1. CHE/ME 109 Heat Transfer in Electronics
LECTURE 16 – EXTERNAL CONVECTION IN SPECIFIC SYSTEMS

2. FLOW ACROSS CYLINDERS AND SPHERES
FLUID FLOW ACROSS A CYLINDER PASSES THROUGH SEVERAL DIFFERENT FLOW REGIMES

3. 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

4. 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

5. 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

6. CFD SIMULATIONS OF VELOCITY PROFILES
LAMINAR FLOW
TURBULENT FLOW

7. 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

8. 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

9. 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

10. 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%

11. 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

12. 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

13. 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:

14. 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

15. CROSS-TUBE PRESSURE DROP CORRELATIONS
CONSIDER TUBE CONFIGURATION AS WELL AS Re NUMBER
THESE GRAPHS ALSO USE THE MAXIMUM VELOCITY TO CALCULATE THE Re

16. 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