CHE/ME 109 Heat Transfer in
Electronics
LECTURE 7 – EXAMPLES OF CONDUCTION MODELS
ONE DIMENSIONAL CONDUCTION SOLUTIONS
• CONDUCTION SOLUTIONS FOR PLANE WALLS• TOTAL HEAT TRANSFER CAN BE EXPRESSED IN TERMS OF
OVERALL OR LOCAL HEAT TRANSFER• LOCAL APPLIES TO A SYSTEM WITH A SINGLE MECHANISM
• WHERE TEMPERATURES ARE SPECIFIED OVER A FIXED THICKNESS AND THERE IS CONSTANT k IS A TYPICAL LOCAL SYSTEM
• ALTERNATELY THIS CAN BE EXPRESSED IN TERMS OF THERMAL RESISTANCE
• COMPARING WITH THE PREVIOUS EQUATION THEN
ELECTRICAL ANALOGS• SHOWN IN FIGURE 3-3 FOR SINGLE
LAYER
• RESISTANCE TERM IS SPECIFIC FOR EACH MODE OF HEAT TRANSFER (EQNS. 3-5, 3.8 & 3.10)
• FIGURE 3.5 SHOWS MULTIPLE MODES – PARALLEL TRANSPORT
OVERALL NETWORK• SERIES OF CONVECTION AND
CONDUCTION MODES
MULTIPLE LAYERS• FOR A SERIES OF LAYERS WHERE
SYSTEM THE FLUX THROUGH EACH LAYER IS CONSTANT, SEE FIGURE 3-9
MULTIPLE LAYERS
• THE FLUX THROUGH EACH LAYER IS THE SAME SO:
• IN TERMS OF RESISTANCE THIS RELATIONSHIP BECOMES:
MULTIPLE LAYERS
• IN OVERALL TERMS, CONSIDER THE DRIVING FORCE TO BE T∞1 - T∞2 AND THEN EXPRESS THE OVERALL RESISTANCE AS
• SO THE OVERALL HEAT TRANSFER CAN THEN BE EXPRESSED AS
THERMAL CONTACT RESISTANCE
• CONTACT RESISTANCE IS CONSIDERED WHEN ONE LAYER OR COMPONENT IS ATTACHED TO ANOTHER
• THE QUALITY OF THE CONTACT DEPENDS ON HOW COMPLETELY THE SURFACES ARE MATED
• SURFACE ROUGHNESS CAN DECREASE THE CONTACT (REFER TO FIGURE 3-14 IN THE TEXT)
THERMAL CONTACT RESISTANCE
• THE QUALITY OF THE CONTACT TYPICALLY INCREASES WITH THE MOUNTING PRESSURE AND THE SURFACE ROUGHNESS
• SEE TABLE 3-2 FOR TYPICAL VALUES
THERMAL CONTACT RESISTANCE
THERMAL CONTACT RESISTANCE
• ALSO SEE RANGE OF VALUES IN THE FOLLOWING TABLE:
THERMAL CONTACT RESISTANCE
• FOR CRITICAL CONNECTIONS, THE RESISTANCE CAN ALSO BE REDUCED BY THE FOLLOWING METHODS:
• USING A SOFT METAL FOIL SHEET• USING A CONDUCTIVE ADHESIVE
(EPOXY)• USING A THERMAL GREASE (SILICON)• USING A GAS WITH A HIGH
CONDUCTIVITY IN THE REGION
THERMAL RESISTANCE NETWORKS
• THE GENERALIZED FORM FOR THE THERMAL RESISTANCE NETWORK IS BASED ON THE ELECTRICAL ANALOGY
• FOR PARALLEL PATHS, THE DRIVING FORCES ARE THE SAME FOR THE SAME TERMINAL TEMPERATURES, AS PER FIGURE (3-19)
THERMAL RESISTANCE NETWORKS
• TOTAL HEAT TRANSFER
• RESISTANCE THROUGH EACH LAYER
• OVERALL EQUATION
• OVERALL RESISTANCE FOR PARALLEL FLOWS:
FOR PARALLEL/SERIES PATHS
• CONSIDER A FLOW THROUGH A SYSTEM OF UNIT WIDTH, WITH FIXED SURFACE TEMPERATURES AND NO CONTACT RESISTANCE
• OVERALL RESISTANCE NETWORK
FOR PARALLEL/SERIES PATHS
• FOR THIS TYPE OF SYSTEM, THE OVERALL RESISTANCE CAN BE EXPRESSED AS A SERIES OF THREE RESISTANCE TERMS
• THE FIRST AND THIRD TERMS ARE BASED ON SINGLE PLANE TERMS
• THE SECOND TERM IS A PARALLEL RESISTANCE TERM OF THE FORM:
• THE REAL SITUATION WILL PROBABLY INCLUDE HEAT TRANSFER BETWEEN THE MIDDLE LAYERS AND A NON-UNIFORM TEMPERATURE AT THE INTERFACES WITH THE MIDDLE SECTION.
FOR PARALLEL/SERIES PATHS
• OTHER RESISTANCE TERMS THAT CAN BE INCLUDED IN THE NETWORK
• CONVECTION RESISTANCE • RADIATION RESISTANCE • .CONTACT RESISTANCE
CONDUCTION IN SPHERES AND CYLINDERS
• RESISTANCE NETWORKS CAN ALSO BE USED FOR CIRCULAR SYSTEMS
• THE PRIMARY CHANGE IS TO ALLOW FOR VARIATION IN THE SURFACE AREA WITH RADIUS, WHICH RESULTS IN A CHANGE IN THE FLUX
CONDUCTION IN SPHERES AND CYLINDERS
• FOR THE CYLINDRICAL SYSTEM FROM AN INNER RADIUS, r1 AND TEMPERATURE T1, TO AND OUTER
RADIUS r2 AND TEMPERATURE T2:
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CONDUCTION IN SPHERES AND CYLINDERS
• FOR A SERIES OF CYLINDRICAL SHELLS, THE SAME ANALYSIS IS USED
• FOR A SPHERICAL SYSTEM (HOLLOW BALL) THE SAME METHOD IS USED
• FOR MULTIPLE LAYERS, THE RESISTANCE FOR EACH LAYER IS INCLUDED IN THE OVERALL TOTAL RESISTANCE
CRITICAL RADIUS OF INSULATION (Section 3.5)
• A SPECIFIC APPLICATION OF THE RESISTANCE CONCEPT
• THIS IS A CALCULATION TO DETERMINE THE OPTIMUM RADIUS FOR AN INSULATING LAYER ON A CYLINDER, WITH CONVECTION ON THE OUTSIDE OF THE INSULATION (SEE FIGURE 3-30)
• AS THE THICKNESS OF THE INSULATION IS INCREASED, THE RESISTANCE OF THE INSULATION INCREASES (SEE FIGURE 3-31)
CRITICAL RADIUS OF INSULATION
• AS THE THICKNESS OF THE INSULATION IS INCREASED, THE EXTERNAL AREA INCREASES, WHICH REDUCES THE CONVECTION RESISTANCE AND INCREASES HEAT TRANSFER
• THE OPTIMUM OCCURS AT THE CRITICAL RADIUS
• AT THINNER RADII, THERE IS MORE HEAT LOSS
• AT THICKER RADII, THERE IS MORE HEAT LOSS