### Shape Factors

• Understand the importance of shape factor for radiation heat transfer.

• Find appropriate view (shape) factors for various configurations.

Shape Factors are also called View Factors, or, Configuration Factors It is the proportion of the radiation which leaves surface A that strikes surface B.

## Reciprocity Relation:

Reciprocity relation relates the shape factors from (1) to (2) and that from (2) to (1) as follows:

$A_i F_{ij} = A_j F_{ji}$

Thus, if the shape factor from (1) to (2) is known, then the shape factor from (2) to (1) can be found by: $F_{2 \rightarrow 1} = \dfrac{A_1}{A_2} F_{1 \rightarrow 2}$

## Summation Rule:

This rule says that the shape factor from a surface (1) to another (2) can be expressed as a sum of the shape factors from (1) to (2a), and (1) to (2b). Using this rule allows you to break up complicated geometry into smaller pieces for which the individual shape factors can be found.

$\sum_{j=1}^{N} F_{ij} = 1$

## Shape Factor for Self Body:

F$_{ii}$ or F$_{11}$ energy received by body 1 out of energy emitted by body 1.

• For a flat surface F$_{ii}$ =0

• For a convex surface F$_{ii}$ = 0

• For a concave surface F$_{ii}$ $\neq$ 0

### Solved Example:

#### 82-4-01

The shape factor of convex surface with respect to itself (F$_{1-1}$) is:

Solution:
If a surface is flat or convex, then the shape factor with respect to itself is zero.