Development of mathematical model for cooling the fish with ice

The cooling of fish with ice as a medium has been studied by using mathematical models. Experiments were conducted by cooling the different quantities of individual Indian major carp Rohu fish (Labeo rohita) with ice in the insulated box. Exponential and asymptotic (logarithmic) models describing the cooling of irregular shape of objects have been investigated. The results were compared to their goodness of fit in terms of coefficient of correlation, standard error and the mean square of the deviation χ². The cooling data like, cooling coefficients, average surface heat transfer coefficient, half cooling time and seven-eighth cooling time were determined for individual fish of different weight. The results show that the half cooling time and seven-eighth cooling time increase and the cooling rate decreases with increase in the weight of fish, respectively. The asymptotic regression model could satisfactorily describe the fish cooling with ice with the values for the coefficient of correlation ranged from 0.9866 to 0.9980; e_s 0.0140 to 0.0301 and χ², 2.0 × 10^-4 to 8.9 × 10^-4. Parabolic regression analyses were performed to relate the coefficient of asymptotic models with weight of the fish. The developed model could predict the cooling of fish with time within an error of 0.50%. The average surface heat transfer coefficient of fish cooling with ice was ranged from 19.84 to 33.01 W m^-2 C^-1.