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CHE/ME 109 Heat Transfer in Electronics

CHE/ME 109 Heat Transfer in Electronics. LECTURE 25 – RADIATION VIEW FACTORS. VIEW FACTORS. THE EQUIVALENT FRACTION OF RADIATION FROM ONE SURFACE THAT IS INTERCEPTED BY A SECOND SURFACE ALSO CALLED THE RADIATION SHAPE FACTOR CONFIGURATION FACTOR. VIEW FACTOR EXAMPLE.

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CHE/ME 109 Heat Transfer in Electronics

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  1. CHE/ME 109 Heat Transfer in Electronics LECTURE 25 – RADIATION VIEW FACTORS

  2. VIEW FACTORS • THE EQUIVALENT FRACTION OF RADIATION FROM ONE SURFACE THAT IS INTERCEPTED BY A SECOND SURFACE • ALSO CALLED THE RADIATION SHAPE FACTOR • CONFIGURATION FACTOR

  3. VIEW FACTOR EXAMPLE • CONSIDER 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, R • THE ANGLE BETWEEN THE PLANES OF THE AREAS

  4. VIEW FACTOR EXAMPLE • TO 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:

  5. RADIOSITY • THE 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

  6. RADIOSITY • IF THE SURFACE IS A DIFFUSE EMITTER AND A DIFFUSE REFLECTOR, THEN THIS RELATIONSHIP BECOMES: • AND FOR THE TOTAL OF ALL WAVELENGTHS THEN:

  7. RADIOSITY AND VIEW FACTOR • THE 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:

  8. SPECIFIC TYPES OF VIEW FACTORS • TABLES 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

  9. VIEW FACTOR RELATIONSHIPS • RECIPROCITY • THE 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:

  10. VIEW FACTOR RELATIONSHIPS • SUMMATION • USED TO DETERMINE THE DISPOSITION OF ALL RADIATION FROM A SOURCE • TOTAL VIEW FACTOR FROM A SOURCE, i, REQUIRES THAT

  11. SUMMATION FOR A CURVED SURFACE • CAN INCLUDE RADIATION TO THE REFERENCE SURFACE • FOR 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

  12. SUMMATION FOR ENCLOSURES • THE 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

  13. SUPERPOSITION • SUPERPOSITION 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:

  14. SYMMETRY • SYMMETRY 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

  15. SYMMETRY • THE 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

  16. INFINITE SURFACES • FOR INFINITE PARALLEL SYSTEMS, THE METHOD OF STRINGS CAN BE USED TO EVALUATE THE VIEW FACTORS

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