Cavity flow in a porous medium driven by differential heating

On the boundary layer structure of differentially heated cavity flow in a stably stratified porous medium

“…Figure 4 shows the solution for τ = 0.213 and R = 1000. In this case the solution consists of a single-cell circulation with an almost-constant temperature core, and is similar to that obtained with an insulated lower boundary (Daniels & Punpocha 2004). In fact for the upper surface profile (2.7), τ c = 0.213 is a critical value of τ for high-Darcy-Rayleigh-number flows: for τ > τ c the flow appears to enter a complex and potentially unstable regime for sufficiently high values of R, whereas for τ < τ c it enters the stably stratified regime typified by the results of figures 2 and 3.…”

On the boundary-layer structure of cavity flow in a porous medium driven by differential heating

“…Clearly a local maximum of φ ∞ is inevitable if, as will be shown below, φ ∞ → 0 at the lower edge of the horizontal boundary layer. The occurrence of a maximum of θ ∞ is also supported by an exact solution of the horizontal boundary-layer system (3.3)-(3.7), in the case where S is given by (2.10), reported by Daniels & Punpocha (2004):…”

“…Numerical solutions of the above problem have been reported by Daniels & Punpocha (2004) for a wide range of Darcy-Rayleigh numbers and aspect ratios, and for both quadratic and cosine temperature distributions at the upper surface. These show that as the Darcy-Rayleigh number increases, a boundary-layer structure emerges, with the main variation in temperature occurring near the upper surface and driving a single-cell circulation about a point near the upper cold corner.…”

“…In many cases of practical interest, the Darcy-Rayleigh number R, which characterizes the importance of buoyancy forces relative to frictional forces, is large. In a previous paper (Daniels & Punpocha 2004), steady-state solutions have been found for the motion generated within a two-dimensional rectangular cavity of aspect ratio L (width/height) by differential heating of the upper surface. If the heating is monotonic and the other three walls of the cavity are thermally insulated, a single-cell circulation is generated, the centre of which moves towards the upper cold corner of the cavity as the Darcy-Rayleigh number increases.…”

Shallow cavity flow in a porous medium driven by differential heating

“…The simplest situation to consider is where only the upper surface is heated, with the other three acting passively as thermal insulators. Progress with this problem has been made by Daniels & Punpocha (2004) who reported numerical solutions for Darcy-Rayleigh numbers in the range 0 < R 6 5000 and aspect ratios 1 4 for monotonic differential heating a single-cell circulation is generated, the centre of which moves towards the upper cold corner of the cavity as R increases. The asymptotic structure of the flow for finite L and large R has been described by Daniels & Punpocha (2005).…”