# Thermal Radiation

### Contents

**Explain Radiative Heat Transfer**1**Explain the radiation properties of surfaces**1**Define Absorptivity, Reflectivity, and Transmissivity**2**Explain the concept of the Black Body and Gray Body**3**Describe the following i. Kirchhoff’s Law ii. Planck’s Law iii. Wien’s Displacement Law iv. Boltzmann Law v. Lambert’s Cosine Law**3**Explain the Intensity of Radiation**4**Define Shape Factor and explain its salient features**5**Define Irradiation and Radiosity**5**Describe the Electrical network analogy for thermal radiation system**6**Recall Heat Exchanger between non-black bodies**6**Describe the Heat Exchanger between infinite parallel plates**7**Describe the Heat Exchanger between infinitely long concentric cylinders**8**Recall Radiation Shields**9

Explain Radiative Heat Transfer

Radiative heat transfer refers to the transfer of heat by the emission of electromagnetic waves, specifically thermal radiation. Unlike conduction and convection, which require a medium for heat transfer, radiative heat transfer can occur in a vacuum, such as in outer space.

In practical applications, radiative heat transfer occurs between objects at different temperatures, and the rate of heat transfer depends on the properties of the emitting and absorbing surfaces, including their temperature, surface area, and emissivity. The emissivity of a surface is a measure of its ability to emit thermal radiation and ranges from 0 to 1, with an emissivity of 1 indicating perfect emission.

The amount of radiative heat transfer between two surfaces can be calculated using the Stefan-Boltzmann law, which states that the total power emitted by a blackbody (a theoretical surface with an emissivity of 1) is proportional to the fourth power of its absolute temperature.

In many engineering applications, radiative heat transfer is combined with conduction and convection, and the total heat transfer is calculated as a combination of all three modes. It is important to accurately predict and model radiative heat transfer in a variety of industrial processes, including furnace design, heat treatment of materials, and thermal management of electronic devices.

Explain the radiation properties of surfaces

The radiation properties of surfaces refer to the ability of a surface to emit, reflect, and absorb electromagnetic radiation. The radiation properties of a surface can be quantified using various parameters such as emissivity, reflectivity, and absorptivity.

Emissivity is the ratio of the radiant energy emitted by a surface to the radiant energy emitted by a blackbody at the same temperature and with the same area. A blackbody is a theoretical object that absorbs all the radiation that falls on it and emits the maximum possible amount of radiation for its temperature.

Reflectivity is the ratio of the radiant energy reflected by a surface to the radiant energy incident on it. The reflectivity of a surface can depend on the angle of incidence of the radiation and the wavelength of the radiation.

Absorptivity is the ratio of the radiant energy absorbed by a surface to the radiant energy incident on it. The absorptivity of a surface can depend on the angle of incidence of the radiation and the wavelength of the radiation.

The radiation properties of a surface play a significant role in radiative heat transfer, which is the transfer of heat by electromagnetic radiation. A surface with high emissivity will emit more radiant energy, while a surface with high reflectivity will reflect more radiant energy. A surface with high absorptivity will absorb more radiant energy, leading to a greater transfer of heat by radiation.

Define Absorptivity, Reflectivity, and Transmissivity

Absorptivity, Reflectivity, and Transmissivity are three important properties that describe the behavior of a surface when it comes to radiative heat transfer.

Absorptivity refers to the fraction of radiation incident on a surface that is absorbed by the surface. It is a measure of the surface’s ability to absorb radiation and is expressed as a dimensionless quantity ranging from 0 to 1, with 0 representing a perfectly reflective surface and 1 representing a perfectly absorbent surface.

Reflectivity refers to the fraction of radiation incident on a surface that is reflected by the surface. It is a measure of the surface’s ability to reflect radiation and is also expressed as a dimensionless quantity ranging from 0 to 1, with 0 representing a perfectly absorbent surface and 1 representing a perfectly reflective surface.

Transmissivity refers to the fraction of radiation incident on a surface that passes through the surface. It is a measure of the surface’s ability to allow radiation to pass through and is also expressed as a dimensionless quantity ranging from 0 to 1, with 0 representing a perfectly opaque surface and 1 representing a perfectly transparent surface.

It’s important to note that the sum of Absorptivity, Reflectivity, and Transmissivity for a given surface always equals 1.

Explain the concept of the Black Body and Gray Body

In the field of thermal radiation, a black body is considered an idealised surface that absorbs all incoming radiation and does not reflect or transmit any of it. This means that a black body is a perfect emitter of radiation and absorbs all the radiation that falls on it. A black body has a unique temperature-dependent emissive power, which is described by the Stefan-Boltzmann law.

A grey body, on the other hand, is a real-world object that is not a perfect emitter or absorber of radiation. It absorbs, reflects and transmits some fraction of the incoming radiation and has emissive power that deviates from the Stefan-Boltzmann law. The degree of deviation depends on the surface properties of the grey body, such as its absorptivity, reflectivity, and transmissivity. The amount of radiation absorbed by a grey body is proportional to its absorptivity, while the amount reflected and transmitted is proportional to its reflectivity and transmissivity, respectively.

Describe the following i. Kirchhoff’s Law ii. Planck’s Law iii. Wien’s Displacement Law iv. Boltzmann Law v. Lambert’s Cosine Law

i. Kirchhoff’s Law: This law states that the ratio of the emissivity to the absorptivity of a material at a given temperature is equal to unity. In other words, an ideal black body absorbs all the radiation incident on it and emits an equal amount of radiation.

ii. Planck’s Law: Planck’s law describes the spectral distribution of blackbody radiation as a function of temperature. It states that the energy emitted by a black body per unit area per unit time per unit wavelength is proportional to the frequency of the radiation raised to the power of 4, and inversely proportional to the exponential of the product of the frequency and temperature.

iii. Wien’s Displacement Law: This law states that the wavelength of maximum radiation from a black body is inversely proportional to its temperature. This means that as the temperature of a black body increases, the wavelength of maximum radiation emitted by it decreases.

iv. Boltzmann Law: Boltzmann law states that the total energy radiated by a black body is proportional to the fourth power of its temperature.

v. Lambert’s Cosine Law: This law states that the radiance of a diffusely emitting surface is proportional to the cosine of the angle between the surface normal and the direction of observation. This law is used to calculate the amount of radiation emitted by a diffuse surface, such as a cloud or a matte surface, in a particular direction.

Explain the Intensity of Radiation

Intensity of radiation refers to the amount of energy being transferred by radiation per unit area per unit time in a particular direction. It is a measure of the strength of the radiation and can be expressed in units of power per unit area or W/m^2. The intensity of radiation depends on various factors such as the temperature of the radiating body, the surface area of the body, and the distance from the radiating body. At a given temperature, the intensity of radiation increases as the surface area of the body increases, and decreases as the distance from the body increases. The concept of intensity of radiation plays a crucial role in various applications of heat transfer, such as in solar radiation, combustion systems, and radiative cooling.

Define Shape Factor and explain its salient features

The Shape Factor (also known as the configuration factor) is a dimensionless quantity that describes the radiative exchange between two surfaces. It represents the ratio of the radiant exchange between two surfaces to the radiant exchange that would occur if the surfaces were black and extended to infinity.

The Shape Factor depends on the size, shape, and orientation of the surfaces, as well as their distance from one another. It is a crucial factor in the calculation of radiative heat transfer in real-world situations, where surfaces are often not ideal (i.e., not black or extended to infinity).

The salient features of the Shape Factor include:

- It is a dimensionless quantity, making it easy to use in calculations.
- It accounts for the real-world conditions of radiative heat transfer, including surface size, shape, orientation, and distance from one another.
- The Shape Factor ranges from 0 to 1, with a value of 1 representing the maximum radiative exchange between two surfaces and a value of 0 representing no radiative exchange.
- The Shape Factor can be calculated using various methods, including analytical models and numerical methods, such as Monte Carlo simulations.

Overall, the Shape Factor plays an important role in the accurate calculation of radiative heat transfer, taking into account the complexities of real-world situations.

Define Irradiation and Radiosity

Irradiation is defined as the rate of incident radiation received per unit surface area at a given point on a surface. It is denoted as I and is expressed in units of power per unit area. Irradiation is the measure of the rate of incoming radiant energy.

Radiosity is defined as the rate of radiant energy emitted by a surface per unit area. It is denoted as J and is expressed in units of power per unit area. Radiosity is the measure of the rate of outgoing radiant energy from a surface.

In a system of multiple surfaces in thermal interaction, irradiation and radiosity are related through Kirchhoff’s law, which states that the emissivity and absorptivity of a surface are equal. This means that a surface that absorbs a certain fraction of incident radiation will also emit radiation at the same rate.

Both irradiation and radiosity play an important role in the calculation of radiative heat transfer and the exchange of energy between surfaces in thermal systems.

Describe the Electrical network analogy for thermal radiation system

The electrical network analogy for thermal radiation systems is a comparison between the flow of heat through radiative heat transfer and the flow of electrical current through a network of resistors. In this analogy, the temperature difference between two surfaces is equivalent to the voltage difference between two electrical nodes, and the heat transfer between the two surfaces is equivalent to the electrical current flowing through a resistor. The resistance in this case is represented by the shape factor, which is a measure of the exchange of radiative heat between two surfaces. By using this analogy, engineers can use well-established methods from electrical engineering to analyze and design thermal radiation systems.

Recall Heat Exchanger between non-black bodies

Heat exchangers are devices that transfer heat from one fluid to another. They are commonly used in a variety of industrial applications to control the temperature of different processes. When the heat exchanger is between non-black bodies, it means that the two fluids that are being exchanged are not ideal black bodies.

Black bodies are theoretical objects that absorb all electromagnetic radiation that falls on them, and they emit radiation proportional to their temperature. In reality, no object is a perfect black body. However, black bodies are often used as a reference for defining the behavior of real objects in thermal radiation.

In a heat exchanger between non-black bodies, the two fluids are not ideal black bodies, meaning that they do not absorb and emit radiation perfectly. This leads to differences in the amount of heat that can be transferred from one fluid to another, as well as the efficiency of the heat exchanger itself. The amount of heat transferred is dependent on various factors such as the temperature difference between the two fluids, the emissivity of the surfaces in contact, and the radiative heat transfer coefficient.

To summarise, a heat exchanger between non-black bodies refers to a heat exchanger in which the two fluids being exchanged are not ideal black bodies and therefore exhibit differences in the amount of heat that can be transferred and the efficiency of the heat exchanger.

Describe the Heat Exchanger between infinite parallel plates

A heat exchanger between infinite parallel plates is a specific type of heat exchanger that uses two parallel plates as the surfaces through which heat is transferred. These plates are typically made of a highly conductive material such as metal, and they are separated by a small gap. The two fluids being exchanged are separated by these plates, and the heat is transferred between them by conduction through the plates.

In this type of heat exchanger, the two parallel plates are assumed to be infinite in size and have a constant temperature. This allows for a simplified analysis of the heat transfer process, as the conditions on the two plates are uniform and do not change with time. The heat transfer rate in this type of heat exchanger is proportional to the temperature difference between the two fluids, the surface area of the plates, and the thermal conductivity of the plates.

One of the benefits of a heat exchanger between infinite parallel plates is that it is relatively simple and inexpensive to manufacture, as the plates are relatively simple in shape and can be made from readily available materials. Additionally, this type of heat exchanger can be designed to transfer heat at high rates, making it suitable for high-temperature applications.

To summarise, a heat exchanger between infinite parallel plates is a type of heat exchanger that uses two parallel plates as the surfaces through which heat is transferred. The plates are assumed to be infinite in size and have a constant temperature, and the heat transfer rate is proportional to the temperature difference between the fluids, the surface area of the plates, and the thermal conductivity of the plates. This type of heat exchanger is simple and inexpensive to manufacture, and it is suitable for high-temperature applications.

Describe the Heat Exchanger between infinitely long concentric cylinders

A heat exchanger between infinitely long concentric cylinders is a type of heat exchanger in which two concentric cylindrical surfaces are used to transfer heat between two fluids. The two cylindrical surfaces are separated by a small gap, and the two fluids being exchanged are separated by these surfaces. The heat is transferred between the two fluids by conduction through the cylindrical surfaces.

In this type of heat exchanger, the two cylindrical surfaces are assumed to be infinitely long, which simplifies the analysis of the heat transfer process. The temperature distribution along the cylinder surfaces is uniform and does not change with time. The heat transfer rate in this type of heat exchanger is proportional to the temperature difference between the two fluids, the surface area of the cylindrical surfaces, and the thermal conductivity of the cylindrical surfaces.

One of the benefits of a heat exchanger between infinitely long concentric cylinders is that it is relatively simple and inexpensive to manufacture, as the cylindrical surfaces are relatively simple in shape and can be made from readily available materials. Additionally, this type of heat exchanger is relatively compact and can be designed to transfer heat at high rates, making it suitable for high-temperature applications.

To summarise, a heat exchanger between infinitely long concentric cylinders is a type of heat exchanger that uses two concentric cylindrical surfaces to transfer heat between two fluids. The cylindrical surfaces are assumed to be infinitely long, and the heat transfer rate is proportional to the temperature difference between the fluids, the surface area of the cylindrical surfaces, and the thermal conductivity of the cylindrical surfaces. This type of heat exchanger is simple and inexpensive to manufacture, and it is relatively compact and suitable for high-temperature applications.

Recall Radiation Shields

Radiation shields are devices that are used to protect sensitive equipment and personnel from the harmful effects of radiant energy. They are typically used in a variety of industrial and scientific applications, including nuclear power plants, particle accelerators, and medical imaging equipment.

Radiation shields are designed to reduce the amount of radiant energy that reaches a protected area by absorbing or reflecting the energy. They are typically made of materials that are highly reflective or absorptive of radiant energy, such as lead or heavy metals. The effectiveness of a radiation shield depends on its thickness and composition, as well as the type and energy of the radiant energy being shielded.

One of the key benefits of radiation shields is that they provide a high level of protection against the harmful effects of radiant energy, such as ionising radiation. They are also relatively simple and inexpensive to manufacture, and they can be designed to fit specific applications.

To summarise, radiation shields are devices that are used to protect sensitive equipment and personnel from the harmful effects of radiant energy. They are typically made of materials that are highly reflective or absorptive of radiant energy and are designed to reduce the amount of radiant energy that reaches a protected area. Radiation shields are effective in providing protection against the harmful effects of radiant energy and are relatively simple and inexpensive to manufacture.