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Basic theory
Assume a kiln is a hollow shape with uniform thickness of fire-brick or other insulating material. The inside is hot and held at temperature Ci. The outside is cool and held at a lower temperature Co. Then there is a heat loss by conduction through the insulating material which is proportional to the temperature difference Ci - Co. The temperature on the inside of the insulation is Ci, on the outside Co, halfway in between (Ci + Co)/2, and so on for all intermediate positions in the thickness. In other words heat loss = k x (Ci - Co), where k is some constant number for all kilns of the same construction.
Now also assume that Ci drops slowly, but so slowly that this relationship is still approximately correct. Assume further that the mass is mostly on the inside and hot. Then by integrating the heat loss, the temperature (heat content x mass / specific heat) will fall as e (2.71828...) to the power -t/T, where t = time, and T is the kiln 'time constant' dependent on the hot mass and the insulation.
T is characteristic of the loaded kiln, and for small loads of glass will not change much. Putting a heavy item inside, such as a clay mold or a thicker shelf, will increase it. More or thicker insulation will increase it by reducing heat loss. Fiber insulation (low mass) may result in a lower T than fire-brick insulation.
Theory approximations
This is what is called a 'lumped model' where I assume all the items are either mass or insulation. It is possible to analyse a 'distributed model' where the distribution of mass through the insulation is taken into account. For typical kiln configurations the effects on the cooling curve are not large because the rate of cooling is so slow.
This theory assumes that the outside temperature of the kiln casing is fixed (heat carried away instantly) or otherwise heat is carried away approximately as the temperature difference between the kiln casing and the room air (same pattern as the insulation conduction mechanism). This is probably a safe assumption, given that the casings are not very hot.
What about kiln size? The total mass of an unloaded kiln is approximately = specific gravity of insulation x external surface area x thickness. Thickness of insulation probably is much the same for large and small kilns, as is the specific gravity and specific heat of the insulation. So the heat content is proportional to the surface area, and so is the rate of heat loss. Therefore large kilns can be expected to have much the same time constant and cooling characteristics as small kilns. Shape is not very relevant.
But this is also an 'engineering approximation'. Kilns have shelves and contents that add mass. Insulation thicknesses may vary. Small kilns have more mass proportional to their area. These introduce differences in the time constant, but a value in the range 2 to 4 hr is probably to be expected over the entire range of home and small business kilns (except for tiny ones). Really light insulation (such as fiber) will bring T lower, but there is really no way for the user to increase the cooling rate except by cooling the inside too (using vents or cracking the lid/door/hat open to let a small amount of hot air out and cool air in). The design of kilns is compromise: lots of insulation makes it easier to reach high temperatures with low power, but may make the cooling rate unacceptably slow.

© Copyright  2000, 2001  AHJ Sale
Page last modified on 2001 October 24