CHE/ME 109 Heat Transfer in Electronics LECTURE 19 NATURAL
CONVECTION FUNDAMENTALS
Slide 2
NATURAL CONVECTION MECHANISMS NATURAL CONVECTION IS THE RESULT
OF LOCALIZED DENSITY DIFFERENCES THESE CAN BE DUE TO DIFFERENCES IN
COMPOSITIONS FOR HEAT TRANSFER THEY ARE GENERALLY RELATED TO
TEMPERATURE DIFFERENCES CONCENTRATION BASED CONVECTION INCLUDES
CLOUD FORMATIONS WATER HAS A LOWER MOLECULAR WEIGHT THAN AIR
CONCENTRATIONS OF WATER WILL TEND TO RISE THROUGH AIR DUE TO
CONVECTION TO FORM CLOUDS CUMULONIMBUS CLOUD FORMATION AS A RESULT
OF CONVECTION. THE CLOUD TRACES THE PATH OF THE CONVECTION
CURRENTS.
http://blogs.sun.com/staso/resource/cumulonimbus-cloud-akbhhf-sw.jpg
Slide 3
CLOUD FORMATION H THIS MECHANISM IS BASED ON NATURAL
CONVECTION
Slide 4
CLOUD FORMATIONS TEMPERATURE DIFFERENCES WILL ALSO RESULT IN
ADVECTION, A HORIZONTAL TRANSFER OF HOT AIR OVER COLD AIR
NIMBOSTRATUS CLOUDS FORMED DUE TO ADVECTION. CLOUDS SHOW THE
HORIZONTAL CURRENTS
http://cimss.ssec.wisc.edu/satmet/modules/clouds/lowclouds2.html
Slide 5
SURFACE WINDS THE RESULT OF PRESSURE DIFFERENCES. THE FLOW OF
COOL AIR FROM THE OCEAN TO THE COAST IS THE RESULT OF THIS TYPE OF
NATURAL CONVECTION THE MOST EXTREME EXAMPLES OF THESE FLOWS CAN
RESULT IN THE FORMATION OF TORNADOES, CYCLONES AND HURRICANES
http://www.berkeleycitycollege.edu/faculty/rhaberlin/images/pwppthl.gif
Slide 6
SEA AND LAND FLOWS THESE ARE BASED ON DENSITY DIFFERENCES THAT
RESULT IN PRESSURE VARIATIONS
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breeze.gif
Slide 7
DENSITY DIFFERENCES DEFINED IN TERMS OF VOLUME EXPANSION
COEFFICIENT DERIVATION OF CHANGES IN DENSITY FOR FLUIDS: VOLUME
EXPANSIVITY: ISOTHERMAL COMPRESSIBILITY:
Slide 8
DENSITY DIFFERENCES FOR IDEAL GASES: SO AROUND AMBIENT
TEMPERATURE = 3.3x10 SO AROUND AMBIENT TEMPERATURE = 3.3x10-3 K -1
= 1.8x10-3 R -1 FOR LIQUIDS THE VALUES ARE ON THE ORDER OF = 3x10-4
K
Slide 9
GRASHOF NUMBER FLUID MOTION OCCURS DUE TO BOUYANCY EFFECTS AS
PER (FIGURE 9-6) ONCE THE FLUID IS IN MOTION, THEN VISCOUS EFFECTS
OCCUR COMPLETING A MOMENTUM BALANCE FOR A NATURAL CONVECTION FLOW
WITH VELOCITIES IN THE x AND y DIRECTION (u AND v RESPECTIVELY)
CONSIDERED YIELDS (9-13):
Slide 10
GRASHOF NUMBER GRASHOF NUMBER IS THE RATIO OF THE BOUYANCY
FORCES TO THE VISCOUS FORCES VALUE OF THE GRASHOF NUMBER CAN BE
LINKED TO FLOW REGIMES FOR NATURAL CONVECTION
Slide 11
NATURAL CONVECTION OVER SURFACES FOR NATURAL CONVECTION HEAT
TRANSFER PROCESSES THE CORRELATIONS FOR HEAT TRANSFER COEFFICIENTS
ARE BASED ON THE RAYLEIGH NUMBER: Ra = GrPr Ra IS THE NATURAL
CONVECTION EQUIVALENT OF THE PECLET NUMBER, Pe = RePr FOR FORCED
CONVECTION
Slide 12
NATURAL CONVECTION OVER SPECIFIC SHAPES VERTICAL FLAT PLATES
BOUNDARY LAYER STAYS AGAINST THE SURFACE AND THE FLOW REGIME
CHANGES WITH DISTANCE. TRANSITION TO TURBULENCE IS GENERALLY
DEFINED IN TERMS OF THE Ra NUMBER AT Ra > 10 9. EQUATIONS ARE
DEVELOPED FOR CONSTANT TEMPERATURE OR CONSTANT HEAT RATE BASED ON
FILM TEMPERATURE EQUAL TO (Ts - T )/2 APPLY EQUALLY TO HOT OR COLD
WALLS, RELATIVE TO T
Slide 13
NATURAL CONVECTION OVER SPECIFIC SHAPES VERTICAL CYLINDERS CAN
BE ANALYZED WITH THE VERTICAL PLATE EQUATIONS AS LONG AS THE
DIAMETER IS LARGE ENOUGH
Slide 14
INCLINED PLATES AND FLAT PLATES HAVE DIFFERENT FLOW PATTERNS
FOR PLATE TEMPERATURES GREATER THAN THE SURROUNDINGS LOWER THAN THE
SURROUNDINGS
Slide 15
INCLINED PLATES AND FLAT PLATES HAVE DIFFERENT CORRELATIONS FOR
TOPS OF PLATES AND BOTTOMS OF PLATES ) )INCLINED PLATES CAN USE
VERTICAL PLATE CORRELATIONS BY REPLACING g IN THE Gr NUMBER WITH
g(cos ): FOR THE TOP OF COOLED PLATES OR THE BOTTOM OF HEATED
PLATES FOR < 60 FOR OTHER SITUATIONS, THE BOUNDARY LAYER BREAKS
UP AND A SINGLE CORRELATION IS NOT PRACTICAL
Slide 16
HORIZONTAL PLATES USE DIFFERENT CORRELATIONS BASED ON L c = A s
/P FOR THE UPPER SURFACE OF A HEATED PLATE OR THE LOWER SURFACE OF
A COOLED PLATE (9-22 & 9-23) THE LOWER SURFACE OF A HEATED
PLATE OR THE UPPER SURFACE OF A COOLED PLATED (9-32)
Slide 17
HORIZONTAL CYLINDERS THE BOUNDARY LAYER FORMS AROUND THE RADIUS
AS SHOWN IN FIGURE 9-12 SINGLE CORRELATION IS PROVIDED (9-25)
APPLIES TO LAMINAR CONDITIONS Ra < 10 12 FOR TURBULENT FLOW Ra
> 10 9 :
Slide 18
OTHER CORRELATIONS FOR CONSTANT SURFACE TEMPERATURE, VALUES ARE
BASED ON THE GENERAL FORMULATION: SPHERES ARE MODELED USING (9-26)
FROM IRVINE & HARTNETT (Eds), ADVANCES IN HEAT TRANSFER, Vol
11, 1975, Pp. 199-264
