What happens when cold air hits warm grain?

Suppose we have one cubic foot of wheat at a temperature of 30 C, and we pass one cubic air through it at 10 C.  We would expect the temperature of the wheat to go down, and the temperature of the air will increase — but by how much?  We will use something called the specific heat; it is the amount of energy that a substance holds due to its temperature.  I looked up the specific heat for wheat and it is 1.67 kJ/kg C, which means for every degree C, one kilogram of wheat holds 1.67 kilo joules of energy or heat.  Likewise the specific heat of air is 0.716 kJ/kg C

We want to get everything in terms of a cubic foot, so we will need some conversion factors.  Air weighs .0807 lbs per cubic foot or .0366 kg per cubic foot. One bushel is 1.2446 cubic feet, and we will assume that wheat is 60 lbs per bushel.

When the air comes into contact with the grain, the grain will lose the same amount of energy as the air gains.  Using the conversion factors we see that one cubic foot of wheat is 48.2 lbs or 21.88 kg. So the specific heat of wheat in terms of a cubic foot would be:    1.67 x 21.88 = 36.53 kJ/ft^3  C

Air weighs  0.0807 lbs per cubic foot   or .0366 kg per cubic foot.  The specific heat in terms of a cubic foot is  0.716 kJ/kg C  x  0.0366 kg/ft^3 = 0.0262 kJ/ft^3 C

So the wheat has way more energy (36.53) than the air (0.0262); in fact it has 36.53/0.0262 =  1,394 times more,  and with difference in temperature, 30 -10 = 20. The wheat will go down in temp, but only 1/1394 x 20 = 0.0143 deg C below 30, 29.98 C and the air will increase 1,393/1,394 x 20 = 19.98  above its 10 to 29.98 C

So to conclude, we see that the air becomes almost the same temperature as the wheat, and because the surface area of the wheat is so large, it is clear that this heat exchange would happen without delay.

Another way to look at this is that one air exchange would move the temperature of the wheat approx  .02/20, one thousandth the difference in temperature, but after many heat exchanges, the temperature of the grain will go down, and the difference becomes less.  So it might take a thousand air exchanges to get the temperature of the wheat from 30 to 20.  If our fans have a flow of 1 CFM/bu. and since one bu is close to one cubic foot, we would get an air exchange every minute.  A thousand air exchanges would take over 16 hours.  The data that we have collected over the years shows that cooling the grain is much faster than this, it can be cooled to near the air temp in a matter of hours with air flow close to 1 CFM/bu.  There is more at play here and there must be something else, the grain is being cooled by water evaporating from the grain into the air.  This is called the latent heat of evaporation; and this will be a topic for another day.

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