CHE/ME 109 Heat Transfer in

Electronics

LECTURE 3 – HEAT TRANSFER MECHANISMS

HEAT TRANSFER MECHANISMS

• HEAT TRANSFER IS ASSUMED TO OCCUR BY THREE PRIMARY MECHANISMS, CONDUCTION, CONVECTION AND RADIATION.

• COMMON DRIVING FORCE IS TEMPERATURE DIFFERENCE.

CONDUCTION

• OCCURS BY DIRECT CONTACT BETWEEN ADJACENT MOLECULES WHICH ARE AT DIFFERENT TEMPERATURES

• APPLIES TO SOLIDS OR STATIC FLUIDS• HEAT FLOW FROM THE HIGHER TEMPERATURE

MOLECULE TO THE LOWER TEMPERATURE.• THE PROCESS TAKES PLACE IN THREE

DIMENSIONS• THE DISTRIBUTION OF HEAT IN THE SYSTEM IS

REFERRED TO AS THERMAL DIFFUSIVITY

CONDUCTION

• USING THE TEMPERATURE BASED DRIVING FORCE, THE GOVERNING EQUATION IS FOURIER’S LAW OF HEAT CONDUCTION (1-22)

– THIS S THE FORM FOR ONE DIMENSIONAL HEAT TRANSFER (IN THE x - DIRECTION)

– THE RATE OF CHANGE OF TEMPERATURE WITH RESPECT TO DISTANCE IS THE TEMPERATURE GRADIENT

• THE NEGATIVE SIGN IS A CONVENTION USED BECAUSE HEAT IS TRANSFERRED IN THE DIRECTION OF DECREASING TEMPERATURE AND DISTANCE IS NORMALLY REFERRED TO AS A POSITIVE VARIABLE.

dx

dTkAQ

THERMAL CONDUCTIVITY

• IS A MEASURE OF THE HEAT TRANSFER THROUGH A UNIT AREA UNDER A SPECIFIC TEMPERATURE GRADIENT

• THIS VALUE IS DETERMINED BY ACTUAL MEASUREMENTS (SEE FIGURE 1-29 FOR A TYPICAL CONFIGURATION FOR MEASUREMENT IN SOLIDS)

• IT IS LOWEST FOR GASES AND HIGHEST FOR SOLIDS (SEE FIGURE 1-26 AND ALSO SEE THE PROPERTY VALUES IN THE APPENDICES

• IT IS SOMEWHAT TEMPERATURETEMPERATURE DEPENDENT IN LIQUIDS AND GASES (SEE FIGURE 1-28)

• AS A RULE OF THUMB, GOOD THERMAL CONDUCTORS ARE ALSO GOOD ELECTRICAL CONDUCTORS

dxdTA

Qk

1

THERMAL CONDUCTIVITY

THERMAL DIFFUSIVITY

• α ISTHE RATIO OF HEAT CONDUCTION TO HEAT STORAGE

• HAS UNITS OF AREA/TIME AND CAN BE USED TO COMPARE THERMAL PROPERTIES OF MATERIALS (TABLE 1-4)

PC

k

CONVECTION

• WHEN A MATERIAL IS CAPABLE OF MOTION, THEN THE MECHANISM OF HEAT TRANSFER INCLUDES CHANGING LOCATION OF MOLECULES WITH TIME

• A MOLECULE MAY HAVE A SLIGHTLY HIGHER TEMPERATURE THAN THOSE MOLECULES IMMEDIATELY ADJACENT TO IT, BUT IN A FLUID PHASE, IT CAN MOVE TO A REGION WHERE THE TEMPERATURES ARE MUCH LOWER

• THIS CHANGE IN POSITION RESULTS IN A HIGHER TEMPERATURE DIFFERENCE AND A HIGHER RATE OF HEAT FLUX

CONVECTION• BASED HEAT TRANSFER TO FIXED

SURFACES• THE GOVERNING EQUATION (1-24) IS

NEWTON’S LAW OF COOLING:

• THE HEAT TRANSFER IS CONSIDERED AS A FLUX NORMAL TO THE SURFACE: Q/A

• THE CONVECTION HEAT TRANSFER COEFFICIENT IS BASED ON THE FLUX THAT RESULTS WITH A SPECIFIED TEMPERATURE DIFFERENCE BETWEEN THE BULK OF THE FLUID AND THE SURFACE) WHERE ΔT IS |TBULK – TSURFACE|

ThAQ

T

AQ

h

CONVECTION COEFFICIENT H

• VARIABLES THAT CAN INFLUENCE THE VALUE OF h INCLUDE:– THE TYPE OF FLUID FLOW - LAMINAR, TURBULENT,

OR TRANSITION– THE TRANSPORT PROPERTIES OF THE FLUID, k, ρ,

TEMPERATURE AND POSSIBLY PRESSURE

• FORCED CONVECTION AND NATURAL CONVECTION

• TYPICAL EXAMPLE: http://www.youtube.com/watch?v=uGU5Zff1DXQ

http://www.energyquest.ca.gov/story/images/chap01_convection.gif

RADIATION HEAT TRANSFER • BASED ON ELECTROMAGNETIC WAVES TRANSMITTED FROM

BODIES WITH TEMPERATURES GREATER THAN ABSOLUTE ZERO

• WHEN TWO BODIES OF DIFFERENT TEMPERATURES ARE ALIGNED SO THERE IS A LINE OF SIGHT BETWEEN THEIR SURFACES, RADIATION HEAT TRANSFER WILL OCCUR

• BOTH BODIES RADIATE ENERGY• THE NET RADIATION IS THE DIFFERENCE IN RADIATION

BETWEEN THE TWO BODIES

http://mabryonline.org/blogs/woolsey/images/radiation_balance_usgs_large-2.jpg

RADIATION HEAT TRANSFER • THE GOVERNING EQUATION IS THE STEFAN-

BOLTZMAN EQUATION (1-25)

• σ IS THE STEFAN-BOLTZMAN CONSTANT THAT REPRESENTS ENERGY TRANSMITTED FROM A PERFECT RADIATOR (BLACKBODY)

• ε IS THE EMISSIVITY AND THIS IS A CORRECTION FACTOR BETWEEN THE REAL (0 < ε < 1) AND IDEAL VALUE– THE EMISSIVITY IS A FUNCTION OF THE MATERIALS

OF CONSTRUCTION OF THE SURFACE AND TEMPERATURE (TABLE 1-6)

– IT RANGES FROM VERY LOW FOR HIGHLY POLISHED CONDUCTORS TO VERY HIGH FOR MOST NATURALLY OCCURRING MATERIALS (SEE TABLE 1.6)

• ABSOLUTE TEMPERATURE IS ALWAYS USED FOR RADIATION CALCULATIONS

4ATQ

RADIATION HEAT TRANSFER• NET RADIANT HEAT TRANSFER BETWEEN TWO

SURFACES• IS BASED ON THE RELATIVE TEMPERATURES,

THE EMISSIVITY, AND THE VIEW FACTOR (PORTION OF THE SURFACE THAT IS ON A LINE OF SIGHT BETWEEN THE SURFACES)

• WHEN THE SURFACE IS COMPLETELY SURROUNDED BY ANOTHER SURFACE THEN THE VIEW FACTOR IS 1 AND THE NET TRANSFER EQUATION IS (1-28):

)( 42

41 TTAQ

PARALLEL MECHANISMS

• MOST REAL HEAT TRANSFER PROCESSES INCLUDE COMBINATIONS OF MECHANISMS

• WHEN ONE MECHANISM IS DOMINANT, THEN THE OTHERS CAN BE EXCLUDED TO SIMPLIFY THE MODELS