 # Simultaneous Heat and Moisture Transfer in a Porous Cylinder

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This Demonstration illustrates a model of heat and moisture transfer accompanied by phase change in a porous cylinder. The porous cylinder is initially at a constant temperature and moisture. It is suddenly placed in contact with a stream of hot air that exchanges heat and moisture by diffusion and convection. The moisture movement and the phase change occurring within the cylinder generate a coupled relationship between mass and heat transfer.

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The governing equations  for this model are the Luikov equations: , .

Here and are temperature and moisture potential, respectively, is the space coordinate, is time, and are positive coupling coefficients determined by moisture and heat migration, respectively, and and represent the temperature and moisture diffusion coefficients.

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Contributed by: Clay Gruesbeck (January 2018)
Open content licensed under CC BY-NC-SA

## Snapshots   ## Details

The Luikov equation coefficients are:    .

The moisture potential is related to moisture content by . The cylinder is assumed to have an infinite length to radius ratio, thus only radial transport is considered; material properties are assumed to be constant.

Nomenclature moisture capacity  heat capacity  convective heat transfer coefficient  convective mass transfer coefficient  moisture conductivity  thermal conductivity  moisture  initial cylinder moisture  moisture of the air  cylinder radius  space coordinate  time  temperature  initial cylinder temperature  temperature of the air   moisture potential Symbols equivalent moisture diffusion coefficient  thermo-gradient coefficient  ratio of vapor diffusion coefficient to coefficient of total diffusion of moisture equivalent temperature diffusion coefficient  heat of vaporization  density  coupling coefficient due to moisture migration  coupling coefficient due to heat conduction At the boundary of the cylinder, the latent heat of vaporization becomes part of the energy balance, and the mass diffusion caused by the temperature and moisture gradients affects the overall mass balance; the boundary conditions at are: and .

The right-hand side of the first boundary condition represents the heat flux due to convection plus the energy transfer due to phase change, and the right-hand side of the second condition represents the mass flux due to convection plus the mass flux due to the temperature gradient.

At because of symmetry we have: .

The initial conditions are  .

The system of Luikov equations is solved using the finite element method as implemented in the built-in Mathematica function NDSolve, and the results are presented in space and time plots for various values of the temperature and moisture diffusion coefficients and .

Reference

 H. R. Thomas, R. W. Lewis and K. Morgan, "An Application of the Finite Element Method to the Drying of Timber," Wood and Fiber Science: Journal of the Society of Wood Science and Technology, 11(4), 1980 pp. 237–243. wfs.swst.org/index.php/wfs/article/download/534/534.

## Permanent Citation

Clay Gruesbeck

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