CHE/ME 109
Heat Transfer in Electronics
LECTURE 19 – NATURAL
CONVECTION
FUNDAMENTALS
NATURAL CONVECTION
MECHANISMS
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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
http://blogs.sun.com/staso/resource/cumulonimbus-cloud-akbhhf-sw.jpg
THE
PATH OF THE CONVECTION CURRENTS.
CLOUD FORMATION H
 THIS
MECHANISM IS BASED ON
NATURAL CONVECTION
CLOUD FORMATIONS
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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
SURFACE WINDS
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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
SEA AND LAND FLOWS
 THESE
ARE BASED ON DENSITY
DIFFERENCES THAT RESULT IN
PRESSURE VARIATIONS
http://www.free-online-private-pilot-ground-school.com/images/sea-landbreeze.gif
DENSITY DIFFERENCES
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DEFINED IN TERMS OF VOLUME
EXPANSION COEFFICIENT
 DERIVATION OF CHANGES IN DENSITY FOR
FLUIDS:
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VOLUME EXPANSIVITY:
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ISOTHERMAL COMPRESSIBILITY:
DENSITY DIFFERENCES
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FOR IDEAL GASES:
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SO AROUND AMBIENT TEMPERATURE
β = 3.3x10-3 K-1 = 1.8x10-3 R-1
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FOR LIQUIDS THE VALUES ARE ON THE
ORDER OF β = 3x10-4 K
GRASHOF NUMBER
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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):
GRASHOF NUMBER
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GRASHOF NUMBER IS THE RATIO OF THE
BOUYANCY FORCES TO THE VISCOUS
FORCES
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VALUE OF THE GRASHOF NUMBER CAN BE
LINKED TO FLOW REGIMES FOR NATURAL
CONVECTION
NATURAL CONVECTION OVER
SURFACES
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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
NATURAL CONVECTION OVER
SPECIFIC SHAPES
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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 > 109.
EQUATIONS ARE DEVELOPED
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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∞
NATURAL CONVECTION OVER
SPECIFIC SHAPES
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VERTICAL CYLINDERS CAN BE ANALYZED
WITH THE VERTICAL PLATE EQUATIONS
AS LONG AS THE DIAMETER IS LARGE
ENOUGH
INCLINED PLATES AND FLAT
PLATES
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HAVE DIFFERENT FLOW PATTERNS FOR
PLATE TEMPERATURES
 GREATER THAN THE SURROUNDINGS
 LOWER THAN THE SURROUNDINGS
INCLINED PLATES AND FLAT
PLATES
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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 θ):
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FOR THE TOP OF COOLED PLATES OR THE
BOTTOM OF HEATED PLATES
FOR θ < 60
FOR OTHER SITUATIONS, THE BOUNDARY
LAYER BREAKS UP AND A SINGLE
CORRELATION IS NOT PRACTICAL
HORIZONTAL PLATES
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USE DIFFERENT
CORRELATIONS BASED ON Lc
= As/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)
HORIZONTAL CYLINDERS
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THE BOUNDARY LAYER FORMS
AROUND THE RADIUS AS SHOWN
IN FIGURE 9-12
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SINGLE CORRELATION IS
PROVIDED (9-25) APPLIES TO
LAMINAR CONDITIONS Ra < 1012
FOR TURBULENT FLOW Ra > 109:
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OTHER CORRELATIONS
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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