THERMAL INSTABILITY AND CONVECTION IN A HORIZONTAL LAYER OF TWO IMMISCIBLE FLUIDS WITH INTERNAL ENERGY GENERATION

Results are reported on experimental and theoretical investigations of thermal convection in a horizontal layer composed of two immiscible fluids with uniform internal energy generation in the lower sublayer. A linear stability analysis, numerical study, and experimental measurements are presented, and an attempt to utilize the overall results to develop a general semi-empirical heat transfer correlation has been made. The fluid layer is bounded from below by a rigid, insulated surface and from above, by a rigid isothermal surface. The fluid in the upper sublayer is varied to provide a range of property values, i.e., heptane over water and silicone oil over water are systems used.; In the stability analysis, conditions for the onset of convection via the linearized perturbation approach are obtained by evaluation of a determinant of a matrix comprising two working matrices that are associated with each fluid sublayer. A simple explicit finite-difference technique is used for the numerical solution of the partial differential equations governing the temperature and flow fields. Results are obtained for Rayleigh numbers up to 10('8), and it is also shown how different treatments of the sublayer interface can affect the flow and temperature fields. Experimental measurements of transient and steady convection up to Rayleigh number of 2 x 10('11) in the internally heated sublayer are presented for both the silicone oil-water and heptane-water systems. Time averaged temperature profiles suggest a flow field nearly like that of Rayleigh-Benard convection in the upper sublayer and a flow field entirely similar to that of an internally heated layer without a superimposed fluid in the lower sublayer. The Nusselt number is generally found to be dependent on the sublayer thickness ratio over the entire range of Rayleigh numbers investigated. A thin upper sublayer first decreases the Nusselt number at a given Rayleigh number; a minimum value is reached and, thereafter, the Nusselt number increases when the upper sublayer thickness is increased. Through a combination of the results of the stability analysis, numerical analysis, and the experiments a semi-empirical expression is developed for the Nusselt number as the function of the Rayleigh number and sublayer thickness ratio from the conduction to the turbulent regimes of convection. This expression is in good agreement with the experimental results on overall Nusselt number.