Thermoconvective instabilities in a horizontal porous annulus with an external wavy wall

This paper investigates the thermal instability in a horizontal porous annulus with an external wavy wall. The porous matrix is supposed to be filled by an incompressible fluid. The model that we consider includes the heat equation and the hydrodynamics equations under the Darcy law and Boussinesq approximation. The derived model with the temperature-stream function is solved numerically using the alternating direction implicit method. Our numerical results indicate that the heat transfer and the convective instability depend strongly on the waviness of the external cylinder. The results of this paper confirm that the heat transfer is enhanced when the waviness amplitude increases. It is noticed that the thermoconvective instabilities are strongly affected by the undulation number.

Figure 1

Schematic of the problem and coordinate system.

Figure 2

Average Nusselt number as function of $\eta$ for $\text{Ra}=100$ and different values of $\lambda$.

Figure 3

Streamlines (left) and isotherms (right) for $\lambda =\eta =0$.

Figure 4

Streamlines (left) and isotherms (right) for $\eta =30$ and different values of $\lambda$.

Figure 5

Critical Rayleigh number as a function of undulation number for different $\lambda$.