Effect of Time Periodic Boundary Conditions on Convective Flows in a Porous Square Enclosure with Non-Uniform Internal Heating

2010 ◽  
Vol 85 (3) ◽  
pp. 885-903 ◽  
Author(s):  
H. Saleh ◽  
I. Hashim ◽  
N. Saeid
Keyword(s):  
Boundary Conditions ◽  
Periodic Boundary ◽  
Periodic Boundary Conditions ◽  
Internal Heating ◽  
Square Enclosure ◽  
Convective Flows ◽  
Time Periodic

Time-periodic solutions to a nonlinear wave equation with periodic or anti-periodic boundary conditions

2008 ◽  
Vol 465 (2103) ◽  
pp. 895-913 ◽  
Author(s):  
Shuguan Ji
Keyword(s):  
Wave Equation ◽  
Boundary Conditions ◽  
Periodic Solutions ◽  
Nonlinear Wave ◽  
Nonlinear Wave Equation ◽  
Periodic Boundary ◽  
Periodic Boundary Conditions ◽  
Main Concept ◽  
Time Periodic Solutions ◽  
Time Periodic

This paper is concerned with the existence of time-periodic solutions to the nonlinear wave equation with x -dependent coefficients u ( x ) y tt − ( u ( x ) y x ) x + au ( x ) y +| y | p −2 y = f ( x ,  t ) on (0,  π )× under the periodic or anti-periodic boundary conditions y (0, t )=± y ( π ,  t ), y x (0,  t )=± y x ( π ,  t ) and the time-periodic conditions y ( x ,  t + T )= y ( x ,  t ), y t ( x ,  t + T )= y t ( x ,  t ). Such a model arises from the forced vibrations of a non-homogeneous string and the propagation of seismic waves in non-isotropic media. A main concept is the notion ‘weak solution’ to be given in §2. For T =2 π / k ( k ∈ ), we establish the existence of time-periodic solutions in the weak sense by investigating some important properties of the wave operator with x -dependent coefficients.

scholarly journals Numerical simulation of natural convection in an inclined porous cavity under time-periodic boundary conditions with a partially active thermal side wall

RSC Advances ◽  
2017 ◽  
Vol 7 (28) ◽  
pp. 17519-17530 ◽  
Author(s):  
Feng Wu ◽  
Gang Wang
Keyword(s):  
Numerical Simulation ◽  
Natural Convection ◽  
Boundary Conditions ◽  
Periodic Boundary ◽  
Side Wall ◽  
Periodic Boundary Conditions ◽  
Porous Cavity ◽  
Thermal Boundary Conditions ◽  
The Right ◽  
Time Periodic

Natural convection in an inclined porous cavity with positively or negatively inclined angles is studied numerically for time-periodic boundary conditions on the left side wall and partially active thermal boundary conditions on the right wall.

Time-periodic solutions to the one-dimensional wave equation with periodic or anti-periodic boundary conditions

2007 ◽  
Vol 137 (2) ◽  
pp. 349-371 ◽  
Author(s):  
Shuguan Ji ◽  
Yong Li
Keyword(s):  
Wave Equation ◽  
Weak Solution ◽  
Boundary Conditions ◽  
Periodic Solutions ◽  
Periodic Boundary ◽  
Periodic Boundary Conditions ◽  
One Dimensional ◽  
Time Periodic Solutions ◽  
Time Periodic ◽  
Dimensional Wave

This paper is devoted to the study of time-periodic solutions to the nonlinear one-dimensional wave equation with x-dependent coefficients u(x)ytt – (u(x)yx)x + g(x,t,y) = f(x,t) on (0,π) × ℝ under the periodic boundary conditions y(0,t) = y(π,t), yx(0,t) = yx(π,t) or anti-periodic boundary conditions y(0, t) = –y(π,t), yx[0,t) = – yx(π,t). Such a model arises from the forced vibrations of a non-homogeneous string and the propagation of seismic waves in non-isotropic media. Our main concept is that of the ‘weak solution’. For T, the rational multiple of π, we prove some important properties of the weak solution operator. Based on these properties, the existence and regularity of weak solutions are obtained.

Modelling of Mass Transport in Porous Materials: Analytical Solutions and Analysis

2014 ◽  
Vol 348 ◽  
pp. 107-112
Author(s):  
Antonio F. Miguel
Keyword(s):  
Mass Transport ◽  
Boundary Conditions ◽  
Periodic Boundary ◽  
Periodic Boundary Conditions ◽  
Analytic Solutions ◽  
Temperature Gradients ◽  
Numerical Techniques ◽  
Physical Insight ◽  
Mass And Heat Transfer ◽  
Time Periodic

The pioneering works in the area of mass transport in porous media go back to the end of last century. The partial differential equations governing the mass and heat transfer can be solved using numerical techniques, and in this paper we solve them analytically under different boundary conditions including time-periodic boundary conditions. The nature of these solutions is discussed. Analytic solutions provide valuable physical insight and are usually easier to compute. In addition, these solutions may help to experimentally determine the parameters in a setting where both the mass and temperature gradients are present, without resorting to a simplified set of equations that govern heat and mass transfer separately.

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