## THERMAL SCIENCE

International Scientific Journal

### MATHEMATICAL MODELING OF FISH BURGER BAKING USING FRACTIONAL CALCULUS

**ABSTRACT**

Tilapia (Oreochromis sp.) is the most important and abundant fish species in Brazil due to its adaptability to different environments. The development of tilapia-based products could be an alternative in order to aggregate value and increase fish meat consumption. However, there is little information available on fishburger freezing and cooking in the literature. In this work, the mathematical modeling of the fish burger baking was studied. Previously to the baking process, the fishburgers were assembled in cylindrical shape of height equal to 8mm and diameter 100mm and then baked in an electrical oven with forced heat convection at 150ºC. A T-type thermocouple was inserted in the burger to obtain its temperature profile at the central position. In order to describe the temperature of the burger during the baking process, lumped-parameter models of integer and fractional order and also a nonlinear model due to heat capacity temperature dependence were considered. The burger physical properties were obtained from the literature. After proper parameter estimation tasks and statistical validation, the fractional order model could better describe the experimental temperature behavior, a value of 0.91±0.02 was obtained for the fractional order of the system with correlation coefficient of 0.99. Therefore, with the better temperature prediction, process control and economic optimization studies of the baking process can be conducted.

**KEYWORDS**

PAPER SUBMITTED: 2016-04-22

PAPER REVISED: 2016-05-24

PAPER ACCEPTED: 2016-06-15

PUBLISHED ONLINE: 2016-10-01

**THERMAL SCIENCE** YEAR

**2017**, VOLUME

**21**, ISSUE

**1**, PAGES [41 - 50]

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