Heat Transfer for Fins (or Extended Surfaces) Handout ...kshollen/ME350/Handouts/Fin_Summary.pdf ·...

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Heat Transfer for Fins (or Extended Surfaces) Handout Table 3.4 Fin temperature distribution, θ = T T , and heat loss, q f , for uniform cross section Table 3.5 Fin Efficiency, η f , for common fin shapes where θ b = T b T η f = actual heat transfer rate with fin maximum heat transfer rate with fin = q f hA f θ b < 1 Fin effectiveness: ε f = heat transfer rate with fin heat transfer rate without fin = q f hA c, b θ b = η f A f A c,b Resistance Analogy: Single fin, θ b = q f R t , f , or fin array, θ b = q t R t ,o , with thermal resistances: R t , f = 1 η f hA f single fin R t , N = 1 N η f hA f N fins in parallel R t ,b = 1 hA b convection from exposed base R t ,o = 1 R t , N + 1 R t ,b 1 overall for fin array without contact resistance R t ,o = ʹ ʹ R t ,c NA c,b + R t , N 1 + 1 R t ,b 1 overall for fin array with contact resistance Overall Efficiency: η o = q t hA t θ b = 1 R t , o hA t = 1 N A f A t 1 η f C 1 , C 1 = 1 + η f hA f ʹʹ R t , c A c, b A total base area (without fins) A c fin cross-sectional area A c,b fin cross-sectional area at base ( A c = A c,b for constant area) A f fin surface area A b area of the exposed base ( A b = A NA c, b ) A t total fin array surface area ( A t = NA f + A b )

Transcript of Heat Transfer for Fins (or Extended Surfaces) Handout ...kshollen/ME350/Handouts/Fin_Summary.pdf ·...

Page 1: 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

Heat Transfer for Fins (or Extended Surfaces) Handout Table 3.4 Fin temperature distribution,

θ = T −T∞, and heat loss, qf, for uniform cross section Table 3.5 Fin Efficiency,

η f , for common fin shapes where

θb = Tb −T∞

η f =actual heat transfer rate with fin

maximum heat transfer rate with fin=

qfh Af θb

<1

Fin effectiveness:

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,

θb = q f Rt, f , or fin array,

θb = qt Rt,o , with thermal resistances:

Rt, f =1

η f h Af

single fin

Rt,N =1

N η f h Af

N fins in parallel

Rt,b =1

h Ab

convection from exposed base

Rt,o =1

Rt,N

+1

Rt ,b

⎝ ⎜

⎠ ⎟

−1

overall for fin array without contact resistance

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 (

Ab = A − N Ac,b) At total fin array surface area (

At = N Af + Ab)

Page 2: 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