Demystifying Heat Transfer

Gary Whittaker

May 1, 2005

Insulation systems–from low-density polymeric foams to medium density fiberglass to high-density calcium silicate–all share a common function. There are many disparate reasons to use insulation; they range from keeping your house warm in the winter and cool in the summer to controlling the noise levels in a commercial airliner. But despite the seeming differences, they share one purpose: resistance to the flow of energy. In the vast majority of cases, insulation is used to control the flow of thermal energy, usually called heat, into or out of whatever is insulated. Heat transfer is the term applied to the movement of heat from one place to another; this is a discussion of its fundamentals.

Any discussion of heat transfer must start with a definition of the second law of thermodynamics. Stated simply, the second law requires that energy always flows spontaneously from high to low. In the case of heat, energy always flows from hot to cold. All insulation designs and all heat transfer systems are grounded in this fundamental law of nature. The purpose of insulation is to resist the flow of energy that comes about as a result of the second law. Where does temperature fit into this discussion?

Temperature is just a measure of the amount of thermal energy contained in a substance. There are different measurement scales that relate temperature to different physical phenomena, such as the freezing point of water (0 C), but, regardless of the basis of the scale, they still just indicate the amount of heat energy present in the substance being measured. The zero point of the Kelvin scale is called absolute zero, and it is the lowest possible temperature. At absolute zero the atoms of which all matter is composed contain no thermal energy and are motionless with respect to adjacent atoms.

There are three distinct ways in which heat is transferred from one location to another, and each is based on a distinct characteristic of matter. The first is conduction; the second is convection, and the last is radiation. Conduction is the transfer of heat energy between two bodies as a result of direct physical contact. When a coffeepot is placed on the hot burner of a stove, heat is conducted from the burner to the pot.

How does this happen? In the case of a stainless steel coffeepot, its atoms are mostly iron and are arranged in a specific crystalline pattern. Let’s assume that the coffee pot was at 0 K, absolute zero, when it was placed on the stove. If you could see the atoms of the pot, you would observe that they were not vibrating before you placed the pot on the stove. The atoms of the stove are at a higher temperature, and you would see that instead of being stationary they are vibrating. As soon as the pot touches the stove, the vibrating stove atoms start to collide with the stationary pot atoms, causing them to vibrate as well. These collisions are a transfer of energy from the hot atoms to the cold atoms. As the pot atoms vibrate, they transfer energy to their neighbors, which also start to vibrate. Over time more collisions occur between the hot atoms of the stove and the cold pot, resulting in increasing vibration of the pot atoms. This ever-increasing vibration is an increase in the thermal energy of the pot and would be measured as an increase in its temperature. If insulation was placed between the pot and the stove, the hot atoms couldn’t bump into the cold atoms and no heat transfer would take place.

All materials have a unique ability to conduct heat, and that ability is expressed as a material constant called the thermal conductivity. Metals as a class of materials are the best conductors of heat, though within the metals family some are better conductors, than others. Copper is a very good heat conductor, which is one of the reasons it ends up on the bottom of many cooking pots. Ceramics and polymers are in general not very good conductors, and this is why they are used to manufacture thermal insulation.

Heat transfer by convection occurs in fluids, either liquid or gas, and results from the motion and interaction of hot and cold fluids. In a liquid or gas the atoms are not locked in position as they are in a solid like the coffeepot; rather, they are free to move around or flow. As the amount of thermal energy in the fluid is increased, the motion of its atoms increases. This causes the average distance between atoms to increase; in other words, the density of the fluid decreases. When fluids of different density are mixed, the denser substance sinks and the less dense substance rises. Hot-air balloons float because the hot air in the balloons is less dense than the cool air outside the balloons.

Let’s apply these principles to the convective heat transfer that occurs in the coffeepot. As the bottom of the pot gets hot, the rate of atomic vibration increases and the atoms on the inside of the pot in contact with the water start to vibrate. Of course, if this illustration were real, the water would be frozen, a minor detail we’ll ignore for the sake of discussion. The vibrating pot atoms collide with the water molecules and transfer heat energy by conduction. As more energy is transferred into the water, it becomes warmer and less dense near the bottom of the pot. The warm water rises and is replaced by cold water that flows into the volume that was occupied by the warm water. The movement of warm water transfers heat from low to high in the pot and is an example of natural convective heat transfer. Insulation controls convective heat transfer by isolating the insulated surface from contact with the moving fluid.

The third method of heat transfer is radiation. So far we have described thermal energy as being the vibration of atoms–the kinetic energy model. It works well when describing conduction and convection, but it falls short when it comes to radiation. All matter–solid, liquid or gas–constantly exchanges thermal energy in the form of electromagnetic radiation (EMR), or light, with its surroundings. If a body is at higher temperature than its surroundings, it emits EMR. If it is at a lower temperature, it absorbs EMR. If the body is at constant temperature the amount of energy it radiates must equal the amount it absorbs; if not, its temperature would change. You will notice this sounds just like the second law of thermodynamics mentioned earlier.

Since the physics of EMR is complex, we’ll limit our discussion to its effects; but there are a few facts about EMR we need to understand. EMR moves in uniformly shaped waves, and its color and energy content depend on wavelength. Wavelength is defined as the distance between identical locations on two adjacent waves; the longer the wavelength, the less energetic the light. As an object gets hotter, its EMR becomes more energetic and its wavelength gets shorter; if it gets sufficiently hot, the radiated light reaches the visible part of the spectrum. To illustrate this effect, consider a piece of steel: At room temperature, it emits no visible light. Now we apply a torch to it, and as the metal warms, it starts to emit visible light, first a deep red that can only be seen in the dark. With rising temperature the color changes from deep red to a brighter orange and finally to a brilliant yellow. This change in color is the result of the increasing energy of the emitted light and its resulting shorter wavelength. Again, the second law of thermodynamics is in play; the hot metal is at a higher energy state than the surrounding environment; so it spontaneously emits EMR in the form of visible light.

You may have noticed I have repeatedly described the spontaneous radiation of EMR from an object as emission. I have used this term because it naturally leads to an important property of all materials called emissivity. Just as conductivity is a unique material property that is a measure of a material’s ability to conduct heat, so is emissivity a measure of a material’s ability to transfer heat by emitting EMR.

A material that is a perfect emitter, that is, it can emit 100 percent of the energy that is available for emission, has an emissivity of 1.0 and is called an ideal blackbody. No material is a perfect blackbody, just as no material is a perfect conductor. Emissivity is defined as the ratio of the actual energy emitted by a surface to the energy emitted by a blackbody. Since nothing in nature is an ideal blackbody, emissivity is always less than 1.0 and is a function of the material and the condition of its surface. A metal surface that is painted black has an emissivity close to 1.0 while the same metal polished to a mirror finish has an emissivity closer to 0.1.

Emission is only half the story of radiation heat transfer; the other half is absorption. I started this discussion by saying that all objects constantly exchange thermal energy with their surroundings. For an object to remain at constant temperature, it must absorb as much energy as it emits. Absorptivity is the absorption counterpart of emissivity. The physicist Gustav Kirchhoff created the concept of the blackbody while studying light. He defined an ideal blackbody as a body that absorbs all incident radiation. The absorbing power of an ideal blackbody is 1.0 and it is less than 1.0 for all other surfaces.

Absorption and emission must always exist together when temperature is constant. When one is greater than the other, temperatures change and there is a net heat transfer. I have always found it difficult to understand how a very absorbent surface could also be a high emitter. We have all experienced black surfaces that get very hot in the summer sun. The natural and correct conclusion is that black is a very good energy absorber, that is probably why Kirchhoff thought to name his perfect absorber a blackbody.

But, if a black surface is such a good absorber, how can it also be a good emitter? The key to understanding this intuitive contradiction lies in the need for equilibrium. If you park your black car in the sun in July, its surface gets very hot because it is a good absorber. If it were not also equally good at radiating heat, its energy content would continue to rise as long as it was in the sun. If this could happen, its temperature would continue to rise without limit. Obviously this doesn’t happen; so when the car reaches a constant temperature it must be radiating as much energy as it is absorbing. Since it’s absorbing a lot of energy, it must also be radiating an equally large amount, which leads to the conclusion that this good absorber must also be a good emitter.

We have now seen that heat transfer occurs in three ways: conduction, convection and radiation. Each process is unique and relatively easy to understand when you boil it down to its basic physical principles. To go further than I have in this column requires some pretty interesting mathematics. All three types of heat transfer can be completely described by equations that are the basis for computer programs like 3E Plus® and the sophisticated finite element heat transfer modeling software that is in common use today.

Finally, now that you understand the fundamentals of heat transfer, you are equipped to understand how any insulation system works. The next time you look at an insulated system, ask yourself where the heat is coming from, where it wants to go and how the insulation interferes with that transfer. If you see the answer, you understand the fundamentals of heat transfer and all the rest you need to know is in the details.

Figure 1