CHE/ME 109 Heat Transfer in

Electronics

LECTURE 17 – INTERNAL FORCED CONVECTION

FUNDAMENTALS

INTERNAL FORCED CONVECTION DESCRIPTIONS

• HEAT TRANSFER IN DUCTS IS A VERY COMMON PROCESS

• USED FOR COOLING FLUIDS FOR RADIATORS AND HEAT SINKS

• USED FOR HEAT REJECTION SYSTEMS IN REFRIGERATORS

• HEAT EXCHANGE PROCESSES MAY TAKE PLACE IN HEAT EXCHANGERS

• NEED A LARGE AMOUNT OF TRANSFER AREA IN A SMALL FLUID VOLUME

• DESIGNED FOR EASE OF FABRICATION

http://www2.electronicproducts.com/Liquid_cooling_targets_advanced_microelectronics-article-farr_cooligy_may2008-html.aspx

CONVECTION HEAT TRANSFER CORRELATIONS

• BASED ON MOMENTUM TRANSFER MODELS

• ERRORS FOR CORRELATIONS + 20%

• MINOR FACTORS SUCH AS VISCOUS HEATING MAY END UP IN THE NOISE FOR THESE CALCULATIONS, SO ARE IGNORED IN MANY SYSTEMS

MEAN VELOCITY AND MEAN TEMPERATURE

• FLOW REGIMES

• LAMINAR FLOW IS DEFINED BY Re < 2300

• THE VELOCITY PROFILE IS TYPICALLY PARABOLIC FOR DEVELOPED LAMINAR FLOW

• SEE DEVELOPMENT IN SECTION 8-2

MEAN VELOCITY

• THE VELOCITY IS ZERO-VALUED AT EACH WALL AND GOES TO A MAXIMUM IN THE CENTER

• THE MEAN VELOCITY IS OBTAINED FROM

• NOTE THE MEAN VELOCITY WILL NOT BE AT THE CENTER OF THE FLOW

MEAN (MIXING CUP) TEMPERATURE

• IS CALCULATED AS THE AVERAGE TEMPERATURE IN A DUCT CROSS SECTION

• THE EQUATION FOR CALCULATION IS:

TURBULENT FLOW • DEFINED BY Re>10000• AVERAGE VELOCITY AND MEAN

TEMPERATURES ARE CALCULATED THE SAME AS FOR LAMINAR SYSTEMS

• THE TURBULENT PROFILE IS TYPICALLY UNIFORM EXCEPT AT THE SURFACES

TURBULENT/TRANSITION FLOW

• THE VALUES FOR AVERAGE VELOCITY AND MEAN TEMPERATURES ARE VERY CLOSE TO THE CENTERLINE VALUES FOR TURBULENT FLOW

• TRANSITION FLOW IS 2300 < Re < 10000

• THERE ARE NO CORRELATIONS FOR THE TRANSITION REGION

NON-CIRCULAR DUCTS

• ADAPTING THESE CORRELATIONS TO NON-CIRCULAR DUCTS

• ACCOMPLISHED USING THE HYDRAULIC DIAMETER IN THE SAME EQUATIONS.

• SAME LIMITS FOR FLOW REGIMES ARE NORMALLY APPLIED TO NON-CIRCULAR DUCTS

ENTRANCE EFFECTS

• THE HYDRODYNAMIC ENTRY LENGTH IS THE SECTION OF THE PIPE FROM THE ENTRY TO FULLY DEVELOPED FLOW AS SHOWN IN THIS FIGURE

ENTRANCE EFFECTS

• THE THERMAL ENTRY LENGTH IS THE SECTION OF THE PIPE FROM THE ENTRY TO FULLY DEVELOPED FLOW AS SHOWN IN THIS FIGURE

ENTRANCE FLOW CHARACTERISTICS

• THE BOUNDARY LAYER IS CONTINUOUSLY CHANGING IN THIS REGION

• THE FRICTION FACTOR CHANGES WITH DISTANCE

• THE HEAT TRANSFER COEFFICIENT CHANGES WITH DISTANCE

• BOUNDARY LAYER IN THE ENTRY LENGTH MAY START AS LAMINAR

• FOR TURBULENT FLOW CONDITIONS, THE BOUNDARY LAYER BECOMES TURBULENT OVER A SHORT DISTANCE

ENTRANCE FLOW CHARACTERISTICS

ENTRY LENGTH LIMITS• FULLY DEVELOPED FLOW IS DEFINED BY

THE FRICTION FACTOR AND HEAT TRANSFER COEFFICIENT STAYING CONSTANT

• ENTRY LENGTH EFFECTS ARE SIGNIFICANT WHEN THE TOTAL LENGTH IS RELATIVELY SHORT (L/DH < 50)

• EXTENT OF ENTRY LENGTHS• FOR LAMINAR FLOW:

• FOR TURBULENT FLOW:

PrRe05.0Re05.0 HThermalHHydro DLDL

HThermHydro DL 10,

LIMITING SYSTEMS

• IDEAL SYSTEM MODELS ARE BASED ON EITHER CONSTANT SURFACE TEMPERATURE OR CONSTANT SURFACE FLUX

• FOR CONSTANT SURFACE HEATING, THE VALUE OF ΔT = Ts - Tm STAYS CONSTANT

• Ts INCREASES AS Tm INCREASES

LIMITING SYSTEMS

• FOR CONSTANT VALUES OF Cp AND As THE RATE OF INCREASE CAN BE EVALUATED AS:

• THIS RELATIONSHIP DOES NOT APPLY IN THE ENTRY LENGTH

LIMITING SYSTEMS

• FOR CONSTANT SURFACE TEMPERATURE• THE VALUE OF ΔT IS ALWAYS CHANGING• EVENTUALLY THE BULK TEMPERATURE

WILL MATCH THE WALL TEMPERATURE• THE DIMENSIONLESS TEMPERATURE CAN

BE EXPRESSED AS AN EXPONENTIAL DECAY FUNCTION:

CONSTANT SURFACE TEMPERATURE

• TOTAL HEAT TRANSFER OVER THE DUCT • USE AN AVERAGE ΔT FOR THE

CALCULATIONS– MATH AVERAGE ΔT:

– LOG-MEAN AVERAGE ΔT