Most, if not all, of us know that heating (and cooling) of parts happens by three mechanisms: radiation, convection and conduction. While simple examples illustrate the basic concepts, the underlying science, while a bit more complex, is something all heat treaters should know. Let’s learn more.
The Science Revealed
Radiation is a method of heat transfer that does not rely upon direct contact between the heat source and the object being heated. For example, we feel heat from the sun (Fig. 1) even though we are not touching it. Radiation is also line-of-sight heating. If an object (such as a component part buried inside a dense load) is not directly in the path of the radiant energy, it will only heat when the surrounding objects (parts, in this example) are heated and re-radiate their heat energy to the buried object. This is why part loading/spacing in high-temperature atmosphere furnaces and in vacuum furnaces is so important.
Everyday experience has taught us that black or dull surfaces are better at absorbing radiant heat energy than shiny, reflective surfaces. What we don’t often appreciate is that the radiant energy (the amount of thermal energy being radiated per second per unit area) is proportional to the fourth power of (absolute) temperature (Eq. 1). Thus, we must be extremely careful when we heat something to ensure that we do not overheat it by radiation. This is why, for example, aerospace specifications do not allow direct exposure of radiant heating sources to the parts (e.g., during the solution heat treating of aluminum), which is performed close to the melting point of the material. Heat loss by radiation can occur in any situation, but it becomes more important as the temperature increases. This is why insulation in high-temperature furnaces must be carefully designed.
The rate of radiant heat transfer is given in equation 1.
Q=A•K•Fe•Fs•(T4radiator – T4receiver) (1)
Q is the heat transferred in watts (Joule/second), A is the surface area in m2, K is a constant (Stefan-Boltzmann), Fe and Fs are the emissivity of the emitter and the surface respectively, and T is the temperature of the radiator and receiver (in °K).
In simplest terms, convection occurs when a (solid) object comes in contact with a liquid or gas at a different temperature. It will always involve the liquid or gas in some state of motion. A hair dryer (Fig. 2) is a simple example in which heated air exits the dryer at a speed such that it transfers heat energy to the object it strikes (wet hands, wet hair, etc.).
The rate of convective heat transfer is given in equation 2.
Q=hc•A•(Tfluid– Tobject) (2)
Q is the heat transferred in watts (Joule/second), hc is the heat-transfer coefficient in W/m2-°K, A is the surface area in m2, T is the temperature in °K, and t is the time in seconds.
Conduction occurs when two objects at different temperatures are in contact with each other. Heat flows from the warmer object to the cooler object until they are both at the same temperature. A classic example of heat transferred between two bodies is when a metal spoon is left in a hot cup of coffee (Fig. 3). Solids are better conductor than liquids, and liquids are better conductor than gases.
The rate of conductive heat transfer is given in equation 3.
Q=k•A•(Thotter – Tcolder) (3)
Q is the heat transferred in watts (Joule/second), k is the thermal conductivity of the material in W/m-°K, A is the surface area in m2, Thotter – T cooler is the temperature difference across the material in °K, and L is the thickness of the material in meters.
While both conduction and convection require physical contact to transfer heat energy, by contrast, radiation does not require contact between the heat source and the object being heated. Thus, the heat transfer to an object at a specific temperature by radiation and convection occurs differently (Fig. 4).
In the real world, it is important for us to keep in mind how heat energy is being transferred to the parts we are processing so that we can avoid issues such as overheating, underheating, distortion and surface/subsurface melting. Here are a few more important takeaways:
• Parts heated by radiation (a T4 relationship) will receive heat energy far more rapidly than parts heated by convection (a T1 relationship).
• Heat transfer by radiation, while (thermally) inefficient at temperatures under about 540°C (1000°F), becomes highly efficient as the temperature increases. This is one reason why radiant furnaces have a difficult time holding temperature uniformity at low temperatures.
• Heat transfer by convection is (thermally) efficient at low temperatures – up to approximately 650°C (1200°F) – but far less efficient as the temperature increases.
• Heat transfer by conduction is responsible for bringing heat to the inside of a part or extracting heat from the interior (core) of a part. Time is an important factor in heating or cooling to ensure the center of the part is at temperature.
• Only a small portion of the heat energy delivered to a furnace or oven is available to heat the load. The balance is lost due to a variety of reasons (e.g., flue losses, wall losses, opening losses, heat storage, etc.). IH
1. Dick Bennett, Janus Technologies, private correspondence
2. How Does Heat Travel, NASA (www.nasa.org or http://coolcosmos.ipac.caltech.edu/cosmic_classroom/light_lessons/thermal/transfer.html)
3. European Space Agency (www.esa.int)