shape factor or view factor

SHAPE FACTOR OR VIEW FACTOR OR CONFIGURATION FACTOR:

Radiation heat transfer between surfaces depends upon the orientation of the surfaces relative to each other as well as their radiation properties and temperatures.

To account for the effects of orientation on radiation heat transfer between the surfaces,

a new parameter VIEW FACTOR is defined which is purely geometric quantity and is independent of radiation properties and temperatures.

Assumptions:

• The surfaces are diffuse emitter.
• The radiation that strikes a surface need not to be absorbed by that surface.
• Radiation that strikes a surface after being reflected by other is not considered in the evaluation of view factor.

The radiation shape factor is represented by the symbol F_ij ,

which means the shape factor form a surface, A_i to another surface A_j.

Thus the radiation shape factor F₁₂ of surface A₁ to surface A₂ is

 

SHAPE FACTOR RELATIONS:

(i) RECIPROCITY RELATION:

A1F12 = A2F21

 Reciprocity Relation is valid between any two surfaces even when there are more than two number of surfaces involved in Radiation Heat Exchange.

(ii) SUMMATION RULE:

If there are n number of surfaces involved in any radiation heat exchange then.

F₁₁ + F₁₂ + F₁₃ + …………….F_1n = 1

F₂₁ + F₂₂ + F₂₃ + ……………. F_2n = 1

.

F_n1 + F_n2 + F_n3 + ………..F_nn + 1

TOTAL SURFACES FOR VIEW FACTORS FOR N SURFACES OF AN ENCLOSURE

• Numbers of relation given by summation rule =N
• Numbers of relations given by reciprocity rule,

     

• The total numbers of view factors that need to be evaluated directly,

      

SUPERPOSITION RULE:

 F_1-(2,3) = F_1-2 + F_1-3

 SYMMETRY RULE:

Two or more surfaces that posses symmetry about a third surface will have identical view factors from that surface.

If the surface 2 and 3 are symmetric about surface 1 then F_1-2=F_1-3

GENERAL CASES:

CROSS STRING METHOD:

The each length is assumed to Be a strings connected between two points.

Cross Strings → The strings which crosses each other.

Uncrossed strings → The strings which do not cross each other.

L_i = length of string on surface i.

AB → 1 surface

CD → 2 surface

Special Case:

(Length)₁ = (Length)₂ Both surface are infinite in plane perpendicular to plane of paper.