Slip boundary condition effect on double‐diffusive convection in a porous medium: Brinkman Model

Abstract

The model of double-diffusive convection in a porous medium layer was analyzed using the Brinkman model and concentration based on an internal heat source. Linear instability analysis of the model was performed. Particularly, we analyzed the effect of slip boundary conditions on the instability of the system. We analyzed when the instability started and computed the critical Rayleigh number as a function of the slip coefficient. K E Y W O R D S Brinkman model, double-diffusive, slip boundary conditions, linear instability, Rayleigh number, slip boundary conditions

Nonlinear stability analysis for double-diffusive convection when the viscosity depends on temperature

“…However, in figure 3, different values of P c have been utilised. The eigenvalue systems of linear instability and nonlinear stability theories have been solved by using the Chebyshev collocation method, for more details see [25][26][27][28][29][30][31][32].…”

Soret effect on stability of Darcy problem in a bidispersive porous medium with an exothermic chemical surface reaction

“…For further details, interested readers may refer to Refs. [53][54][55][56][57][58][59]. The initial step in applying this method involves transforming the solution domains of 𝑢 𝑓 , 𝑢 𝑝 , 𝜃 and 𝜙 to (−1, 1), which corresponds to the domain of the Chebyshev polynomials of the first kind, 𝑇 𝚤 (𝑧).…”

Chemical Reaction Effect on Convection in Bidispersive Porous Medium

“…In this section, the Chebyshev collection method is employed to solve the eigenvalue systems (3.4) and (4.11). For more details see Harfash (2014a, b, c), Harfash (2015, 2016a, Harfash and Nashmi (2017), Challoob (2018, 2019); Harfash and Meften (2020), Meften (2018, 2019), Hameed and Harfash (2019) and Challoob et al (2020). In this method, system (3.4) is rewritten in terms of second-order derivatives only.…”