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doi:10.1016/j.biosystemseng.2006.04.006PH—Postharvest Technology

Biosystems Engineering (2006) 94 (3), 429–435

Determination of Convective Heat and Mass Transfer Coefficientsfor Solar Drying of Fish

Dilip Jain

Central Institute of Post Harvest Engineering and Technology, PAU Campus, Ludhiana 141 004, India; e-mail: jaindilip25@rediffmail.com

(Received 15 July 2005; accepted in revised form 7 April 2006; published online 5 June 2006)

Solar drying (natural convection) of Indian minor fish species, such as prawn (Macrobrachium lamarrei) andcarp (chelwa) (Oxygaster bacaila), has been studied. The hourly data for the rate of moisture evaporation, fishtemperature and relative humidity of surrounding air have been recorded for complete drying of fish. Thesedata were used for determination of the coefficients of convective heat and mass transfer. Convective heat andmass transfer coefficients are mainly dependent on the rate of moisture transfer under the drying process,which have been determined as the function of drying time and moisture content of fish. The convective masstransfer coefficient varied from 8�958 to 0�402 mms�1 for prawn and from 7�613 to 0�320 mms�1 for chelwafish. The empirical rational models have been developed to predict the convective heat and mass transfercoefficients with moisture contents. The goodness of fit of the model described with higher coefficient ofdetermination 0�9996 and low root mean square error 0�05079 for drying of chelwa fish.r 2006 IAgrE. All rights reserved

Published by Elsevier Ltd

1. Introduction

India ranks fourth in global fish production with anannual production of 6Mt equivalent to 1�4% of thegross domestic product (GDP). The share of inland fishproduction increased to 50% of the total landings. Indiahas 19 370 reservoirs covering 3 153 366 ha. Fish hastraditionally been viewed as a source of high-qualityanimal protein, supplying approximately 6% of globalprotein requirement and 16% of the total animal protein(Ayyappan & Diwan, 2003). Minor fish species con-sumed with bones and shell (chitin) body, are a goodsource of calcium, protein, vitamin B and vitamin B12.Fish is highly perishable with a short storage life.

Cooling is a widely used and important preservationtechnique to maintain quality and prevent the spoilage(Dincer, 1995) and the simplest method of cooling offish is icing (Jain et al., 2005; Govindan, 1985). When,the fresh fish is not utilised by consumers and convertedinto finished product then it remains surplus and goeswaste. Around 20% of fish is wasted due to poor andinsufficient methods of cold storage and improper post-harvest practices in India (Prakash et al., 2003). Minor

1537-5110/$32.00 429

fish species such as prawn and carp (chelwa) are dried innorthern India (Punekar & Mandape, 2003). Solardrying is very common practice of fish in manydeveloping countries.

Drying is a process of heat and mass transfersimultaneously. Where, the heat energy applied to thefish is utilised to increase the temperature of fish and tovaporise the moisture present in the fish throughprovision of latent heat of vaporisation. The removalof moisture from the interior of the fish takes place dueto induced vapour pressure difference between the fishand surrounding medium. The desired difference ofvapour pressure may be obtained either by increasingthe vapour pressure of the fish surface or by decreasingthe vapour pressure of the surrounding or by both. Theabove parameters may be employed for controllingdrying rate under the controlled conditions of drying.However, this is not true with the open solar drying,since it is weather-dependent process.

Several empirical models such as Page model,Henderson and Pabis model and logarithmic modelhave been fitted to represent the onion drying process,where the operating parameters are under control and

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Published by Elsevier Ltd

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Notation

At area of fish (tray), m2

C coefficientCv specific heat of humid air, J kg�1 1C�1

Cf specific heat of fish, J kg�1 1C�1

c constantERMS root mean square errorGr Grashof number ( ¼ bgX3rv

2DT1/m2)g acceleration of gravity, m s�2

hc convective heat transfer coefficient of fish,Wm�2 1C�1

hc,pre predicted convective heat transfer coefficient offish, Wm�2 1C�1

Kv thermal conductivity of humid air, Wm�1 1C�1

kg convective mass transfer coefficient, m s�1 ormms�1

kG convective mass transfer coefficient, kgmolm�2 s�1 Pa�1 or ngmolm�2 s�1 Pa�1

L characteristic dimension, mm gradientmev moisture evaporated, kgNu Nusselt number ( ¼ hcL/Kv)n coefficientPr Prandtl number ( ¼ mv Cv/Kv)

P(T) partial vapour pressure at temperature T, Nm�2

Qe rate of heat utilised to evaporate moisture,Jm�2 s�1

R universal gas constant ( ¼ 8314�3), JK�1mol�1

r2 coefficient of determinationTf surface temperature of fish, 1CTe temperature of humid air above the fish

surface, 1CTi average of fish and humid air temperature, 1CDT1 effective temperature difference, 1Ct time, sXd moisture content of fish on dry basis, kg [H2O]/

kg [dry matter (DM)]Xw moisture content of fish on wet basis, kg [H2O]/

kg [fish]x, y independent and dependent variableZ functionb coefficient of volumetric expansion, C�1

g relative humidity (dec.)l latent heat of vaporisation, J kg�1

mv dynamic viscosity of humid air, kgm�1 s�1

rf density of fish, kgm�3

rv density of humid air, kgm�3

D. JAIN430

constant during the whole drying process (Jain &Pathare, 2004; Doymaz et al., 2004). The dryingcoefficient could be correlated with the operatingparameters. Similar expressions were tried to representthe solar drying process of aromatic plant (Akpinar,2005), where the drying coefficients with the operatingparameters could not be correlated, since these weretime and weather dependent.The modelling of heat and mass transfer mechanism

for solar drying of fish is complex. The convective heattransfer coefficient is an important parameter in dryingrate simulation since the temperature difference betweenthe air and fish varies with this coefficient. Jain andTiwari (2003) evaluated the convective heat transfercoefficient for some crops (green chillies, green peas,white gram, onions, potatoes, and cauliflower) undersolar drying and developed a mathematical modelfor predicting the drying parameters. Jain and Tiwari(2004) further studied the dependence of convectiveheat transfer coefficient on the drying time duringcomplete solar drying process of green peas andcabbage. The convective heat transfer coefficient ofjaggery under solar drying has been evaluated by Tiwariet al. (2004).The present studies were undertaken to determine

the convective heat and mass transfer coefficients at

different durations of the drying time and moisturecontent of the two varieties of fish (invertebrateand vertebrate) under the natural conditions of solardrying.

2. Theoretical consideration

2.1. Convective heat and mass transfer coefficient

The Nusselt number Nu for natural convection is afunction of Grashof Gr and Prandtl Pr numbers. Asingle equation correlates both the laminar and turbu-lent regimes well (Pitts & Sissom, 1977)‘:

hcL

Kv

¼ Nu ¼ CðGr PrÞn (1)

where: hc is the convective heat transfer coefficient inWm�2 1C�1; L is the characteristics length in m; Kv is thethermal conductivity of the humid air in Wm�1 1C�1; andC and n are the equation coefficient and exponent.

Thus, the convective heat transfer coefficient can bedetermined as

hc ¼Kv

LCðGr PrÞn (2)

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SOLARDRYING OF FISH 431

The rate of heat utilised Qe in Jm�2 s�1 to evaporatemoisture is given as (Malik et al., 1982)

Qe ¼ 0�016hc½PðTf Þ � gPðTeÞ� (3)

where P(Tf) and P(Te) are the partial vapour pressuresof air at the temperatures in 1C of the fish surface Tf andsurrounding humid air Te at relative humidity g,respectively.By substituting hc from Eqn (2), then Eqn (3) can be

written as

Qe ¼ 0�016Kv

LCðGrPrÞn½PðTf Þ � gPðTeÞ� (4)

The moisture evaporated mev in kg is determined bydividing Eqn (4) by the latent heat of vaporisation l inJ kg�1 and multiplying the area of the fish in tray At inm2 and time interval t in s

mev ¼Qe

lAtt ¼ 0�016

Kv

LlCðGr PrÞn

� ½PðTf Þ � gPðTeÞ�Att ¼ ZCðGr PrÞn ð5Þ

where the function Z is given by

Z ¼ 0�016Kv

Ll½PðTf Þ � gPðTeÞ�tAt (6)

Rearranging terms

mev

Z¼ CðGr PrÞn (7)

Taking logarithm of both sides of Eqn (7)

lnmev

Z

h i¼ n ln½Gr Pr� þ lnC (8)

This is the form of a linear equation, y ¼ mx+c, wherex and y are the independent and dependent variables, m

is the gradient and c is the constant, such that y ¼

ln½mev

Z�; m ¼ n; x ¼ ln½GrPr� and c ¼ ln C: Thus,

C ¼ expðcÞ (9)

Once the numerical values of C and n are known,the convective heat transfer coefficient is computed byEqn (2). The convective mass transfer coefficient kg inm s�1 is determined by using Lewis relation (Saravacos,1995) as

kg ¼hc

rf Cf

(10)

where: rf is the density in kgm�3; and Cf is the specificheat of fish in J kg�1 1C�1.Equation (10) may be written for convective mass

transfer coefficient in kgmol s�1m�2 Pa�1 as

kG ¼kg

RðTf þ 273�15Þ(11)

where: R is the universal gas constant in JK�1mol�1;and Tf is the surface temperature of fish.

2.2. Physical properties of humid air

The following expressions were used for calculatingvalues of the physical properties of air, such as specificheat Cv in J kg�1 1C�1, thermal conductivity Kv inWm�1 1C�1, density rv in kgm�3 and dynamic viscositymv in kgm�1 s�1 and the partial vapour pressure P inNm�2 (Jain & Tiwari, 2003). For obtaining the physicalproperties of humid air, Ti is taken as the average of thefish temperature Tf and the temperature just above thefish surface Te

Cv ¼ 999�2þ 0�1434Ti þ 1�101� 10�4T2i

� 6�7581� 10�8T3i ð12Þ

Kv ¼ 0�0244þ 0�6773� 10�4Ti (13)

rv ¼353�44

Ti þ 273�15(14)

mv ¼ 1�718� 10�5 þ 4�620� 10�8Ti (15)

PðTÞ ¼ exp 25�317�5144

Ti þ 273�15

� �(16)

2.3. Thermal and physical properties of fish

The following expression was used for thermal andphysical properties of fish.

The specific heat Cf in J kg�1 1C�1 of fish can beestimated (Siebel, 1982) as

Cf ¼ 837þ 334�9X w (17)

where Xw is moisture content of fish on wet basis in kg[H2O]/kg [fish].

Shrinkage factor during drying of fish muscles can becalculated (Balaban & Pigott, 1986) with the help ofchange in density of fish rf in kgm�3 with moisturecontent as

rf ¼ 1�4� 0�5X w (18)

where the value for the coefficient of determination r2 is0�875.

3. Materials and methods

3.1. Experimentation

Indian minor carp (chelwa) (Oxygaster bacaila);vertebrate and prawn (Macrobrachium lamarrei); inver-tebrate fish were considered for drying. The fresh fishpurchased from local market was washed with fresh

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D. JAIN432

water. The initial moisture of the fish was determinedby the method of drying at a temperature 130 1Cdescribed by Gerasimov and Antonova (1979) andobserved as 3�621 and 2�676 kg[H2O]/ kg[dry matter(DM)] in prawn and chelwa fish, respectively. Theinitial volume of the fish was measured by water-displacement technique. Surface water was removedby blotting with absorbent paper. A steel wire meshtray of 0�26m by 0�22m was used during solar dryingof the fish. The fish were arranged in a single layerin the drying tray. The tray with fish was kept in the sun,in a sheltered position to ensure disturbance from thewind was kept to a minimum. Experiments wereconducted in April 2005 between 10:00 and 17:00 hunder the climatic condition of Ludhiana, India(Latitude 301450N; Longitude 751480E). The solarradiation ranged during these hours between 460 and820Wm�2.A non-contact thermometer (Raytek-MT4; least

count of 0�5 1C and accuracy of 72%) was used formeasurement the temperature of fish surface. A digitalhygro-thermometer (Exteck-45320; least count of 1%relative humidity, accuracy of 73% and 0�1 1C,accuracy of71%) was used to measure the relativehumidity and temperature of air above the fishsurface. A top loading digital balance (CitizenCTG-1000) of 1 kg weighing capacity with leastount of 0�1 g was used to weigh the sample duringthe drying. The difference in weight gave themoisture evaporated during that observed timeinterval.

3.2. Computation technique

The average surface temperature of fish Tf andtemperature above the fish surface Te were calculatedat hourly intervals for corresponding moisture evapo-rated. The physical properties of humid air wereevaluated for the mean temperatures of Tf and Te

using Eqns (12)–(16). These physical properties wereutilised for calculating the values for the Grashof Gr andPrandtl numbers Pr. The initial area of fish At forcomputation was taken as the area of tray. The changein area of fish (in the tray) during drying was computedusing the shrinkage ratio obtained by the expressiongiven by Balaban and Pigott (1986) for density as thefunction of moisture content. The values of C and n inEqn (2) were obtained by linear regression techniqueexpressed in Eqn (8) at the increment of every hour ofobservation and thus the mean values of hc werecomputed at the corresponding hour of drying. Thecomputer program was prepared in the Matlab software6�1 (Mathworks, Inc.).

4. Results and discussion

The computed values of convective heat and masstransfer coefficients for prawn (invertebrates) fish duringnatural sun drying are summarised in Table 1. It took14 h (two sunny days) to dry the prawn fish from aninitial moisture content of 3�621 kg[H2O]/kg[DM] to thefinal moisture content as 0�081 kg[H2O]/ kg[DM]. Themoisture evaporation rate was higher in the initial fewhours (3–4 h) of drying. The Grashof number Gr rangedfrom 1�56� 106 to 0�019� 106 and Prandtl number Pr

remained steady as 0�705 throughout the drying process.The product of Grashof and Prandtl number (Gr

Prp107) indicates that the entire drying falls within alaminar flow regime (Holman, 1992; Jain & Tiwari,2004).

The convective heat transfer coefficient hc for prawnfish drying ranged from 9�929 to 0�472 Wm�2 1C�1. Theconvective heat transfer coefficient decreased with adecrease in moisture content of fish. Similarly, theconvective mass transfer coefficient kg varied from 8�958to 0�402 mms�1 and reduced with decreasing in moisturecontent. The convective mass transfer coefficient kG alsofollows the declining trend with moisture content andvaries from 3�554 to 0�155 ngmolm�2 s�1 Pa�1.

The dependence of convective heat transfer coefficientof prawn fish on the moisture content is presented inFig. 1. A linear rational model has been establishedbetween the convective heat transfer coefficient andmoisture content as

hc;pre ¼1�778X 2

d þ 4�41X d � 0�1499

X d þ 0�2499(19)

where: hc,pre is predicted convective heat transfercoefficient in Wm�2 1C�1; Xd is moisture content in kg[H2O]/kg [DM]; and where the values for coefficient ofdetermination r2 and the root mean square error ERMS

are 0�9967 and 0�1941, respectively.The convective heat and mass transfer coefficients for

chelwa (vertebrates) fish drying under natural sun arepresented in Table 2. The moisture evaporation rate wasslower compared to prawn fish throughout the drying.Therefore, the complete drying took longer duration as21 h (three sunny days) and to dry from an initialmoisture content 2�676 kg[H2O]/kg[DM] to the finalmoisture content as 0�138 kg[H2O]/kg [DM]. TheGrashof and Prandtl numbers once again explain thatentire drying process within the laminar flow regime(Gr Prp107). The convective heat transfer coefficient ofthe chelwa fish ranged from 8�524 to 0�376 Wm�2 1C�1,which was lower than that of the prawn fish. Theconvective mass transfer coefficient of chelwa fish variedfrom 7�613 to 0�320 mms�1. The convective mass

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0 0.5 1 1.5 2 2.5 3 3.5 40

1

2

3

4

5

6

7

8

9

10

11

Moisture content, kg[H2O]/ kg[DM]

Con

vect

ive

heat

tran

sfer

coe

ffic

ient

, W m

−2 C

−1

Fig. 1. Dependence of convective heat transfer coefficient on moisture content of prawn fish during solar drying; J, computedconvective heat transfer coefficient (hc), &, predicted convective heat transfer coefficient (hc,pre)

Table 1

Hourly observations and heat and mass transfer coefficients of prawn fish (invertebrates) (initial weight, 0.1633 kg; number

of fish, 305)

Day Dryingtime, h

Tf , 1C Te, 1C g mev, g Xd, kg[H2O]/kg

[dry matter]

Gr� 106 Pr C n hc,W m�2 C�1

kg,mm s�1

kG, ngmol m�2

s�1 Pa�1

1st 1 30�00 35�45 0�190 45�5 3�621 1�565 0�7051 1�000 0�227 9�929 8�958 3�5542 30�75 36�35 0�190 30�1 2�333 1�376 0�7051 0�998 0�212 8�086 7�188 2�8453 33�00 36�75 0�190 15�4 1�481 0�756 0�7052 0�968 0�192 5�889 5�156 2�0264 35�25 36�65 0�185 12�4 1�046 0�241 0�7053 0�900 0�184 4�699 4�073 1�5885 35�00 35�45 0�160 9�2 0�695 0�070 0�7052 0�806 0�183 3�951 3�393 1�3246 35�00 34�40 0�140 4�9 0�434 0�084 0�7052 0�690 0�180 3�176 2�711 1�0587 35�75 32�10 0�145 2�8 0�296 0�481 0�7051 0�704 0�155 2�391 2�036 0�793

2nd 8 36�00 31�35 0�155 1�9 0�217 0�584 0�7051 0�737 0�129 1�837 1�563 0�6089 36�25 34�20 0�155 1�6 0�163 0�232 0�7052 0�678 0�119 1�501 1�277 0�49610 37�00 36�75 0�155 0�7 0�118 0�025 0�7053 0�439 0�139 1�233 1�049 0�40711 38�00 38�10 0�160 0�3 0�098 0�019 0�7054 0�229 0�177 1�007 0�857 0�33112 38�75 38�50 0�150 0�2 0�089 0�023 0�7054 0�141 0�200 0�802 0�683 0�26313 39�00 38�20 0�145 0�1 0�084 0�074 0�7054 0�108 0�199 0�606 0�516 0�19914 39�50 38�60 0�140 0�1 0�081 0�082 0�7054 0�088 0�196 0�472 0�402 0�155

Tf hourly average surface temperature of fish; Te hourly average temperature of air above the fish surface; g hourly average relative humidity of

air above the fish surface; mev, hourly moisture evaporated; Gr, Grashof number; Pr, Prandtl number; C and n, coefficient and exponent; hc,

convective heat transfer coefficient; kg, convective mass transfer coefficient; kG, convective mass transfer coefficient.

SOLARDRYING OF FISH 433

transfer coefficient kG of chelwa fish ranged from 3�020to 0�121 ngmolm�2 s�1 Pa�1.The convective heat transfer coefficient of chelwa fish

is also a function of moisture content. Figure 2 presentsthe relationship of convective heat transfer coefficient ofchelwa fish with moisture content during sun dryingprocess. The following rational expression explains the

linear relation of moisture content and convective heattransfer coefficient as

hc; pre ¼2�925X 2

d þ 0�4577X d � 0�09773

X d þ 0�08512(20)

where the values for r2 and ERMS are 0�9996 and0�05079, respectively.

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Table 2

Hourly observations and heat and mass transfer coefficients of chelwa fish (vertebrates) (initial weight, 0.2141 kg; number

of fish, 101)

Day Dryingtime, h

Tf 1C Te g mev, g Xd, kg

[H2O]/kg[dry matter]

Gr� 106 Pr C n hc, W m�2

C�1kg,

mm s�1kG,

ng mol m�2

s�1 Pa�1

1st 1 30�00 35�55 0�295 29�5 2�676 1�306 0�7051 1�000 0�214 8�524 7�613 3�0202 30�75 36�45 0�275 21�3 2�170 1�218 0�7051 0�999 0�199 7�027 6�231 2�4663 33�00 36�60 0�275 18�8 1�804 0�691 0�7052 0�987 0�191 6�007 5�293 2�0794 38�00 39�55 0�260 15�6 1�481 0�240 0�7054 0�937 0�184 4�967 4�349 1�6815 41�00 41�55 0�235 12�0 1�213 0�073 0�7056 0�841 0�183 4�129 3�594 1�3766 41�50 42�05 0�255 11�2 1�007 0�067 0�7056 0�771 0�182 3�602 3�119 1�1927 41�50 42�85 0�270 8�8 0�815 0�152 0�7056 0�729 0�176 3�142 2�707 1�035

2nd 8 43�50 40�85 0�275 6�8 0�664 0�280 0�7056 0�719 0�164 2�671 2�293 0�8719 47�25 38�30 0�265 6�5 0�547 0�875 0�7056 0�804 0�139 2�237 1�914 0�71910 48�00 38�10 0�225 4�8 0�435 0�902 0�7057 0�898 0�114 1�873 1�599 0�59911 47�25 40�05 0�200 3�1 0�353 0�611 0�7057 0�950 0�095 1�574 1�342 0�50412 46�25 41�45 0�195 2�2 0�300 0�391 0�7057 0�941 0�082 1�341 1�142 0�43013 42�75 41�60 0�195 2�0 0�262 0�096 0�7056 0�800 0�086 1�200 1�021 0�38914 41�75 42�05 0�195 1�7 0�228 0�025 0�7056 0�610 0�101 1�097 0�934 0�357

3rd 15 43�00 42�10 0�180 1�2 0�198 0�071 0�7056 0�503 0�107 0�979 0�832 0�31716 44�00 41�55 0�155 0�8 0�178 0�189 0�7056 0�469 0�101 0�849 0�722 0�27417 44�75 41�45 0�135 0�6 0�164 0�249 0�7057 0�457 0�091 0�731 0�622 0�23518 42�75 40�85 0�135 0�4 0�154 0�148 0�7056 0�406 0�089 0�635 0�540 0�20619 43�25 39�25 0�125 0�3 0�147 0�317 0�7056 0�418 0�073 0�544 0�463 0�17620 45�75 36�35 0�105 0�2 0�142 0�746 0�7055 0�526 0�039 0�455 0�387 0�14621 43�75 34�25 0�100 0�1 0�138 0�810 0�7054 0�681 0�002 0�376 0�320 0�121

Tf ; hourly average surface temperature of fish; Te; hourly average temperature of air above the fish surface; g; hourly average relative humidity of

air above the fish surface; mev, hourly moisture evaporated; Gr, Grashof number; Pr, Prandtl number; C and n, coefficient and exponent; hc,

convective heat transfer coefficient; kg, convective mass transfer coefficient; kG, convective mass transfer coefficient.

9

8

7

6

5

4

3

2

1

00 0.5

Con

vect

ive

heat

tran

sfer

coe

ffic

ient

, W m

−2 C

−1

1.5 2.5 321

Moisture content, kg[H2 O]/ kg[DM]

Fig. 2. Dependence of convective heat transfer coefficient on moisture content of chelwa fish during solar drying; J, computedconvective heat transfer coefficient (hc), &, predicted convective heat transfer coefficient (hc,pre)

D. JAIN434

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SOLARDRYING OF FISH 435

The convective heat transfer coefficient of prawn andchelwa fish can be quantified using Eqns (19) and (20),respectively, by having the knowledge of moisturecontent of fish. Furthermore, the convective masstransfer coefficient can be evaluated with knowledge ofdensity and specific heat of fish, which are again thefunction of the moisture content of fish [Eqns (17) and(18)].

5. Conclusion

The convective heat and mass transfer coefficients ofminor fish species like prawn (invertebrates) and chelwa(vertebrates) have been determined under sun dryingcondition at different drying times and moisturecontents. Convective heat and mass transfer coefficientwas a function of moisture removal, physical propertiesof moist air, operating temperature and surface area.The values of convective heat and mass transfercoefficient varied significantly with the type of fish. Thiswas mainly because of porosity, shape, size and initialmoisture content of the fish. The convective masstransfer coefficient varied from 8�958 to 0�402 mms�1

for prawn and from 7�613 to 0�320 mms�1 for chelwafish. The developed mathematical models successfullypredict the convective heat and mass transfer coefficientsas the function of moisture content of prawn and chelwafish.

Acknowledgements

Author gratefully acknowledges Dr. S. Ayyappan,Deputy Director General (Fisheries) ICAR for hisinspiration and encouragements. Help in conductingexperiment given by Er. Pankaj Pathare and Mr. SudayPrasad is thankfully acknowledged.

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