13
Radiation Exchange in a Nonparticipating
Medium
13.1 Radiation Exchange between Gray Diffuse Isothermal
Surfaces in an Enclosure
Since we know how to get surface radiation properties such as emissivity,
reflectivity, and absorptivity and how to determine the view factor between
two surfaces, the following shows how to determine radiation heat transfer
between surfaces in an enclosure [1–4]. Assume that there are N gray diffuse
and isothermal surfaces. This implies that each surface at T i has uniform
radiosity J i (emission plus reflection). Figure 13.1 shows an energy balance
on each surface i and an energy balance between surface i and the rest of
enclosure surfaces j.
Based on the assumptions, each surface radiation properties can be given
as follows.
α i = ε i , for gray and diffuse surfaces
τ i = 0, for the opaque body
ρ i = 1 − α i = 1 − ε i
There are three types of radiation problems for electric furnace applications.
1. Given each surface temperature T i to determine each surface heat
flux (q/A) i =?
2. Given each surface heat flux (q/A) i to determine each surface
temperature T i =?
3. Combination of 1 and 2, some surfaces given temperature but heat
flux unknown, and some surfaces given heat flux but temperature
unknown.
Perform energy balance on the i surface: net energy = energy out (radiosity) − energy in (irradiation)
q i A i ( J i G i )
(13.1)
=
−
257
Radiation Exchange in a Nonparticipating
Medium
13.1 Radiation Exchange between Gray Diffuse Isothermal
Surfaces in an Enclosure
Since we know how to get surface radiation properties such as emissivity,
reflectivity, and absorptivity and how to determine the view factor between
two surfaces, the following shows how to determine radiation heat transfer
between surfaces in an enclosure [1–4]. Assume that there are N gray diffuse
and isothermal surfaces. This implies that each surface at T i has uniform
radiosity J i (emission plus reflection). Figure 13.1 shows an energy balance
on each surface i and an energy balance between surface i and the rest of
enclosure surfaces j.
Based on the assumptions, each surface radiation properties can be given
as follows.
α i = ε i , for gray and diffuse surfaces
τ i = 0, for the opaque body
ρ i = 1 − α i = 1 − ε i
There are three types of radiation problems for electric furnace applications.
1. Given each surface temperature T i to determine each surface heat
flux (q/A) i =?
2. Given each surface heat flux (q/A) i to determine each surface
temperature T i =?
3. Combination of 1 and 2, some surfaces given temperature but heat
flux unknown, and some surfaces given heat flux but temperature
unknown.
Perform energy balance on the i surface: net energy = energy out (radiosity) − energy in (irradiation)
q i A i ( J i G i )
(13.1)
=
−
257