Configuration factor at the axis of a cylinder

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Configuration factor at the axis of a cylinder

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CANADA Ser TKL 7392 no. 38 c. 2 BrnG

CONFIGURATION FACTOR

AT

THE AXIS

OF

A CYLINDER by

5. H. McGuire

(3)

CONFIGURATION FACTOR

AT

THE AXIS O F A C Y L m E R

Expr es s ions, gr apbs and tables relating to the configuration

factors for most of the commonly encountered surfaces are already

available. Ref. 1 include8 a fairly comprehensive List of expre B sions, a number of tables and a list of references t o other sourcea of i d o r

-

mation.

Nevertheless, a problem arose recently involving a swface

for which the solution to the configuration factor w a s not readily avail-

able. The problem was €he specification of the radial clearance necessary

to protect a building, located in a forest, from undesirable levels of

thermal radiation in the event of a forest fire. In addition to other

information, an expression was required for the configuration factor of the interior surface of a finite cylinder at a receiving surface on. the axis of the cylinder.

The problem is illustrated in_{Fig. 9.} _The_{general expression}

for the configuration factor

+

of a radiator with respect to a receiving

element i~ (1)

+

z-11

n- d o . c o s a

where d o is the s o l i d angle subtended at the receiver by an element of

4

radiator, and a is the angle NOP between the normal t o the receiver

(ON)

(4)

F o r the integration use spherical co-ordinates

1 c,

0 ) choosing

the origin of 0 such that the normal to the receiver

[ON),

the axis of

I T

the cylindrical radiator (OZ) and the line 8

=

0,

5 =

_-[OY)

are

2

co-planar ,

T o determine cos a u s e the carkesian co-ordinates

OX,

O Y

and

O Z

and the direction cosine rule

I

cos a

= & &

+ a rnf

+

z a'.

Considering

OM,

the normal to the receiver,

0 , m = c o s p a n d n = s i n p .

Considering

OP,

1'

need not be evaluated since A!

=

0 ,

OY'

OP

sira

6

cos 0

- 1 x- =

OP O P = sin f coa 8

and n'

=

eos

6.

Therefore cos a r cos

p

sin

5

cos 0

+

sin.

p

cos

5 .

Reverting t o the spherical co-ordinates and the general express ion

f o r a configuration factor,

d w

=

d e . d 8 .

she.

Therefore

52 ,-BZ

(5)

h the practical application of thia a p r e s sian particular heed

must be paid to a feature of almost all mathematically derived expres-

sions for confignration factors. Radiation incident on the rear surface

of the receiver is aesociated'witb, a negative configuration factor. F o r

any one calculation, therefore, the area taken as the radiator, deiined by the Limits of f, and 0 , must be i4within. the field of view1' of the

receiving surface.

It

might be useful t o bear in mind that the above expres d o n

applies to any surface

(e.

g. spherical) with limits

el.

e2.

g1

and

c2.

Reference

1. McGuire,

J.

H. Heat Transfer by Radiation. H. M. S. 0.

,

5. _F-

_R.

_0.

(6)

REC

ELE

FIGURE

I