Transient Double Diffusion in a Fluid Layer Extending Over a Permeable Substrate

The problem of transient double diffusion in a composite layer is studied numerically. The composite layer consists of a fluid region extending over a fluid-saturated permeable substrate. Initially, the fluid in the system is motionless, isothermal, and stably stratified with a linear salt distribution. A constant uniform heat flux is then suddenly applied to the bottom wall of the system. The resulting coupled flow, temperature, and concentration fields as they evolve in time are obtained numerically. The flow in the fluid region was determined by solving the complete form of the two-dimensional laminar governing equations subjected to the usual Boussinesq approximations. The flow in the porous region was modeled using the general flow model, which includes both the effects of macroscopic shear (Brinkman effect) and flow inertia (Forchheimer effect). Interesting results were obtained and are presented in a systematic manner so as to document the effect of changing the important system parameters, which include the height of the permeable substrate, its permeability, and the ratio of the thermal to the solutal Rayleigh number. It was found that these parameters had a major impact on the system behavior and their effects are thoroughly discussed.