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Analytical Solution to Partial Differential Equations Derived from Thermo-Hydro-Mechanical Analysis

Yazdani, Davood | 2017

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  1. Type of Document: M.Sc. Thesis
  2. Language: Farsi
  3. Document No: 50936 (09)
  4. University: Sharif University of Technology
  5. Department: Civil Engineering
  6. Advisor(s): Pak, Ali
  7. Abstract:
  8. In this research an analytical and semi analytical solution to the differential eqautions derived from coupled analysis of heat transfer, moisture transfer and solid deformation in porous materials is presented. In first section, differential equations derived from Hydro-mechanical analysis of an unsaturated soil layer with limited thickness was considered and it is assumed that pore air pressure is equal to atmospheric pressure. To solve the system of equations laplace transform is used.In second section, the effect of daily changes in temperature on transient heat and moisture transfer in semi infinite layer is studied in three dimension. Energy conservation equation and pore liquid mass conservation equation is considered and temperature changes was applied to the problem as a boundary condition. the solution to the problem is computed by linearization of the equations and the use of Laplace-fourier transform. In last section, an analytical solution for a system of coupled differential equations, derived from thermo-hydro-mechanical analysis of a three-phase porous media is presented in one dimension. Initially, a system of coupled differential equations, including energy conservation, dry air mass conservation, pore liquid-vapor mass conservation and momentum conservation is considered and a method called AGM is used to solve the system of equations. The method is simple and perspicuous and can be used to solve various differential equations such as nonlinear partial differential equations. The values of the error functions are calculated by placing the obtained solution in the equation. The results display the accuracy of the applied method for solving nonlinear partial differential equations
  9. Keywords:
  10. Porous Materials ; Unsaturated Soil ; Coupled Analysis ; Laplace Trasformation ; Fourier Transform ; Thermohydraulic Analysis ; Akbari-Ganji (AG)Method

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