In the last issue, I began exploring the relationship between a product's properties and the ease with which it absorbs heat in an oven or dryer. As part of that discussion, I introduced the properties of specific heat, which is the amount of thermal energy required to elevate a certain weight of a material through a given temperature rise, and thermal conductivity, which is a measure of how readily heat can flow through a material.
In determining how quickly you can heat something, you must consider these two properties. High thermal conductivity is good -- it says you can move heat to the interior of the product quickly, assuming there's any heat left when you get there. That's where specific heat, combined with material density, comes into play. These three properties determine how quickly and uniformly you can heat a material.
Consider a few examples. To keep things simple, assume that the density and weight of the material are the same in all cases.
Scenario 1: High/ High. I'll begin with a material that has high thermal conductivity and high specific heat. If you follow a parcel of BTUs as they make their way from the surface to the center of this material, you see that they move quickly. However, as they travel deeper and deeper into the material, large numbers of them are siphoned off because of the material's high specific heat. Unless you can bring large amounts of thermal energy to the surface to make up for this attrition, the depths of the material will be slow to heat, and you'll have a steep temperature differential from the surface to the interior. On the plus side, materials like these are hard to overheat, so oven temperature control may not be critical.
Scenario 2: High/Low. Now I'll consider a material with high thermal conductivity and low specific heat. Under these conditions, heat moves quickly through the material, and only small amounts are removed by the material it passes through. Ample heat reaches the material's interior quickly, and surface-to-interior temperatures are relatively uniform. You need a light touch to avoid overheating the material, but if you could choose the properties of the materials you were heating, these would be ideal.
Scenario 3: Low/High. For this scenario, you have a material with low thermal conductivity and high specific heat. Heat travels through the material slowly, and large amounts of it are absorbed en route. This is the worst combination because it ensures large surface-to-interior temperature differentials and slow heating of the interior. There's a temptation to push the process by raising oven temperatures higher than normal, but because of the material's low conductivity, if you do so, you risk overheating the surface.
Scenario 4: Low/Low. In this example, assume you have a material with low thermal conductivity and low specific heat. Energy travels slowly through the material, but little of it is required to satisfy the heating needs. Heating will have to be done carefully to avoid overheating the surface, but temperature gradients will tend to be fairly uniform. The temperature profile developed in this situation is similar to the one where both conductivity and specific heat are high. The major differences are the amount of heat required by the product and the time required to do it.
Figure 1 shows, in general, the types of surface-to-center temperature profiles that tend to develop in these scenarios. The true shapes of the curves will vary, of course, with the absolute values of the conductivities, specific heats and material densities.
Thermal conductivity, specific heat and material density (which affects the amount of heat a given volume of material will absorb) have been combined into a property called thermal diffusivity. It suggests how uniformly thermal energy will spread throughout a material and, as a result, how uniform internal temperatures will be. It's expressed in square feet per hour or equivalent metric units.
Thermal diffusivity equals:
The higher the diffusivity, the more uniform the heat and temperature distribution.
This seems like a useful concept -- why, you ask, haven't you ever seen it before? I can only speculate, but it's probably because we're in the habit of describing products' diffusivity in less specific terms like, "It doesn't take a lot of heat, but you have to baby it along," or "Just throw the coals to it -- it'll come up quickly. You can't overheat it even if you try." If you've had any prior experience with a material, you've developed an instinctive feel for its diffusivity, and that becomes your guide on how to approach the task of heating it.
So far, I've dealt only with single- component materials, and their behavior is fairly easy to describe. Next time [links at bottom of page], I'll look at two-component loads, where heat is traveling into the material and moisture or a solvent is traveling in the opposite direction; in other words, drying.
In my previous column (January/ February 2001, p. 25), I cited an incorrect value. (Blame it on a Senior Moment.) I should have said the specific heat of water is 1 BTU/lb-oF. This information has been corrected online at www.process-heating.com.