Heat Transfer From Extended Surfaces: Conduction-convection Systems (fins)

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Mech 346: Heat Transfer Chapter 3:Heat Transfer from Extended Surfaces: Conduction-Convection Systems J.G. Pharoah 214 – McLaughlin Hall 533-6579

Department of Mechanical Engineering Queen's University Kingston, Ontario, Canada, K7L 3N6

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H

TE EA

D

SU

AC RF

C onduc

E

Convection to fluid

tion

contact resistance Radiation

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2

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dx

H

L

W

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3

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Additional Resource Text • http://web.mit.edu/lienhard/www/ahtt.html

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Variable h • Small differences in temperature distribution result in large changes in Q •The fin becomes less effective as the length increases •Base gradient is best to visualize fin performance.

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Same Geometry, Different k • Flux in now proportional to k dT/dx Æ base gradient misleading in isolation •As the conductivity decreases, less and less of the fin is working •Look at effectiveness and efficiency •Careful of Bi

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What you Dare to Dream ... •In this case, at least, effectiveness is misleading •K=1 has an effectiveness of over 6 and yet it is very wasteful. Based on the previous figure a proper design of this fin would be about 15% of this length.

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•Conductivities below 1 (for this geometry convection coefficient) are extremely suspect with a 1D analysis

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