An Inverse Explicit Method for Obtaining Convective Mass Transfer Coefficient Plus Exponentially and Linearly Variable Diffusion Coefficient from Experimental Data

سال انتشار: 1403
محل انتشار: سی و دومین همایش سالانه بین المللی انجمن مهندسان مکانیک ایران
کد COI اختصاصی: ISME32_366
زبان مقاله: انگلیسی
تعداد مشاهده: 188

نویسندگان

Assistant Professor, Mechanical Engineering Group, Shahrekord University, ۲nd Kilometer of Soumoun Road, Shahrekord, Iran

چکیده

In this research, for one dimensional unsteady diffusion problem, the diffusion coefficient, D, has been considered as either a linear or exponential function of the local moisture content. By these assumptions, the governing differential equation and its initial and boundary conditions were transformed into dimensionless form in a newly proposed method. Then the dimensionless numerical solution for average moisture content, X*av, versus dimensionless time, t* or Fo, were obtained for many different cases by writing and running a Fortran program based on Finite Volume formulation. The mathematical features of such plots, X*av versus t*, were obtained by using a curve fitting software. These mathematical features were of two major types: dimensionless time required to reach a certain average moisture content (X*av-۰=۰.۱۲۵, ۰.۲۵, ۰.۵), and the slope of the mentioned curve at these cases (dX*av/dFo) or the inverse of the slope. Then by using a three dimensional curve fitting software, it was tried to obtain mathematical relationships among these sets of features and another set of important dimensionless parameter which also specify the dimensionless solution, e.g. the Bi number based on the initial diffusion coefficient at initial time. Here, there are three important parameters that should be explicitly determined from experimental data of average moisture content of specimen versus time. They are: the initial diffusion coefficient, Di, average convective mass transfer coefficient, hm, and another parameter related to the linear or exponential function. The mentioned mathematical relationships among the sets of dimensionless features should be in such a format that, when converted to dimensional form and after simplification, they can explicitly determine these parameters. Such a work is not found in published literature. This was carried out for both linear and exponential cases. Then the proposed relationships have been applied to a set of experimental data leading to successful obtaining of the mentioned parameters. The parameters were used in the written program to produce the numerical results for linear and exponential cases in addition to the case of constant diffusion coefficient. In all three cases, the numerical results of average moisture content of specimen versus time were in good agreement with experiments. Results show that at the beginning and end of drying process, the accuracy of exponential case is better than others, while the linear case was generally the worst. The exponential case also predicted the total time required for drying better.

کلیدواژه ها

kiln drying, mass diffusion coefficient, mass convection coefficient, inverse problem

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