An Inverse Explicit Method for Determining Constant Diffusion and Convective Mass Transfer Coefficients from Experimental data

In this research, a new inverse explicit method is proposed for obtaining the constant diffusion, D, and convective mass transfer, hm, coefficients from experimental data of average moisture content of specimen versus time. It is shown that in one dimensional diffusion problem, the mathematical features of the curve of dimensionless average moisture content, X*av, versus dimensionless time, Fo, are only functions of Bi number for mass transfer. Here, first for ۶۰ different Bi numbers in the range of ۰.۰۰۱ to ۱۰۰, and for X*av-۰=۰.۵, ۰.۲۵, ۰.۱۲۵, two mathematical features of such plots, Fo(X*av-۰) and dX*av/dFo, have been obtained by curve fitting of plots. Then by using a software of SPSS family, the possible functions for relationships between such features were studied in order to obtain the best functions relating them that can explicitly determine the D values. Two relationships were obtained that have the accuracy of less than ۱.۵%. Also two other functions were distinguished that can relate Bi number to two other mathematical features of such plots. From these latter relationships and by having values of D, the values of hm can be obtained by less than ۱% accuracy in the whole Bi number domain. For verification of these equations, they were applied to four sets of experimental data and successfully D and hm were calculated for each test. The obtained values have been used for a Fortran program, written in this study to solve the one dimensional diffusion process, to produce numerical results of Xav versus time. The numerical plots were successfully in good agreement with experimental ones. Also for two dimensional case of drying of square shape objects, the same procedure was carried out leading to two equations for obtaining D and hm explicitly. These equations were applied to a set of experimental data which resulted to successful calculation of D and hm. These values were used in another Fortran program written in this work for solving the two dimensional diffusion numerically. The numerical results of Xav versus time were also in good agreement with experimental data.

کلیدواژه ها:

western hemlock ، wood drying ، convection in kilns ، mass diffusion coefficient ، mass convection coefficient ، inverse problem