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# Lecture2 - 1 Conduction A Microscopic view(gases(kinetic...

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1. Conduction A. Microscopic view (gases) – (kinetic theory) T (temperature) < 2 1 mv 2 > Average kinetic energy of molecules Random thermal motion behavior T+ + - q x e.g. (T+ > T-) (heat) q x : transfer of energy/time across ……….surface line A: normal surface area n: # of molecules /volume m: mass of molecule v: characteristic (rms) are velocity of molecules q x = nvA(T + - T - ) T + - T - l x T - l : mean free path between collisions 1

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ty conductivi thermal : k flux heat " x x x q x T nvl A q x T nvAl q = - = - = One-dimensional conduction: x T kA q x - = Fourier’s law of heat conduction Units: [English] ft Btu [SI] sec ] [ 2 2 2 " hr m W m Joul q x - = = - = Units of: [SI] or ] [ C K m Watt dx AdT q K ° ° - = = R F ft hr Btu ° ° - - [English] 2
Notes: Elastic random motion irreversible process No driving force to diffusion Slow process (molecule to molecule transfer of energy) These results are more difficult to obtain for liquids and solids Conduction (& electrical current) is highly dependent upon flow of free electrons Good electrical conductors = good thermal conduction 3

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B.Macroscopic (continuum) [liquid/solids] 1 Btu = British thermal unit = 10 3 x 1.055 J Fourier’s law of heat conduction x T KA q x - = Analogy y u = μ τ A is at uniform temp. (W/m°C) because q ┴ A Defines the thermal conductivity useful only if K = K(T,P) x T k k k (isotropic) Generally true for (gases, liquids & solids) consider e.g. air oil, liquid & metals gas k k ( μ ) ( μ ) 0°C T T K air = .024 w/m°C Check figures in text 1-4, 5, 6 K oil = .147 w/m/°C 4
Pressure effect is much smaller K Al = 202 w/m°C K diamond = 1050 w/°C

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