Double Pipe HEAT EXCHANGERS with Low Thermal Resistance

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Double Pipe HEAT EXCHANGERS with Low Thermal
Resistance

• P M V Subbarao
• Professor
• Mechanical Engineering Department
• I I T Delhi

Ideas for Creation of Isotropically Compact HX!!!
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Need for Compact HXs

• Double Pipe Hxs are long, even for moderate
  capacities.
• Unviable to accommodate in an industrial space.
• The size of heat exchanger is very large in those
  applications where gas is a medium of heat
  exchange.
• Continuous research is focused on development of
  Compact Heat Exchangers --- High rates of heat
  transfer per unit volume.
• The rate of heat exchange is proportional to
• The value of Overall heat transfer coefficient.
• The surface area of heat transfer available.
• The mean temperature difference.

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Large surface area Heat Exchangers

• The use of extended surfaces will reduce the gas
  side thermal resistance.
• To reduce size and weight of heat exchangers,
  many compact heat exchangers with various fin
  patterns were developed to reduce the air side
  thermal resistance.
• Fins on the outside the tube may be categorized
  as
• 1) flat or continuous (plain, wavy or
  interrupted) external fins on arrays of tubes,
• 2) Normal fins on individual tubes,
• 3) Longitudinal fins on individual tubes.

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Innovative Designs for Extended Surfaces
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Geometrical Classification
Longitudinal or strip
Radial
Pins
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Anatomy of A STRIP FIN
Flow Direction
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Basic Geometric Features of Longitudinal Extended
Surfaces
profile
PROFILE AREA
cross-section
CROSS-SECTION AREA
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Complex Geometry in Nature
An optimum body size is essential for the ability
to regulate body temperature by blood-borne heat
exchange. For animals in air, this optimum size
is a little over 5 kg. For animals living in
water, the optimum size is much larger, on the
order of 100 kg or so.
This may explain why large reptiles today are
largely aquatic and terrestrial reptiles are
smaller.
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Longitudinal Extended Surfaces with Variable C.S.A

Straight fin of triangular profile rectangular
C.S.
Straight fin of parabolic profile rectangular C.S.
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For a constant cross section area
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Most Practicable Boundary Condition
Corrected adiabatic tip
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Rate of Heat Transfer through a constant Area Fin
Fin Efficiency
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How to decide the height of fin for a Double Pipe
HX ?
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Strip Fin of Least Material

• The heat flux is not constant throughout the fin
  surface area.
• It decreases as some function of distance from
  the fin base.
• Two models are possible
• For a constant heat flux, the cross-section of
  the fin must also decrease as some function of
  distance from the base.
• Schmidt reasoned that the problem reduced to the
  determination of a fin width function, d(x), that
  would yield minimum profile area.

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Longitudinal Fin of Least Material Constant Heat
Flux Model
Consider
With A a function of x. Then
For a constant heat flux (with k a constant by
assumption)
and
which is a linear temperature excess profile. The
practical feasibility of this solution depends on
ease of manufacturing.
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Strip Fin of Least Material OPTIMUM SHAPES

• Least profile area for a given rate of heat
  transfer can be modified as maximum rate of heat
  transfer for a given profile area Ap
• For a Longitudinal fin of Rectangular Cross
  Section with L 1

( L1)
, let
With
Hence
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Optimum Shapes Strip Fin
Find the best shape where
and get
Solving iteratively gives bR1.4192
Find the optimum shape for a given Ap
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LONGITUDINAL FIN OF CONCAVE PARABOLIC PROFILE
The differential equation for temperature excess
is an Euler equation
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The particular solution for temperature excess
is
And the heat dissipation (L1) is
Efficiency
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Longitudinal Fins
Gardners curves for the fin efficiency of
several types of longitudinal fins.
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nth order Longitudinal Fins
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More Ideas to Save Material..
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Performance of Optimum Profiles Strip Fin(L1)
Heat dissipated
Optimum fin width (mb1.4192)
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Performance of Optimum Profiles
Optimum shape for a given qb qb
And solve for Ap with tanh (1.4192) 0.8894
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Selection of Fin Material
Rectangular Profile
Consider three popular materials
Steel Aluminum Copper
7249 2704 8895
43.3 202.5 389.4
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Selection of Fin Material
For a given length, fin mass is proportional to
Ap. Ap is inversely proportional to thermal
conductivity.
For given h, qb, and qb
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Comparison of Longitudinal Fin
profile area varies as the cube of
To double the heat flow, you use two fins or
make one fin eight times as large.
There is a virtue in using short stubby fins.
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LONGITUDINAL FIN OF TRIANGULAR PROFILE
The differential equation for temperature excess