Investigation The Finite Volume Method Of 2D Heat Conduction Through A Composite Wall By Using The 1D Analytical Solution

2017 ◽  
pp. 1
Author(s):  
Abdulhamid El Edris Saad
Keyword(s):  
Heat Conduction ◽  
Analytical Solution ◽  
Finite Volume Method ◽  
Finite Volume ◽  
Composite Wall ◽  
Volume Method

Heat Conduction Equation Finite Volume Method to Achieve on MATLAB

2012 ◽  
Vol 195-196 ◽  
pp. 712-717
Author(s):  
Qiong Xue ◽  
Xiao Feng Xiao ◽  
Niang Zhi Fan
Keyword(s):  
Differential Equation ◽  
Partial Differential Equation ◽  
Heat Conduction ◽  
Finite Volume Method ◽  
Finite Volume ◽  
Heat Conduction Equation ◽  
Conduction Equation ◽  
Two Dimensional ◽  
Partial Differential ◽  
Volume Method

Diffusion only, two dimensional heat conduction has been described on partial differential equation. Based on Finite Volume Method, Discretized algebraic Equation of partial differential equation have been deduced. different coefficients and source terms have been discussed under different boundary conditions, which include prescribed heat flux, prescribed temperature, convection and insulated. Transient heat conduction analysises of infinite plate with uniform thickness and two dimensional rectangle region have been realized by programming using MATLAB. It is useful to make the heat conduction equation more understandable by its solution with graphical expression, feasibility and stability of numerical method have been demonstrated by running result.

Heat Conduction Equation Finite Volume Method to Achieve on MATLAB

2012 ◽  
Vol 510 ◽  
pp. 205-210
Author(s):  
Xiao Feng Xiao ◽  
Qiong Xue
Keyword(s):  
Differential Equation ◽  
Partial Differential Equation ◽  
Heat Conduction ◽  
Finite Volume Method ◽  
Finite Volume ◽  
Heat Conduction Equation ◽  
Conduction Equation ◽  
Two Dimensional ◽  
Partial Differential ◽  
Volume Method

Diffusion only, two dimensional heat conduction has been described on partial differential equation. Based on Finite Volume Method, Discretized algebraic Equation of partial differential equation have been deduced. different coefficients and source terms have been discussed under different boundary conditions, which include prescribed heat flux, prescribed temperature, convection and insulated.. Transient heat conduction analysis of infinite plate with uniform thickness and two dimensional rectangle region are realized by programming using MATLAB. It is useful to make the heat conduction equation more understandable by its solution with graphical expression, feasibility and stability of numerical method have been demonstrated by running result.

scholarly journals A Quasi-3D Numerical Model for Grout Injection in a Parallel Fracture Based on Finite Volume Method

Complexity ◽  
2019 ◽  
Vol 2019 ◽  
pp. 1-18
Author(s):  
Xiaolong Li ◽  
Meimei Hao ◽  
Yanhui Zhong ◽  
Bei Zhang ◽  
Fuming Wang ◽  
...  
Keyword(s):  
Analytical Solution ◽  
Finite Volume Method ◽  
Finite Volume ◽  
Rock Fracture ◽  
Diffusion Mechanism ◽  
Three Dimensional ◽  
Fracture Aperture ◽  
Grout Injection ◽  
New Model ◽  
Volume Method

The purpose of the present work is to develop a quasi-3D numerical method that can be used to study the diffusion mechanism of grout injection in a rock fracture based on the collocated structured grid of the finite volume method (FVM). Considering the characteristics of fracture in geometry that the aperture is much less than its length and width, the Hele-Shaw model is introduced to deduce the z-derivatives of velocities u and v at walls, which is a function of the relevant average velocity and the fracture aperture. The traditional difference scheme for the diffusive term is partly substituted with the derived analytical expressions; hence a three-dimensional problem of grout flow in the parallel fracture can be transformed into a two-dimensional one that concerns fracture aperture. The new model is validated by the analytical solution and experimental data on three cases of grouting in the parallel-plate fracture. Compared with the results from ANSYS-Fluent software, the present model shows better agreement with the analytical solution for the distribution of pressure and velocity. Furthermore, the new model needs less grid unit, spends less time, but achieves greater accuracy. The complexity of the grout flow field in the rock fracture is reduced; thus the computational efficiency can be improved significantly.

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