Radiative Heat Transfer - 2 | Heat Transfer - Mechanical Engineering PDF Download

7.1.3 Irradiation

It is the term used to denote the rate, per unit area, at which thermal radiation is incident upon a surface (from all the directions). The irradiative incident upon a surface is the result of emission and reflection from other surfaces and may thus be spectrally dependent.

               (7.5)

where, G and G_λ are the total and monochromatic irradiation.
Reflection from a surface may be of two types specular or diffusive as shown in fig.7.1.

Fig. 7.1: (a) Specular, and (b) diffusive radiation

Thus,

J = E + ρG                (7.6)

7.1.4 Absorptivity, reflectivity, and transmitting
The emissive power, radiosity, and irradiation of a surface are inter-related by the reflective, absorptive, and transmissive properties of the system.
When thermal radiation is incident on a surface, a part of the radiation may be reflected by the surface, a part may be absorbed by the surface and a part may be transmitted through the surface as shown in fig.7.2. These fractions of reflected, absorbed, and transmitted energy are interpreted as system properties called reflectivity, absorptivity, and transmissivity, respectively.

Fig. 7.2: Reflection, absorption and transmitted energy

Thus using energy conservation,

              (7.7)

               (7.7)

where,  are total reflectivity, total absorptivity, and total transmissivity. The subscript λ indicates the monochromatic property.

In general the monochromatic and total surface properties are dependent on the system composition, its roughness, and on its temperature.

Monochromatic properties are dependent on the wavelength of the incident radiation, and the total properties are dependent on the spectral distribution of the incident energy.

Most gases have high transmissivity, i.e.  (like air at atmospheric pressure). However, some other gases (water vapour, CO₂ etc.) may be highly absorptive to thermal radiation, at least at certain wavelength.

Most solids encountered in engineering practice are opaque to thermal radiation  Thus for thermally opaque solid surfaces,

ρ + α = 1                (7.6)

Another important property of the surface of a substance is its ability to emit radiation. Emission and radiation have different concept. Reflection may occur only when the surface receives radiation whereas emission always occurs if the temperature of the surface is above the absolute zero. Emissivity  of the surface is a measure of how good it is an emitter.

7.2 Blackbody radiation

In order to evaluate the radiation characteristics and properties of a real surface it is useful to define an ideal surface such as the perfect blackbody. The perfect blackbody is defined as one which absorbs all incident radiation regardless of the spectral distribution or directional characteristic of the incident radiation.

A blackbody is black because it does not reflect any radiation. The only radiation leaving a blackbody surface is original emission since a blackbody absorbs all incident radiation. The emissive power of a blackbody is represented by , and depends on the surface temperature only.

Fig. 7.3: Example of a near perfect blackbody

It is possible to produce a near perfect blackbody as shown in fig.7.3.

Figure 7.2 shows a cavity with a small opening. The body is at isothermal state, where a ray of incident radiation enters through the opening will undergo a number of internal reflections. A portion of the radiation absorbed at each internal reflection and a very little of the incident beam ever find the way out through the small hole. Thus, the radiation found to be evacuating from the hole will appear to that coming from a nearly perfect blackbody.

7.2.1 Planck’s law
A surface emits radiation of different wavelengths at a given temperature (theoretically zero to infinite wavelengths). At a fixed wavelength, the surface radiates more energy as the temperature increases. Monochromatic emissive power of a blackbody is given by eq.7.10.

                (7.7)

Where; h = 6.6256 X 10^-34 JS; Planck’s constant

c = 3 X 10⁸ m/s; speed of light

T  = absolute temperature of the blackbody

λ = wavelenght of the monochromatic radiation emitted

k = Boltzmann constant.

Equation 7.10 is known as Planck’s law. Figure 7.4 shows the representative plot for Planck’s distribution.

Fig. 7.4: Representative plot for Planck’s distribution