scholarly journals Continuous dependence on the heat supply for the Boussinesq equations with a cubic density law

1991 ◽  
Vol 161 (1) ◽  
pp. 258-273
Author(s):  
Geoffrey McKay
Keyword(s):  
Continuous Dependence ◽  
Heat Supply ◽  
Boussinesq Equations ◽  
Cubic Density

scholarly journals Structural stability for the Boussinesq equations interfacing with Darcy equations in a bounded domain

2021 ◽  
Vol 2021 (1) ◽  
Author(s):  
Yuanfei Li ◽  
Shuanghu Zhang ◽  
Changhao Lin
Keyword(s):  
Bounded Domain ◽  
Structural Stability ◽  
Differential Inequality ◽  
Continuous Dependence ◽  
A Priori ◽  
Boussinesq Equations ◽  
Interface Boundary ◽  
A Priori Bounds ◽  
First Order ◽  
Darcy Equations

AbstractA priori bounds were derived for the flow in a bounded domain for the viscous-porous interfacing fluids. We assumed that the viscous fluid was slow in $\Omega _{1}$ Ω 1 , which was governed by the Boussinesq equations. For a porous medium in $\Omega _{2}$ Ω 2 , we supposed that the flow satisfied the Darcy equations. With the aid of these a priori bounds we were able to demonstrate the result of the continuous dependence type for the Boussinesq coefficient λ. Following the method of a first-order differential inequality, we can further obtain the result that the solution depends continuously on the interface boundary coefficient α. These results showed that the structural stability is valid for the interfacing problem.

On the Exact Soliton Solutions of Some Nonlinear PDE by Tan-Cot Method

2018 ◽  
Vol 5 (1) ◽  
pp. 31-36
Author(s):  
Md Monirul Islam ◽  
Muztuba Ahbab ◽  
Md Robiul Islam ◽  
Md Humayun Kabir
Keyword(s):  
Solitary Wave ◽  
Acoustic Waves ◽  
Water Waves ◽  
Wave Equations ◽  
Rectangular Channel ◽  
Soliton Solutions ◽  
Boussinesq Equations ◽  
Travelling Wave ◽  
Ion Acoustic Waves ◽  
Analytical System

For many solitary wave applications, various approximate models have been proposed. Certainly, the most famous solitary wave equations are the K-dV, BBM and Boussinesq equations. The K-dV equation was originally derived to describe shallow water waves in a rectangular channel. Surprisingly, the equation also models ion-acoustic waves and magneto-hydrodynamic waves in plasmas, waves in elastic rods, equatorial planetary waves, acoustic waves on a crystal lattice, and more. If we describe all of the above situation, we must be needed a solution function of their governing equations. The Tan-cot method is applied to obtain exact travelling wave solutions to the generalized Korteweg-de Vries (gK-dV) equation and generalized Benjamin-Bona- Mahony (BBM) equation which are important equations to evaluate wide variety of physical applications. In this paper we described the soliton behavior of gK-dV and BBM equations by analytical system especially using Tan-cot method and shown in graphically. GUB JOURNAL OF SCIENCE AND ENGINEERING, Vol 5(1), Dec 2018 P 31-36

Autonomous energy supply based on the wind-energy complex and hydrogen energy storage

2019 ◽  
pp. 12-26
Author(s):  
S. I. Nefedkin ◽  
A. O. Barsukov ◽  
M. I. Mozgova ◽  
M. S. Shichkov ◽  
M. A. Klimova
Keyword(s):  
Wind Speed ◽  
Wind Energy ◽  
Power Supply ◽  
Energy Supply ◽  
Heat Supply ◽  
Hot Water ◽  
Successful Implementation ◽  
High Wind ◽  
Wind Generators ◽  
Weak Wind

The paper proposes an alternative scheme of guaranteed electricity and heat supply of an energy-insulated facility with a high potential of wind energy without the use of imported or local fuel. The scheme represents a wind power complex containing the park of wind generators located at the points with high wind potential. The wind generators provide guaranteed power supply even in periods of weak wind. For heat supply of the consumer, all surplus of the electric power goes on thermoelectric heating of water in tanks of accumulators, and also on receiving hydrogen by a method of electrolysis of water. The current heat supply is carried out with the use of hot water storage tanks, and the heat supply during the heat shortage is carried out by burning the stored hydrogen in condensing hydrogen boilers. We have developed the algorithm of calculation and the program "Wind in energy" which allows calculating annual balance of energy and picking up necessary quantity of the equipment for implementation of the scheme proceeding from the annual schedule of thermal and electric loading, and also potential of wind energy in the chosen region. The calculation-substantiation of the scheme proposed in relation to the real energy-insulated object Ust-Kamchatsk (Kamchatka) is carried out. The equipment for the implementation of an alternative energy supply scheme without the use of imported fuel is selected and compared with the traditional energy supply scheme based on a diesel power plant and a boiler house operating on imported fuel. With the introduction of an alternative power supply scheme, the equipment of the traditional scheme that has exhausted its resource can be used for backup power supply. Using climate databases, a number of energy-insulated facilities in the North and East of Russia with high wind energy potential are considered and the conditions for the successful implementation of the energy supply scheme are analyzed. This requires not only a high average annual wind speed, but also a minimum number of days of weak wind. In addition, it is necessary that the profile of the wind speed distribution in the annual section coincides with the profile of the heat load consumption.

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