Simulations of onset of convection in a non-newtonian liquid induced by unsteady-state heat conduction - Ting, Kee Chien (2001)
The onset of convection in an initially static non-Newtonian liquid under Fixed Surface Temperature (FST) and Constant Heat Flux (CHF) boundary conditions was simulated using a CFD package. Steady-state and unsteady-state simulations were successfully conducted for bottom surface heating of shear thinning non-Newtonian liquids. Simulations on Newtonian liquid water and glycerine were conducted to verify the simulation setup. Fourier's law of heat conduction was used to validate the steady-state simulation results. Simulations conducted for non-Newtonian liquid with Tien et al.'s (1969) experimental data were found to agree well with Fourier's law at conduction phase. Tien et al.'s definition of non-Newtonian power-law Rayleigh number was found to be inadequate in representing the onset of convection in non-Newtonian liquid. Attempts to determine the Rayleigh number for non-Newtonian liquid using apparent viscosity was successfully carried out. A more realistic critical Rayleigh number for non-Newtonian liquid was successfully determined with local values of Rayleigh number around a convection cell successfully obtained. For simulations conducted for unsteady-state heat conduction in non-Newtonian liquid, transient heat conduction theory was used to validate the results. Convection was found to occur in a continuous deep fluid bounded by two horizontal rigid surfaces and adiabatic vertical walls. Transient critical Rayleigh number for non-Newtonian liquid under unsteady state heat conduction defined by Tan (1994) was successfully applied. Transient critical Rayleigh number for non-Newtonian liquid was found to vary with flow behavior n of the Power Law model. A more realistic transient critical Rayleigh number for non-Newtonian liquid was successfully determined using apparent viscosity. Development of thermal plumes in viscous non-Newtonian liquid were found to differ slightly from the development of thermal plumes in non-viscous Newtonian liquid. The NUmax for unsteady-state simulations of Newtonian and non-Newtonian liquid were observed to be 3.8 ± 2.0 for FST cases and 2.7 ± 1.8 for CHF cases. Effect of boundary condition at interface on onset of transient convection were studied. Velocity boundary condition of a top surface solid were found to be best approximated using top-cooling simulations. Bottom-heating simulations in a deep fluid revealed that the upper interface boundary has the property between a solid and a free surface.