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CHE/ME 109 Heat Transfer in Electronics

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This lecture focuses on the view factors, also known as radiation shape factors or configuration factors, essential in analyzing heat transfer in electronic systems. It explains how the fraction of radiation emitted from one surface and intercepted by another varies based on distance and angle. Essential terms such as radiosity and the relationship between view factors are discussed, along with examples and rules for calculating view factors in various configurations. This knowledge is crucial for optimizing thermal management in electronic applications.

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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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