Prediction of freezing time

With respect to an individual food piece, the unit operation of freezing involves unsteady-state heat transfer in other words, the temperature of the food changes with time. In these circumstances heat transfer by conduction is described by Fourier s first law 

Fourier s equafion does nof fake into account convection, which in the case of food freezing governs heat transfer befween fhe food surface and fhe refrigerafing medium, for example cold air in the case of a fluidized bed. Second, and more importanfly, if cannof accounf for fhe removal of lafenf heaf and fhe resultant phase change. Of the models available to predict freezing time. Plank s equation (Plank, 1913, 1941) is one of fhe simplesf and most widely used and is derived in many standard texts (Singh and Heldman, 2001 Smith, 2003). The principal 

Nagaoka s equation (Nagaoka et al, 1955) is an extension of Plank s model and takes into account the time required to reduce the temperature from an initial temperature T, above the freezing poinf. The lafenf heat of fusion in equafion 3.3 is replaced by the total enthalpy change A/i which includes the sensible heat which must be removed in reducing the temperature from an initial T and in addition an empirical correction factor is included. Thus 

When frozen from both surfaces a = half thickness for freezing from one surface. 

Here Tfind is the final temperature and and Cp are the heat capacities of the unfrozen and frozen food respectively 

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