lecture 25 – radiation view factors. view factors the equivalent fraction of radiation from one...
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CHE/ME 109 Heat Transfer in
ElectronicsLECTURE 25 –
RADIATION VIEW FACTORS
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VIEW FACTORSTHE EQUIVALENT FRACTION OF RADIATION
FROM ONE SURFACE THAT IS INTERCEPTED BY A SECOND SURFACE
ALSO CALLED THE RADIATION SHAPE FACTOR
CONFIGURATION FACTOR
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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
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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
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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
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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
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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
`
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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
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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
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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
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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
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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( )
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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
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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
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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.
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INFINITE SURFACESFOR INFINITE PARALLEL SYSTEMS, THE
METHOD OF STRINGS CAN BE USED TO EVALUATE THE VIEW FACTORS