Fast technological developments and availability of sophisticated cultivation techniques have brought green revolution in India and this has led India to become a nearly self-sufficient country in terms of food requirements. The differential growing conditions of foods in our country lead to their seasonal availability. To ensure their off season availability, it is an excellent idea to exploit proper preservation techniques, developed time to time, worldwide. Preservation of food reduces the growth rate of fungi, bacteria or other micro-organisms and retards the oxidation of fat also that spoils the food. Preservation of food includes the processes that inhibit deterioration, like enzymatic reaction in potato after these are cut during food preparation. Some food preservation methods drastically change the characteristics of the foods. Among all food preservation methods, the cold preservation method is most suitable for fruits and vegetables as it retains their original flavour, nutritional value, colour, aroma and texture.

Cold preservation of food

At normal temperature, biological and chemical reactions are present in food products, which deteriorate the quality of fruits and vegetables that cannot be completely stopped by canning, dehydration blanching, ohmic heating, radio-frequency heating, pulsed electric field processing, pasteurization, sterilization, ultra violet light processing, microwave heating and electron beam processing. These methods also cause loss the texture, flavour and nutrition value of foods. Therefore, low temperature preservation is the only means of food preservation, which can maintain the important qualities of foods. Food products continuously generate heat that is called heat of respiration. As the temperature of food products decreases the heat of respiration also decreases. Food products freeze over a wide range of temperatures. The rate of freezing greatly affects the quality of frozen foods. The velocity of cooling air during cold preservation affects the loss of moisture from the food products in addition to the rate of heat transfer. Besides this initial temperature and cooling air (refrigeration) temperature etc. has great impact on the rate of freezing and thus freezing time.

Properties of fruits and vegetables

Each fruit and vegetable can grow only in some specific environmental conditions and thermo-physical properties of these products depend on the growing conditions. So, for food preservation, it is necessary to determine these properties, viz. specific heat, mass density, thermal conductivity, latent heat of fusion and moisture content of fruits and vegetables, which are commonly preserved. Since cold storages are designed according to the purpose of requirement, the above data of properties of food products is necessary for the design of cold preservation equipment.

Freezing time estimation by numerical modeling

Freezing time estimation by conducting actual experiments is quite costly affair. Therefore, numerical models for freezing time estimation have been developed in past by Plank in 1941, which is valid for spherical, cylindrical and rectangular shapes. A number of models have also been developed after Plank. But all these methods provide inaccuracies when compared with experimental results. Nagaoka in 1956 modified the Plank’s model by considering the sensible heat during precooling and post freezing and applied this technique on the regular shaped food products. Rolfe (1967), Cleland and Earle (1977), Lacroix and Castaigne (1987) and Varshney and Ansari (2003) have given the mathematical models that can be solved by hand only. These models are applicable for regular shaped food products only. Cleland (1985) has given mathematical model based on numerical methods for regular and irregular shapes. Wilson and Singh (1986) have given numerical model and conducted experiments for freezing time of spherical peas.

Description of experimental setup

The measurement of freezing time by experimental method is the main objective of this work as it ascertains accuracy of results. For this an experimental setup was fabricated, the line diagram of which is shown in Figure 1. The pea samples were placed inside the wooden test section and supported with a wire mesh. This test section was connected end to end with the deep freezer through the circular pipes made of PVC. In the circular pipe section two blowers were placed. Each blower was powered by a 275W electric motor. These blowers forced the air inside the duct and over the samples. The valves were able to control the velocity of air inside the test section and different constant velocities could be obtained. The air velocity could be easily varied between 3 and 14.9 m/s. The temperature inside the deep freezer could be maintained between 0°C to -86°C as per cooling condition requirement. Cooling air was blown between -24°C and -36°C temperature over the sample of peas.  Cooled air in the deep freezer was used to freeze the pea grains in the test section by forced convection. Pea samples and frozen samples have been shown in Figure 2 and 3, respectively.

Fig. 1 Line diagram of experimental setup…
Fig. 2 Photograph of sample of pea grains…
Fig. 3 Photograph of frozen peas…

Results of numerical and experimental study

The moisture content in the pea samples has been found to be 76.03% through measurements. The thermo-physical properties of food products are greatly affected by water content – so these vary slightly in frozen state. One hundred twenty six experiments were conducted for estimation of freezing time by varying different parameters.

Although, peas are generally frozen in packets but individual pea grains have been frozen in the experiments to determine the freezing time accurately. The freezing point temperature of food products decreases with the advancement of freezing because water part in food commodities is always in bond state with the dispersed food, which is in matrix form and percentage concentration of unfrozen (dispersed) food increases as the water content in the food freezes. The variation of freezing time, when the pea samples are frozen under different operating conditions, has been shown in Figure 4 and 5.

Effect of cooling air temperature

Pea samples of identical shapes were frozen under different cooling air temperature considering initial temperature and cooling air velocity as constant. Figure 4 shows the variation of temperature of peas with time during precooling, freezing and post freezing of pea samples as obtained from numerical model and experimental data.  From Figure 4, it is clear that as cooling air temperature decreases, freezing rate increases and freezing time decreases.

Fig. 4 Numerical time-temperature variation in freezing of spherical pea samples for variable cooling air temperature
using numerical model of variable freezing temperature (v=5.2 m/s and Ti = 32.97°C)…
Fig. 5 Numerical time-temperature variation in freezing of spherical pea samples for variable cooling air velocity using
numerical model of variable freezing temperature (Ti=32°Cand Tc = -28.5°C)…

Effect of cooling air velocity

Figure 5 shows the numerically and experimentally obtained time-temperature variation with variation in cooling air velocity. It also indicates that as cooling air velocity increases, freezing rate increases and freezing time decreases. For different initial temperature of peas, there were insignificant variations in the temperature profiles as well as in freezing times. Therefore, time-temperature variations for variable initial temperature are not plotted for this case.

Comparison of experimental freezing time and predicted freezing times

Figure 6 shows the comparison between experimental freezing time and predicted freezing time using numerical model. The correlation coefficient of linear regression, R2, is 0.97 which denotes that both the freezing times are in good agreement. The maximum and minimum errors in numerical freezing time are 5.17% and 5.04%, respectively.

Fig. 6 Comparison between experimental freezing time and numerical freezing time…


Numerical model for freezing time estimation of peas has been developed considering that latent heat of fusion is removed at successively decreasing freezing point, which happens in the case of actual freezing.

An experimental setup has been designed and fabricated to calculate experimental freezing times of pea samples. The freezing temperatures measured in experiments were compared with the temperatures predicted by the numerical model. It was found that for variable cooling air temperature, the deviations in experimental freezing times with numerical freezing times are within acceptable limit.

Similarly, for variable cooling air velocity the deviations are within acceptable limits. Thus, it was concluded that predicted results using numerical method showed very good agreement when compared with experimental results.

The effect of three operating parameters, viz. cooling air temperature, cooling air velocity and initial temperature, were studied on freezing time of peas. It was found that initial temperature of pea samples has negligible effect on freezing time. However, increase in cooling air velocity and decrease in cooling air temperature both increase the freezing rate and hence decrease freezing time significantly.

Dr. A. K. Pratihar is a Professor in the Department of Mechanical Engineering, College of Technology, G. B. Pant University of Agriculture & Technology, Uttarakhand, India.  He received his Ph.D. from I. I. T. Delhi. He is a member of ISHRAE (Indian Society of Heating Refrigerating and Air conditioning Engineers) and Fellow of Institution of Engineers (India). His areas of interest are Thermodynamics, Refrigeration and Air conditioning and Solar Energy.

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