Brandão, Teresa R. S.

Ramos, Inês N.

Silva, Cristina L. M.

English

Repositório Institucional da Universidade Católica Portuguesa

Inês N. Ramos, Teresa R. S. Brandão, Cristina L. M. SilvaKinetic approach:Normalised Newton modelMATERIALS & METHODS1) to develop a computer program in order to simulate solardrying, which includes an integrated mass and heat transfermodel.2) to quickly assess kinetics and total drying time of field solardrying of grapes submitted to different pre-treatments.OBJECTIVESINTRODUCTIONIntegrated heat and mass transfer model for solar drying simulation of grapes• The consistent increase of society demand for a sustainabledevelopment is reinforcing the use of solar drying, due to being arenewable energy technology.• Raisins are easily produced with solar energy, and are an excellentsource for providing vitamins, minerals (essentially iron) polyphenols,flavonoids, crude fibre and antioxidants in general. Besides theirnutritive value, they also present functional properties, benefitinghuman health.• In order to design drying equipment, it is essential to model theprocess. Mathematical modelling is also important to predict andsimulate the drying behaviour. Drying is a complex phenomenonsimultaneously involving mass and heat transfer.CONCLUSIONSREFERENCES:Charles-Edwards, D.A.; Acock, B. 1977. Growth response of a chrysanthemum crop to the environment. IImathematical analysis relating photosynthesis and growth. Annals of Botany 1977, 41, 49-58. Quoted in France,Thornley, J.H.M.; Weather. In Mathematical models in agriculture - a quantitative approach to problems in agricultureand related sciences; Butterworth: Kent, 1984; 95-113.ACKNOWLEDGEMENTS: The authors Inês N. Ramos and Teresa R. S. Brandão would like to acknowledge, respectively,PRAXIS XXI PhD grant nr. 18543/98 and Post-Doctoral grant SFRH/BPD/11580/2002, to Fundação para a Ciência eTecnologia, Portugal. The authors are also grateful to Direcção Regional de Agricultura de Trás-os-Montes, Portugal,for providing the equipment and technical support, in particular to Engº Manuel Pascoal.Fig. 2 Schematic flowsheet of the computer programfor prediction of grapes solar drying curves.Fig. 1 Solar dryer at Mirandela, Portugal.00.20.40.60.810 5 10 15time (days)X / X 0untreatedblanched in 0.1% oilblanched in waternormalised Newton modelFig. 4 Comparison between different pretreatments on grape drying kinetics.Fig. 3 Simulation of solar drying curves (4 experimental replicates) for grapes blanched in water during 15 s.The modelling and simulation of dynamic experimental drying with cyclic airconditions, using water content gradients and shrinkage simultaneously, wereinnovative and represent a contribution in Food Engineering.A good representation of experimental solar drying curves was attained bysimulation. The computer program may be easily applied for simulating solardrying of different foods, once known the specific characteristics of theproduct.RESULTS & DISCUSSIONt)k ( exp XXe1XXeXX000• Red seedless grapes, Monukka cultivar Heat and mass transfer approachTHEORETICAL CONSIDERATIONSMeteorological model: To generate data of climatic diurnal variation in radiation, developed by Charles-Edwards and Acock (1977).• Fick’s second law and a heat balance equation  - solved by explicit finite differences. • Negligible resistance to external mass transfer and to internal heat transfer • Integrated model considering:1. changes in effective mass diffusivity and thermal properties with water content and temperature, along drying and within grapes (non-isotropic characteristics)2. shrinkage of the product with subsequent changes on its surface and projected areas, and distance between nodes3. changing boundary conditions (equilibrium changes with variable air conditions).Developed equation to express mass diffusivity dependence on water content and temperature: av20i0i0iT1-T1c- XXb  XXa exp DDF )T(T σ ε Adt)m (λ d - )T-(TA hI(t)A dt T)Cp (m d 4a4swasp Heat transfer model:• It was observed that pre-treated samples (blanched in hot water or in a 0.1emulsion of sunflower edible oil at 99ºC, for approximately 15 seconds) hadfaster drying rates (Newton model) than untreated grapes, not implyingnoteworthy difference in total drying time. However, pre-treatments had animportant role accelerating initial drying rates, thus preventing moulds andbacterial grow and consequently increasing farmers’ income.  NdNNdg 20.5tcos1gJ)I(t01234560 2 4 6 8 10 12 14time (days)water content (kg H2O / kg dm)replicate 1simulated01234560 2 4 6 8 10 12 14time (days)water content (kg H2O / kg dm)replicate 2simulated01234560 2 4 6 8 10 12 14time (days)water content (kg H2O / kg dm)replicate 3simulated01234560 2 4 6 8 10 12 14time (days)water content (kg H2O / kg dm)replicate 4simulatedMass and Heat transfer approachTraysAir inletSolar chimneyProtectionThermocouplesAir humidityprobesSTARTINPUT:nnodes, ntimes, tmass diffusivity parameters      D = f (X, T) shrinkage parameters       R, As, Ap = f (X) GAB coefficients     Xe = f (RH, Ta)  data of    Ta, RH, Iinitial conditions:   X0, R0heat transfer parameters      , , h, parameters of    Cp = f (X) initial conditions:    m0, As0, Ap0t = t0CALCULATE:position rit   DitXit  CALCULATE:                    i=1CALCULATE:Qc, Qr = f (T, Ta,      )Qe = f (      )Cp, As, Ap = f(      )TptNOYESt+1STOPi = nnodes-1i-1t = ntimesNOYESCALCULATE:  Xe, Cp tX)(XfRt  tX tX tX

Integrated heat and mass transfer model for solar drying simulation of grapes

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Integrated heat and mass transfer model for solar drying simulation of grapes

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Repositório Institucional da Universidade Católica Portuguesa