Annals of Warsaw University of Life Sciences - SGGW.

46 M. Sojak, Sz. GłowackiMODELLING OF VEGETABLECHIPS DRYINGProcess of convectional drying ofvery moist solid bodies occurs in twosignificantly different drying periods. Inthe first period the process is influencedby conditions of water particle transportfrom the surface of body subjected todrying through the boundary layer ofgas; in conventional second period ofdrying, the process is influenced bythe conditions of internal diffusion ofthese particles to body surface. In fact,transition from the first to second periodproceeds constantly. This period is calleda transitory period and it is not welllearned theoretically, while only partsof its mathematical models are known(Jaros and Pabis 2006). The kineticmodel considering the effect of dryingshrinkage was checked in this work inthe range (u 0 , u cr ) (Pabis 1999):u() τ⎡N⎛ b= ub Nu k ⎞⎢1⎤⎜ τ⎟− ⎥0 1− 1− ⎢1−⎝ 0 ⎠bb0 1−⎥⎣⎦(1)This model was proved with maximallocal error not bigger than 11% in therange of water content from 7.5 to about2 kg·kg –1 and for coefficient b = 0.056,determined in drying process of anotherpumpkin variety (Sojak 2000).The exponent N value in equation(1) can be determined eg.: by trial-anderror method or it can be calculated(Pabis and Jaros 2002) basing on resultsof measurements on changes in shapeparameters (Sojak and Jaros 1999).The second model to be verified forthe range (u 0 , u cr ) is:u() τ = ue + ( ucr −ue) exp(− Kτ)(2)Equation (2) was proved withmaximal local error not bigger than 15%in the range of water content from about2 to about 0.02–0.16 kg·kg –1 .In respect to maintaining of processcontinuity in point u = u cr , drying speedsin the first and second periods must beequal, thus, (du/dτ ) I = (du/dτ ) II (Sojak2000).Then, coefficient of drying speed canbe calculated (Jaros and Pabis, 2006)from equation:K =k0ucr− ue( )⎛ Nb−−−1⎜Nu k ⎞1 1 cr ⎟⎝ 0 0 τ (3)⎠VERIFICATION OF MODELSFOR THE FIRST AND SECONDDRYING PERIODSFigure 1 presents results of threerepetitions of measurements on changesin water content in pumpkin slices ofthickness 5 and 10 mm at drying mediumtemperature 80°C and drying mediumspeed 1.2 m·s –1 . Changes in water contentwere described with the mean functionsin the form of cubic polynomials selectedso, that relative error was lower then 1%;their graphical interpretation is presentedin Figure 1.Coefficient N in model (1) wasdetermined by subsequent approximationsso, that model relative error of watercontent was possibly lowest according tomethod given by Jaros and Pabis (2006).The value of k 0 coefficient of initialdrying speed was determined by linearregression method, basing on watercontent initial measurements.