Radiative Heat Transfer - 1 | Heat Transfer - Mechanical Engineering PDF Download

In the previous chapters it has been observed that the heat transfer studies were based on the fact that the temperature of a body, a portion of a body, which is hotter than its surroundings, tends to decrease with time. The decrease in temperature indicates a flow of energy from the body. In all the previous chapters, limitation was that a physical medium was necessary for the transport of the energy from the high temperature source to the low temperature sink. The heat transport was related to conduction and convection and the rate of heat transport was proportional to the temperature difference between the source and the sink.

Now, if we observe the heat transfer from the Sun to the earth atmosphere, we can understand that there is no medium exists between the source (the Sun) and the sink (earth atmosphere). However, still the heat transfer takes place, which is entirely a different energy transfer mechanism takes place and it is called thermal radiation.

Thermal radiation is referred when a body is heated or exhibits the loss of energy by radiation. However, more general form “radiation energy” is used to cover all the other forms. The emission of other form of radiant energy may be caused when a body is excited by oscillating electrical current, electronic bombardment, chemical reaction etc. Moreover, when radiation energy strikes a body and is absorbed, it may manifest itself in the form of thermal internal energy, a chemical reaction, an electromotive force, etc. depending on the nature of the incident radiation and the substance of which the body is composed.

In this chapter, we will concentrate on thermal radiation (emission or absorption) that on radiation produced by or while produces thermal excitation of a body.

There are many theories available in literature which explains the transport of energy by radiation. However, a dual theory is generally accepted which enables to explain the radiant energy in the characterisation of a wave motion (electromagnetic wave motion) and discontinuous emission (discrete packets or quanta of energy).

An electromagnetic wave propagates at the speed of light (3×10⁸ m/s). It is characterised by its wavelength λ or its frequency ν related by

c = λv                   (7.1)

Emission of radiation is not continuous, but occurs only in the form of discrete quanta. Each quantum has energy

E = hv                   (7.2)

where, = 6.6246×10^-34 J.s, is known as Planck’s constant.

Table 7.1 shows the electromagnetic radiation covering the entire spectrum of wavelength

Table 7.1: Electromagnetic radiation for entire spectrum of wavelength

It is to be noted that the above band is in approximate values and do not have any sharp boundary.

7.1 Basic definition pertaining to radiation 
Before we further study about the radiation it would be better to get familiarised with the basic terminology and properties of the radiant energy and how to characterise it.

As observed in the table 7.1 that the thermal radiation is defined between wavelength of about 1×10^-1 and 1×10² μm of the electromagnetic radiation. If the thermal radiation is emitted by a surface, which is divided into its spectrum over the wavelength band, it would be found that the radiation is not equally distributed over all wavelength. Similarly, radiation incident on a system, reflected by a system, absorbed by a system, etc. may be wavelength dependent. The dependence on the wavelength is generally different from case to case, system to system, etc. The wavelength dependency of any radiative quantity or surface property will be referred to as a spectral dependency. The radiation quantity may be monochromatic (applicable at a single wavelength) or total (applicable at entire thermal radiation spectrum). It is to be noted that radiation quantity may be dependent on the direction and wavelength both but we will not consider any directional dependency. This chapter will not consider directional effect and the emissive power will always used to be (hemispherical) summed overall direction in the hemisphere above the surface.

7.1.1 Emissive power
It is the emitted thermal radiation leaving a system per unit time, per unit area of surface. The total emissive power of a surface is all the emitted energy, summed over all the direction and all wavelengths, and is usually denoted as E. The total emissive power is found to be dependent upon the temperature of the emitting surface, the subsystem which this system is composed, and the nature of the surface structure or texture.

The monochromatic emissive power E_λ, is defined as the rate, per unit area, at which the surface emits thermal radiation at a particular wavelength λ. Thus the total and monochromatic hemispherical emissive power are related by

                   (7.3)

and the functional dependency of E_λ on λ must be known to evaluate E.

7.1.2 Radiosity
It is the term used to indicate all the radiation leaving a surface, per unit time and unit area.

                  (7.4)

where, J and J_λ are the total and monochromatic radiosity.
The radiosity includes reflected energy as well as original emission whereas emissive power consists of only original emission leaving the system. The emissive power does not include any energy leaving a system that is the result of the reflection of any incident radiation.