Stability analysis of natural convection in porous cavities through integral transforms

Alves, Leonardo Santos de Brito; Cotta, Renato M.; Pontes, J.

doi:10.1016/s0017-9310(01)00231-9

Cited by 36 publications

(15 citation statements)

References 6 publications

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“…Hence, it is possible to conclude that subcritical instabilities are not present. This behaviour is consistent with the non-dissipative nature of the GITT, which does not force the solution to converge towards an unstable steady state even when the initial conditions are very close to it [32]. Furthermore, it is important to note that an absolute instability is observed in the nonlinear simulations, because perturbations grow exponentially in time beyond threshold values of Λ.…”

Section: Numerical Analysissupporting

confidence: 68%

Nonlinear stability analysis of Darcy’s flow with viscous heating

2016

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The nonlinear stability of a rectangular porous channel saturated by a fluid is here investigated. The aspect ratio of the channel is assumed to be variable. The channel walls are considered impermeable and adiabatic except for the horizontal top which is assumed to be isothermal. The viscous dissipation is acting inside the channel as internal heat generator. A basic throughflow is imposed, and the nonlinear convective stability is investigated by means of the generalized integral transform technique. The neutral stability curve is compared with the one obtained by the linear stability analysis already present in the literature. The growth rate analysis of different unstable modes is performed. The Nusselt number is investigated for several supercritical configurations in order to better understand how the system behaves when conditions far away from neutral stability are considered. The patterns of the neutrally stable convective cells are also reported. Nonlinear simulations support the results obtained by means of the linear stability analysis, confirming that viscous dissipation alone is indeed capable of inducing mixed convection. Low Gebhart or high Péclet numbers lead to a transient overheating of the originally motionless fluid before it settles in its convective steady state.

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Section: Numerical Analysissupporting

confidence: 68%

Nonlinear stability analysis of Darcy’s flow with viscous heating

2016

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“…Equations (19) and (20), with initial and boundary conditions (10) and using combined property dependences (21) to (25) as well as property (17) (see figs. 1 to 4), form the system of equations that governs the unsteady near critical heat transfer process.…”

Section: Solution Methodologymentioning

confidence: 99%

“…It is a hybrid numerical-analytical solution methodology with global error control that has been applied to many different problems in heat and mass transfer [18]. Finally, it is chosen for the current study due to the successful experience of the author in using it to simulate natural convection in porous media [19], non-linear convection-diffusion flows [20], and Rayleigh-Benard instability in porous media [21].…”

Section: Introductionmentioning

confidence: 99%

An integral transform solution for unsteady compressible heat transfer in fluids near their thermodynamic critical point

2013

THERM SCI

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The classical thermodynamic model for near critical heat transfer is an integral-differential equation with constant coefficients. It is similar to the heat equation, except for a source term containing the time derivative of the bulk temperature. Despite its simple form, analytical methods required the use of approximations to generate solutions for it, such as an approximate Fourier transformation or a numerical Laplace inversion. Recently, the Generalized Integral Transform Technique or GITT has been successfully applied to this problem, providing a highly accurate analytical solution for it and a new expression of its relaxation time. Nevertheless, very small temperature differences, on the order of mK, have to be imposed so that constant thermal properties can be assumed very close to the critical point. The present paper generalizes this study by relaxing its restriction and accounting for the strong dependence on temperature and pressure of supercritical fluid properties, demonstrating that a) the GITT can be applied to realistic nonlinear unsteady compressible heat transfer in fluids with diverging thermal properties and b) temperature and pressure have opposite effects on all properties, but their variation causes no additional thermo-acoustic effect, increasing the validity range of the constant property model

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“…There is a vast literature about this subject, including papers and books that become impossible to mention all of them. But, for instance, we mention the works of [31,32,33,34], etc. In this chapter, we restrict our attention to the linear problem, because for nonlinear problem the linear result is iteratively used after the linearization of nonlinear transformed equation.…”

Section: Giltt Approach Solutionmentioning

confidence: 99%