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Unformatted text preview: 21-Sep-2010 1 of 10 CHE 3013 Rate Operations I Heat Transfer by Conduction Fouriers Law dxdTkAqx=(2.1) or dxdTkAqq"x==(2.2) where q= rate of heat transfer, Btu/hr (W) q= heat flux, Btu/hrft2(W/m2) A= cross-sectional area normal to direction of flow, ft2(m2) T= temperature, F (K) x= distance in direction of flow, ft (m) k= thermal conductivity, Btu/hr ft2F/ft or Btu/hr ft F (W/mK) 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 F Solid 0.1 to 10 Liquid 0.01 Gas 0.001 The general form of Fouriers 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=++++++&Dividing by xyzand taking the limit as x, y,andzapproach zero, ( )...
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