The Mathematical Model of Carrot Slices Drying

Abstract

Drying of carrots slices was investigated in a laboratory dryer with a heater with thermostat. Carrots were grated in slices with a thickness of 1-2 mm, width of 4-5 mm and placed in the perforated container with layer thickness 30-35 mm. Based on the experimental data, the time dependency of moisture content and drying rate were calculated and presented. Using drying rate, the layer of carrot slices drying was simulated and receiving results compared with experimental data. Obtained measurement results are in high correlation with calculations. Presented mathematical model contains system of partial differential equations including the matter and environmental temperatures ( Θ(x,t ) and T(x,t) ) and mass exchange (W(x,t), d(x,t)) and it can be used for thick, porous medium layers, containing small particles, drying. Experimental and theoretical results showed that the carrot slices 3.5 cm thick layer was dry in 8 hours using a convective airflow with temperature 37 oC

Sušenje usitnjene šargarepe bilo je ispitivano u laboratorijskoj sušari sa grejačem sa termostatom. Šargarepa je usitnjena u rezance debljine 1-2 mm i širine 4-5 mm, a smeštena u perforirani sud, u sloj debljine 30-35 mm. Na osnovu eksperimentalnih podataka izračunate su i predstavljene zavisnosti sadržaja vlage i dinamike sušenja u funkciji vremena. Koristeći brzinu sušenja simulirano je sušenje sloja rezanaca šargarepe, a dobijeni rezultati su poređeni sa eksperimentalnim podacima. Dobijeni rezultati merenja su u visokoj korelaciji sa rezultatima proračuna. Predstavljeni matematički model sadrži sistem parcijalnih diferencijalnih jednačina koje uključuju temperature materijala i okoline ( Θ(x,t ) i T(x,t) ) i razmenu mase (W(x,t), d(x,t)). Može biti primenjen na sušenje debelih, srednje poroznih, slojeva koji se sastoje od malih rezanaca. Eksperimentalni i teorijski rezultati su pokazali da je sloj rezanaca šargarepe debljine 3.5 cm bio osušen za 8 časova, korišćenjem konvektivne vazdušne struje temperature 37 oC.