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Effect of Solid Particles on the ThermalConductivity of Mango Juice in a ShearFlow FieldD.I.O. Ikhu-Omoregbe aa Department of Chemical Engineering , Cape Peninsula University ofTechnology , Bellville, Cape Town, South AfricaPublished online: 21 Aug 2009.

To cite this article: D.I.O. Ikhu-Omoregbe (2009) Effect of Solid Particles on the Thermal Conductivityof Mango Juice in a Shear Flow Field, International Journal of Food Properties, 12:4, 885-895, DOI:10.1080/10942910802105452

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International Journal of Food Properties, 12: 885–895, 2009Copyright © Taylor & Francis Group, LLCISSN: 1094-2912 print / 1532-2386 onlineDOI: 10.1080/10942910802105452

885

EFFECT OF SOLID PARTICLES ON THE THERMAL CONDUCTIVITY OF MANGO JUICE IN A SHEAR FLOW FIELD

D.I.O. Ikhu-OmoregbeDepartment of Chemical Engineering, Cape Peninsula University of Technology,Bellville, Cape Town, South Africa

The effect of solids on the thermal conductivity of mango juice concentrate obtained from aSouth African supermarket was studied in a shear flow field using a coaxial cylinder appa-ratus with a rotating outer cylinder. The fluid was observed to be shear thinning and thermalconductivity increased with temperature, shearing rate and particle size. The thermal con-ductivity of the juice with coarse particles was found to be significantly different from thatwithout particles at a given temperature and shear rate. Significantly different values wereobtained when the solid concentration is 50 mg/l. Temperature and shear rate dependentmodels were tested with the data and were found to correlate the observed data fairly wellwith a correlation coefficient of above 0.95.

Keywords: Thermal conductivity, Solids, Mango juice, Shear rate, Couette flow.

INTRODUCTION

Good engineering analysis and design of production systems and product qualityevaluation of food substances often rely on reliable thermophysical and transportproperty data. The transfer of heat to and from a product has significant interest inproduct quality control during heating or cooling of food. The successful managementof heat transfer processes depends on the availability of thermophysical data such asthermal conductivity. The thermal properties of food substances are used in quantita-tive analysis for various thermal processes, such as heating, cooking, sterilization,drying and extrusion cooking.[1] The processing of fruit juices often requires heatingand sterilization.

Non-Newtonian liquid and semi-solid food substances have varying viscosity undera shearing environment. It is therefore reasonable to suggest that there will be changes inthe thermal conductivities when these substances are subjected to a shearing field. There issignificant information on the effect of temperature, moisture content and composition onthermal conductivity of food substances in literature.[2-10] However, not much data isavailable on the effect of shear stress-shear rate on the thermal conductivity of foods. Thisis because available data (values) for most liquid foods have been measured under static

Received 20 July 2007; accepted 6 April 2008.Address correspondence to D.I.O. Ikhu-Omoregbe, Department of Chemical Engineering, Cape Peninsula

University of Technology, Bellville, Cape Town, 7535, South Africa. E-mail: ikhuomoregbed@cput.ac.za

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conditions. If a shear rate effect exists on the thermal conductivity such as in the case withapparent viscosity, then measurements must be made over a range of shear rates when thefluid is in motion with respect to a static boundary.

The effects of shear rate on thermal conductivity of viscoelastic polymer fluids havebeen fairly reported in literature. Cocci and Picot[11] reported that the thermal conductivityof Dow 200 fluids increase with increase in shear rate in the region of ( ).Chitrangad and Picot[12] and Picot et al.[13] reported that at low shear rates of ( ),the thermal conductivity of DOW 200 fluids and polyethylene melts increased withincreasing shear rate, reached a maximum point and then decreased with increasing shearrate ( ). Lee and Irvine[14] observed for non-Newtonian fluids such asaqueous CMC and Separan solutions, that there were as much as 70% and 50% increasesin thermal conductivities for CMC and Separan respectively depending on the shear rate,polymer concentration and temperature. Their results showed a linear relationshipbetween shear rate and thermal conductivity. Shin and Lee[15] carried out thermal conduc-tivity measurements of polymer suspensions under a rotating couette flow conditions witha varying rotational speed of the outer cylinder. The thermal conductivity of the test sus-pensions in shear flow increased with shear rate and displayed asymptotic plateau valuesat high shear rates. Furthermore, the shear rate dependent conductivity was stronglyaffected by both particle size and volume concentration in shear flow field. Xu Qi Linet al.[16] and Ikhu-Omoregbe and Chen[17] used similar flow conditions to measure thethermal conductivity of two fruit juices and sauces obtained from a supermarket in Auckland,New Zealand, respectively, observed trends as those for the polymer materials. That thermalconductivity increases linearly as shear rate increases.

A number of models have been proposed in literature[6,8,18,19] to predict the thermalconductivity of two-phase systems. These models were based on the geometry of the compo-nents in the two phases. Furthermore, some have been extended to predict multi-componentsystems. Maroulis et al.[20] applied some of these models to predict the thermal conductivity ofgelatinized starch at different temperatures and compositions. Two types of thermal con-ductivity prediction models can be identified in the literature.[6] The first relates tempera-ture to thermal conductivity while the second relates composition to thermal conductivity(a structural model). However, both cover only non-shearing cases. Empirical models willbe proposed to correlate the effect of shear rate and/or temperature on thermal conductivity.The thermal conductivities of most substances are known to be functions of temperatureand are of the form:

where a, b, and c are constants and T is temperature (ºC). In this paper a model of the formwas used:

where is shear rate (s−1). The objectives of this investigation were to: determine theeffect of shear rate on the thermal conductivity at three temperatures of mango fruit juice;investigate the effect of size and concentration of solids on the thermal conductivity of thisjuice in a shearing environment; and propose some empirical models to demonstrate theeffect of shear rate on apparent thermal conductivity.

0 00≤ ≤ −&g 3 s 1

&g ≤ −2 s 100

200 400 1≤ ≤ −&g s

k a bT cT 2= + + (1)

k a + bT + cT + f ( )2= &g (2)

&g

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THERMAL CONDUCTIVITY OF MANGO JUICE 887

MATERIAL AND METHODS

Materials

A number of solution mixtures were made with the mango juice concentrate by add-ing known quantities and sizes of thyme solids. Both materials were obtained from asupermarket in Durban, South Africa. The mango juice concentrate (Bromo Foods (Pty)Ltd. Salt River, South Africa) consisted of mango puree, guava puree, orange juice, sugar,water, acidifying agent (E330), stabilizer (E412), sodium benzoate, sulphur dioxide, fla-vourants, colourants, and vitamin C.

Three different size fractions of thyme (The Spice People, South Africa) were usedas with a size ranges of 750–1000 microns (coarse fraction), 300–750 microns (mediumfraction) and 150–300 microns as the fines fraction. The concentrations of the solids usedin this set of runs were 25.0 g per litre of juice. In another set of runs the fines particleswere used but the concentrations were 10, 20, 25, 35, and 50 mg/l, respectively.

Method

The equipment and procedure adopted in this work are similar to those described in detailsby Qi Lin et al.[16] and Ikhu-Omoregbe and Chen.[17] The equipment consists of two con-centric cylinders, in which the inner cylinder is stationary and the outer one can be rotated.Both cylinders were made from materials such as copper with high thermal conductivities,so that the temperature drop across each is negligible compared to that across the testfluid. The test fluid is contained in the annular space (1.5 mm) between the two cylinders.One of the advantages of couette method is the non-existence of Taylor vortices especiallyif the gap is narrow[21,22] and the annular space of ro/ri of 1.074 satisfies the elementaryrequirement of ISO 3219 for narrow gap. The rest of the system consists of a constant tem-perature bath, a main heater, a guard heater, thermocouple to measure the inner cylinderand bath temperatures, and Pico data acquisition system. To commence the run, the speedof rotation is set and the system was allowed to reach a steady state which takes about10–15 min. Then the temperatures, voltage and current are recorded every 10 s for 10 minthrough the data acquisition system; the speed of rotation of the outer cylinder was alsorecorded. The speed was varied as to give a shear rate of between 0 and 700 s−1. The meanvalue of these readings at a set shear rate was taken as one experimental point. All thermalconductivity measurements were in triplicates and showed a variation of not more than±5%. The effect of time of shear on thermal conductivity of the pure juice was examinedat shear rates of 204, 409, and 546 s−1 and at a temperature of 30ºC.

If we assume that Fourier’s law of conduction is applicable, the shear rate variationacross the gap (annulus) is negligible, the thermal conductivity of the liquid (test fluid) inthe gap is considered to be independent of temperature, at steady state the following equa-tion can be written for thermal conductivity, k:

where Q is heat input calculated from current and voltage measurements Q is current (A)× voltage (V); do is outer diameter (m); di is inner diameter (m),l is length of the testingsection (m); and DT is temperature difference across the testing fluid (ºC). For a

kQ d /d

l Ti=

ln 0( )2p Δ

(3)

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narrow gap” ≈1.5 mm between the cylinders, regardless of fluid type, the velocity profilecan be assumed to be linear over this distance. The shear rate ( ), s−1 within the gap canthus be considered to be uniform and can be calculated as:

where n is rotational speed, (rpm.); do and di are as defined above. The rheologicalmeasurements (shear stress – shear rate and viscosity) of the test fluids were madeusing an Anton Paar MC51 rheometer (Anton Paar GmbH, Ostfilden, Germany). Themeasurement system used for this work consisted of a measuring cup of radius 21 mmand bob of radius 19.5 mm. The gap length was 60 mm and cone angle of the measuringbob was 120°. A constant temperature circulator (Viscotherm VT2, Anton Paar GmbH)with a temperature range of −20 and 180°C (± 0.1°C) was used to control measurementtemperature. The rheological measurements were at various shear rates ranging from 1to 800 s−1, and at a temperature of 30°C. The rheological measurements were made todemonstrate that the fluids used in this work are non-Newtonian fluids. The suitabilityof this apparatus set up for this study was determined in another publication.[19] Also inthat work the presence and effect of secondary flow on the measurement wasexplained.

RESULTS AND DISCUSSION

Figure 1 shows that the mango juice concentrate (pure and mixed with solids) isnon-Newtonian and that its viscosity decreases with increasing shear rate suggesting thatthis fluid is shear thinning. The apparent viscosity of the pure juice varied from 0.40 Pa.sat low shear rate to 0.17 Pa.s at high shear rate at a temperature of 30°C. Furthermore, theresults show that its viscosity decreases with increasing temperature as the moleculesbecome elongated or expand. Application of the power law viscosity model to the puremango juice gives values for consistency index, K as 0.94 and flow behaviour index, n as0.251. The results also show a correlation coefficient, R2 > 99.6%, suggesting a good fit.There were no significant viscosity changes with the presence of solids as similar patternsand values were obtained (Figure 1b).

&g

&gp

=( )

−( )n

d di

d + di0

60 0

(4)

Figure 1 Viscosity-shear rate curves for (a) pure mango juice and (b) with solids.

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THERMAL CONDUCTIVITY OF MANGO JUICE 889

The results in Table 1 show the values of thermal conductivity with shear rate formango juice, with the fine, medium and coarse particle fractions respectively at the differenttemperatures of 30, 40, and 50°C. It can be observed that the thermal conductivity valuesfor the juice without solids varied from 0.30 W/m K at zero shear rate and 30°C tempera-ture, to 0.76 W/m K at a shear rate of 700 s−1 and at 50°C temperature. Similar values forthe mixture with fines varied from 0.34 W/m K at zero shear rate and 30°C to 0.98 W/m Kat a temperature of 50°C and shear rate of 615 s−1. These increased to 0.37 W/m K at 30°Cand zero shear rates, and 1.43 W/m K and a temperature of 50°C for the fluid containingthe coarse fraction. These values compare well with those obtained for mango pulp byTelis et al.[19] The results also show that thermal conductivities for the fluids with particlesare higher than that without the particles for a given shear rate. The fluid with the coarseparticles also has higher conductivity values at a given shear rate. Furthermore the resultsshow that thermal conductivity values increase significantly with increasing shear rate fora given temperature. Also for a given shear rate the conductivity increases with tempera-ture. It can be observed from Table 2 that the apparent thermal conductivity tends toincrease with solids concentration for a give shear rate. However, a least significant differ-ent (LSD) analysis indicated that the effects of particle size and solids concentration arenot significant (p < 0.05) except for the 50 mg/l concentration and for the coarse particlesfor the solid contents particle size and shear rates investigated. Furthermore, correlationanalysis for the comparative effects of particle size and solids concentration does not indi-cate which had a more pronounced effect on thermal conductivity of the substance,although there is more variation with particle size compared to concentration.

Based on a critical Reynolds number of 1000 after which instabilities and turbulencein the gap start to significantly affect the results, critical shear rates were determined forthe various fluid mixtures used in this work. A critical shear rate of 2970 s−1 was obtainedfor the least viscosity value of 0.073 Pa·s for any of the material condition. This value ismuch higher than the maximum shear rate of 800 s−1 experienced in the thermal conduc-tivity measurements. Furthermore the maximum Reynolds number experienced during theexperiments was 300 for the least viscous conditions. As the critical shear rate and

Table 1 Thermal conductivity, W/mK values at various shear rate, particle size and temperature for mangojuice.

Temp. ºC

Shear rate, 1/s

0 68.2 136.4 204.6 272.8 341.0 409.2 477.5 545.7 619.9

No solid 30 0.301 0.403 0.468 0.485 0.497 0.511 0.516 0.521 0.532 0.54040 0.341 0.471 0.485 0.535 0.563 0.589 0.607 0.618 0.627 0.63550 0.401 0.597 0.632 0.654 0.671 0.706 0.729 0.727 0.748 0.755

Juice + fines 30 0.337 0.438 0.505 0.554 0.589 0.641 0.675 0.706 0.715 0.73840 0.418 0.524 0.676 0.707 0.735 0.747 0.766 0.775 0.787 0.80250 0.576 0.675 0.746 0.808 0.855 0.875 0.933 0.948 0.964 0.981

Juice + medium solids 30 0.316 0.422 0.508 0.594 0.643 0.721 0.763 0.797 0.835 0.85840 0.434 0.514 0.609 0.672 0.789 0.848 0.911 1.092 1.158 1.21450 0.602 0.616 0.741 0.838 0.905 0.982 1.144 1.273 1.308 1.343

Juice+coarse solids 30 0.368 0.658 0.807 0.906 0.960 0.997 1.040 1.066 1.100 1.11040 0.471 0.703 0.876 0.953 1.112 1.178 1.188 1.207 1.287 1.31150 0.627 0.755 0.919 1.013 1.167 1.254 1.309 1.393 1.419 1.428

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Reynolds number were not exceeded, it is thus correct to state that instabilities due toturbulence would not have had any significant effect on the results obtained.

Correlation analysis suggests that there is a strong linear correlation between thermalconductivity and shear rate (R2 > 0.95) for all the composition and solids sizes on one hand andbetween thermal conductivity and temperature (R2 > 0.95) for all the composition and sol-ids sizes investigated on the other hand. The analysis of the results also show that thermal con-ductivity for the conditions studied increase significantly with increasing shear rate for agiven temperature. These observations are in agreement with literature[11,14,16] that thermalconductivity of non-Newtonian fluids increase with shear rate. A number of reasons havebeen given for the effect of shear rate on thermal conductivity.

Cocci and Picot[11] explained it to be due to either preferred orientation or clusterrotation of the polymer molecules. Shin and Lee[15] suggested that the shear rate dependentconductivity was strongly affected by both particle size and volume concentration in shearflow field which is agreement with the findings of this work. Xu Qi Lin et al.[16] suggestedthat the higher thermal conductivity at higher shear rates is due to the fluid structurebecoming more aligned along the streamlines and hence becoming ordered. This was apparentbecause one of the fluids (mango concentrate) contained some fibres. Though the puremango juice used in this work did not contain mango fibres, the presence of the thyme solids isthought to have possible similar effects.

A common phenomenon when a material is continuously being sheared is the occur-rence of viscous dissipation resulting in local heating and temperature distribution andconsequently affecting the thermal properties obtained. The contribution of viscous energycan be determined by estimating the Brinkman number and viscous heat production. Analysisof the system and results gave a Brinkman number less than 0.01 and a viscous heat con-tribution of 2.81% for the most viscous condition and at highest shear rate of 800 s−1. Theimplication of this is that viscous dissipation did not significantly affect the resultsobtained.

Figure 2 shows that the thermal conductivity of mango juice increases with the timeof stress at the beginning and then remains fairly constant after about 10 min. This is aperiod of unsteady state with reference to thermal conductivity when shearing action iscommenced. This observation suggests a realignment of the polymer structure due toshearing forces. It is also possible that the polymer structure could have become“stretched” resulting in increased rate of heat transfer across the material.

Table 2 Effect of solids concentration on thermal conductivity at various shear rates and 30ºC.

Shear rate, 1/s

Solids concentration, mg/l

0 10 20 25 35 50

0 0.301 0.306 0.314 0.308 0.375 0.43268.2 0.403 0.417 0.427 0.438 0.475 0.505136.4 0.468 0.452 0.475 0.483 0.547 0.564204.6 0.485 0.488 0.494 0.505 0.594 0.642272.8 0.497 0.508 0.513 0.516 0.632 0.686341.0 0.511 0.522 0.551 0.569 0.657 0.736409.2 0.516 0.562 0.570 0.575 0.706 0.771477.5 0.521 0.578 0.581 0.586 0.734 0.801545.7 0.532 0.589 0.595 0.606 0.746 0.825

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THERMAL CONDUCTIVITY OF MANGO JUICE 891

The effect of time on viscosity at constant shear rate is shown in Figure 3 for a shearrate of 100 s−1 and 30ºC temperature. The results show that the apparent viscositydecreases slightly with increasing duration of shear. It can be observed that while viscosityis decreasing thermal conductivity is increasing, suggesting that as the bond forces arebeing ‘stretched’ (sheared), the ability of the material to conduct heat is enhanced agreeingwith the observations of Ikhu-Omoregbe and Chen.[17] Similar shear decay curves wereobserved for mustard suspensions,[23] chickpea flour dispersion,[24] mango pulp,[25] and fruitsauces.[26] The effect is less pronounced for the mixture with the highest solids content.

Thermal Conductivity Models

A number of models have been proposed in literature[6,15] to predict the thermal con-ductivity of two-phase systems. These models were based on the geometry and composition ofthe components in the two phases. Furthermore, some have been extended to predictmulti-component systems in a non-shearing field. In this paper attempt is made to accountfor the effect of shear rate/shear stress on the thermal conductivities of food substances.The thermal conductivity of most materials is known to be a function of temperature andis of the form of Eq. (1).

Figure 2 Thermal conductivity vs time shear for mango juice at 30ºC.

0

0.1

0.2

0.3

0.4

0.5

0.6

0 10 20 30 40Time, mins

Con

duct

ivity

, W/m

.K204 1/s 409 1/s 545.7 1/s

Figure 3 Viscosity vs time of shear at constant shear rate of 100 s−1.

0

0.1

0.2

0.3

0.4

0.5

0 20 40 60Time, mins

App

aren

t vis

cosi

ty, P

a.s

50 mg/l

10 mg/l

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Correlation analysis of the relationship between thermal conductivity and shear ratesuggest a linear relationship. Hence it is possible to deduce empirical models of the formof Eq. (2), which incorporate the effects of the rates of shear to correlate the data. From theresults, the following models can be deduced to relate conductivity, temperature and shearrate for these materials.

1. Pure mango juice:

(a)

(b)

(c)

2. Mango juice with fine solids:

(a)

(b)

(c)

3. Mango juice with medium solids:

(a)

(b)

(c)

4. Mango juice with coarse solids

(a)

(b)

(c)

where s is the slope of conductivity-shear rate curve and is shear rate. Figures 4(a-d)show the thermal conductivity values predicted using the three shear-rate dependent modelsfor the pure mango juice, juice with fine particles, juice with the medium particles andjuice with the coarse particles, respectively. The above results suggest that both equationsA and C best correlate the data while model B did not fairly correlate the data. The modelstend to correlate the data better at the lower shear rates than at the higher values. The perfor-mance of these empirical models suggests that the relationship between thermal conduc-tivity and shear rate can be said to be linear rather than exponential.

Statistical analysis of the results shows good correlation between experimental and pre-dicted values using the models. An analysis of the standard errors and standard % errorbetween predicted values and experimental thermal conductivities for the different solid sizemixtures was carried out in order to compare the performance of the proposed models. It wasobserved from the analysis results that models A and C gave the lowest standard error values

k 0.301 3.0T 10 1.0T 10 s3 2 4= − × + × +− − &g

k 0.301 3.0T 10 1.0T 10 T3 2 4 2.16= − × + × +− − −&g

k 0.301 3.0T 10 1.0T 10 0.098 T 103 2 4 5= − × + × + ×− − −&g

k 0.266 5.8T 10 2.4T 10 s3 2 4= − × + × +− − &g

k 0.266 5.8T 10 2.4T 10 T3 2 4 2.07= − × + × +− − −&g

k 0.266 5.8T 10 2.4T 10 0.133 T 103 2 4 5= − × + × + ×− − −&g

k 0.262 5.7T 10 2.5T 10 s3 2 4= − × + × +− − &g

k 0.262 5.7 T 10 2.5T 10 T3 2 4 2.07= − × + × +− − −&g

k 0.262 5.7T 10 2.5T 10 0.296 T 103 2 4 5= − × + × + ×− − −&g

k 0.372 8.0T 10 2.62T 10 s3 2 4= − × + × +− − &g

k 0.372 8.0T 10 2.62T 10 T3 2 4 1.84= − × + × +− − &gk 0.372 8.0T 10 2.62T 10 0.308 103 2 4 4= − × + × + ×− − −&g

&g

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THERMAL CONDUCTIVITY OF MANGO JUICE 893

for all temperatures and solid content. For example whilst model A gave a standard error of0.027 and standard % error of 3.23 at 40ºC for the mixture containing medium sized particles,model B gave respective values of 0.292 and 35.42 at the same temperature and material. Thisimplies that the predicted values of thermal conductivity values were in closer agreement withexperimental values using models A and C for the various solids contents used in this work.The performances of both models agree with earlier assertion that the relationship betweenshear rate and thermal conductivity is rather linear as these models are based on linear rela-tionship between thermal conductivity and shear rate. The performance of the models for thedifferent solid contents does not show any defined trend. The values of the standard errors andstandard % errors are not significantly different for a given temperature except for the coarsesolids. The solids are not dissolved in the fluid and therefore the effect of the presence of solidsthought to be that of possible scattering or bouncing off heat or a type of convective transferrather than conduction. It is apparent that this is better played by the larger particles, compar-atively. The form of these models are empirical hence the specific model parameters or/andconstants may not be applicable to other materials, but its form could be suitable for predict-ing the thermal conductivity for liquid food material in a shear fields.

CONCLUSION

The effects of solid particles on the thermal conductivity of mango juice obtainedfrom the market have been studied in a shearing environment using a coaxial cylinder

Figure 4 Predicted thermal conductivity values for: (a) pure juice at 50ºC; (b) with fines at 30ºC; (c) withmedium particles at 40ºC; and (d) with coarse particles at 50ºC.

(a)

0

0.2

0.4

0.6

0.8

1

0 200 400 600Shear rate, 1/s

Con

duct

ivity

, W/m

.K

Exptl. Eqn. A Eqn. B Eqn. C

(b)

0

0.2

0.4

0.6

0.8

1

0 200 400 600 800Shear rate, 1/s

Con

duct

ivity

, W/m

.K

Exptl. Eqn. A Eqn. B Eqn. C

(c)

0

0.5

1

1.5

Shear rate, 1/s

Con

duct

ivity

, W/m

.K

0 200 400 600

Exptl. Eqn. A Eqn. B Eqn. C

(d)

0

0.5

1

1.5

2

Shear rate, 1/s

Con

duct

ivity

, W/m

.K.

Exptl. Eqn. A Eqn. B Eqn. C

0 200 400 600

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apparatus with a rotating outer cylinder. The juice concentrate was found to be shear thin-ning and the thermal conductivity values increased with increasing rate of shear. The ther-mal conductivities were also found to increase with the presence of solids in the juice.Furthermore, the thermal conductivity values were found to be significantly higher withthe coarser particles and at a concentration of 50 mg/l for a given temperature and shearrate. The thermal conductivity was also observed to increase asymptotically to a constantvalue with time of shear. The results were not significantly affected by viscous dissipationcontribution. Three temperature and shear rate dependent empirical models for the con-ductivities have been proposed and tested. The models were based on the assumption thatthe relationship between thermal conductivity and shear rate is linear. Two of these modelswere found to fit the data fairly well with correlation coefficient above 0.95.

ACKNOWLEDGMENT

The author would like to thank the University of KwaZulu-Natal for providing the funds for this work.

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2. Sweat, E.V.; Parmelee, C.E. Measurement of thermal conductivity of dairy products and marga-rines. Journal of Food Process Engineering 1978, 2, 187–197.

3. Wang, N.; Brennan, J.G. Thermal conductivity of potato as a function of moisture content. Journal ofFood Engineering 1992, 17, 152–160.

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