การแก้แบบจำลองทางคณิตศาสตร์ของเครื่องปฏิกรณ์ TAP ด้วยวิธีกลุ่มของลี

Solving the Mathematical Model of TAP Reactor using Lie Group Method

Name: เพ็ญวิภา สาสนรักกิจ

Organization : มหาวิทยาลัยเทคโนโลยีพระจอมเกล้าธนบุรี

keyword: Lie Group

; Lie Algebras

; Infinitesimal Symmetries

; Group Invariant Solution

; Symmetry Group

; Optimal System

Abstract: The objective of this thesis is to apply Lie group method for solving the mathematical nonlinear model of TAP (Temporal Analysis of product) reactor. There are four TAP models of 1. Diffusion TAP Model, 2. Diffusion and First order Irreversible Adsorption/Reaction TAP Model, 3. Diffusion and Second order Irreversible Adsorption/Reaction TAP Model, and 4. Diffusion and First order Reversible Adsorption/Reaction TAP Model. TAP model is one of partial differential equation. In application of Lie group to system of partial differential equations, the symmetry group usually doesn’t want any determination of the general solution but it determines special types of solutions, which are invariant under some subgroup of the full symmetry group of the system. In this thesis, the results are continued to the step of finding Lie algebra of infinitesimal symmetries of the model. The Lie algebras of infinitesimal symmetries of each model are 1. six vectors, 2. six vectors, 3. three vectors and 4. four vectors respectively. The accuracy of results is proved by Lie 5.1 software [8]. The comparison shows the very good agreement results. Therefore, the Lie algebras of infinitesimal symmetries of TAP models are acceptable. Next step is to find the optimal system of subalgebras and then the group invariant solution of differential equation. Since this step required deeply understandable of many theories for example, adjoint representation, invariant theory, transformation group, killing form. The thesis need to be scoped down and skipped this step. The last step is to find the group invariant solutions for each of the one dimensional subgroups in the optimal system. This step is straightforward and shows only for Diffusion Model. Finally the numerical solutions of TAP model are presented. The accuracy of numerical program is checked by comparing the result to the existing analytical result. The numerical results of program are agreed to the analytical results. Then the numerical results of second order irreversible adsorption/reaction are created. The results found that the dimensionless exit flow depends on the order of reaction and the number of moles or molecules of A in the inlet pulse.

มหาวิทยาลัยเทคโนโลยีพระจอมเกล้าธนบุรี

Address: กรุงเทพมหานคร (Bangkok)

Email: info.lib@mail.kmutt.ac.th

Name: Assoc.Prof. Thongchai Srinophakun

Role: Supervisor

Created: 2546

Issued: 2005-10-12

Modified: 2006-05-09

วิทยานิพนธ์/Thesis

ISBN: 9741833318

CallNumber: CHE1516

tha

DegreeName: Master of Engineering

Level: Master's Degree

Descipline: Chemical Engineering

Grantor: King Mongkut's University of Technology Thonburi

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