I guess it's inevitable. Start talking about one phase of heat transfer, and you feel obligated to rattle on about the others, too. Just as you can't picture Larry without Curly and Moe, my last column's discussion of convection begs for followups on conduction and radiation. I'll take on conduction first.

I guess it's inevitable. Start talking about one phase of heat transfer, and you feel obligated to rattle on about the others, too. Just like you can't picture Larry without Curly and Moe, my last column's discussion of convection just begs for followups on conduction and radiation. I'll take on conduction first.

Conduction is heat transfer through materials or between objects in physical contact with one another. Conduction heat transfer is described by this relationship:

where
Q represents the amount of heat transferred per unit time (BTU/hr or equivalent units)
A is the cross-sectional area of the material the heat is passing through
ΔT is the temperature difference across the thickness of the material
k is the thermal conductivity of the material

Conductivity is expressed in terms like BTU foot/square foot- hour-^oF (BTU-ft/ft²-hr-^oF) or Joule-cm/square cm-second-^oC (J-cm/cm²-sec-^oC).

Figure 1 shows this relationship graphically. The solid object is shown as a round bar; it could just as well have any other shape, or it could represent a small section of something larger.

Understanding conduction is pretty straightforward -- the rate of heat flow increases with the thermal conductivity of the material (heat flows more readily), the cross-sectional area available for it to pass through (larger heat-flow path) and the temperature difference from one side to the other (driving force for the heat flow). It decreases as material thickness increases -- the longer the path, the longer it takes the heat to get from one point to another.

Where does conduction come into play in an oven or dryer? Two places, primarily -- the product being heated and the insulation in the walls, roof and floor of the oven.

Although convection and radiation usually are responsible for bringing heat to the load, their job ends when they unload the thermal energy at the product's surface. More often than not, conduction carries the heat into the product interior. Consequently, the thermal conductivity of the product has a great deal of influence over how quickly it reaches a uniform processing temperature.

Heat is lost through oven walls by conduction, so to keep those losses to an economical minimum, you can do one of two things -- increase the thickness of the wall ("L" in the equation above) or decrease the value of k, the thermal conductivity of the material from which the wall is made.

This raises an interesting question. Most oven walls consist of mineral wool or ceramic-fiber board or blanket sandwiched between two sheets of metal. Thermal conductivity of these insulating materials runs between 0.25 and 0.40 BTU/hr-ft² per inch of thickness. At typical oven temperatures, however, air has a conductivity of only 0.18 to 0.24 BTU/hr-ft² per inch of thickness (conductivity varies with temperature). Why, then, don't oven manufacturers simply leave an open air space between the inner and outer panel walls? Wouldn't heat losses be lower because of air's lower conductivity?

In theory, yes, if there were no natural convection inside the wall panel. The problem, as shown in figure 2, is that the air resting against the inside of the hot wall becomes heated and rises. Eventually, it bumps into the top of the panel or some other barrier and is forced over to the cold side panel, where it begins to lose heat. As it cools, it slides down the cold side, finally hitting the bottom of the cavity and drifting back to the hot side panel, where it heats up again, repeating the cycle.

Packing the cavity with mineral wool or ceramic fiber does increase the thermal conductivity of the wall, but this is more than offset by the fact that it breaks up those air circulation patterns. It's the same principle as insulating the walls and attic of your house.

Another interesting point is that the effective thermal conductivity of the insulating materials is a function of the form they're in. For example, at full density, the raw materials used to make insulation have thermal conductivities in the range of 8 to 10 BTU/hr-ft² per inch of thickness. When they're spun or blown into fibers and fabricated into blankets or boards containing lots of air pockets, the effective conductivity is only a small fraction of that value.

Links

• Energy Notes: Convection
• Energy Notes: Conduction
• Energy Notes: Radiation, Part 1
• Energy Notes: Radiation, Part 2
• Energy Notes: Archives