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Unformatted text preview: 21-Sep-2010 1 of 10 CHE 3013 Rate Operations I Heat Transfer by Conduction Fourier’s Law dxdTkAqx−=(2.1) or dxdTkAqq"x−==(2.2) where q= rate of heat transfer, Btu/hr (W) q”= heat flux, Btu/hr⋅ft2(W/m2) A= cross-sectional area normal to direction of flow, ft2(m2) T= temperature, ºF (K) x= distance in direction of flow, ft (m) k= thermal conductivity, Btu/hr ft2ºF/ft or Btu/hr ft ºF (W/m⋅K) KmW678.5Ffthr Btu22=oKmW7307.1Fft hr Btu=oThe thermal conductivity is a transport property of the material and is a function of temperature. For mostsolids and liquids, kdecreases with increasing temperature; kincreases with temperature for gases. Material Order of magnitude, Btu/hr ft ºF Solid 0.1 to 10 Liquid 0.01 Gas 0.001 The general form of Fourier’s law for an anisotropicmaterial in Cartesian coordinates is ⎟⎟⎠⎞⎜⎜⎝⎛∂∂+∂∂+∂∂−=zTkyTkxTkzyxq"21-Sep-2010 2 of 10 For an isotropicmaterial, ⎟⎟⎠⎞⎜⎜⎝⎛∂∂+∂∂+∂∂−=zTyTxTkq"Conservation of Energy Input – Output + Generation = Accumulation ( )tTCzyxzyxqAqAqyxAqAqzxAqAqzypzzzzzyyyyyxxxxx∂∂ΔΔΔ=ΔΔΔ+⎟⎟⎠⎞⎜⎜⎝⎛−ΔΔ+⎟⎟⎠⎞⎜⎜⎝⎛−ΔΔ+⎟⎟⎠⎞⎜⎜⎝⎛−ΔΔΔ+Δ+Δ+ρ&Dividing by ΔxΔyΔzand taking the limit as Δx, Δy,andΔzapproach zero, ( )...
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This note was uploaded on 10/11/2011 for the course CHE 3013 taught by Professor Staff during the Fall '11 term at Oklahoma State.
- Fall '11