CHE/ME 109 Heat Transfer in Electronics LECTURE 19 – NATURAL CONVECTION FUNDAMENTALS

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.

CLOUD FORMATION H  THIS MECHANISM IS BASED ON NATURAL CONVECTION

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

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

SEA AND LAND FLOWS  THESE ARE BASED ON DENSITY DIFFERENCES THAT RESULT IN PRESSURE VARIATIONS breeze.gif

DENSITY DIFFERENCES   DEFINED IN TERMS OF VOLUME EXPANSION COEFFICIENT   DERIVATION OF CHANGES IN DENSITY FOR FLUIDS:  VOLUME EXPANSIVITY:  ISOTHERMAL COMPRESSIBILITY:

DENSITY DIFFERENCES   FOR IDEAL GASES:  SO AROUND AMBIENT TEMPERATURE β = 3.3x10  SO AROUND AMBIENT TEMPERATURE β = 3.3x10-3 K -1 = 1.8x10-3 R -1   FOR LIQUIDS THE VALUES ARE ON THE ORDER OF β = 3x10-4 K

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):

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

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

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 >   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 ∞

NATURAL CONVECTION OVER SPECIFIC SHAPES   VERTICAL CYLINDERS CAN BE ANALYZED WITH THE VERTICAL PLATE EQUATIONS AS LONG AS THE DIAMETER IS LARGE ENOUGH

INCLINED PLATES AND FLAT PLATES   HAVE DIFFERENT FLOW PATTERNS FOR PLATE TEMPERATURES   GREATER THAN THE SURROUNDINGS   LOWER THAN THE SURROUNDINGS

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 θ): 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   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)

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 <   FOR TURBULENT FLOW Ra > 10 9 :

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