CHE/ME 109 Heat Transfer in

Electronics

LECTURE 16 – EXTERNAL CONVECTION IN SPECIFIC SYSTEMS

FLOW ACROSS CYLINDERS AND SPHERES FLUID FLOW ACROSS A CYLINDER

PASSES THROUGH SEVERAL DIFFERENT FLOW REGIMES

VELOCITY PATTERNS THE VELOCITY AT THE CENTERLINE IS

ZERO AT THE FORWARD STAGNATION POINT

A BOUNDARY LAYER FORMS AS THE FLUID ACCELERATES AROUND THE CYLINDER WITH DECREASING PRESSURE

THERE IS A POINT WHERE

AND THE VELOCITY REACHES A MAXIMUM

Incropera & DeWitt, Fundamentals of Heat and Mass Transfer, 4th Edition, Wiley, 1996

VELOCITY PATTERNS

BEYOND THIS POINT, THERE IS A REVERSAL OF THE PRESSURE AND THE MATERIAL SEPARATES FROM THE BOUNDARY LAYER

VORTICES ARE FORMED AND THE WAKE DEVELOPS SEPARATION POINTS

FOR LAMINAR FLOW (Re < 2x10^5) THE SEPARATION OCCURS AT ~ 80◦ FROM THE STAGNATION POINT

AS Re INCREASES TO HIGHER LEVELS, THE SEPARATION POINT MOVES AROUND TO A MAXIMUM OF ~ 140∘

THE SIZE OF THE WAKE IS INVERSELY PROPORTIONAL TO THE FORM DRAG

SURFACE ROUGHNESS EFFECTS ON DRAG

BREAKING UP THE BOUNDARY LAYER (USING DIMPLES ON GOLF BALLS OR SPOILERS ON HIGH SPEED VEHICLES) WILL REDUCE THE PRESSURE DRAG.

THE DRAG COEFFICIENT CAN BE REDUCED BY INDUCING TURBULENCE AT A LOWER REYNOLD’S NUMBER

CFD SIMULATIONS OF VELOCITY PROFILES

LAMINAR FLOW

TURBULENT FLOW

http://www.math.rug.nl/~veldman/figures/dns-zoom.jpg

FLOW PARALLEL TO THE CYLINDER AXIS

MOMENTUM AND HEAT TRANSFER IS MODELED USING THE FLAT PLATE CORRELATIONS

FOR SPHERES THE SAME EFFECTS ARE PRESENT IN THREE DIMENSIONS

PRESSURE DROP CORRELATIONS ARE SHOWN IN FIGURE 7-17

HEAT TRANSFER COEFFICIENTS

HEAT TRANSFER COEFFICIENTS FOR CYLINDERS AND SPHERES ARE OF THE FORM:

EXAMPLES ARE (7-35) AND (7-36) PROPERTIES ARE EVALUATED AT FILM

TEMPERATURES, EXCEPT FOR THE WALL VISCOSITY

THESE CORRELATIONS INCLUDE A LAMINAR AND A TURBULENT PORTION

FLOW ACROSS A RANGE OF EXTERNAL FORMS

A MORE GENERAL FORM IS Nu = CRemPrn

VALUES FOR FLOW ACROSS A RANGE OF EXTERNAL FORMS ARE SHOWN IN TABLE 7-1

ALL FLUID PROPERTIES ARE BASED ON THE FILM TEMPERATURE

A VARIATION OF THIS EXPRESSION IS:

FOR THIS VERSION ALL PROPERTIES EXCEPT THE PrSurf ARE EVALUATED AT THE MEAN STREAM TEMPERATURE

LIMITATIONS FOR CORRELATIONS

THESE CORRELATIONS ARE ALL BASED ON:

A SPECIFIC FLUID SPECIFIC FLOW REGIMES SPECIFIC SURFACE ROUGHNESS SPECIFIC RANGES OF Pr AND Re EXPECTED ACCURACY IS + 20%

FLOW ACROSS TUBE BANKS

EXTERNAL FLOWS OVER BANKS OF TUBES ARE INFLUENCED BY THE RELATIVE POSITIONS OF THE TUBES

THERE CAN BE SHADOWING - WHERE THE WAKE OF AN UPSTREAM TUBE AFFECTS THE BOUNDARY LAYER FORMATION ON A DOWNSTREAM TUBE

THERE CAN BE ADDITIONAL MOMENTUM INTERACTIONS BETWEEN ADJACENT TUBES

FLOW ACROSS TUBE BANKS

TUBE PATTERNS

TUBES CAN BE INSTALLED WITH ALIGNED OR STAGGERED LAYOUTS (SEE FIGURE 7-25)

LOCATIONS ARE CHARACTERIZED IN TERMS OF PITCH (SEE FIGURE 7-26) OR DISTANCE BETWEEN TUBE CENTERS

TRANSVERSE PITCH, ST, IS THE DISTANCE BETWEEN TUBES NORMAL TO FLOW

LONGITUDINAL PITCH, SL, IS THE DISTANCE DIAGONAL PITCH, SD, IS BASED ON THE

DISTANCE BETWEEN TUBE CENTERS IN ALTERNATE ROWS FOR STAGGERED CONFIGURATIONS

CROSS TUBE HEAT TRANSFER

CORRELATIONS THE CORRELATIONS ARE BASED ON THE MAXIMUM

FLUID VELOCITY IN THE TUBE BUNDLE, WHICH IS USED TO CALCULATE Re FOR THE FLUID

THIS CAN BE RELATED TO THE FREE STREAM VELOCITY AS FOR ALIGNED LAYOUTS AS:

FOR STAGGERED LAYOUTS THE SAME EXPRESSION APPLIES WHEN 2(SD - D)>(ST -

D) FOR 2(SD - D)<(ST - D) THEN THE MAXIMUM IS

CALCULATED:

CROSS-TUBE HEAT TRANSFER

CORRELATIONS THE GENERAL FORM OF THE CORRELATION

IS

FLUID PROPERTIES ARE CALCULATED AT THE MEAN TEMPERATURE WHICH IS THE AVERAGE BETWEEN THE ENTRY AND EXIT OVER THE TUBE BANK

RECOMMENDED EQUATIONS ARE SHOWN IN TABLE 7-2

CROSS-TUBE PRESSURE DROP CORRELATIONS

CONSIDER TUBE CONFIGURATION AS WELL AS Re NUMBER

THESE GRAPHS ALSO USE THE MAXIMUM VELOCITY TO CALCULATE THE Re

HEAT TRANSFER IN ELECTRONICS COOLING

SIGNIFICANCE OF PRINTED CIRCUIT BOARDS ARE EXAMPLES OF FLAT PLATE INSTALLATIONS

IN HIGH HEAT LOAD SERVICES, THE HEAT TRANSFER MAY INCLUDE PASSING COOLING AIR OVER TUBE BUNDLES TO REDUCE TEMPERATURE

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