Back
 MSCE  Vol.4 No.4 , April 2016
Application of Finite Fourier Transform and Similarity Approach in a Binary System of the Diffusion of Water in a Polymer
Hisham A. Maddah1
Show more
Abstract: This paper describes the method of two important mathematical techniques used in chemical engineering applications. Solving a mass transfer problem, weather in finite or semi-infinite domain, may seem difficult without the practice of Finite Fourier Transform (FFT) and Similarity Transformation. Finite systems refer to any closed system that has a specific boundary that can be determined. For example, polymer sheets, membranes, storage tanks, oil reservoirs and a human stomach are determined to be finite systems where FFT is applicable to derive expressions for concentration profiles of the materials in the system. However, Similarity Transformation method is used to identify the concentration profile in semi-infinite systems that have no limits. It has been approved that we may also use the similarity procedure for finite systems since our results are almost the same. Methodologies of both techniques have been discussed thoroughly in order to apply them to a water-polymer diffusion system for the determination of the concentration of water in a polymer sheet of PET. Discussion and comparison between FFT and similarity is included to illustrate the power of each mathematical procedure in predicting and modeling mass concentrations.
Keywords: Similarity, Fininte Fourier Transfrom, Modeling, Mass Transfer, Concentration Profile
Cite this paper: Maddah, H. (2016) Application of Finite Fourier Transform and Similarity Approach in a Binary System of the Diffusion of Water in a Polymer. Journal of Materials Science and Chemical Engineering, 4, 20-30. doi: 10.4236/msce.2016.44003.
References

[1]   Bird, R.B., Stewart, W.E. and Lightfoot, E.N. (2002) Transport Phenomena. 2nd Edition, John Wiley & Sons Ltd., New York.
http://dx.doi.org/10.1115/1.1424298

[2]   Trim, D.W. (1990) Applied Partial Differential Equations. 1st Edition, Pws Pub Co., Boston.

[3]   Welty, J., Wicks, C.E., Wilson, R.E. and Rorrer, G.L. (2007) Fundamentals of Momentum, Heat, and Mass Transfer. 5th Edition, John Wiley & Sons Ltd., New York.

[4]   Deen, W.M. (2011) Analysis of Transport Phenomena. 2nd Edition, Oxford University Press, New York.

[5]   Ramachandran, P.A. (2014) Advanced Transport Phenomena: Analysis, Modeling, and Computations. 1st Edition, Cambridge University Press, New York.

[6]   Bergman, T.L., Lavine, A.S., Incropera, F.P. and DeWitt D.P. (2011) Fundamentals of Heat and Mass Transfer. 7th Edition, John Wiley & Sons Ltd., New York.

[7]   Greenberg, M.D. (1998) Advanced Engineering Mathematics. 2nd Edition, Prentice Hall, New Delhi.

[8]   Kreyszig, E. (2011) Advanced Engineering Mathematics. 10th Edition, John Wiley & Sons Ltd., New Delhi.

[9]   Myint-U, T. and Debnath, L. (2006) Linear Partial Differential Equations for Scientists and Engineers. 4th Edition, Birkhäuser, Boston.

[10]   Cushman-Roisin, B. (2012) Environmental Transport and Fate. 1st Edition, Dartmouth College, USA.

[11]   Green, D.W. and Perry, R.H. (2007) Perry’s Chemical Engineers’ Handbook. 8th Edition, McGraw-Hill Professional, New York.

 
 
Top