VM164

VM164
Drying of a Thick Wooden Slab (Diffusion Analogy)

Overview

Reference:	W. M. Rohsenow, H. Y. Choi, Heat, Mass and Momentum Transfer, 2nd Printing, Prentice-Hall, Inc., Englewood Cliffs, NJ, 1963, pg. 392, article 15.4.
Analysis Type(s):	Transient Thermal Analysis (ANTYPE = 4) with Analogous Diffusion Variables
Element Type(s):	3D Conduction Bar Elements (LINK33)
Input Listing:	vm164.dat

Test Case

A slab of wood of thickness b originally has a uniform moisture concentration c_i (relative to dry wood) when a drying period begins. The ambient moisture concentration of the drying air is c_e. Determine the moisture concentration c at the centerline of the slab after 127 hours.

Figure 231: Wooden Slab Problem Sketch

Material Properties

Geometric Properties

D = 4 x 10^-5 ft²/hr

b = 2 in = (2/12) ft

c_i = 30%

c_e = 5%

Analysis Assumptions and Modeling Notes

The thermal analysis, which solves the Laplace equation, is used to solve this problem since the diffusion problem is also governed by the Laplace equation. The following analogy (thermal : diffusion) of input and output variables is used: (temperature : moisture concentration), (thermal conductivity : diffusion coefficient). The slab is assumed to have a large surface area compared with its thickness and a negligible surface resistance. The density and specific heat properties are arbitrarily set to 1.0 and the thermal conductivity is used for the diffusion coefficient input. The solution is obtained for an arbitrary cross-sectional area of 1 ft².

The initial integration time step of 0.434 hr. is determined from δ²/4D, where δ is a characteristic element length (0.008333 ft) and D is the diffusion coefficient. Automatic time stepping is used to reduce the number of iterations if possible.

Results Comparison

	Target[1]	Mechanical APDL	Ratio[1]
c, %	10.0	10.3	1.027

Based on graphical estimates.