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Conductive Heat Transfer

Last week, we talked about that mug of coffee and transient heat flow. The temperature of many surfaces is constantly changing because of an imbalance in the transfer of energy with the surroundings. When things balance, reaching what we call steady-state transfer, then temperatures stabilize.

We have all heard about the three modes of heat transfer: conduction, convection and radiation. Conduction happens in solids. When you touch that coffee mug, heat is transferred by conduction between the mug and your hand. How much heat is transferred is determined by the conductivity of the materials involved, the difference in their temperature and, if we are concerned about total energy transfer, the area over which transfer is happening. Scientists have determined rates of conductivity in laboratories and published these for many common materials.

Fourier’s Law succinctly describes conductive heat transfer:

Q = k • ΔT • A

In which:

Q = total conductive heat transfer

K = conductivity

ΔT = temperature difference between the transfer surfaces

A = Area of surfaces over which transfer is taking place

When the mug is warmer, the net flow of energy is into your hand. If it is cold, your hand supplies heat to the mug. An extremely hot mug may be too hot to touch comfortably because a great deal of energy is transferred to your hand. There may be instances where the mug and your hand are exactly the same temperature, in which case ΔT equals zero and no heat transfer happens!

All these containers are filled with hot coffee of the same temperature so ΔT is the same in all cases. They exhibit different surface temperatures based on difference in conductive heat transfer. From left to right, compare the plain paper cup to a ceramic mug to an insulated cup to a vacuum bottle. Note the thermal reflections on the counter in front of the two on the left and the reflections off the surfaces of the two on the right.

We commonly change the conductive properties to control heat transfer. If we want to keep coffee warm (or our beer cold!) for a longer time period, we can put it in an insulated—less conductive—container. We can keep our fingers comfortable by adding a material that is less conductive, like a paper sleeve.

Insulating our home reduces conductive transfer and as a result, keeps us warmer in the winter and cooler in the summer. We know that in extreme climates, either hot or cold, we need more insulation if we are to effectively control heat loss and gain. Also buildings with a greater surface area will lose/gain more energy, so just minimizing area is another viable way to control total heat transfer. Typically, we talk about resistance to heat transfer, or R-value, when describing insulation. Stated simply R = 1/k.

Thermographers must fully understand conductive heat transfer, one of the main reasons it is integral to the Level I curriculum.  You can learn more on your own as well by getting out your imager, filling a cup of coffee (or two) and having some fun exploring this important topic. Next week we’ll review convective heat transfer.

Thinking Thermally,

John Snell—The Snell Group, a Fluke Thermal Imaging Blog content partner

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