Modi et al. / International Journal of Heat and Mass Transfer 78 (2014) 354–359
where K = Thermal conductivity of unknown material, (W/m °C). Kw = Thermal conductivity of Water, 0.614 W/m °C. Ks = Thermal conductivity of Solids, 0.2597 W/m °C. M = Moisture content of material in decimal. 5. Results and discussion Experiments were conducted to determine the thermal conductivity of Guava fruit at different instant of time, temperature and density with the moisture content ranging from 40% to 80% (wb). 5.1. Assay of thermal conductivity of guava fruit Fig. 1. Schematic representation of the apparatus used for measuring thermal conductivity [14].
4.2. Methodology A known mass of defined moisture content is filled in the cylindrical sample tube. The open end of the tube was sealed off with a polyethylene foil before the Teflon top cover was placed in order to prevent the evaporation of moisture. The sample in the tube is allowed to equilibrate with the ambient temperature. When the sample attains the constant temperature with ambient temperature, the power and stop watch were switched ON simultaneously. The core temperature shown by the thermocouple was noted for every 30 s up to 20 min. The current was determined to an accuracy of 0.01 A by measuring at Regulated Power Supply. The thermal conductivity values are determined using Eq. (3). The moisture content of the sample were measured before and after the test and found to be no considerable changes. Predicted model: Sweat [15] and Anderson [16] models were used to compare thermal conductivity with the experimental values: Sweat model:
K ¼ 0:148 þ 0:00493 M
ð4Þ
where, M = moisture content of the material in% (wb). Anderson model:
K ¼ MK w þ ð1 MÞK s
ð5Þ
Variation of thermal conductivity at different instant of time in the range of 40% to 80% (wb) moisture content for densities of 911 kg/m3 (D1) and 1062 kg/m3 (D2) are depicted in Figs. 2 and 3. It is observed that at all moisture contents, thermal conductivity of guava fruit increases with increase in time. But at lower moisture levels Thermal conductivity is relatively low with higher moisture levels with increase in temperature or time. Because, as the moisture evaporates the sample shrinks and the rate of shrinkage in the initial stage of heating is more, leading to porosity i.e. entrapped air which is a bad conductor of heat, hence decrease in the thermal conductivity [17,18]. It is observed that thermal conductivity increases with increase in time at all moisture contents. The analysis shows that at higher moisture contents (70% and 80% (wb)), thermal conductivity values lie in the range of 0.3027 W/m °C to 0.5775 W/m °C and 0.3210 W/ m °C to 0.6037 W/m °C results in increased thermal conductivity. Similarly at lower level moisture contents (50% and 40% (wb)), the thermal conductivity values lie in the range of 0.265 W/m °C to 0.5019 W/m °C and 0.1526 W/m °C to 0.4595 W/m °C respectively. This is due to low density, void spaces present and nonhomogeneity in the sample structure apparently causes the reduction the thermal conductivity. The variation of thermal conductivity with respect to center temperature of guava fruit (at different instant of time) in the range of 40% to 80% (wb) moisture content for densities D1 and D2 are shown in Figs. 4 and 5 respectively. It is observed that thermal conductivity increases with increase in center temperature for all moisture content 40% to 80% (wb). This behavior suggests that the structural characteristics of fruit
Fig. 2. Variation of thermal conductivity v/s time for various moisture content (for density of 911 kg/m3).
S.K. Modi et al. / International Journal of Heat and Mass Transfer 78 (2014) 354–359
Fig. 3. Variation of thermal conductivity v/s time for various moisture content (for density of 1062 kg/m3).
Fig. 4. Variation of thermal conductivity v/s centre temperature for various moisture content (for density of 911 kg/m3).
Fig. 5. Variation of thermal conductivity v/s centre temperature for various moisture content (for density of 1062 kg/m3).
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Fig. 6. Variation of thermal conductivity v/s moisture content at different time (for density of 911 kg/m3).
Fig. 7. Variation of thermal conductivity v/s moisture content at different time (for density of 1062 kg/m3).
permit rapid moisture migration in response to increase in temperature. In the initial stage of heating at all moisture contents the thermal conductivity increases more rapidly because of presence of more suspended water particles on the surface of the sample making it wet. The Thermal conductivity increases rapidly in the beginning and attain steady state until final stage. Effect of moisture content (40% to 80% (wb)) on thermal conductivity of guava fruit at different timings for densities D1 and D2 shown in Figs. 6 and 7. Thermal conductivity increases with the increase in moisture content because moisture contained in the sample leads to heat transfer by conduction hence increase in the thermal conductivity values with increase in time. It is also observed that, at higher moisture content (60–80% (wb)), thermal conductivity values lie in the range of 0.2908– 0.5438 W/m °C, and 0.3210–0.6037 W/m °C results in increase in thermal conductivity values. This is because high density and moisture content present in the sample has by far greater influence on the increase of thermal conductivity values [9]. Similarly at lower moisture content i.e. less than 60% moisture content thermal conductivity decreases due to surface
Fig. 8. Variation of thermal conductivity v/s time for different densities at 40% and 80% moisture content.
S.K. Modi et al. / International Journal of Heat and Mass Transfer 78 (2014) 354–359
moisture being evaporated causing the case hardening of the surface. At 40% (wb) the thermal conductivity lies in the range of 0.1526–0.4595 W/m °C. The variation of thermal conductivity with time for two densities (D1, D2) at 80% and 40% moisture content are shown in Fig. 8. It is observed that, at different bulk densities (D1 and D2) of 80% and 40% (wb) moisture content, thermal conductivity values increases with increase in time/temperature and corresponding increase in density. This indicates that thermal conductivity is not merely a function of physical properties like density, temperature and moisture content but also is a function of physical structure of food sample [10]. 6. Conclusion Experimental investigations have been carried out in order to investigate the effect of moisture content (MC) and temperature on thermal conductivity (K) of guava fruit. From the above discussion the following conclusion were made: 1. Significant variation in thermal conductivity was observed with changes in moisture content and temperature. 2. It is observed that, the thermal conductivity increases with increase in moisture content, caused mainly by conduction heat transfer of water particles of the sample. 3. The thermal conductivity also increases with increase in density, due to higher thermal contact between particle structures of the sample and also structure is nonporous with fewer voids (i.e. the volume of pores reduced, resulting in higher Thermal conductivity). 4. The variation of thermal conductivity may occur due to nonhomogeneity and positioning of temperature measurement within the sample. 5. The deviation of experimental results of thermal conductivity with the standard models is in the range of 10.15% to 18.38% (Sweat) and 12.08% to 14.29% (Anderson), and found to be in good agreement.
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