Continuous dependence for double diffusive convection in a Brinkman model with variable viscosity

Meften, Ghazi Abed; Ali, Ali Hasan

doi:10.2478/ausm-2022-0009

Cited by 7 publications

(7 citation statements)

References 12 publications

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“…Resources of this direction can be obtained in an intensive study that was first conducted by Straughan [1]. In addition, new elaborations of this study were conducted by Aulisa et al [8], Ciarletta et al [9], Hoang and Ibragimov [10], Liu [11], Liu et al [12,13], and Ghazi and Ali [14][15][16][17]. Our current paper is an advancement of the work conducted by Straughan [18] and Gentile and Straughan [19] who studied the continuous dependence and the structural stability of the supplier of heat in a penetrating convection type and in the porous medium of Forchheimer, such that the density relies quadratically or cubically on the temperature field.…”

Section: Introductionmentioning

confidence: 90%

A Study of Continuous Dependence and Symmetric Properties of Double Diffusive Convection: Forchheimer Model

et al. 2022

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In this recent work, the continuous dependence of double diffusive convection was studied theoretically in a porous medium of the Forchheimer model along with a variable viscosity. The analysis depicts that the density of saturating fluid under consideration shows a linear relationship with its concentration and a cubic dependence on the temperature. In this model, the equations for convection fluid motion were examined when viscosity changed with temperature linearly. This problem allowed the possibility of resonance between internal layers in thermal convection. Furthermore, we investigated the continuous dependence of this solution based on the changes in viscosity. Throughout the paper, we found an “a priori estimate” with coefficients that relied only on initial values, boundary data, and the geometry of the problem that demonstrated the continuous dependence of the solution on changes in the viscosity, which also helped us to state the relationship between the continuous dependence of the solution and the changes in viscosity. Moreover, we deduced a convergence result based on the Forchheimer model at the stage when the variable viscosity trends toward a constant value by assuming a couple of solutions to the boundary-initial-value problems and defining a difference solution of variables that satisfy a given boundary-initial-value problem.

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Section: Introductionmentioning

confidence: 90%

A Study of Continuous Dependence and Symmetric Properties of Double Diffusive Convection: Forchheimer Model

et al. 2022

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“…The above equations in (35) are called the Euler Lagrange equations, where ς ,i represents the Lagrange multiplier. Now, by taking the third component in (35) 1 , one can remove the Lagrange multiplier. Thus, we obtain…”

Section: Linear Instabilitymentioning

confidence: 99%

“…The impact of porous medium anisotropy on double diffusive convection was explained in [20]. Further studies with many different applications such as solidify and centrifugal casting of minerals, bio-mechanics, petroleum manufacture, chemical operations and food, rotating machinery, and geophysical problem are found in [21][22][23][24][25][26][27][28][29][30][31][32][33][34][35].…”

Section: Introductionmentioning

confidence: 99%

Nonlinear Stability and Linear Instability of Double-Diffusive Convection in a Rotating with LTNE Effects and Symmetric Properties: Brinkmann-Forchheimer Model

Meften

Ali

Al-Ghafri³

et al. 2022

Symmetry

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The major finding of this paper is studying the stability of a double diffusive convection using the so-called local thermal non-equilibrium (LTNE) effects. A new combined model that we call it a Brinkmann-Forchheimer model was considered in this inquiry. Using both linear and non-linear stability analysis, a double diffusive convection is used in a saturated rotating porous layer when fluid and solid phases are not in the state of local thermal non-equilibrium. In addition, we discussed several related topics such as the effect of solute Rayleigh number, symmetric properties, Brinkman coefficient, Taylor number, inter-phase heat transfer coefficient on the stability of the system, and porosity modified conductivity ratio. Moreover, two cases were investigated in non-linear theory, the case of the Forchheimer coefficient F=0 and the case of the Taylor-Darcy number τ=0. For the validation of this work, some numerical experiments were made in the non-linear energy stability and the linear instability theories.

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“…Differential equations have been widely recognized as a successful modeling approach. Meanwhile, fuzzy group theory serves as a potent tool in handling unknown variables and processing fuzzy or subjective information in mathematical models [1,5,9,18]. It may be necessary to use such mathematical modeling, and to use fuzzy differential equations (FDEs) that involve a system of elementary value problems.…”

Section: Introductionmentioning

confidence: 99%

Solving Fuzzy System of Boundary Value Problems by Homotopy Perturbation Method with Green’s Function

Al-Hayani

Younis

2023

Eur. J. Pure Appl. Math.

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In this research, we successfully demonstrated the use of the homotopy perturbation method with Green's function to find approximate solutions for the fuzzy system of boundary value problems. Our results showcase the effectiveness of this method in providing accurate and reliable solutions. Our results showcase the effectiveness of this method in providing accurate and reliable solutions. The consistent way to reduce the size of the computation gives to reach the exact solution is one of the best methods adopted to determine the behavior of the solution directly in order to determine the approximate solution analytically, Finally, the problems that have been addressed confirmed the validity of the method applied analytically in this research using comparison with some numerical problems

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Continuous dependence for double diffusive convection in a Brinkman model with variable viscosity

Cited by 7 publications

References 12 publications

A Study of Continuous Dependence and Symmetric Properties of Double Diffusive Convection: Forchheimer Model

A Study of Continuous Dependence and Symmetric Properties of Double Diffusive Convection: Forchheimer Model

Nonlinear Stability and Linear Instability of Double-Diffusive Convection in a Rotating with LTNE Effects and Symmetric Properties: Brinkmann-Forchheimer Model

Solving Fuzzy System of Boundary Value Problems by Homotopy Perturbation Method with Green’s Function

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