Abstract
In this paper, we consider the steady-state base flow for natural convection in a vertical porous slab with permeable boundaries. Although recent work proposed a one-dimensional solution for this flow, we make a strong case for this flow to be two-dimensional; this centres on an oversight in the use of the Oberbeck–Boussinesq approximation in the earlier work. Two-dimensional numerical solutions for this flow are then obtained using a pressure–temperature formulation, and the results are backed up using asymptotic analysis. The relevance of these findings to other recent work on the stability of convection in porous slabs with permeable boundaries is also briefly discussed.
Highlights
Variants of the problem of natural convection in a porous vertical slab where there is a temperature differential between the vertical bounding planes, both of which are impermeable, have been considered by numerous authors since the original work by Gill (1969); for a summary, see Barletta (2015)
There has been interest in the problem when both bounding planes are permeable, in particular since this situation is believed to be of relevance to systems such as ‘breathing walls’ (Imbabi 2006; Barletta 2015; Alongi, Angelotti & Mazzarella 2021), which are a novel concept in the building industry that is aimed at achieving better indoor air quality by allowing air inflow/outflow through insulated building walls
Our purpose is to investigate whether the steady-state base flow is one-dimensional when the bounding planes are permeable; for simplicity, we limit ourselves to the case of a porous vertical slab
Summary
Variants of the problem of natural convection in a porous vertical slab where there is a temperature differential between the vertical bounding planes, both of which are impermeable, have been considered by numerous authors since the original work by Gill (1969); for a summary, see Barletta (2015). There have appeared many works that have considered porous layers with permeable boundaries, all of which have used a one-dimensional steady-state base flow (Barletta 2016; Celli, Barletta & Rees 2017; Barletta & Celli 2018; Barletta & Rees 2019). Our purpose is to investigate whether the steady-state base flow is one-dimensional when the bounding planes are permeable; for simplicity, we limit ourselves to the case of a porous vertical slab.
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