Series solution to coupled nonlinear heat and moisture transfer in slabs with temperature-dependent diffusivities
The two-dimensional differential transform method (DTM) is applied to solve the one-dimensional coupled heat and moisture diffusion problem for a slab with temperature-dependent thermal and moisture diffusivities, which are expressed by a linear function and an exponential function of temp...
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De Gruyter
2014-12-01
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| Series: | Nonlinear Engineering |
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| Online Access: | https://doi.org/10.1515/nleng-2014-0020 |
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doaj-e2818f5b57754a0895a668714172e0762021-09-06T19:21:06ZengDe GruyterNonlinear Engineering2192-80102192-80292014-12-013421522510.1515/nleng-2014-0020Series solution to coupled nonlinear heat and moisture transfer in slabs with temperature-dependent diffusivitiesChiba Ryoichi0Department of mechanical systems engineering, Asahikawa National College of Technology, 2-2-1-6 Shunkodai, Asahikawa 071-8142, Japan The two-dimensional differential transform method (DTM) is applied to solve the one-dimensional coupled heat and moisture diffusion problem for a slab with temperature-dependent thermal and moisture diffusivities, which are expressed by a linear function and an exponential function of temperature, respectively. One surface of the slab is subjected to convective hygrothermal loading and the other has constant prescribed temperature and moisture. Approximate analytical (series) solutions for the temperature and moisture profiles in the slab are derived. The transformed functions included in the solutions are obtained through a simple recursive procedure. Numerical results for a slab subjected to a sudden change in surface temperature illustrate the effects of temperature-dependent diffusivities on the transient temperature and moisture profiles of the slab. The results indicate that the nonlinear effect originating from the varying moisture diffusivity is not negligible for resin composites. The DTMis a useful new analytical method for solving nonlinear coupled transient problems.https://doi.org/10.1515/nleng-2014-0020differential transform methodseries solution coupled heat and mass transfer temperature-dependent property |
| collection |
DOAJ |
| language |
English |
| format |
Article |
| sources |
DOAJ |
| author |
Chiba Ryoichi |
| spellingShingle |
Chiba Ryoichi Series solution to coupled nonlinear heat and moisture transfer in slabs with temperature-dependent diffusivities Nonlinear Engineering differential transform method series solution coupled heat and mass transfer temperature-dependent property |
| author_facet |
Chiba Ryoichi |
| author_sort |
Chiba Ryoichi |
| title |
Series solution to coupled nonlinear heat and
moisture transfer in slabs with
temperature-dependent diffusivities |
| title_short |
Series solution to coupled nonlinear heat and
moisture transfer in slabs with
temperature-dependent diffusivities |
| title_full |
Series solution to coupled nonlinear heat and
moisture transfer in slabs with
temperature-dependent diffusivities |
| title_fullStr |
Series solution to coupled nonlinear heat and
moisture transfer in slabs with
temperature-dependent diffusivities |
| title_full_unstemmed |
Series solution to coupled nonlinear heat and
moisture transfer in slabs with
temperature-dependent diffusivities |
| title_sort |
series solution to coupled nonlinear heat and
moisture transfer in slabs with
temperature-dependent diffusivities |
| publisher |
De Gruyter |
| series |
Nonlinear Engineering |
| issn |
2192-8010 2192-8029 |
| publishDate |
2014-12-01 |
| description |
The two-dimensional differential transform
method (DTM) is applied to solve the one-dimensional
coupled heat and moisture diffusion problem for a slab
with temperature-dependent thermal and moisture diffusivities,
which are expressed by a linear function and
an exponential function of temperature, respectively. One
surface of the slab is subjected to convective hygrothermal
loading and the other has constant prescribed temperature
and moisture. Approximate analytical (series) solutions
for the temperature and moisture profiles in the
slab are derived. The transformed functions included in
the solutions are obtained through a simple recursive procedure.
Numerical results for a slab subjected to a sudden
change in surface temperature illustrate the effects of
temperature-dependent diffusivities on the transient temperature
and moisture profiles of the slab. The results indicate
that the nonlinear effect originating from the varying
moisture diffusivity is not negligible for resin composites.
The DTMis a useful new analytical method for solving
nonlinear coupled transient problems. |
| topic |
differential transform method series solution coupled heat and mass transfer temperature-dependent property |
| url |
https://doi.org/10.1515/nleng-2014-0020 |
| work_keys_str_mv |
AT chibaryoichi seriessolutiontocouplednonlinearheatandmoisturetransferinslabswithtemperaturedependentdiffusivities |
| _version_ |
1717775222900260864 |