A thermal non-equilibrium model with Cattaneo effect for convection in a Brinkman porous layer

Abstract

a b s t r a c tThis paper aims to investigate the onset of thermal convection in a layer of fluid-saturated Brinkman porous medium taking into account fluid inertia and local thermal non-equilibrium (LTNE) between the solid and fluid phases with Cattaneo effect in the solid. A two-field model is used for the energy equations each representing the solid and fluid phases separately. The usual Fourier heat-transfer law is retained in the fluid phase while the solid phase is allowed to transfer heat via a Cattaneo heat flux theory. It is observed that the Cattaneo effect has a profound influence on the nature of convective instability. In contrast to the standard Brinkman convection with LTNE model, instability is found to occur through oscillatory convection depending on the value of solid thermal relaxation time parameter which in turn depends on other parametric values. The instability characteristics of the system are analyzed in detail for a wide range of parametric values including those for copper oxide and aluminium oxide solid skeletons.

Penetrative Brinkman ferroconvection via internal heating in high porosity anisotropic porous layer: influence of boundaries

“…To understand the heat transfer characteristics in a FF-saturated porous medium, FTC in a porous medium has also been studied extensively (Sekar et al [11], Shivakumara et al [12,13], Nanjundappa et al [14,15,16]). Besides, the implications of additional effects such as magnetic field dependent viscosity (Nanjundappa et al [17,18], Shivakumara et al [19,20]), rotation (Shivakumara et al [21], Nanjundappa et al [22]), internal heating (Nanjundappa et al [23,24]), throughflow (Nanjundappa et al [25]), non-uniform basic temperature gradients (Nanjundappa et al [26]), local thermal nonequilibrium (Shivakumara et al [27,28,29,30]), Cattaneo heat flux law (Shivakumara et al [31,32]) have also been investigated on FTC in porous media.…”

Numerical Study of Natural Convection Flow of Nanofluid Past a Circular Cone with Cattaneo–Christov Heat and Mass Flux Models

“…Kumar et al [29] studied the MHD flow over a cone and a wedge with the Cattaneo-Christov heat flux model and shows that the heat transfer rate in the fluid flow over a cone is higher than that of the flow over a wedge. Further, numerous researchers [30][31][32][33][34][35] used the Cattaneo-Christov heat flux model to formulate energy equations and discuss the flow and heat transfer phenomenon for different types of non-Newtonian fluids.…”

On cattaneo-christov heat flux analysis with magneto-hydrodynamic and heat generation effects in a Carreau nano-fluid over a stretching sheet

“…Haddad [33] examined the heat flux in a Brinkman porous channel embedded with fluid inertia. Shivakumara et al [34] observed the thermal convection with Cattaneo effects in the solid and found that its impacts on the nature of convective instability are efficient. Mustafa et al [35] studied the rotating flow upon linearly stretching disk.…”