A numerical treatment of the natural convection and passive dispersion in symmetrically interconnected tilted layers embedded in a rock which is subject to a constant vertical temperature gradient is presented. Such a system is a faithful model of configurations commonly found in the geophysical context. There, flow movements and temperature distributions are closely connected to phenomena of interest such as transport of contaminants and diagenesis. The important case of large thermal conductivity of the rock compared with that of the material filling the layer is discussed in order to show the decisive role of the temperature distribution and the geometrical parameters on the convective flow. The present analysis treats two cases, the fluid-filled layer and the saturated porous layer. Convective flows were calculated for small Rayleigh numbers and the resulting velocity fields were included in the analysis of the transport of a passive contaminant that was initially located where layers connect with each other. Transport of contaminants in the isotropic porous layer was studied by using a model which includes hydrodynamic dispersion terms. How far the tracer transports through the layers and the rate the tracer enters into the system were analysed. The influence of the angle of tilt has also been included. The molecular diffusive Péclet number which relates convective to diffusive species transport is closely associated to a considerable transporting rate, and for the porous layer the hydrodynamic dispersion appears to be an important effect to consider.