Boundary and thermal non-equilibrium effects on the onset of Darcy–Brinkman convection in a porous layer

Abstract

A local thermal non-equilibrium model for the temperature representing the solid and fluid phases separately is used to study the onset of free convection in a sparsely packed porous layer using the Brinkman-extended Darcy model. The lower boundary of the porous layer is considered to be rigid and isothermal, while the upper isothermal boundary is assumed to be either rigid or free. The Galerkin method is used to obtain the eigenvalue equation, which is then solved numerically. The effects of thermal non-equilibrium and other physical parameters on the onset of convection are analyzed and compared for two types velocity boundary conditions considered. Besides, some known results available in the literature are compared with those obtained from the present study and good agreement is found.

Boundary and thermal non-equilibrium effects on convective instability in an anisotropic porous layer

“…The critical Darcy-Rayleigh numbers are found to converge to the desired degree of accuracy by taking seven terms (i.e., 7 n = ) in Eq. (13). The critical stability parameters computed for the isotropic case ( are compared with those of Guo and Kaloni [18] and Postelnicu [11] in Ta (see Fig.…”

“…Postelnicu [11] has studied the onset of Darcy-Brinkman convection using a LTNE model for rigid isothermal boundaries. Recently, Shivakumara et al [12,13] have analyzed temperature dependent viscosity and quadratic density as well as boundary effects on the onset of free convection in a porous layer using a LTNE model, whereas Lee et al [14] have discussed the effect of various forms of non-uniform basic temperature gradients on the problem to assess their impact on the criterion for the onset of convection.…”

Instability of a horizontal porous layer with local thermal non-equilibrium: Effects of free surface and convective boundary conditions

“…The analysis of the effects of LTNE on the Darcy-Bénard instability has been further developed in the last years considering several aspects such as modified boundary conditions, non-Darcy effects, internal heat generation, throughflow, mass diffusion, heterogeneous or anisotropic porous media, and inclination of the layer to the horizontal [10][11][12][13][14][15][16][17][18][19][20][21][22][23][24][25][26].…”

Effect of rotation on ferromagnetic porous convection with a thermal non-equilibrium model

“…Therefore, the recent trend in the study of thermal convective instability problems in porous media is to account for LTNE effects by considering a two-field model for energy equation each representing the fluid and solid phases separately. Copious literature is available on natural convection in an ordinary viscous fluid saturating a porous layer using a LTNE model (Rees and Pop [16], Nield and Bejan [17]; Shivakumara et al [18] and references therein). Nonetheless, limited attention has been given to assess LTNE effects on the criterion for the onset of ferromagnetic convection in a porous medium despite its relevance and importance in many heat transfer problems as mentioned above [19][20][21][22].…”