Heat Transfer for Fins (or Extended Surfaces) Handout ...kshollen/ME350/Handouts/Fin_Summary.pdf ·...
Transcript of Heat Transfer for Fins (or Extended Surfaces) Handout ...kshollen/ME350/Handouts/Fin_Summary.pdf ·...
Heat Transfer for Fins (or Extended Surfaces) Handout Table 3.4 Fin temperature distribution,
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θ = T −T∞, and heat loss, qf, for uniform cross section Table 3.5 Fin Efficiency,
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η f , for common fin shapes where
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θb = Tb −T∞
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η f =actual heat transfer rate with fin
maximum heat transfer rate with fin=
qfh Af θb
<1
Fin effectiveness:
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ε f =heat transfer rate with fin
heat transfer rate without fin=
q f
h Ac,b θb
=η f
Af
Ac,b
⎛
⎝ ⎜
⎞
⎠ ⎟
Resistance Analogy: Single fin,
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θb = q f Rt, f , or fin array,
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θb = qt Rt,o , with thermal resistances:
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Rt, f =1
η f h Af
single fin
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Rt,N =1
N η f h Af
N fins in parallel
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Rt,b =1
h Ab
convection from exposed base
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Rt,o =1
Rt,N
+1
Rt ,b
⎛
⎝ ⎜
⎞
⎠ ⎟
−1
overall for fin array without contact resistance
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Rt,o =ʹ ́ R t ,c
N Ac,b
+ Rt,N
⎛
⎝ ⎜
⎞
⎠ ⎟
−1
+1
Rt ,b
⎡
⎣ ⎢ ⎢
⎤
⎦ ⎥ ⎥
−1
overall for fin array with contact resistance
Overall Efficiency: ηo =qt
h At θb=
1Rt,o h At
=1− NAf
At
⎛
⎝⎜
⎞
⎠⎟ 1−
η f
C1
⎛
⎝⎜
⎞
⎠⎟ , C1 =1+η f h Af
ʹ́Rt,cAc,b
⎛
⎝⎜⎜
⎞
⎠⎟⎟
A total base area (without fins) Ac fin cross-sectional area Ac,b fin cross-sectional area at base ( Ac = Ac,b for constant area) Af fin surface area Ab area of the exposed base (
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Ab = A − N Ac,b) At total fin array surface area (
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At = N Af + Ab)