# Conduction, Convection, and Radiation

When heat is transferred from one substance or body to another, it is done in one of three ways: conduction, convection, and radiation. Often, heat will be transferred in a combination of methods. Let's take a closer look.

*Conduction* is the direct transfer of heat between two objects in contact with each other, or through
an object in contact with both of the other objects. When you put your spoon in a cup of hot coffee, the spoon heats up. In a nutshell, the coffee warms the molecules at one end of the spoon,
increasing their kinetic energy. These molecules, in turn, bounce into other molecules in the spoon and increase the KE of those molecules. And so it goes until all of the molecules in the spoon have
reached thermal equilibrium with the coffee. Of course, there is a loss of heat by the coffee, and heat is lost at the end of the spoon to the atmosphere. Ultimately, the coffee cools
down.

When heat is transferred via conduction, certain factors affect the rate of heat flow. These include the type of material, the length between the objects, and the cross sectional area of the material heat is being transferred through. Mathematically, we can say:

where l is the length or distance between the two objects (or the length of
the conductor), A is the cross sectional area of the conductor, T_{1} and T_{2} are the temperatures of the two objects, and k is the *Thermal Conductivity* of the conductor. k
is measured in J/sec- m-^{o}C and the higher the value of k, the better of a conductor the substance is. Materials that are not good conductors (that have low values of k) are called
*insulators*. An analysis of the above equation tells us that we get a pretty good rate of heat transfer if:

- k is high, or the cross sectional area, A is high, or the path length for heat transfer (l) is small, or
- there is a large temperature difference between the two objects.

If you go to a hardware store and look at insulation in building materials,
you will see that it is referred to in terms of its R value. This is *thermal resistance* and a materials R-value is given by the equation

where l is the thickness of the material and k is the conductivity. Thus, you get good R values for thick materials that are poor conductors. But you probably already surmised that.

Similar to conduction is *convection*. Fluids (gases and liquids)
tend to be poor conductors. Heat is generally transferred through convection in fluids and gases. Convection is the rapid and mass movement of molecules in a substance. This movement causes
excitation of other molecules, raising the overall kinetic energy of the system. Ocean currents and air currents are examples of heat being transferred through convection. A convection oven forces
hot air around the food to provide faster movement of the molecules and to exchange the hot molecules for cooler molecules near the food's surface. You can see convection currents in a pot of water
as you heat it up.

Both convection and conduction require a medium to transfer heat. But the
third type, *radiation* can transfer heat energy even in a vacuum. Radiation consists of electromagnetic waves (such as Infrared and

Ultraviolet energy) and these have the ability to transfer in a vacuum. This is how the sun's energy gets to us.

Radiation has some unique characteristics. The first is that the rate of heat transfer is proportional to the temperature of the radiating body (in Kelvin) raised to the 4th power. If an object is twice as hot as a second object, it radiates heat at a rate 16 times as fast. The actual formula for heat transfer by radiation is given by the Stefan-Boltzman equation:

where **s** is a universal constant called the Stefan- Boltzman constant and is equal to 5.67 x
10^{-8} Watts/m^{2} K^{4},

and *e* is a factor called emissivity that is a characteristic of the material. A is the cross sectional area of the object. T is the temperature in Kelvin. Dark objects have an emissivity
close to 1, while shiny or white objects have an *e* closer to 0. Objects that emit less radiation also absorb less radiation, which is why we wear light colored clothing on hot, sunny
days.

For more on the topics, try:

http://www.mansfieldct.org/schools/mms/staff/hand/convcondrad.htm

http://hyperphysics.phy-astr.gsu.edu/hbase/hframe.html (follow the road map)

For Practice Problems, Try: *Giancoli Multiple Choice Practice Questions (Try them all!)*