Series solution to coupled nonlinear heat and moisture transfer in slabs with temperature-dependent diffusivities

Abstract

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.

Keywords

• differential transform method
• series solution
• coupled heat and mass transfer
• temperature-dependent property