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CHE/ME 109 Heat Transfer in Electronics

CHE/ME 109 Heat Transfer in Electronics. LECTURE 8 – SPECIFIC CONDUCTION MODELS. SOLUTIONS FOR EXTENDED (FINNED) SURFACES. FINS ARE ADDED TO A SURFACE TO PROVIDE ADDITIONAL HEAT TRANSFER AREA

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CHE/ME 109 Heat Transfer in Electronics

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  1. CHE/ME 109 Heat Transfer in Electronics LECTURE 8 – SPECIFIC CONDUCTION MODELS

  2. SOLUTIONS FOR EXTENDED (FINNED) SURFACES • FINS ARE ADDED TO A SURFACE TO PROVIDE ADDITIONAL HEAT TRANSFER AREA • THE TEMPERATURE OF THE FIN RANGES FROM THE HIGH VALUE AT THE BASE TO A GRADUALLY LOWER VALUE AS THE DISTANCE INCREASES FROM THE BASE

  3. SOLUTIONS FOR FINS • BASIC HEAT BALANCE OVER AN ELEMENT OF THE FIN INCLUDES CONDUCTION FROM THE BASE, CONDUCTION TO THE TIP, AND CONVECTION TO THE SURROUNDINGS WHICH MATHEMATICALLY IS

  4. SOLUTIONS FOR FINS • FOR UNIFORM VALUES OF k AND h, THIS EQUATION CAN BE WRITTEN AS: • THE GENERAL SOLUTION TO THIS SECOND-ORDER LINEAR DIFFERENTIAL EQUATION IS: • AT THE BOUNDARY CONDITION REPRESENTED BY THE BASED CONNECTION TO THE PLATE: T = To AT x = 0, THE SOLUTION BECOMES:

  5. NEED ONE MORE BOUNDARY CONDITION TO SOLVE FOR THE ACTUAL VALUES THERE ARE 3 CONDITIONS THAT PROVIDE ALTERNATE SOLUTIONS INFINITELY LONG FIN SO THE TIP TEMPERATURE APPROACHES T∞: SOLUTIONS FOR FINS

  6. SOLUTIONS FOR FINS • SO THE FINAL FORM OF THIS MODEL IS AN EXPONENTIALLY DECREASING PROFILE • WITH THIS PROFILE, THE TOTAL HEAT TRANSFER CAN BE EVALUATED • CONSIDERING THE CONDUCTION THROUGH THE BASE AS EQUAL TO THE TOTAL CONVECTION

  7. SOLUTIONS FOR FINS • TAKING THE DERIVATIVE OF (3-60) AND SUBSTITUTING AT x = 0, YIELDS • THE SAME RESULT COMES FROM A CALCULATION OF THE TOTAL CONVECTED HEAT

  8. SOLUTIONS FOR FINS • FINITE LENGTH WITH INSULATED TIP OR INSIGNIFICANT SO THE TEMPERATURE GRADIENT AT x = L WILL BE • VALUES CALCULATED FOR C1 AND C2 USING THIS BOUNDARY CONDITION ARE

  9. SOLUTIONS FOR FINS • THIS LEADS TO A TEMPERATURE PROFILE OF THE FORM: • THE TOTAL HEAT FROM THIS SYSTEM CAN BE EVALUATED USING THE TEMPERATURE GRADIENT AT THE BASE TO YIELD

  10. SOLUTIONS FOR FINS • ALLOWING FOR CONVECTION AT THE TIP • THE CORRECTED LENGTH (3-66) APPROACH CAN BE USED WITH EQUATIONS (3-64 AND 3-65) • ALTERNATELY, ALLOWING FOR A DIFFERENT FORM FOR THE CONVECTION COEFFICIENT AT THE TIP, hL, THEN THE HEAT BALANCE AT THE TIP IS

  11. SOLUTIONS FOR FINS • THE RESULTING TEMPERATURE PROFILE IS • AND THE TOTAL HEAT TRANSFER BECOMES

  12. FIN EFFICIENCY • THE RATIO OF ACTUAL HEAT TRANSFER TO IDEAL HEAT TRANSFER WITH A FIN • IDEAL TRANSFER ASSUMES THE ROOT TEMPERATURE EXTENDS OUT THE LENGTH OF THE FIN • REAL TRANSFER IS BASED ON THE ACTUAL TEMPERATURE PROFILE • FOR THE LONG FIN

  13. FIN EFFICIENCY • SIMILARLY, FOR A FIN WITH AN INSULATED TIP: • FIN EFFECTIVENESS INDICATES HOW MUCH THE TOTAL HEAT TRANSFER INCREASES RELATIVE TO THE NON-FINNED SURFACE • IT IS A FUNCTION OF • RELATIVE HEAT TRANSFER AREA • TEMPERATURE DISTRIBUTION • CAN BE RELATED TO EFFICIENCY

  14. HEAT SINKSH • EXTENDED AREA DEVICES • TYPICAL DESIGNS ARE SHOWN IN TABLE 3-6 • TYPICAL LEVELS OF LOADING http://www.techarp.com/showarticle.aspx?artno=337&pgno=2

  15. OTHER COMMON SYSTEM MODELS • USE OF CONDUCTION SHAPE FACTORS TO CALCULATE HEAT TRANSFER • FOR TRANSFER BETWEEN SURFACES MAINTAINED AT CONSTANT TEMPERATURE, THROUGH A CONDUCTING MEDIA • FOR TWO DIMENSIONAL TRANSFER • THE SHAPE FACTOR, S, RESULTS IN AN EQUATION OF THE FORM Q`= SkdT

  16. SHAPE FACTORS • THE METHOD OF SHAPE FACTORS COMES FROM A GRAPHICAL METHOD WHICH ATTEMPTS TO DETERMINE THE ISOTHERMS AND ADIABATIC LINES FOR A HEAT TRANSFER SYSTEM • AN EXAMPLE IS FOR HEAT TRANSFER FROM AN INSIDE TO AN OUTSIDE CORNER, WHICH REPRESENTS A SYMMETRIC QUARTER SECTION OF A SYSTEM WITH THE CROSS-SECTION AS SHOWN IN THIS SKETCH

  17. TEMPERATURE PROFILES • THIS SKETCH SHOWS THE CORNER WITH ISOTHERMAL WALLS AT TEMPERATURES T1 AND T2 • TAKEN FROM Kreith, F., Principles of Heat Transfer, 3rd Edition, Harper & Row, 1973

  18. TEMPERATURE PROFILES • THIS SKETCH SHOWS THE CORNER WITH ISOTHERMAL WALLS AT TEMPERATURES T1 AND T2 • THE CONSTRUCTION IS CAN BE MANUAL OR AUTOMATED • n LINES ARE CONSTRUCTED MORE OR LESS PARALLEL TO THE SURFACES THAT REPRESENT ISOTHERMS • A SECOND SET OF m LINES ARE CONSTRUCTED NORMALTO THE ISOTHERMS AS ADIABATS (LINES OF NO HEAT TRANSFER) AND THE NUMBER IS ARBITRARY

  19. TEMPERATURE PROFILES • THE TOTAL HEAT FLUX FROM SURFACE 1 TO SURFACE 2, THROUGH m ADIABATIC CHANNELS AND OVER n TEMPERATURE INTERVALS IS: • THE SHAPE FACTOR IS DEFINED AS S = m/n, SO THE FLUX EQUATION BECOMES: . • GENERATION OF THE MESH IS THE CRITICAL COMPONENT IN THIS TYPE OF CALCULATION • .TABLE 3-5 SUMMARIZES THE VALUES FOR EQUATIONS FOR VARIOUS SHAPE FACTORS

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