Computation of FREE CONVECTION

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Computation of FREE CONVECTION

• P M V Subbarao
• Associate Professor
• Mechanical Engineering Department
• IIT Delhi

Quantification of Free .
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Governing Equations

• Now, we can see buoyancy effects replace pressure
  gradient in the momentum equation.

• The buoyancy effects are confined to the momentum
  equation, so the mass and energy equations are
  the same.

Strongly coupled and must be solved simultaneously
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Dimensionless Similarity Parameter

• The x-momentum and energy equations are

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Dimensionless Similarity Parameter

• Define new dimensionless parameter,

• Grashof number in natural convection is analogous
  to the Reynolds number in forced convection.
• Grashof number indicates the ratio of the
  buoyancy force to the viscous force.
• Higher Gr number means increased natural
  convection flow

natural
forced
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Laminar Free Convection on Vertical Surface

• As y ? ? u 0, T T?
• As y ? 0 u 0, T Ts
• With little or no external driving flow, Re ? 0
  and forced convection effects can be safely
  neglects

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• Analytical similarity solution for the local
  Nusselt number in laminar free convection

Where
Average Nusselt
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Effects of Turbulence

• Just like in forced convection flow, hydrodynamic
  instabilities may result in the flow.
• For example, illustrated for a heated vertical
  surface
• Define the Rayleigh number for relativemagnitude
  of buoyancy and viscous forces

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Effects of Turbulence

• Transition to turbulent flow greatly effects heat
  transfer rate.

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Empirical Correlations
Typical correlations for heat transfer
coefficient developed from experimental data are
expressed as
For Turbulent
For Laminar
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Vertical Plate at constant Ts
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• Alternative applicable to entire Rayleigh number
  range (for constant Ts)

• Vertical Cylinders
• Use same correlations for vertical flat plate if

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Free Convection from Inclined Plate
Cold plate or Hot fluid
Hot plate or Cold fluid
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Horizontal Plate
Cold Plate (Ts lt T?)
Hot Plate (Ts gt T?)
Active Upper Surface
Active Lower Surface
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Empirical Correlations Horizontal Plate

• Define the characteristic length, L as

• Upper surface of heated plate, or Lower surface
  of cooled plate

• Lower surface of heated plate, or Upper surface
  of cooled plate

Note Use fluid properties at the film temperature
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Empirical Correlations Long Horizontal Cylinder

• Very common geometry (pipes, wires)
• For isothermal cylinder surface, use general form
  equation for computing Nusselt

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Constants for general Nusselt number Equation
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free convection turbulent heat transfer in an
enclosure

• Turbulent flow in an enclosed cavity or box is a
  model for many flows of practical interest
• Heating of a room.
• Flow in a double glazing Window.
• Spreading of fire and fire generated gases in an
  building.

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Velocity Vectors on A Central Vertical Plane
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Isotherms on A Central Vertical Plane
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Nusselt Number Correlations
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Natural Convection in A Pool of Saturated Liquid
Tsat
Onset of Convection
Tsurface
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Further Behavior of Saturated Liquid
Natural Convection
Increasing DT
Onset of Boiling
Isolated Bubble Regime
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High Overshoots !!!
A
B
A Onset of Natural convection
B Onset of Nucleate Boiling
Heat Flux
Overshoot
Wall Superheat (DTTs Tsat)
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BOILING HEAT TRANSFER

• P M V Subbarao
• Associate Professor
• Mechanical Engineering Department
• IIT Delhi

A Basic means of Power Generation A science
which made Einstein Very Happy!!!
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Boiling

• In a steam power plant convective heat transfer
  is used to remove heat from a heat transfer
  surface.
• The  liquid  used  for  cooling  is  usually  in
   a  compressed  state,  (that   is,  a  subcooled
   fluid)  at pressures higher than the normal
  saturation pressure for  the given temperature.
• Under certain conditions some type of boiling can
  take place.
• It is  an important  process  in nuclear  field
   when  discussing convection heat transfer.
• More  than  one  type  of  boiling  can  take
   place  within  a  
• nuclear facility.

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Nuclear Power Plant
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Steam Boiler
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Classification of Boiling

• Microscopic classification or Boiling Science
  basis
• Nucleated Boiling
• Bulk Boiling
• Film Boiling
• Macroscopic Classification or Boiling Technology
  basis
• Flow Boiling
• Pool Boiling

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Nucleate Boiling

• The most common type of local boiling encountered
  in nuclear facilities is nucleate boiling.
• In nucleate boiling, steam bubbles form at the
  heat transfer surface and then break away and are
  carried into the main stream of the fluid.  
• Such movement enhances heat transfer because the
  heat generated at the surface is carried directly
  into the fluid stream.   
• In the main fluid stream, the bubbles collapse
  because the bulk temperature of the fluid is not
  as high as the heat transfer surface  temperature
   where  the  bubbles  were  created.   
• This  heat  transfer  process  is  sometimes
  desirable  because  the  energy  created  at  the
   heat  transfer  surface  is  quickly  and
   efficiently "carried" away.

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Bulk Boiling

• As  system  temperature  increases  or  system
   pressure drops,  the  bulk  fluid  can  reach
   saturation conditions.  
• At this point, the bubbles entering the coolant
  channel will not collapse.  
• The bubbles will tend to join together and form
  bigger steam bubbles.  
• This phenomenon is referred to as bulk boiling.
• Bulk  boiling  can  provide  adequate  heat
   transfer  provided  that  the  steam  bubbles
   are carried  away  from  the  heat  transfer
   surface  and  the  
• surface  is  continually  wetted  with
   liquid water.   
• When this cannot occur film boiling results.

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Film Boiling

• When the pressure of a system drops or the flow
  decreases, the bubbles cannot escape as quickly
  from  the  heat  transfer  surface.    
• Likewise,  if  the  temperature  of  the  heat
   transfer  surface  is increased, more bubbles
  are created.  
• As the temperature continues to increase, more
  bubbles are formed  than  can  be  efficiently
   carried  away.   
• The  bubbles  grow  and  group  together,
   covering small  areas  of  the  heat  transfer
   surface  with  a  film  of  steam.    
• This  is  known  as  partial  film boiling.    
• Since  steam  has  a  lower  convective  heat
   transfer  coefficient  than  water,  the  steam
  patches on the heat transfer surface act to
  insulate the surface making heat transfer more
  difficult.
• As  the  area  of  the  heat  transfer  surface
   covered  with  steam  increases,  the
   temperature  of  the surface  increases
   dramatically,  while  the  heat  flux  from  the
   surface  decreases.   

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• This  unstable situation continues until the
  affected surface is covered by a stable blanket
  of steam, preventing contact between the heat
  transfer surface and the liquid in the center of
  the flow channel.   
• The condition after the stable steam blanket has
  formed is referred to as film boiling.
• The process of going from nucleate boiling to
  film boiling is graphically represented in
  Figure.   
• The figure illustrates the effect of boiling on
  the relationship between the heat flux and the
  temperature difference between the heat transfer
  surface and the fluid passing it.

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Boiling Curve