The theory of conservation of energy tells us energy cannot be created nor destroyed. It can only be transformed into different forms. Thermal energy is heat energy in the form of heat, which is transferred when a temperature difference is present. Thermal energy can only be transferred from a higher-temperature body to a lower-temperature body until both bodies reach thermal equilibrium.
Thermal equilibrium
Thermal equilibrium is a state where two substances of matter have reached the same temperature and hence there is no longer transfer of thermal energy between them. It can also be described as an isothermal condition. In order for it to be counted as an isothermal condition, the two bodies need to be in contact with each other.
If a block of ice with a temperature of -5°C is positioned on a table with a temperature of 25°C, will thermal equilibrium be reached?
Solution
The thermal energy of the table will transfer to the ice due to the temperature difference (ΔΤ) of 20°C, until these two objects reach thermal equilibrium. So thermal equilibrium will be reached when these two objects reach the same temperature.
The direction of heat transfer
The temperature of the two regions under the present temperature gradient will provide the direction of the heat transfer. The direction of thermal energy will always be from the higher temperature body to the lower temperature body, when no external heat additions are in the system. In the above example, the direction of heat transfer is from the table to the ice as the table has a higher temperature.
Methods of heat transfer
There are three main methods by which heat transfer can occur. These include convection, conduction, and radiation.
Convection
Also known as convective heat transfer, this entails the transfer of heat through the movement of a fluid that might be in the form of gas or liquid. When a fluid moves, thermal energy is being transferred from the motion of particles in the fluid.
Moving hot fluid inside a pipeline will cause the pipe to heat up as thermal energy will transfer from the hot fluid to the pipeline walls, causing the material to heat up.
Conduction
This is a method of heat transfer that occurs due to collisions between particles and subatomic particles within a body. When subatomic particles collide with each other, there is a transfer of kinetic energy known as internal energy, which creates heat.
When a hot pan is removed from the stove and positioned on a table, the thermal energy from the hot pan will transfer locally to the surface of the table by the collision of particles between the two surfaces.
Radiation
Radiation is a method of heat transfer in the form of light or electromagnetic waves. This type of energy is emitted by certain matters around us.
An example of radiation heat transfer is the heating of a room from the thermal energy emitted by a fireplace. In this example, heat transfer through conduction also occurs in the room, but at a lower rate.
Heat transfer coefficient
This is a physical property of an object, used to express how well heat is being transferred. If the heat transfer coefficient (h) is large, then heat will be transferred from one object to another more easily and quickly, and vice versa. The heat transfer coefficient depends on two parameters - thermal conductivity, and the thickness of the materials in which heat transfer occurs.
Thermal conductivity is a measure of the ability of a material to conduct heat. If thermal conductivity is high, the heat transfer coefficient will also be higher. And also, if the material is quite thick, the resulting heat transfer coefficient will be lower.
The equation for heat transfer
The rate at which heat transfer occurs can be described by the following equation. Keep in mind:
- h is the heat transfer coefficient.
- Q is the heat transferred measured in Watts.
- ΔΤ is the temperature difference between the two objects of interest (it is measured in Kelvin).
- A is the surface area of the conduction zone in m2.
- T1 and T2 are the temperatures of the surface and surroundings respectively.
\[Q = h \cdot A \cdot \Delta T = h \cdot A \cdot (T_2 - T_1)\]
A pan with a diameter of 20cm and a depth of 5cm is being heated. Energy is transferred by convection from the stove to the bottom of the pan at a rate of 600 W. The resulting temperature on the outer bottom of the pan is 380 K. Find the heat transfer coefficient if the temperature at the inner bottom surface is 300 K.
Solution
We first need to find the surface area in SI units. We do that by converting 20 cm into meters and then converting diameter into radius to find the area as shown below.
\(D = 20 \space cm = 20 \cdot 10^{-2} \space m\)
\(R = \frac{20 \cdot 10^{-2} \space m}{2} = 0.1 \space mA = \pi \cdot r^2 = \pi \cdot 0.1^2 m^2 = 0.0314 \space m^2\)
Find the heat transfer coefficient by rearranging the heat transfer rate equation.
\(Q = h \cdot A \cdot (T_2 - T_1) \rightarrow h = \frac{Q}{A \cdot (T_2-T_1)}\)
Finally, we substitute the given values in the final equation to find the heat transfer coefficient.
\(h = \frac{Q}{A \cdot (T_2-T_1} = \frac{600}{0.0314 \cdot (380-300)} [W/m^2K] = 238.85 [W/m^2K]\)
Heat Transfer - Key takeaways
Thermal energy transfer is the transfer of thermal energy between two bodies due to temperature differences.
Thermal energy can be transferred by three main methods.
Convection, conduction, and radiation are the methods of thermal energy transfer.
The heat transfer coefficient is a characteristic of the thermal conductivity of a material, which measures how well heat is being transferred through the material.
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