## Friday, January 2, 2015

### Thermal Conduction in Transmission of Heat

Heat is a form of energy. Heat always flows from a body of higher temperature to a body of lower temperature, when there is a temperature difference between the two bodies and they are connected.

There are broadly three ways of the transmission of the heat from one place to another place. They are conduction, convection and radiation.

Conduction

Conduction is a phenomenon of the transmission of the heat where no particle of the medium has a permanent displacement.

After receiving the heat energy each particle starts vibrating about its mean position and passes the energy to the next particles.

Once after the transfer of the heat energy is done from one particle to other particle, the original particle comes back the state of rest. Thus the vibration of the each particle is just a temporary until it passes the heat energy to the next particles.

This kind of transmission happens through a solid media. It is just because the force of attraction between the molecules of the solid is very strong and they always preferred to come back to their original positions.

Among all the three different types of transmission, conduction is the slowest process.

How much heat energy is passing through a solid medium depends on the nature of the media.

The amount of the heat energy that is passing through a given solid media is directly proportional to its area of cross-section, temperature difference between the two ends, and time of the flow and inversely proportional to the length of the conductor.

To eliminate the proportionality with can put a constant and the constant is called coefficient of thermal conductivity.

Coefficient of thermal conductivity is a characteristic property of the material and it is independent of the physical dimensions of the body.

We can define coefficient of thermal conductivity as the rate of the flow of the heat through a material of unit area of cross-section and unit length when the temperature difference between the ends is only 1°C.

Problem and solution

A metal rod is having a length of 80 cm. One end of the rod is in steam and other end is in ice. Find the temperature at a point where the distance is 20 cm from the cold end?

While solving this problem we shall understand one point that the same heat will flow through the entire rod per second.

The impact of the heat energy into different points of the rod is different and hence each part is going to have different temperature. By equating the rate of flow of heat between the two parts of the rod we can get the answer as shown below.

Problem and solution

Three different materials having the same physical dimensions are connected in the Y-shape as shown. Find the temperature at the junction?

Even in solving this problem, we are going to follow the same approach. From one rod heat energy starts flowing and at the junction which spreads into two parts. How much heat energy is going to be shared among them depends on the nature of the rod and its physical dimensions.

Anyway the rate of flow of the heat energy is conserved and by applying that concept we can get the temperature at the junction.

We can also understand one more point that the heat always flows from a body of higher temperature to your body of lower temperature.

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