THE VIEW FACTOR/SHAPE FACTOR

It is a purely geometric quantity and is independent of the surface properties and temperature. It is also known as configuration factor and angle factor.

The view factor from a surface i to a surface j is denoted by Fi → j or just Fij, and is defined as

Fij = the fraction of the radiation leaving surface i that strikes surface j directly

Fij=QijQi

Here,            Qij =  fraction of rate of energy leaving surface i reaching surface j

                    Qi = Rate of total energy radiated by surface i

• In general, 0 ≤ Fij ≤ 1.

• The view factor from a surface to itself is zero for plane or convex surfaces and nonzero for concave surfaces.

Reciprocity Relation

A1F12=A2F21

Summation Rule

The sum of the view factors from surface i of an enclosure to all surfaces of the enclosure, including to itself, must equal unity.

∑j=1NFij=1

F11=0

F11+F12=1   (Summation Rule)

hence F12=1

A1F12=A2F21   (Reciprocity Rule)

F21=A1A2

F21+F22=1   (Summation Rule)  

F22=1−F21=1−A1A2

Superposition Rule

The view factor from a surface i to a surface j is equal to the sum of the view factors from surface i to the parts of surface j. 

Note : The reverse of this is not true.

 

F1(23)=F12+F13

Symmetry Rule

This Rule can be expressed as two (or more) surfaces that possess symmetry about a third surface will have identical view factors from that surface.

The Crossed-Strings Method

View Factors between Infinitely Long Surfaces is given by

F12=(L5+L6)−(L3+L4)2∗L1

Fij=∑(CrossedStrings)−∑(UncrossedStrings)2∗(Stringonsurface′i′)

Net Radiation Heat Transfer to or from a Surface

Net Energy Leaving a Surface

The net energy leaving from the surface will be equal to the difference between the energy leaving a surface and the energy received by a surface 

Qi=Ai(Ji−Gi)

J=εEb+ρG

If Surface is opaque, ρ = 1 – α 

J = ε Eb + (1 – α) G

we get,   Qi=Eb−JiRi and Ri=1−εiAiεi is the surface resistance to the radiation.

Net Exchange Between Surfaces

The net rate of radiation heat transfer from surface i to surface j can be expressed as

Qij=AiJiFij−AjJjFji

Qij=Ji−JjRij

where Rij=1AiFij is the space resistance to the radiation.

Electrical circuit representation of two surfaces which can see each other nothing else

Total resistance      Rt=1−ε1ε1A1+1A1F12+1−ε2ε2A2

Q12=Eb1−Eb2Rt

Radiation Shields

Assume two flat infinite long flate surfaces 1 and 2 have N shields in between.

Net Heat Transfer without any shield:

Q=Aσ(T41−T42)1ε1+1ε2−1

Net Heat transfer with N shields

Q=Aσ(T41−T42)(1ε1+1ε2−1)+∑Nj=1(1εj,1+1εj,2−1)