scholarly journals COMPARISON OF THE THEORETICAL AND NUMERICAL SOLUTION BY THE FINITE ELEMENT METHOD FOR STEADY STATE AIR FLOW IN SOIL TOWARD AN EXTRACTION WELL

2006 ◽  
Vol 62 (4) ◽  
pp. 391-402 ◽  
Author(s):  
Yoshihiko HIBI ◽  
Kenji JINNO ◽  
Nobuyuki EGUSA ◽  
Junichi KAWABATA ◽  
Masanori SHIMOMURA
Keyword(s):  
Finite Element Method ◽  
Finite Element ◽  
Steady State ◽  
Numerical Solution ◽  
Air Flow ◽  
The Finite Element Method ◽  
Element Method

scholarly journals Finite Element Analysis of Thermoelastic Contact Stability

1994 ◽  
Vol 61 (4) ◽  
pp. 919-922 ◽  
Author(s):  
Taein Yeo ◽  
J. R. Barber
Keyword(s):  
Finite Element Method ◽  
Finite Element ◽  
Steady State ◽  
Eigenvalue Problem ◽  
Linear Perturbation ◽  
Dimensional System ◽  
The Finite Element Method ◽  
One Dimensional ◽  
Thermoelastic Contact ◽  
Element Method

When heat is conducted across an interface between two dissimilar materials, theimoelastic distortion affects the contact pressure distribution. The existence of a pressure-sensitive thermal contact resistance at the interface can cause such systems to be unstable in the steady-state. Stability analysis for thermoelastic contact has been conducted by linear perturbation methods for one-dimensional and simple two-dimensional geometries, but analytical solutions become very complicated for finite geometries. A method is therefore proposed in which the finite element method is used to reduce the stability problem to an eigenvalue problem. The linearity of the underlying perturbation problem enables us to conclude that solutions can be obtained in separated-variable form with exponential variation in time. This factor can therefore be removed from the governing equations and the finite element method is used to obtain a time-independent set of homogeneous equations in which the exponential growth rate appears as a linear parameter. We therefore obtain a linear eigenvalue problem and stability of the system requires that all the resulting eigenvalues should have negative real part. The method is discussed in application to the simple one-dimensional system of two contacting rods. The results show good agreement with previous analytical investigations and give additional information about the migration of eigenvalues in the complex plane as the steady-state heat flux is varied.

Stratification and Buoyancy Effect of Heat Transportation in Magnetohydrodynamics Micropolar Fluid Flow Passing Over a Porous Shrinking Sheet Using the Finite Element Method

2019 ◽  
Vol 8 (8) ◽  
pp. 1640-1647 ◽  
Author(s):  
Shahid Ali Khan ◽  
Yufeng Nie ◽  
Bagh Ali
Keyword(s):  
Finite Element Method ◽  
Finite Element ◽  
Numerical Solution ◽  
Mesh Size ◽  
Stratified Medium ◽  
Shrinking Sheet ◽  
The Finite Element Method ◽  
Nonlinear Odes ◽  
Micropolar Fluid Flow ◽  
Element Method

The current study investigates the numerical solution of steady heat transportation in magnetohydrodynamics flow of micropolar fluids over a porous shrinking/stretching sheet with stratified medium and buoyancy force. Based on similarity transformation, the partial differential governing equations are assimilated into a set of nonlinear ODEs, which are numerically solved by the finite element method. All obtained unknown functions are discussed in detail after plotting the numerical results against different arising thermophysical parameters namely, suction, magnetic, stratification, heat source, and buoyancy parameter. Under the limiting case, the numerical solution of the velocity and temperature is compared with present work. Better consistency between the two sets of solutions was determined. To verify the convergence of the numerical solution, the calculation is made by reducing the mesh size. The present study finds applications in materials processing and demonstrates convergence characteristics for the finite element method code.

Sign in / Sign up

Export Citation Format

Share Document