Heat Transfer Mechanisms

Heat is transferred from a substance of higher temperature to one with lower temperature. But how is it transferred? In this page, we will discuss about the different processes in which heat energy can be transferred from one substance to the other.

There are three different methods in which heat can be transferred, namely – conduction, convection, and radiation.

Conduction is the transfer of heat due to the collision of the particles of the object. When an object is heated, the particles move more rapidly, increasing the kinetic energy. Hotter regions have higher kinetic energy than the cooler regions. As the particles in the hotter region are moving faster, they collide with their neighbor particles in the cooler region, making them move and continue colliding. The process continues until all the particles in all parts of the object is moving. The collision of the particles all throughout the object makes the kinetic energy of the particles more similar thus making the temperature uniform all throughout the object. The particles don’t move from one region to the other in an object, but their energy does.

In a metal, the conduction of heat is of more different process. Some of the electrons can separate from the atoms and move around the metal.  These “free” electrons can carry energy from hotter area to cooler area in a metal. This process within a metal makes it as a good conductor of heat.

During conduction, the heat flows from the region of higher temperature to the region of lower temperature. The ratio of the heat flow in a material is dQ \over dt, in which dQ is the amount of heat dQ transferred in the material at time dt. This ratio is called as the heat current which is denoted by the letter H. For a metal rod, experiments show that the heat current varies directly to the rod’s cross-sectional area, A and to the change in the temperature TH – TC and varies inversely to the length of the rod, L. Mathematically, this can be expressed as

$$H = kA\; {T_H – T_C \over L}$$

where the quantity $$T_H – T_C \over L$$ is the temperature difference per unit length which is called as the temperature gradient, k is the numerical value of the thermal conductivity. Different materials have different thermal conductivity, that is, the one with large thermal conductivity value are good conductors of heat and the ones with small thermal conductivity value are poor conductors which are commonly known as the insulators. L is also called as the length of the heat-flow path.

The unit for heat current is Watts, W or joule/second, J/s. The temperature is in Kelvin, K, the area is in m2, length is in meter, m and the thermal conductivity is in $$J/s\cdot m \cdot K$$ or in $$W/m \cdot K$$.

Example 1.

A rod made of copper with length of 1.00 m and a cross-sectional area of 0.03 m2 is heated at a temperature of 750 K. if the region with lower temperature of the rod is 400 K, what is the heat current through the rod? The thermal conductivity of copper is 385 $$W/m \cdot K$$.

Given:

L = 1.00 m

A = 0.03 m2

T_C = 400 K

T_H = 750 K

k = 385 $$W/m \cdot K$$

Solution:

$$H = kA\; {T_H – T_C \over L}$$

$$H = (385\; W/m \cdot K) (0.03\;m^2) \begin{pmatrix} {750\;K – 400\;K \over 1.00\; m} \end{pmatrix}$$

$$H = 4,042.5\;W$$

Convection

Convection type of heat transfer occurs when the heated particles are moving from one region to another in a material or system. When air or water is in contact with a heat source, the temperature rises on the part which is near or in contact with the heat, making that part to expand and become less dense. The expanded part is lighter than the cooler part. Buoyant force will cause the hotter particles to rise. The cooler particles will then occupy the part vacated by the hotter particles, and then the process continues.

Convection can be forced or free. If the circulation of the gas or fluid particles is due to a blower or pump, the process is called forced convection. Free convection happens if the heat flow is caused by the differences in density due to thermal expansion.

Convection is a complicated process and no equation is used to illustrate and solve it but it plays important role in any processes. In natural processes, the free convention in the atmosphere helps in determining the variation of the daily weather and global climate patterns. Also, the convection in the ocean is an important global heat-transfer mechanism. Convection is also the only heat transfer method that happens in the Earth’s mantle which is important in the distribution of heat in the Earth’s layer. It is also because of the convection in the Earth’s mantle that the tectonic plates are able to move around the Earth’s surface.

The hot-air and hot-water heating systems and the cooling system of an automobile engine are also examples of application of convection.

Most importantly is the convection in our body which is needed to maintain nearly constant temperature in different environment. The circulation of our blood is an example of forced convection in which the heart is the pump.

The heat transfer is caused by electromagnetic waves such as visible light, infrared, and ultraviolet radiation. We feel the heat of the sun even if its hundred million kilometers away from the Earth. When cooking, we can feel the heat of the fire even if we don’t touch it. In this way, we absorb the thermal energy from the Sun and the fire, increasing our thermal energy. Heat can be transferred through the process of radiation without any medium used as path of the heat. Even if the heat source and the one absorbing the heat is distance apart, heat is still transferred.

The rate of heat emitted by a radiation source is directly proportional to its surface area, A and to the fourth power of the absolute temperature, T4. Mathematically, this relationship can be expressed as

$$H = A \varepsilon \sigma T^4$$

where $$\varepsilon$$ is the emissivity of the object’s surface and $$\sigma$$ is the Stefan–Boltzmann constant which has a current best numerical value as 5.670373(21) x 10-8 W/m2 $$\cdot$$ K4. This relationship is also called as the Stefan–Boltzmann law in honor of its late-19th-century discoverers - Josef Stefan and Ludwig Boltzmann.

Example 1.

An iron rod with a surface area of 0.08 m2 is heated at 1,123 K. Solve for the total rate of radiation of energy from the rod if the emissivity is 0.9.

Given:

A = 0.08 m2

T = 1, 123 K

$$\varepsilon$$ = 0.9

$$\sigma$$ = 5.670373(21) x 10-8 W/m2 $$\cdot$$ K4

Solution:

To solve the problem we use the equation $$H = A \varepsilon \sigma T^4$$. Now we substitute all the given values

$$H = (0.08\;m^2)(0.9)(5.67 \times 10^{-8}\;W/m^2 \cdot K^4)(1, 123\;K)^4=6,492.84\;W$$

The total rate of radiation of energy from the rod is 6, 492.84 W.