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Measurementandmodellingtheeffectoftemperature,relativehumidityandstoragedurationonthetranspirationrateofthreebananacultivars

ArticleinScientiaHorticulturae·September2016

DOI:10.1016/j.scienta.2016.06.011

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SanchitaMurmu

IndianInstituteofTechnologyKharagpur

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HariNMishra

IndianInstituteofTechnologyKharagpur

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Scientia Horticulturae 209 (2016) 124–131

Contents lists available at ScienceDirect

Scientia Horticulturae

journa l homepage: www.e lsev ier .com/ locate /sc ihor t i

easurement and modelling the effect of temperature, relativeumidity and storage duration on the transpiration rate of threeanana cultivars

anchita Biswas Murmu ∗, Hari Niwas Mishragricultural and Food Engineering Department, Indian Institute of Technology, Kharagpur, 721302 West Bengal, India

r t i c l e i n f o

rticle history:eceived 8 November 2015eceived in revised form 31 May 2016ccepted 10 June 2016

eywords:ranspiration rateananaass transferodel

nergy balance

a b s t r a c t

Transpiration rate (TR) of three cultivars of banana (triplicates of each experimental run, 2 nos. presentin each run) was measured at different temperatures (10, 20 and 30 ◦C) and relative humidity (RH) (70,80 and 90%) and storage time (2, 3 and 6 days). Models based on unsteady state energy balance equationand regression equation was fitted to the TR data. Best fitting model was validated at 15 ◦C and 70, 80and 90% RH and on 2nd, 3rd and 6th day of storage. Using the TR data design parameters for equilibriumhumidity packaging for three banana varieties had been estimated. While the TR of banana increased withrise in temperature, it decreased with rise in storage RH and with progress of storage duration. BananaCv. Singapuri had significantly low (P < 0.05) average TR (21.69 g/kg-day), while the average TR of G9(34.96 g/kg-day) and Chapa (29.53 g/kg-day) cultivars were similar (P > 0.05), and these two varieties (G9and Chapa) were least affected by variation in temperature and relative humidities. The energy balancemodel (R2 = 0.61–0.81) fitted the TR data better than the regression model at all RH and temperaturestudied. Temperature of the banana surface was determined from the model and was found to be greaterthan the wet bulb temperature of banana. Heat transfer from banana surface by convection was found to

◦

provide approximately 70% of the heat required for transpiration. At 15 C, the predicted TR was plottedagainst the experimental data corresponding to storage RH, and duration. For these two predictions themean relative percentage deviation modulus was 10.27% and 18.35%, respectively. The required watervapour transmission rate for designing equilibrium humidity packaging of three variety of banana rangedfrom 172 to 618 g/m2day at 10–20 ◦C.

© 2016 Elsevier B.V. All rights reserved.

. Introduction

India with annual production of 29.72 million metric tonnMMT) is the leading producer of banana in the world contribut-ng 27.8% of total world production. Also, the production increasedt 2.08% average rate per year for the last five years (Indianorticulture Database, 2014). Of the total production in India, only.12% is exported to more than nine countries of the world includ-

ng USA (14000 MT), Soudi Arabia (4809 MT), Oman (3521 MT) etc.

arning an export value of about 1.56 billion Indian rupee (APEDA,015).

∗ Corresponding author.E-mail addresses: sanchita1600@agfe.iitkgp.ernet.in, sanchita1600@gmail.com

S.B. Murmu).

ttp://dx.doi.org/10.1016/j.scienta.2016.06.011304-4238/© 2016 Elsevier B.V. All rights reserved.

The shelf-life of banana is limited due to its climactericnature. Storage under modified atmosphere or humidity packaging(MAP/MHP) extends shelf-life of banana without use of any chemi-cal preservatives (Chauhan et al., 2006). To design MHP for bananait is essential to have the information about rate of water evap-oration from banana surface, which should be balanced with thewater vapour transmission rate of the packaging film constitutingthe MHP. Otherwise, water vapour will condense on the walls of thepackage and enhance bacterial and mould growth on the commod-ity. On the other hand extremely low in-package humidity resultsin weight loss of banana. Where fruit is sold on a weight basis,loss of water is equivalent to economic loss. Water loss also detori-ates visual acceptability and had been reported to causes plantain

cultivars of banana to lose its firmness, the peel becomes soft andshriveled, and ripening period reduces (Mu-bo et al., 2015). There-fore, study of the transpiration rate (TR), which is the rate of waterevaporated from banana surface per unit mass per unit time of

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S.B. Murmu, H.N. Mishra / Scient

anana is highly important in MHP design study. Water loss hadeen described as the most important factor effecting shelf life ofepper cultivars in MAP by Lownds et al. (1994).

Mathematical models are used to predict TR of a commodityt any time and any temperature. In the literature there are sev-ral models for estimating TR of different commodities but theyave limited applications due to their specific assumptions. For ex.,ang and Lee (1998) estimated TR of apple by using respiratoryeat as the latent heat required for water evaporation under sat-rated storage conditions in controlled atmosphere. Their modelssumed a steady state condition and did not consider any changen temperature on the fruit surface due to energy transfer. Modi-ed model was used for blueberries by Song et al. (2002) who used

he overall energy balance equation inside MAP to estimate rate ofater evaporation but convection heat transfer inside the pack was

ot considered.Model based on Fick’s law of diffusion was developed by

ahajan et al. (2008) who included temperature term to predictranspiration rate of mushrooms at any temperature. Sousa-allagher et al. (2013) used the model developed by Mahajan et al.

2008) to estimate water vapour transmission rate of polymer filmequired for MA storage of strawberries. Sastry and Buffington1983) described water loss from tomato using mass transfer equa-ion, which required information about water vapour diffusivity,haracteristic dimension, air viscosity and air density.

In all the models TR has been considered constant and the effectf time has not been considered. Also, it appears that no model

s present to detect the TR of banana considering unsteady statenergy balance equation. The aim of this work was to (i) measurehe TR of three cultivars of banana at different temperatures, rel-tive humidity conditions and storage durations and (ii) developodel based on unsteady state energy equation and regression

quation to predict TR of banana at any storage duration.

. Materials and methods

.1. Transpiration rate measurement

Banana of ‘Singapuri’ (Musa spp.) and ‘Chapa’ (Musa spp.) vari-ty were purchased from the local market of Kharagpur (India)n the same day of their harvest whereas that of Grand NainiG9) (Musa acuminata, AAA group) variety were procured from thexperimental farm of Agriculture and Food Engineering Departmet,IT khargpur. The banana bunches were quickly brought to the Foodhemistry and Technology Laboratory, Indian Institute of Technol-gy, Kharagpur and washed with tap water followed by surfaceiping with blotting paper and drying in ambient air.

Sorting of the fruits of each variety was done based on unifor-ity of weight, length and surface greenness (a* value) mentioned

n Table 1. The initial weight of banana was measured using anlectronic balance (Afcoset, GmbH); length, breadth and diame-er were measured with a vernier calliper (Mitutoyo, Japan) andeel outer surface color was measured with colorimeter (Konicainolta, CM-5).

To evaluate the TR of banana, a weight loss technique was used.wo bananas were stored inside an environmental test chamberRemi Instruments) at thermostatically controlled temperature andelative humidity (RH) conditions; taken out at specific time inter-al and weight loss was measured. TR was calculated from thehanges in weight of banana over time from Eq. (1). Temperaturend RH inside the environment chamber were monitored contin-ously using temperature and RH probe and data displayed on the

nstrument display screen.

R = M − Mi

t × Mi1000

(1)

ticulturae 209 (2016) 124–131 125

Where, TR is the transpiration rate in g/kg day; Mi is the initialweight (g), and M is the weight of banana (g) at time t (day).Experiments were performed according to a full factorial design,considering 4 factors at three levels (34), i.e., banana variety (Sin-gapuri, G9 and Chapa), temperature (10, 20 and 30 ◦C), RH (70%,80% and 90%) and storage period (2, 3 and 6 days). Experimentswere replicated three times.

2.2. Measurement of respiration heat

Respiration may be assumed as oxidation of glucose (Eq. (2)) andexpressed as average of rate of O2 consumption and CO2 evolution(Eq. (3)) (Song et al., 2002).

C6H12O6 + 6O2 = 6CO2 + 6H2O + 2, 816, 000 J ↑ (2)

Qs = 12

[rO2 + rCO2

]× 2, 814, 000

6J (3)

Where, Qs is the respiratory heat generation J/mol; rO2 is the res-piration rate of banana in terms of O2 consumption, and rCO2 is therespiration rate of banana in terms of CO2 evolution in kg-mol/kg-day, measured by closed system method (Mangaraj and Goswami,2011). The change in% O2 and% CO2 with time on the headspace ofthe 1.8 L jar containing banana at any temperature was determinedby a head space analyzer (Systech Illinois, 6600).

2.3. Development of transpiration rate model

2.3.1. Energy balance modelAn energy balance was done on the evaporating surface of the

fruit (Eq. (4)) as used by Kang and Lee (1998) and Song et al. (2002).It was assumed that the respiratory heat was the only source ofinternal heat and the head space was assumed to be small and wasat thermal equilibrium with the storage environment. Banana fruitwas assumed to be cylindrical in geometry.

Qs × RR × M + hs × A × (Ts − Tb,t) = TR × M × � + M × Cp,f

×dTb,tdt

(4)

Where, A is surface area of fruit, m2; Ts is the temperature (◦C)of the storage environment; Tb is the surface temperature (◦C) ofthe banana at any time, and was assumed to be initially at the wetbulb temperature of the storage environment; � is the latent heatof evaporation of water in kJ/kg at Ts; Cp,f is the specific heat of thefruit 3.35 kJ/kg ◦C (The engineering tool box website, 2016); dt isthe time interval; hs is the convective heat transfer co-efficient andis calculated by Eq. (5) by assuming natural convection and laminarflow past a cylinder (Kang and Lee, 1998).

hs = 1.32 × 3600 × 24 × 4

√(Ts − Tb,t)

d(5)

Where, Where, Tw,t = wet bulb temperature of the banana surface,d is characteristic dimension of the fruit in m and was calculated bydividing volume by surface area of banana (Table 1). By integratingthe energy balance model with time Eq. (6) was obtained.[Mb(RR × Qr − � × TR) + (h × Ab × (Ts − Tb,t))

]Day 2[

Mb(RR × Qr − � × TR) + (h × Ab × (Ts − Tb,t))]

Day 1

= e−h×Ab×(t2−t1)

M×Cp (6)

2.3.2. Regression modelRegression model Eq. (7) including the effect of time, RH, their

interaction and quadratic terms was fitted to the experimental data

126 S.B. Murmu, H.N. Mishra / Scientia Horticulturae 209 (2016) 124–131

Table 1Initial physical properties used for sorting three varieties of banana for transpiration rate measurement.

Variety Weight, g Surface greeness,a*

Length, mm Breadth, mm Width, mm Surface area,mm2

Characteristicdimention, mm

Initial moisturecontent (% w.b.)

G9 158.37 ± 24.25 −9.77 ± 2.36 120.38 ± 12.13 26.66 ± 5.74 29.61 ± 2.59 22,407.62 74.69 ± 9.24 75.91 ± 1.03± 4.56 30.61 ± 1.33 21,407.62 74.09 ± 7.21 76.57 ± 2.78± 2.64 26.00 ± 0.73 20,687.33 75.40 ± 6.33 73.73 ± 1.78

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Table 2Effect of three storage temperatures, storage relative humidity and storage durationon the average transpiration rate of three banana cultivars (n = 6).

Factors Levels Transpiration rate, g/kg-day

Variety Singapuri 21.59 aG9 34.96 bChapa 29.53 b

Singapuri G9 Chapa

Temperature,◦C 10 17.84 a 35.35 a 30.05 a20 16.17 a 24.05 b 24.70 ab30 26.22 b 45.21 c 33.83 ac

Relative Humidity, % 70 24.31 a 34.31 a 32.20 a80 22.92 a 38.96 a 26.87 a90 13.01 b 31.33 a 29.51 a

Storage Duration, Days 2 32.93 a 37.91 a 25.69 a3 13.02 b 35.51 a 28.37 a

Singapuri 77.50 ± 20.97 −5.23 ± 1.01 103.38 ± 15.13 25.66

Chapa 40.42 ± 07.85 −10.51 ± 2.01 71.16 ± 10.68 21.41

* Indicate the CIE color scale.

f TR of three variety of banana at each temperature.

y = ˇ0 + ˇ1x1 + ˇ2x2 + ˇ12x1x2 + ˇ11x12 + ˇ22x2

2 + ˇ112x12x2

+ˇ122x1x22 (7)

here, x1 is temperature; x2 is RH and x3 is storage duration and terms represent co-efficients.

Eqs. (6) and (7) were used to fit the experimental data obtainedt the combinations of temperature and RH reported earlier, andhe constant coefficients (Tb,t of heat balance model and � termsf regression model) were estimated by minimizing sum of squareesidual using solver tool of the Microsoft Excel, 2007 software.xperimental data were subjected to analysis of variance usingesign Expert 7, software. When the significant difference wasbserved, mean treatments were compared using Turkey’s test.

An additional set of similar experiment mentioned in Sections.1 and 2.2 was carried out at 15 ◦C and 70, 80 and 90% RH toetermine respiration rate and TR in order to validate the devel-ped model. The mean relative percentage deviation modulus wasalculated to evaluate the goodness of fit of the predicted andxperimental data.

. Results and discussion

.1. Effect of storage temperature

The tanspiration rate of banana increased with rise in temper-ture, decrease in RH and progess of storage duration (Table 2).ingapuri had significantly low (P < 0.05) average value of TR21.69 g/kg-day), while the average TR of G9 (34.96 g/kg-day) andhapa (29.53 g/kg-day) cultivars were similar (P > 0.05), and thesewo varieties were least affected by variation in temperature andelative humidities.

The observed TR of banana was higher than transpiration rate ofther commodities which do not have any protective covering. Forxample, Sousa-Gallagher et al. (2013) reported that TR of straw-erries was in the range of 5–24 g/kg-day over temperature rangef 5–15 ◦C and RH range of 76–96%. Similarly, Caleb et al., (2013)eported lower TR of non-climacteric pomegranate arils between.4–16.75 g/kg-day at a temperature range of 5–15 ◦C and 75–90%H and also reported that highest water loss of the arils were at

ow temperature and low RH. This comparison shows that bananas highly transpiring fruit and stresses the importance of measure-

ent of banana TR before engineering design of its MHP.The interaction effect of storage temperature × storage relative

umidity (P < 0.05) and storage temperature × storage duration isignificant (Fig. 1). The variation of RH causes greater variation inR at higher temperature only for all the studied cultivars. Also atny temperature TR decreases with storage duration initally afterhich it increases (for Singapuri and Chapa) or remains constant

G9) variety.When banana was stored at 30 ◦C and 70% RH mould growth

as observed on the fruit surface after only four days of storage

t 30 ◦C and 70% RH. Surprisingly, within four days banana did notipen as indicated by the skin color (data not shown). The aforesaidtorage condition was also found to support Botrytis decay result-ng in excessive softening of the infected part of the fruit advancing

6 14.29 b 31.20 a 34.51 b

a, b, c has significance of p < 0.05.

with storage time, therefore the experiment was terminated aftersix days. Whereas, storage at 90% RH and 10 ◦C induced peel brown-ing/blackening affecting overall visual acceptability of the banana.Contradictorily, at 20 ◦C and 80–90% RH no mould growth wasobserved till banana was fully ripened to yellow color following7 days of storage. This indicates that in-pack RH of 80–90% may befavorable for MAP banana.

To prevent water condensation inside the packaging film at anytemperature, it is required to match the water vapour transmissionrate of the packaging film with banana transpiration rate at thattemperature (Mahajan et al., 2008). Considering this, the designconsiderations for equilibrium humidity packaging of one kg Sin-gapuri banana (approximately 8–10 fingers) is demonstrated at10 ◦C.

The required packaging film area (Af) was calculated by usingbanana finger dimentions from Table 1 as Af = 2 × (width of onefinger × length of one finger) × (1 kg/weight of each finger). Withthis 20% extra area can be obtained providing enough space forsealing etc. Total area thus calculated was Af,total = 936 cm2.

The required water vapour transmission rate (WVTRr)of the packaging film at any temperature was cal-culated as WVTRr = Average TR of banana at thattemperature/Af,total = 190.59 g/m2-day. In the similar way WVTRrwas determined for other cultivars of banana at three temperaturesand presented in Table 3. The WVTRr of the packaging films isdifferent for each variety of bananas and is sensetive to fluctuationin temperature.

When the WVTR of the available film is lower than the WVTRrwater vapour would condense inside MAP. To avoid inpackagecondensation calculated mass of scrubber may be included in equi-librium humidity packaging. For example, packaging film with highWVTR of about 300 g/m2day had been used by Mahajan et al. (2008)for mushrooms. Using film having WVTR of 300 g/m2day for pack-

aging one kg G9 banana at 10 ◦C for storage of 14 days, total massof water accumulation (Mw) inside the designed packaging may becalculated as Mw = (WVTRr − WVTR available) × Af × Storage dura-tion = 244.86 g.

S.B. Murmu, H.N. Mishra / Scientia Horticulturae 209 (2016) 124–131 127

10

15

20

25

30

70.00

75.00

80.00

85.00

90.00

0

7.75

15.5

23.25

31

TR

B: TEMP C: RH

(A-a)

10

15

20

25

30

2.00

3.00

4.00

5.00

6.00

2

19.5

37

54.5

72

TR

B: TEMP D: STORAGE TIME

(B-a)

10

15

20

25

30

70.00

75.00

80.00

85.00

90.00

18

25

32

39

46

TR

B: TEMP C: RH

(A-b)

10

15

20

25

30

2.00

3.00

4.00

5.00

6.00

0

27.5

55

82.5

110 T

R

B: TEMP D: STORAGE TIME

(B-b)

10

15

20

25

30

70.00

75.00

80.00

85.00

90.00

14

19.75

25.5

31.25

37

TR

B: TEMP C: RH

(A-c)

10

15

20

25

30

2.00

3.00

4.00

5.00

6.00

11

22.25

33.5

44.75

56

TR

B: TEMP D: STORAGE TIME

(B-c)

Fig. 1. Effect of interaction between (A) RH and temperature on the 4th day of storage anChapa variety of banana.

Table 3The required water vapour transmission rate for design of equilibrium humiditypackaging of one kg banana for Singapuri, G9 and Chapa cultivars at 10, 20 and30 ◦C.

Required water vapour transmission rate,g/m2-day

Temperature, ◦C 10 20 30VarietySingapuri 247 172 280

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apfaaelt

G9 618 436 818Chapa 271 223 305

This mass of accumulated water must be absorbed by theelected moisture scrubber. Average absorbtion capacity of silicael is 0.4 g water/g silica. Hence, 612.15 g silica is required for effec-ive shelf-life of 1 kg G9 banana. This mass of required silica gel isery high for incorporating in MAP. Hence, moisture absorber hav-ng higher absorbing capacity e.g. clay and mesoporous materialsEng-Poh and Mintova, 2008) may be used instead of silica gel.

.2. Transpiration rate models and comparison

The regression equations for three cultivars of banana at 10, 20nd 30 ◦C are shown in Table 4. Linear relationship was suggested toredict TR as a function of storage RH and storage duration at 10 ◦C

or the three cultivars, equations involving interaction terms of RHnd storage duration and their quadratic terms were fitted at 20nd 30 ◦C. The co-efficient of determination (R2) of the regression

quations at all the temperatures ranged from 0.14–0.76; with theower values of R2 indicating unsatisfactory fit of the predicted datao the observed data.

d (B) storage duration and temperature at 80% RH for (a) Singapuri (b) G9 and (c)

To predict TR of banana by energy balance model the neces-sary parameters including the respiration rate in terms of oxygenconsumption, carbon dioxide evolution and the correspondingestimated respiratory heat generation are shown in Table 5. Therespiration rate and consequently the generated respiratory heatfollowed the expected climacteric pattern. The respiratory heatwas heighest for Singapuri cultivar (1.33–23.12 J/kg-h) compared tothat of G9 (0.34–4.04 J/kg-h) and Chapa cultivars (0.57–18.40 J/kg-h) at all the studied temperatures.

The only unknown parameter in the energy balance model wasthe temperatures of banana surface at any storage temperature,humidity and storage duration. The estimated temperature at thebanana surface was relatively less than the wet bulb temperatureat 10 ◦C and was more than the wet bulb temperature at 20 and30 ◦C for all the cultivars (Fig. 2a–c). This indicated that the devel-oped energy balance model considered the evaporative cooling ofthe banana surface due to transpiration as well as rise in tempera-ture of the banana surface due to heat of respiration. By analyzingthe model it was found that respiratory heat contributed 3–30%,0.01% and 0.1–0.03% of the total heat required for transpiration forsingapuri, G9 and Chapa cultivars, respectively at the three studiedtemperatures. This indicated that majority of the heat required fortranspiration was provided by heat transfer by convection from thesurface.

The co-efficient of determination of the energy balance modelwas 0.71, 0.76, and 0.81 for the Singapuri cultivar; 0.81, 0.76, and0.71 for G9 cultivar; and 0.61, 0.67, and 0.69 for Chapa cultivar at10, 20 and 30 ◦C, respectively. As this model had higher co-efficient

of determination, therefore it was selected over the regressionmodel to predict TR of banana. This could be further confirmedfrom Fig. 3(a–c) which show the observed TR and predicted values

128 S.B. Murmu, H.N. Mishra / Scientia Horticulturae 209 (2016) 124–131

Fig. 2. Relative variation in temperature of banana surface estimated from energy balance model from the wet bulb temperature for (a) Singapuri (b) G9 and (c) Chapacultivars of banana at 10, 20 and 30 ◦C and 70, 80 and 90% storae RH.

S.B. Murmu, H.N. Mishra / Scientia Horticulturae 209 (2016) 124–131 129

Fig. 3. Observed and predicted transpiration rate of (a) Singapuri (b) G9, and (c) Chapa cultivars by regression model and heat balance model at 10, 20 and 30 ◦C and 70% RHon the 2nd day of storage and (d) during the storage duration for Singapuri cultivar at 10 ◦C and 70% RH.

130 S.B. Murmu, H.N. Mishra / Scientia Horticulturae 209 (2016) 124–131

Table 4Regression equation to predict transpiration rate of three varieties of banana at 10, 20 and 30 ◦C with their corresponding co-efficient of regression (R2) values.

Banana Variety Temperature, ◦C Regression Equation R2

Singapuri 10 TR = 63.40 − 0.31 *x1 − 5.29 * x2 0.3620 TR = − 196.88 + 9.33 * x1 − 71.71 * x2 + 0.32x1 * x2 0.3930 TR = 405.35 − 5.68x1 − 73.72 * x2 + 0.06x1 * x2 + 0.03x1

2 − 7.81 * x22 0.73

G9 10 TR = −105.63+ 1.88 * x1 − 3.08 * x2 0.3720 TR = −927.99 + 24.62 * x1 − 10.18x2 − 0.16 * x1 * x2 − 0.15x1

2 + 2.64 * x22 0.48

30 TR = 181.04 −0.74 * x1 + 0.67 * x2 0.45

Chapa 10 TR = −59.72 + 1.23 * x1 + 22.89 * x2 − 0.31x1 * x2 0.1420 TR = 118.40 − 1.24 * x1 − 29.75 * x2 + 0.39x1 * x2 0.2330 TR = 1046.56 − 24.80 * x1 − 12.97 * x2 + 0.30x1 * x2 + 0.14 * x1

2 − 1.20 * x22 0.46

Table 5Experimentally observed respiration rates and estimated respiratory heat of three cultivars of banana on the 2nd, 3rd and 6th day of storage at 10, 20 and 30 ◦C.

Variety Temperature, ◦C 10 20 30

Storage time, days RCO2 × 10−5 RO2 × 10−5 Ravg × 10−5 Qs RCO2 × 10−5 RO2 × 10−5 Ravg × 10−5 Qs RCO2 × 10−5 RO2 × 10−5 Ravg × 10−5 Qs

2 0.85 0.3 1.21 2.71 0.98 1.30 1.16 5.45 3.2 3.4 3.37 15.83Singapuri 3 0.18 0.37 1.18 1.33 0.73 0.73 0.73 3.44 1.6 1.10 1.38 6.49

6 0.18 0.55 1.54 1.74 2.30 2.10 2.10 10.53 5.5 4.20 4.92 23.12

G9 2 0.22 0.22 0.22 1.05 0.98 0.91 0.94 4.45 0.85 0.86 0.86 4.043 0.15 0.07 0.11 0.54 0.77 0.72 0.01 3.52 0.69 0.75 0.72 3.386 0.18 0.03 0.07 0.34 0.63 0.54 0.59 2.77 0.45 0.52 0.45 2.29

Chapa 2 0.61 0.44 0.53 2.49 2.99 2.45 2.72 12.76 4.13 3.70 0.01 18.403 0.16 0.11 0.13 0.64 2.33 1.8 2.06 9.70 2.45 1.11 0.01 8.376 0.14 0.01 0.12 0.57 1.68 1.51 0.01 7.49 2.03 2.15 2.09 9.82

Where RO2 and RCO2 are respiration rate of banana in kg mol/kg-day and Qs is respiration heat in J/kg-day.

F energy balance model at 15 ◦C (a) on 2nd day of storage at different RH (b) 90% RH.

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Table 6Regression equations with their corresponding co-efficient of determinations to pre-dict the temperature of banana surface at any storage temperature, relative humidityand storage duration for Singapuri, G9 and Chapa banana cultivars.

Banana variety Equation to predict temperature of banana surface R2

Singapuri T = − 0.67 + 1.13 * y + 0.24* y 0.99

ig. 4. Transpiration rate of banana of Singapuri cultivar observed and predicted by

f TR of banana by regression model and energy balance model atll the temperatures. The energy balance model also predicted TRf banana with respect to time. An example of such TR predictionith respect to storage duration for Singapuri cultivar at 10 ◦C and

0% RH is shown in Fig. 3(d).To predict TR of banana at any unknown temperature and rela-

ive humidity the corresponding banana surface temperature (Tb)s required. This temperature was found to depend linearly on thetorage wet bulb temperature (y1) and storage duration (y2). Suchegression equations for three studied banana cultivars and theirorresponding co-efficient of determinations are shown in Table 6.hese equations may be combined with the enrgy balance modelo predict the TR of the selected banana cultivars at any storage

emperature, relative humidity and storage duration.

Transpiration rate of banana of Singapuri cultivar observed at5 ◦C and different storage RH are presented in Fig. 4(a) while theredicted value at 15 ◦C and 70% RH as a function of storage duration

b 1 2

G9 Tb = 3.36 + 0.98 * y1 − 0.42 0.09* y2 0.96Chapa Tb = − 1.00 + 1.15 * y1 + 0.12* y2 0.98

is shown in Fig. 4(b). For these two predictions the mean relativepercentage deviation modulus is 10.27% and 18.35%, respectively.

4. Conclusion

Transpiration rate of three variety of banana in the tempera-ture range of 10–30 ◦C varied from 17 to 26, 35–45, 30–33 g/kg-hrfor Singapuri, G9 and Chapa cultivars, respectively. TR increased

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Sousa-Gallagher, M.J., Mahajan, P.V., Mezdad, T., 2013. Engineering packaging

S.B. Murmu, H.N. Mishra / Scient

ith rise in storage temperature and decreased with rise in stor-ge humidity and progrss of storage time. Maximum in-packagetorage temperature and RH for minimum transpiration and qual-ty deterioration may be 20 ◦C and 90% RH. Unsteady state energyalance model fitted the TR data of banana at all RH and tempera-ures. The coefficient of determination of the model was 0.61-0.81hich provided a better fit of the experimental data than regres-

ion equation. Surface temperature of banana was less than storagenvironment temperature at a particular RH. Convective heat trans-er between the storage environment and banana surface provided

ajority of the heat energy required for water evaporation. Theequired water vapour transmission rate for designing equilibriumumidity packaging of three variety of banana ranged from 172 to18 g/m2day at 10–20 ◦C.

cknowledgement

The financial support from the Department of Biotechnology,overnment of India, is thankfully acknowledged.

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http://www.engineeringtoolbox.com/specific-heat-capacity-food-d 295.html. Asseen on 30th May, 2016.