Finite difference solution in predicting temperature profile for chilling process of Malaysian mackerel fish slab

Chilling is very important to maintain the freshness and quality of fish after harvesting. Chilling will also extend fish shelf life and improve fish marketability. The aim of this study is to develop a mathematical model based on finite difference method to predict the temperature profile generated form the fish subjected to chilling and to optimize the finite difference solution by comparing theoretical data against experimental data. Experimental work was done by calculating the thermophysical properties of fish such as thermal conductivity, thermal diffusivity, specific heat and mass density. Thermophysical properties value obtained was inserted into the finite difference model. Air blast cooling system was designed to generate the experimental temperature profile. Time-temperature relationship graph obtained from the system was used as reference in the prediction of temperature profile. For theoretical work, initially the general heat conduction equation was incorporated into the finite difference model. The finite difference model was then converted into a time-temperature relationship graph by plotting points according to the data generated by the finite difference solution. Two types of mathematical approach were used namely the explicit and implicit models. Both explicit and implicit graphs were then compared against experimental graph and analyzed. A combination of explicit-implicit mathematical model was then produced to determine the best weighing factor (β) for finite difference solution which displayed similar timetemperature history graph as the experimental graph. It was found that temperature decreased rapidly at the surface and decreased subtly at the centre of the fish slab. The point located near the surface showed a decrease from room temperature to 1ºC in 20 minutes whereas the centre point took about 40 minutes. Generally, the implicit model showed more accuracy than explicit model when compared to experimental data. However, the explicit model was able to predict sample 1 time-temperature curve more accurately than the implicit one whereas sample 2 was predicted more accurately by the implicit model. Optimization was done by manipulating the weighing factor (β) and number of nodes (n). The mixture model, a combination of explicit-implicit model showed high accuracy especially with weighing factor, β = 0.6. Accuracy increased up to 40% and the decrease in the predicted temperature range was about ±0.152°C. Number nodes, n = 10 displayed the best result with error equals to 0.250 and computation time 20 seconds.

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