CHE/ME 109 Heat Transfer in

ElectronicsLECTURE 25 –

RADIATION VIEW FACTORS

VIEW FACTORSTHE EQUIVALENT FRACTION OF RADIATION

FROM ONE SURFACE THAT IS INTERCEPTED BY A SECOND SURFACE

ALSO CALLED THE RADIATION SHAPE FACTOR

CONFIGURATION FACTOR

VIEW FACTOR EXAMPLECONSIDER THE FOLLOWING SKETCH

THE ENERGY TRANSFERRED FROM

AREA A1 IS ASSUMED TO BE DIFFUSE

SO IT IS DIRECTED IN ALL DIRECTIONS

ABOVE THE PLANE OF THE AREA

THE PORTION THAT REACHES AREA A2

VARIES IN INTENSITY BASED ON:THE DISTANCE TO THE RECEIVER, RTHE ANGLE BETWEEN THE PLANES OF THE AREAS

A1

A2

1

2

R

VIEW FACTOR EXAMPLETO DETERMINE THE TOTAL

RECEIVED, IT IS NECESSARY TO INTEGRATE FROM EACH DIFFERENTIAL AREA ON A1 ACROSS THE ENTIRE SURFACE OF A2.

THE AMOUNT OF RADIATION FROM DIFFERENTIAL AREAS dA1 TO dA2 IS:

Q IdA dA

RdA dA`co s cos

1 2 11 1 2 2

2

A1

A2

1

2

R

RADIOSITYTHE TOTAL RADIATION FROM dA1 IS

COMPRISED OF THE EMITTED AND REFLECTED ENERGY

THIS COMBINATION IS REFERRED TO AS THE RADIOSITY, J

J CAN BE A FUNCTION OF ANGLE AND WAVELENGTH SO THE TOTAL IS EVALUATED FROM

J I d d de r

,

/( , , ) co s sin

0

2

0

2

0

RADIOSITYIF THE SURFACE IS A DIFFUSE EMITTER AND A

DIFFUSE REFLECTOR, THEN THIS RELATIONSHIP BECOMES:

AND FOR THE TOTAL OF ALL WAVELENGTHS THEN:

J I e r ( ) ,

J I e r

RADIOSITY AND VIEW FACTORTHE TOTAL RADIATION FROM A1 TO A2

BECOMES THE INTEGRAL OF ALL THE VALUES SO:

.THE VIEW FACTOR IS THEN DEFINED AS THE FRACTION OF THE TOTAL RADIATION FROM A1 THAT INTERCEPTS A2:

Q JdA dA

RAA`

co s cos1 2 1

1 2 1 2221

FQ

A J121 2

1 1

`

SPECIFIC TYPES OF VIEW FACTORSTABLES 13-1 AND 13-2 PROVIDE SOME VIEW

FACTOR EQUATIONS FOR COMMON CONFIGURATIONS

SIMILAR DATA IS PRESENTED GRAPHICALLY AS FIGURES 13-5 THROUGH 13-8

THIS DATA CAN BE COMBINED TO ALLOW EVALUATION OF OTHER TYPES OF CONFIGURATIONS USING VIEW FACTOR ALGEBRA OR VIEW FACTOR RELATIONS

VIEW FACTOR RELATIONSHIPSRECIPROCITYTHE RELATIONSHIP BETWEEN

VIEW FACTORS FOR TWO SURFACES IS

A SIMPLE EXAMPLE IS FOR THE CASE OF AN INFINITE CYLINDER INSIDE ANOTHER CYLINDER

THE VIEW FACTOR FROM A2 TO A1 IS:

A F A F1 12 2 21

F21 1

A1 A2

VIEW FACTOR RELATIONSHIPSSUMMATIONUSED TO DETERMINE THE

DISPOSITION OF ALL RADIATION FROM A SOURCE

TOTAL VIEW FACTOR FROM A SOURCE, i, REQUIRES THAT

F dFi j i jj

n

, 1

1

SUMMATION FOR A CURVED SURFACECAN INCLUDE RADIATION TO THE

REFERENCE SURFACEFOR THE EXAMPLE OF A CYLINDER (OR

SPHERE) INSIDE AN ARC, THE RADIATION FROM A1 IS INTERCEPTED BY A2 AND ALSO A1.

FOR THE SITUATION WHERE THE VIEW FACTOR CAN BE EXPLICITLY CALCULATED FOR ALL THE SURFACES BUT ONE, THE FINAL ONE IS OBTAINED BY DIFFERENCE

A1

A2

F FUNKNOWN KNOWN 1

SUMMATION FOR ENCLOSURESTHE TOTAL NUMBER OF VIEW FACTOR

RELATIONSHIPS FOR AN ENCLOSURE WITH N SURFACES IS

NUMBER OF VIEW FACTORS THAT NEED TO BE EXPLICITLY .

OTHER VALUES CAN BE EVALUATED BY A COMBINATION OF SUMMATION AND RECIPROCITY

F NN ENCLOSURE 2

F N NEXPLIC IT 1

21( )

SUPERPOSITIONSUPERPOSITION LETS THE VIEW FACTOR

BETWEEN SURFACES BE SUBDIVIDED INTO THE SUM OF VIEW FACTORS BETWEEN SEVERAL SURFACES

THIS RELATIONSHIP IS USEFUL WHEN A SECTION OF A SURFACE, TRANSMITTING OR RECEIVING IS OPEN

.HIS IS ACTUALLY A VARIATION ON THE SUMMATION RULE AND HAS THE FORM:

F FN ii

N1 11

SYMMETRYSYMMETRY RULE IS A DERIVATIVE

FROM THE RECIPROCITY RELATIONSHIP

.THE VIEW FACTOR BETWEEN SIMILAR CONFIGURATIONS IS THE SAME

.CONSIDER AS AN EXAMPLE, AN OPEN TOP CUBICAL BOX WITH RADIATION FROM THE BASE.

)THE VALUE OF THE RADIATION TO ONE OF THE SIDES CAN BE DETERMINED FROM FIGURE 12-6 TO BE

SYMMETRYTHE VALUE OF THE RADIATION TO ONE

OF THE SIDES CAN BE DETERMINED FROM FIGURE 13-6 TO BE

USING SYMMETRY, THE OTHER 3 SIDES HAVE THE SAME VIEW FACTOR

BY DIFFERENCE, THE VIEW FACTOR TO THE TOP IS

WHICH CAN BE VALIDATED FROM FIGURE 13-5

FBASE SIDE 0 2.

FBASE TOP 0 2.

INFINITE SURFACESFOR INFINITE PARALLEL SYSTEMS, THE

METHOD OF STRINGS CAN BE USED TO EVALUATE THE VIEW FACTORS