An inverse problem in simultaneously estimating boundary moisture fluxes in a porous annular cylinder Y.-C. Yang, H.-L. Lee, and W.-J. Chang, Tainan, Taiwan Received February 2, 2005; revised March 31, 2005 Published online: September 8, 2005 Ó Springer-Verlag 2005 Summary. Based on the conjugate gradient method, this study presents a means of solving the inverse boundary value problem of coupled heat and moisture transport in a porous annular cylinder. While knowing the moisture history at the measuring positions, the unknown time-dependent inner-and-outer boundary moisture fluxes can be simultaneously determined. It is assumed that no prior information is available on the functional form of the unknown moisture fluxes. The accuracy of this inverse heat and moisture transport problem is examined by using the simulated exact and inexact moisture measurements in the numerical experiments. Results show that excellent estimation on the time- dependent boundary moisture fluxes can be obtained with any arbitrary initial guesses. Moreover, the methodology presented in this paper can also be used to calculate the cutting forces in nanomachining by atomic force microscopy (AFM), and to determine the heat sources in an X-ray lithographic process. Nomenclature C Dimensionless concentration of moisture D Equilibrium diffusion coefficient of moisture content J Functional L Equilibrium diffusion coefficient of temperature M Total number of measuring positions in r-direction p Direction of decent q Moisture flux r Dimensionless radius r 1 Dimensionless inner radius of cylinder (r 1 =1) r 2 Dimensionless outer radius of cylinder (r 2 =2) t Dimensionless time T Dimensionless temperature Greek symbols b Step size D Small variation quality Acta Mechanica 179, 131–144 (2005) DOI 10.1007/s00707-005-0256-9 Acta Mechanica Printed in Austria