HEAT TRANSFER: LAWS, FORMS OF TRANSMISSION, EXAMPLES - PHYSICAL - 2025

There is heat transfer when energy goes from one body to another due to the difference in temperature between the two. The heat transfer process ceases as soon as the temperatures of the bodies in contact equal or when the contact between them is removed.

The amount of energy transferred from one body to another in a given period of time is called transferred heat. One body can give heat to another, or it can absorb it, but the heat always goes from the body with the highest temperature to the body with the lowest temperature.

Figure 1. In a bonfire there are the three mechanisms of heat transfer: conduction, convection and radiation. Source: Pixabay.

The units of heat are the same as those of energy and in the international system of measurements (SI) it is the joule (J). Other frequently used units of heat are the calorie and the BTU.

As for the mathematical laws that govern heat transfer, they depend on the mechanism involved in the exchange.

When heat is conducted from one body to another, the rate at which heat is exchanged is proportional to the temperature differential. This is known as Fourier's law of thermal conductivity, which leads to Newton's law of cooling.

Forms / mechanisms of heat transmission

They are the ways in which heat can be exchanged between two bodies. Three mechanisms are recognized:

-Driving

-Convection

-Radiation

In a pot like the one shown in the figure above, there are these three heat transfer mechanisms:

-The metal in the pot is heated mainly by conduction.

-The water and air are heated and rise by convection.

-People near the pot are heated by the radiation emitted.

Driving

Heat conduction occurs mostly in solids and in particular in metals.

For example, the stove in the kitchen transmits heat to the food inside the pot through the conduction mechanism through the metal of the bottom and the metal walls of the container. In thermal conduction there is no material transport, only energy.

Convection

The convection mechanism is typical of liquids and gases. These are almost always less dense at higher temperatures, for this reason there is an upward transport of heat from the hotter fluid portions to the higher regions with colder fluid portions. In the convection mechanism there is material transport.

Radiation

For its part, the radiation mechanism allows heat exchange between two bodies even when they are not in contact. The immediate example is the Sun, which heats the Earth through the empty space between them.

All bodies emit and absorb electromagnetic radiation. If you have two bodies at different temperatures, even being in a vacuum, after a while they will reach the same temperature due to heat exchange by electromagnetic radiation.

Heat transfer rate

In equilibrium thermodynamic systems, the amount of total heat exchanged with the environment matters, so that the system passes from one state of equilibrium to another.

On the other hand, in heat transfer, the interest is focused on the transitory phenomenon, when the systems have not yet reached thermal equilibrium. It is important to note that the amount of heat is exchanged in a certain period of time, that is, there is a speed of heat transfer.

Examples

- Examples of heat conduction

In thermal conductivity, the heat energy is transmitted through collisions between the atoms and molecules of the material, whether this is solid, liquid or gas.

Solids are better conductors of heat than gases and liquids. In metals there are free electrons that can move through the metal.

As free electrons have great mobility, they are capable of transmitting kinetic energy through collisions more efficiently, which is why metals have high thermal conductivity.

From a macroscopic point of view, thermal conductivity is measured as the amount of heat transferred per unit time, or caloric current H:

Figure 2. Heat conduction through a bar. Prepared by Fanny Zapata.

The caloric current H is proportional to the cross section of area A and the variation in temperature per unit of longitudinal distance.

This equation is applied to calculate the caloric current H of a bar like the one in figure 2, which is between two reservoirs of temperatures T ₁ and T ₂ respectively, where T ₁ > T ₂.

Thermal conductivities of materials

Below is a list of the thermal conductivity of some materials in watts per meter per kelvin: W / (m. K)

Aluminum -------- 205

Copper --------- 385

Silver ---------- 400

Steel ---------– 50

Cork or Fiberglass - 0.04

Concrete or glass ----- 0.8

Wood ----- 0.05 to 0.015

Air --------– 0.024

- Examples of convection heat

In heat convection, energy is transferred due to the movement of the fluid, which, at different temperatures, has different densities. For example, when water is boiled in a pot, the water near the bottom increases its temperature, so it expands.

This expansion makes the hot water rise, while the cold one goes down to occupy the space left by the hot water that rose. The result is a circulation movement that continues until the temperatures of all levels equalize.

Convection is what determines the movement of large air masses in the Earth's atmosphere and also determines the circulation of marine currents.

- Examples of radiation heat

In the mechanisms of heat transmission by conduction and by convection, the presence of a material is required for the heat to be transmitted. In contrast, in the radiation mechanism, heat can pass from one body to another through a vacuum.

This is the mechanism by which the Sun, at a higher temperature than the Earth, transmits energy to our planet directly through the vacuum of space. Radiation comes to us through electromagnetic waves.

All materials are capable of emitting and absorbing electromagnetic radiation. The maximum of the emitted or absorbed frequency depends on the temperature of the material and this frequency increases with the temperature.

The predominant wavelength in the emission or absorption spectrum of a black body follows Wien's law, which states that the predominant wavelength is proportional to the inverse of body temperature.

On the other hand, the power (in watts) with which a body emits or absorbs heat energy by electromagnetic radiation is proportional to the fourth power of the absolute temperature. This is known as Stefan's law:

P = εAσT ⁴

In the above expression σ is Stefan's constant and its value is 5.67 x 10-8 W / m ² K ⁴. A is the surface area of ​​the body and ε is the emissivity of the material, a dimensionless constant whose value is between 0 and 1, and depends on the material.

Exercise resolved

Consider the bar in Figure 2. Suppose the bar is 5 cm long, 1 cm in radius, and made of copper.

The bar is placed between two walls that keep its temperature constant. The first wall has a temperature T1 = 100ºC, while the other is at T2 = 20ºC. Determine:

a.- The value of the thermal current H

b.- The temperature of the copper bar at 2 cm, at 3 cm and at 4 cm from the wall of temperature T1.

Solution to

As the copper bar is placed between two walls whose walls maintain the same temperature at all times, it can be said that it is in a steady state. In other words, the thermal current H has the same value for any instant.

To calculate this current we apply the formula that relates the current H with the difference in temperatures and the length of the bar.

The cross sectional area is:

A = πR ² = 3.14 * (1 × 10 ^-2 m) ² = 3.14 x 10 ^-4 m ²

The temperature difference between the ends of the bar is

ΔT = (100ºC - 20ºC) = (373K - 293K) = 80K

Δx = 5 cm = 5 x 10 ^-2 m

H = 385 W / (m K) * 3.14 x 10 ^-4 m ² * (80K / 5 x 10 ^-2 m) = 193.4 W

This current is the same at any point on the bar and at any instant, since the steady state has been reached.

Solution b

In this part we are asked to calculate the temperature Tp at a point P located at a distance Xp from the wall T ₁.

The expression that gives the caloric current H at point P is:

From this expression, Tp can be calculated by:

Let's calculate the temperature Tp at the 2 cm, 3 cm and 4 cm positions respectively, substituting numerical values:

• Tp = 340.6K = 67.6 ° C; 2 cm from T1
• Tp = 324.4K = 51.4 ° C; 3 cm from T1
• Tp = 308.2K = 35.2 ° C; 4 cm from T1

References

1. Figueroa, D. 2005. Series: Physics for Sciences and Engineering. Volume 5. Fluids and Thermodynamics. Edited by Douglas Figueroa (USB).
2. Kirkpatrick, L. 2007. Physics: A Look at the World. 6th abridged edition. Cengage Learning.
3. Lay, J. 2004. General Physics for Engineers. USACH.
4. Mott, R. 2006. Fluid Mechanics. 4th. Edition. Pearson Education.
5. Strangeways, I. 2003. Measuring the Natural Environment. 2nd. Edition. Cambridge University Press.
6. Wikipedia. Thermal conductivity. Recovered from: es.wikipedia.com