Analytic calculation to find temperature at distance x

L, Length of the fin

0.15 m

w, width of the fin

0.1 m

t, thickness of the fin

0.015 m

h, heat transfer coeff.

5.489 w/m2-k (for Al)

p, perimeter

0.23 m

Ac, cross section Area

0.0015 m2

k, thermal conductivity

236 w/m-k (for Al)

m

1.888

Tbase

200˚C

Tinfinity

20˚C

L(inm)

x(in m)

Numerator

Denominator

Theta(a)/theta(b)

T(x), ˚C

0.15

0

1.0439

1.0439

1.0000

200.0

0.015

1.0358

1.0439

0.9923

198.6

0.03

1.0286

1.0439

0.9823

197.4

0.045

1.0222

1.0439

0.9792

196.3

0.06

1.0166

1.0439

0.9738

195.3

0.075

1.0118

1.0439

0.9692

194.5

0.09

1.0078

1.0439

0.9654

193.8

0.105

1.0047

1.0439

0.9624

193.2

0.12

1.0023

1.0439

0.9601

192.8

0.135

1.0008

1.0439

0.9586

192.6

0.15

1.0000

1.0439

0.9579

192.4