Chapter 13b Flashcards
Radiation heat exchange depends on
orientation of the surfaces relative to each other accounted for by view factor
View factor is
purely geometric quantity, independent of surface properties and temp
view factor also called
shape factor configuration factor and angle factor
diffuse view factor based on
assumption that the surfaces are diffuse emitters and diffuse reflectors
specular view factor
assumption that the surfaces are diffuse emitters and specular reflectors
Fij
the fraction of the radiation leaving surface i that strikes surface j directly
Radiosity is
total rate at which radiation leaves differential surfaces via emission and reflection in all direction
radiosity =
J = pi()*I
Heat transfer from surface Q. =
JA = pi()I*A
Reciporcity relation for view factors
A1F12 = A2F21
F11=
fraction of radiation leaving surface 1 that strikes itself directly
non zero for concave surfaces
underlying assumption of view factor
radiation a surface receives from a source is directly proportional to the angle the surface subtends when viewed from the source
case when surfaces are isothermal and diffuse emitters and reflectors and separated by nonparticipating medium such as air
issue with assumption of view factor
only the case if the radiation coming off the source is uniform in all directions throughout its surface and the medium between the surfaces doe not absorb emit or scatter radiation
What is the reciprocity relation
F12 = F21 if A1 = A2 A1F12 = A2F21
radiatio analysis on an enclosure consisting of N surfaces requires the evaluation of
N^2 view factors
The summation rule
sum of the view factors from a surface i of an enclsure to all surfaces of the enclosure including to itself must equal unity
sum of Fij from j=1 to N =1
total number of viewfactors that need to be evaluated directly for an N surface enclosure =
1/2 N(N-1)
The superposition rule
view factor from a surface i to a surface j is equal to the sum of the view factors surface i to the parts of surface j
F1(2,3) = F12 + F13
The superposition rule fraction of surfaces
F(2,3)1 = (A2F21 + A3F31)/A2 + A3
The symmetry rule
two or more surfaces the possess symmetry about a third surface will have identical view factors from that surface
if surface j and k are symmetric about surface i
Fij=Fik and Fji = Fki
View factors between infinitely long surfaces
the crossed strings method
Fij = (sum of crossed strings - sum of uncrossed strings)/(2 * string on surface i)
When can crossed strings method be applied
changes and ducts vlong in one direction relative to other directions, therefore consider 2D
modeled as inf long
net rate of radiation when approximated as blackbodies
Q.12 = Radiation leaving the entire surface 1 that strikes surface 2 - Radiation leaving the entire surface 2 that strikes surface 1
=A1Eb1F12 - AEb2F21
=A1F12sigma(T1^4 - T2^4)
Net heat transfer from any surface i of an N surface enclosure =
Q.i = sum from j=1 to N AiFijsigma(Ti^4-Tj^4)
issue with non black surfaces heat transfer
reflections make very complicated
what are assumptions to get around reflection
opaque diffuse gray
isothermal surfaces and incoming and outgoing radiation is uniform
What is radiosity J
the total radiation energy leaving a surface per unit time per unit area
reflected radiation + emitted radiation
for surface that is gray and opaque with is radiosity
epsilon = alhpa alhpa + rho = 1
J = radiation emitted by surface i + radiation reflected by surface i
= EPSiEbi + RHOiGi
= EPSiEbi + (1 - EPSi)Gi (W/m^2)
Net radiation heat transfer to or from a surface
Q.i = (radiation leaving a surface i) - (radiation incident on entire surface i)
= Ai (Ji-Gi)
Net radiation heat transfer to or from a surface Q.i =
Ai*EPSi/(1-EPSi) * (Ebi - Ji) = (Ebi - Ji)/Ri
surface resistance to radiation
Ri = 1 - EPSi / Ai*EPSi
What is a reradiating surface
surface modeled as adiabatic since their back sides are well insulated and the net heat transfer through them is zeo
Ji = Ebi = sigma * T^4
Space resistance to radiation
Rij = 1/Ai*Fij
Draw a network representation of net radiation heat transfer from surface i to the remaining N surfaces of an enclosure
see book
the net radiation flow from a surface through its surface resistance =
the sum of the radiation flows from that surface to all other surfaces through corresponding space resistance
Direct method If net heat transfer rate is given for radiation analysis of an enclosure
Q.i = Ai sum from j=1 to N of Fij (Ji-Jj)
Direct If surfaces with specified temperature Ti is given for radiation analysis of an enclosure
sigma*T^4 = Ji + (1-EPSi)/EPSi * sum from j=1 to N of Fij (Ji-Jj)
When is the network method no longer practical
for enclosures with more than three of four surfaces
Draw the schematic of a two surface enclosure
see book
Draw schematic of a three surface enclosure
see book
