Thammasat Int. J. Sc. Tech.. Vl. I l. N. l. Januarv-March 2006 A Mathematical Mdeling Study f Ht Air Drying fr Sme Agricultural Prducts Jmpb Waewsak Renewable Energy System Research and Demnstratin Center (RESRDeC) Department f Physics, Faculty f Science, Thaksin University, Phatthalung, 93 I 10, Thailand Sirinuch Chindaruksa Graduate Student, Department f Physics, Faculty f Science, Naresuan University Phitsanulk, 65000, Thailand Chantana Punlek Department f Physics, Faculty f Science, Naresuan University, Phitsanulk, 65000, Thailand Abstract The aim f this paper is t investigate the applicability f simplified mathematical drying mdels frm the research wrks prpsed by several investigatrs t the drying f sme agricultural prducts. Drying experiments were cnducted using a cnventinal bimass lngan dryer at drying air velcity 1.34 m/s and drying air temperature 80C fr red chili peppers, 70"C fr lemn grass and 60"C fr leech lime leaves. Drying curues btained frm the experimental data were then fitted t the empirical drying mdels. Thirleen different mathematical drying mdels were cmpared accrding t their cefficients f cmelatin in rder t estimate the drying curves f thse prducts. The results have shwn that amng the mdels, the Midilli et al. mdel was fund t be the best mdel fr describing the drying behavir f red chili peppers and leech lime leaves, whereas the Wangh and Singh mdel was the mst suitable fr lemn grass. Keywrds: Agricultural Prducts, Drying, Energy, Fd Engineering and Misture Rati l. Intrductin Drying prcesses play an imprtant rle in the preservatin f agricultural prducts. they are defined as a prcess f misture remval due t simultaneus heat and mass transfer ]. The mst impftant reasns fr the ppularity f dried prducts are lnger shelf-life, prduct diversity as well as substantial vlume reductin. This culd be expanded further with imprvements in prduct quality and prcess applicatins. The applicatin f dryers in develping cuntries, especially in Thailand, reduce lsses and significantly imprve the quality f the dried prduct when cmpared t the traditinal means f drying such as pen sun drying. Nt nly that, pen sun drying is nt always suited t large-scale prductin due t the lack f ability t cntrl the drying cnditins prperly, the lnger drying time, the uncertainties f ambient cnditins. larse area requirements, insect infestatin and the cntaminatin f dust [2]. Cnsequently, studies based n simulatin mdels are needed fr the design and peratin f dryers. Hence, the drying characteristics f specific prducts shuld be determined. Furlhermre. simulatin mdels are als useful in imprving the existing drying system. The drying kinetics l rnaterials may be described using the transpft prperties such as thermal cnductivity, thermal diffusivity, misture diffusivity as well as interface heat and mass transfer cetficients [2]. The investigatin f the drying behavir f different agricultural prducts has recently been carried ut by several investigatrs, fr example, green peppers [3], nins [4], red peppers [5-7], rugh rice [8], bananas [9], mushrms 0], ptats I l], grapes [12] and pistachis [3]. All the mentined agricultural prducts have the same manner f drying characteristics which are t4
Thammasat Int. J. Sc. Tech., Vl. 11, N. l, January-March 2006 described by the law fexpnents. Accrding t the meal habits f Thai peple, sme f the vegetables are dried during the peak seasn f harvesting and supplied fr cnsuming during ff-seasn. Red chili peppers, leech lime leaves and lemn grass are the best examples f these kinds f vegetables. They are traditinally cnsumed in different kinds f meals. The bjective f this wrk is t study the applicability f several simplified mathematical mdels selected frm the literature t the drying f red chili peppers, lemn grass and leech lime leaves and t fit drying data int the mst suitable mdels by apprpriate regressin analysis in rder t investigate the best mdel fr describing the drying characteristic f sme f the agricultural prducts that are mentined abve. 2. Experimental Setup and a Mathematical Mdeling Study 2.1 Experimental Setup The drying experiments were carried ut using a bimass lngan dryer which cnsists f a blwer, a cmbustin chamber, a drying chamber and a ducting system with air recycling as shwn in Fig. L The drying chamber was cnstructed frm steel sheet as a rectangular dryer f 1.2 m length, \.2 m width and I m height. The Lngan dryer is perated by wd fuel cmbustin fr ht air drying. Ht air is fed int the drying chamber fr the drying prcess via the blwer. A type K thermcuple was used t measure the temperature at varius pints f the dryer and cnnected t a 20-channel data lgger (YOKOKAWA mdel HR 1300 Hybrid Recrder). with reading accuracy f ' 0. lc. The air mass flw rate f air culd be calculated frm the velciry fair passing thrugh the duct system, which is measured by an air velcity meter (TSI incrpratin mdel 8345 htwire type). The misture cntents f red chili peppers, lemn grass and leech lime leaves were recrded each hur during the drying prcess fr the determinatin f drying curves by a digital balance (SARTORIUS MCI analytic mdel AC 2l0s), with reading accuracy f +0001 g. The same sample f each prduct was brught ut f the drying chamber fr weight measurements. Frm the literature survey, it was fund that a suitable drying air temperature fr the drying f chilis. lemn srass and leech lime leaves was in the range f 60-80 "C. In additin, the drying air temperature fr drying f chilis, lemn grass and leech lime leaves shuld be 80 "C, 70 "C and 60 "C respectively. Cnsequently, the drying air was fixed t 80"C fr red chili peppers. 70"C fr lemn grass and 60"C fr leech lime leaves drying. The drying prcess was cntinued frm the initial misture cntent f 250/ db fr red chili peppers, 3l0/ db fr lemn grass and 165% db fr leech lime leaves until the final misture cntent reached 13% db fr red chili peppers and l2/ db fr lemn grass and leech lime leaves, which are the desired and apprpriate final misture cntent as seen in the market. During the experiments, the mass flw rate f air was 0. 198 kg/s crrespnding t a drying air velcity f 1.34 m/s. The ambient temperature and inlet as well as the utlet air temperature f the drying chamber were als recrded. The psitins f the temperature and velcity measurements are shwn in Fig. L 2.2 AMathematical Mdeling Study Althugh the effects f drying air temperature, initial and final misture cntent, relative humidity as well as velcity f drying air n the drying cnstants, were investigated by many researchers!4-16], in this study these parameters were nt taken int accunt. The main bjective is t study the crrelatinship between the misture rati (MR) and the drying time at specific and ptimum drying cnditins, which were surveyed frm the literature [7-18]. The MR is usually expressed as (M- M")/(M"-M") where M is the misture cntent (/" db), M. is an initial misture cntent (% db) and M" is an equilibrium misture cntent. Hwever, it culd be simplified t M/M" instead f (M-M.)/(M"-M"), because the relative humidity f the inlet drying air culd nt cntrlled, whereas the drying air velcity was cntrlled. Furthermre, the equilibrium misture cntent f agricultural prducts is nt high. This effect was clearly presented by the natural sun drying prcess [2]. The recrded misture cntent f red chili peppers, lemn grass and leech lime leaves in the experiments were then used t plt drying curves. Mathematical mdeling f the drying behavir f different agricultural prducts ften requires statistical methds f regressin and crrelatin t5
Thammasat Int. J. Sc. Tech.. Vl. I l. N. 1. Januarv-March 2006 analysis. Linear and nn-linear regressin mdels are imprtant tls t find the relatinships between different variables. In this study, the relatinships f the cnstants f the mdel were determined by a regressin technique using an expnential functin which is the mst cmmn mathematical expressin fr describing drying characteristics. Drying curves were fitted t the experimental data using thirteen different misture rati equatins as expressed in Table I in rder t identify the best mdel. Frm Table 1, the cnstant parameters are the fllwing: e, b and c, whereas the drying cnstants are k, g and h, respectively. These parameters imprve the quality f fit. Several mathematical drying mdels applied t drying curves as shwn in Table I were tested t select the best mdel based n the quality f fit fr describing the drying curve f the red chili peppers, lemn grass and leech lime leaves by chsing the maximum crrelatin cefficient frm regressin. The regressin analysis was perfrmed using cmputer sftware, namely, STATISTICA versin 5.0. Regressin wrk was dne based n the Quasi- Newtn methd. The crrelatin cefficient (r) is the majr criterin fr selecting the best equatin t describe the drying cun/e. Air utlet Recycle air duct Air inlet & Temperature Measurement r\ Velcity Measurement w w w & Drying chamber Cmbustin chamber E E E I Ht air inlet Damper Blwer Fig. I The cnfiguratin f a cnventinal bimass lngan dryer. l6
Thammasat Int. J. Sc. Tech., Vl. Thammasat Int. J. Sc. Tcch., Vl I 1. N. l, January-March 2006 I I, N. l, January-March 2006 Table 1. Mathematical mdel f drying curves [1]. Mdel N Mdel Name Mdel Equatin I 2 3 4 5 7 8 9 l0 lt I2 l3 Newtn Page Mdified Page Hendersn and Pabis Lgaritmic Tw Tcrm Tw Term Expnential Wang and Singh Thmpsn Diffus in Apprximatin Verma et al. Mdified Hendersn and Pabis Midilli et al. MR - exp(-kr) MR: exp(-fr1') MR: exp[(-ft0"] MR - acxp(-ft1) MR: aexp(-tl) + c MR - aexp(-lr) + bexp(-ftr) MR - aexp(-tr) + (l - a)exp(-lr) MR- l+ftbf I: aln(mr)+blln(mr)l: MR - aexp(-ft + (l - a)exp(-kbr) MR = rzexp(-frr) + (l - a)exp(-gr) MR : aexp(-frt) + 6exp(-gr) + cexp(-ht) MR-aexp(-/r/')+bl 3. Results and Discussin [19] The misture cntent f red chili peppers, lemn grass and leech lime leaves during the drying prcess was bsenred in rder t study the behavir f drying. Since the migratin f misture and the evapratin rate frm prduct surfaces t air decreased with decreasing f the prduct misture, the drying rate clearly decreased. The drying time is shrter when the temperature is higher, which is explained by the increase in the drying rate. This increase is due t the increased heat transfer ptential between thc air and the prducts, thus favring the evapratin f the water frm the prducts. The effect f temperature n drying rate was well presented in [20]. The change f misture rati with drying time f experiments and regressin is shwn in Fig. 2, Fig. 3 and Fig. 4 respectively. Features f the drying curves are similar t ther agricultural prducts, that is the misture rati decreased expnentially. The best mdel fr describing the drying characteristic f red chili peppers, lemn grass and leech lime leaves was selected when the crrelatin cefficient (r) was the highest value. The results reveal that the best mathematical mdel fr red chili peppers and leech lime leaves is Midilli et al. when r is 0.99998 where the mdel is the fllwine: MR-aexp(-kt")+bt Where a: 0.999857 k - 0.t 17399 n: 45196 b - -03134 The best mathematical mdel fr lemn grass is Wang and Singh mdel when r is abut 0.99968 where the mdel is the fllwing: MR-1+at+bt' Where a - -66254 b:18578 The best mathematical mdel fr leech lime leaves is Midilli et al. when r is abut 0.99991 and the cnstant parameters as well as drying cnstants are the fllwing: 0188, k:84292. n:0.839248 and 6 - -34214. The mdel perfrmance can be evaluated by the percentage f Rt-Mean-Square errr (RMSE (%)) as expressed in terms f predicted ( p, ) and bserved (, ) values given by: RMSE(%) = The difference between the predicted and bserved value is a residual. In this paper the RMSE (%) was investigated and shwn. RMSE t1
Thammasat Int. J. Sc. Tech.. Vl. I l. N. 1. Januarv-March 2006 (%) f the best mdels fr these agricultural prducts are given in Table 2. The predicted and bserved value fr chili peppers, leech lime leaves and lemn grass drying were pltted and shwn in Fig. 3, Fig. 5 and Fig. 7, respectively. It was fbund that the difference between the predicted and bserved values are very lw. This result is shwn by the RMSE (%). This means that the mdel has very high perfrmance fr describing the characteristics f drying culves. Table 2. RMSE (%) f chilis, lemn grass and leech lime leaves mathematical mdel. Asricultural Prduct RMSE (%) chili 0078098 Lemn Grass 0444855 Leech Lime Leaf 1864375 4. Cnclusin Accrding t the results f the mathematical mdeling f the drying f red chili peppers, lemn grass and leech lime leaves, the best mdel fr describing the drying characteristic f red chili peppers and leech lime leaves is Midilli et al., whereas Wang and Singh mdel is the mst suitable fr lemn grass. The results f regressin analysis indicated that these mdels culd be used t mdel the drying behavir which is useful fr simulatin studies f drvins systems. Drying air temperature is 80"C and drying air velcjty is L34 nts 1.4 1.2 E.s &. 0.4 fime (hr) 20 Fig.2 Variatin f misture rati with drying time fr red chili peppers. (J G " i.) lr O.E 5.50178 ' 0.4 0.6 0.8 Obscrvcd Valuc Fig.3 Plt f predicted and bserved values fr red chili peppers drying mdeling. Drying air temperature is 70"C and clrying air velcity is L34 m"s 1.4 t.2 E.s z. f,,. z 0.4 - - 5 0.E 0.6 0) O n / li A 2 4 6 8 Time (hr) Fig.4 Variatin f misture rati with drying time fr leech lime leafves b.0574 /\ 0.5.53300 0.t7.0.t6212 7. 7-r r2 6c 0 6xt tj6<,/.).,,,,'-'-"'u'"'" 2l'-,,^,,,, u tq. u.t8?4 0.4 0.6 Observed Value l. 0.s9985 0. I (x)()19 0.12. 0 '7 1 81' 7 Fig.5 Plt f predicted and bserved values fr leech lime leaves drvine mdeline. 18
Thammasat Int. J. Sc. Tech.. Vl. I l. N. l. Januarv-March 2006 Drying air tcmpcraturc is 60"C and drying air velcity is. 1.34 nls 1.4 1.2 I E.s &. 0.4 0 I.s c 0.6 L (\A 2 1 6 Tirnc (hr) 3. s n n Fig.6 Variatin f misture rati with drying time fr lemn grass 0.4 0.6 0.u Obsen'ed Value Fig.7 Plt f predicted and bserved values fr lemn grass drying mdeling. 5. Acknwledgement The authrs wish t thank the Department f Alten.rative Energy Develpment and Efficiency (DEDE) fr prviding a cnventinal lngan dryer fr the tests. 6. References t1l Ertekin, C. and Yaldiz, O., Drying l Eggplant and Selectin f a Suitable Thinlayer Drying Mdel, Jurnal f Fd Engineering, Vl.63, pp.349-359, 2004. [2] Tgrul, I. T. and Pehlivan, D., Mdelling f Thin Layer Drying Kinetics f Sme Fruits under Open-air Sun Drying Prcess, Jurnal f Fd Engineering, Vl.65, pp. 413-425.2004. 6 t3l Yaldiz, O.and Ertekin, C., Thin Layer Slar Drying f Sme Vegetables, Drying Technlgy, Vl. I 9, pp.583-596, 2001. [4] Sarsavadia, P. N., Sawhney, R. L. Pangavhane, D. R. and Singh, S. P., Drying Behavir f Brined Onin Slices. Jumal f Fd Engineering, Vl.40, pp.2l9-226, t999. t5l Passami,V. and Saravia, L.,Relatinship Between a Slar Drying Mdel f Red Pepper and the Kinetics f Pure Water Evapratin I, Drying Technlgy, Vl.l5, N.5, pp.l419-1432. l99l. t6l E. K. Akpinar, Yasar Bicer, Cingiz Yildiz, Thin Layer Drying f Red Pepper, Jurnal f Fd Engineering, 59, pp.99- I 04, 2003. [7] Basunia, M. A. and Abe, T., Thin Layer Slar Drying Characteristics f Rugh Rice under Natural Cnvectin.Jumal f Fd Engineering, Y 1.41, pp.295-30 l, 200 I. tt3l Dandamrngrak, R.,Yung, G. and Masn, R.. Evaluatin f Varius Pre-Treatments fr the Dehydratin fbananaand Selectin f Suitable Drying Mdels, umal f Fd Engineering, Vl.55, pp.139-46, 2002,. t9l Midilli, A. Olgun, H. and Ayhan, T., Experimental Studies n Mushrm and Pllen Drying. Intematinal Jurnal f Agricultural Engineering Research, Vl. t6, pp.223-244, 1999.!01 Dimante, L. M. and Munr, P. A., Mathematical Mdelling f Ht Air Dryingf Sweet Ptat Slices, Internatinal Jurnal f Science and Technlgy, Vl. 26. pp.99- I 09. I qq l.! ll Dincer, 1., Sun Drying f Sultana Crapes, Drying Technlgy, Vl.l4, pp.l827-1838, 1996. [l21 Midilli, A.. Determinatin f Pistachi Drying Behavir and Cnditins in a Slar DryingSystem, Intematinal Jumal Of Energy Research, Vl.25, pp.7 l5-725, 2001.!31 Kulkarni,S. D.. Bhle, N. G. and Sawarkar, S. K., Dehydratin f Sybeans during High Temperature Prcessing, Drying Technlgy. Vl.I l, N.l, pp.229-240, I 993.!41 Prabhanjan, D. G., Ramaswamy, H. S. and Raghavan, G. S. V., Micrwaveassisted Cnvective Air Drying f Thin Layer Carrts, Jurnal f Fd Engineering, Vl.25, pp.283-293, 995. 19
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