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The thermodynamic significance of the local volume averaged temperature

Hager, Jörgen LU and Whitaker, S (2002) In Transport in Porous Media 46(1). p.19-35
Abstract
Since the temperature is not an additive function, the traditional thermodynamic point of view suggests that the volume integral of the temperature has no precise physical meaning. This observation conflicts with the customary analysis of non-isothermal catalytic reactors, heat pipes, driers, geothermal processes, etc., in which the volume averaged temperature plays a crucial role. In this paper we identify the thermodynamic significance of the volume averaged temperature in terms of a simple two-phase heat transfer process. Given the internal energy as a function of the point temperature and the density e(beta) = F (T-beta, rho(beta)), we show that the volume averaged internal energy is represented by [e(beta)](beta) = F([T-beta](beta),... (More)
Since the temperature is not an additive function, the traditional thermodynamic point of view suggests that the volume integral of the temperature has no precise physical meaning. This observation conflicts with the customary analysis of non-isothermal catalytic reactors, heat pipes, driers, geothermal processes, etc., in which the volume averaged temperature plays a crucial role. In this paper we identify the thermodynamic significance of the volume averaged temperature in terms of a simple two-phase heat transfer process. Given the internal energy as a function of the point temperature and the density e(beta) = F (T-beta, rho(beta)), we show that the volume averaged internal energy is represented by [e(beta)](beta) = F([T-beta](beta), [rho(beta)](beta)), when e(beta) is a linear function of T-beta and rho(beta), or when the traditional length-scale constraints associated with the method of volume averaging are satisfied. When these conditions are not met, higher order terms involving the temperature gradient and the density gradient appear in the representation for [e(beta)](beta). (Less)
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author
organization
publishing date
type
Contribution to journal
publication status
published
subject
keywords
volume averaging, temperature, thermodynamics
in
Transport in Porous Media
volume
46
issue
1
pages
19 - 35
publisher
Kluwer
external identifiers
  • wos:000173349100002
  • scopus:0036176078
ISSN
0169-3913
DOI
10.1023/A:1013801627353
language
English
LU publication?
yes
id
e0a4bc10-f6e4-4995-8243-d27cf8e9a8f2 (old id 344648)
date added to LUP
2007-08-22 15:36:28
date last changed
2017-10-08 04:24:02
@article{e0a4bc10-f6e4-4995-8243-d27cf8e9a8f2,
  abstract     = {Since the temperature is not an additive function, the traditional thermodynamic point of view suggests that the volume integral of the temperature has no precise physical meaning. This observation conflicts with the customary analysis of non-isothermal catalytic reactors, heat pipes, driers, geothermal processes, etc., in which the volume averaged temperature plays a crucial role. In this paper we identify the thermodynamic significance of the volume averaged temperature in terms of a simple two-phase heat transfer process. Given the internal energy as a function of the point temperature and the density e(beta) = F (T-beta, rho(beta)), we show that the volume averaged internal energy is represented by [e(beta)](beta) = F([T-beta](beta), [rho(beta)](beta)), when e(beta) is a linear function of T-beta and rho(beta), or when the traditional length-scale constraints associated with the method of volume averaging are satisfied. When these conditions are not met, higher order terms involving the temperature gradient and the density gradient appear in the representation for [e(beta)](beta).},
  author       = {Hager, Jörgen and Whitaker, S},
  issn         = {0169-3913},
  keyword      = {volume averaging,temperature,thermodynamics},
  language     = {eng},
  number       = {1},
  pages        = {19--35},
  publisher    = {Kluwer},
  series       = {Transport in Porous Media},
  title        = {The thermodynamic significance of the local volume averaged temperature},
  url          = {http://dx.doi.org/10.1023/A:1013801627353},
  volume       = {46},
  year         = {2002},
}