In this paper, an upscaling study of solid–fluid combustion in porous medium with homogeneous and heterogeneous heat sources is carried out using a volume averaging theory. For the sake of simplicity, the reaction rate is assumed to be of first-order Arrhenius type and convection is not taken into account. Local thermal non-equilibrium is considered between the solid and fluid phases. During th...

A major challenge in flow through porous media is to better understand the link between microstructure and macroscale transport. For idealised microstructures, mathematical framework of homogenisation theory can be used for this purpose. Here, we consider a two-dimensional comprising an array obstacles smooth but arbitrary shape, size spacing which vary along length medium. We use via method mu...

In the present paper, we have studied MHD free convective two dimensional unsteady viscous incompressible flows through a porous effect bounded by an infinite vertical porous plate with constant suction. The permeability of the porous medium fluctuates in time about a constant mean, and the viscosity of fluid is assumed to vary as a linear function of temperature. The flow is permitted under th...

The infinite Darcy-Prandtl number model is an effective reduced model for describing convection in a fluid-saturated porous medium. It is well known that the deterministic model does not possess a unique invariant measure. In this work we study the dynamics of the infinite Darcy-Prandtl number model, under an additive stochastic forcing of its low modes. This is the so-called stochastic infinit...