Islamic Azad University Karaj Branch

Chapter 3 Extended Surfaces / Fins

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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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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Typical Fin Configurations

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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.

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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:

where p is the fin perimeter

Define:

(3.6.1)

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Boundary Conditions

•  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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Solutions of Differential Equation

(3.6.2)

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Selection of fin material (Example 3.9)

kCu>kAl>kSS

(1)

(2)

(3)

SS

Al Cu

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Problem 3.116 Assessment of cooling scheme for gas turbine blade. (a)  Determine whether the blade temperature is less than the maximum

allowable value (1050 °C) for the prescribed operating conditions (b)  Evaluate blade cooling rate.

Assume that convective heat losses from the surface are negligible, i.e. adiabatic tip condition.

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Fin Performance

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

!  ef should be as large as possible (at least >2)

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

where qb=Tb-T!, and Ac,b is the fin cross-sectional area at the base

(3.6.3)

(3.6.4)

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•  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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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

!  We can use the efficiency to calculate the fin resistance

(3.6.5)

(3.6.6)

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Fin Performance

•  Define the overall efficiency, ho as

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

•  Thermal resistance of the fin array

(3.6.7)

(3.6.8)

(3.6.9)

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Fin Arrays

Fin Manufacturing

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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 75°C. Suggest ways to maximize heat dissipation.

Top view Side view

Air, T!=20°C

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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 (>700 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

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