Extended Surfaces Fins

1
Extended Surfaces / Fins

• Sections 3.6, 11.2

2
Extended Surfaces (Fins)

• An extended surface (also known as a combined
  conduction-convection system or a fin) is a solid
  within which heat transfer by conduction is
  assumed to be one dimensional, while heat is also
  transferred by convection (and/or radiation) from
  the surface in a direction transverse to that of
  conduction

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3
Heat Transfer from Extended Surfaces

• Extended surfaces may exist in many situations
  but are commonly used as fins to enhance heat
  transfer by increasing the surface area available
  for convection (and/or radiation).

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4
Typical Fin Configurations
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5
True or False?

• Heat is transferred from hot water flowing
  through a tube to air flowing over the tube. To
  enhance the heat transfer rate the fins should be
  installed on the tube interior surface (the hot
  water side)
• Fins are particularly beneficial when h is small
  (typical for a gas or when only natural
  convection exists).
• Ideally the fin material should have a large
  thermal conductivity to minimize temperature
  variations from its base to its tip.

6
Fins of Uniform Cross-Sectional Area

• Assuming one-dimensional, steady-state
  conduction in an extended surface of constant
  conductivity and uniform cross-sectional area
  with negligible generation and radiation, the fin
  equation is of the form

(3.6.1)
where p is the fin perimeter
Define
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7
Boundary Conditions
Case A

• At the base T Tb or q(0)qb
• At the tip
• Case A Convection heat transfer
• Case B Adiabatic tip
• Case C Prescribed temperature, q(L)qL
• Case D Infinite fin, T(L)T? or q(L)0

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8
Solutions of Differential Equation
(3.6.2)
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9
Selection of fin material (Example 3.9)
(1)
SS
(2)
Al
kCugtkAlgtkSS
Cu
(3)
10
Example Problem 3.116

• Assessment of cooling scheme for gas turbine
  blade.
• Determine whether the blade temperature is less
  than the maximum allowable value (1050 C) for
  the prescribed operating conditions
• Evaluate blade cooling rate.
• Assume that convective heat losses from the
  surface are negligible, i.e. adiabatic tip
  condition.

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11
Fin Performance

• Fin effectiveness Ratio of the fin heat transfer
  rate qf to the heat transfer rate that would
  exist without the fin

where qbTb-T?, and Ac,b is the fin
cross-sectional area at the base
(3.6.3)

• ef should be as large as possible (at least gt2)

• For a very long (infinite) fin (Case D boundary
  condition)

(3.6.4)
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12
Fin Performance

• Fin heat transfer rate

where Rt,f is the fin resistance

• Can express fin effectiveness as a ratio of
  thermal resistances

where Rt,b is the resistance due to convection
of the exposed base (1/hAc,b)
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13
Fin Performance

• Fin efficiency The ratio of the actual heat
  transfer rate from the fin to the maximum rate at
  which a fin could dissipate energy

See Table 3.5 and Figures 3.18 and 3.19 for the
efficiencies of common fin shapes
(3.6.5)

• We can use the efficiency to calculate the fin
  resistance

(3.6.6)
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14
Fin Arrays

• Define the overall efficiency, ho as

(3.6.7)
where N is the number of fins in the array, Af
the surface area of each fin and At the total
surface area.

• We can then calculate the heat rate for the fin
  array

(3.6.8)

• Thermal resistance of the fin array

(3.6.9)
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15
Fin Manufacturing

• Care must be exercised to ensure that the
  thermal contact resistance does not adversely
  influence the overall fin performance

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16
Example

• As more components are placed on a single
  intergrated circuit (chip), the amount of heat
  dissipated increases. The maximum allowable chip
  operating temperature, is approximately 75C.
  Suggest ways to maximize heat dissipation.

Air, T?20C
Side view
Top view
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17
Fins in Heat Exchangers

• Widely used to achieve large heat rates per unit
  volume, particularly when one or both fluids is a
  gas.
• Characterized by large heat transfer surface
  areas per unit volume (gt700 m2/m3), small flow
  passages, and laminar flow.

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Fin (extended surface) effects

• Fins reduce the resistance to convection heat
  transfer, by increasing surface area.
• The expression for the overall heat transfer
  coefficient includes overall surface efficiency,
  or temperature efficiency, ho, of the finned
  surface, which depends on the type of fin (see
  also Ch. 3.6.5)

(11.5)
where c is for cold and h for hot fluids
respectively