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

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, r 1 AND TEMPERATURE T 1, TO AND OUTER RADIUS r 2 AND TEMPERATURE T 2 :

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