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Our limited knowledge of convection and its poor representation in climate models is one of the factors that most hamper our ability to understand and predict the climate system. In this thesis, the dynamics of shallow cumulus convection are probed using Large-eddy simulations (LES) and simple models. / Earth and Planetary Sciences

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A basic physical model of electrodecantation has been developed and tested. Experimental data of Belongia (1999) were used to compare with computational results obtained from the model. The model was developed to calculate the transient velocity field, electric potential and particle distribution for the parameter space encountered in stable colloidal dispersions. The model included the effects of a spatially nonuniform electric field that existed in the experiments of Belongia (1999) because of the type and position of the electrodes used. As a result, the model required numerical methods for its solution. The problem was found to depend largely on three dimensionless groups: Re, a Reynolds number, Pe an electric Péclet number and ¤ a large dimensionless parameter denoting the Grashof number divided by the Reynolds number. Because A^(1/3) >> 1, nonuniform computational meshes were needed to resolve the exceedingly thin natural convection boundary layers that occur. Additionally, because Pe >> 1, a flux-limiting (FCT) numerical method was used to solve the particle transport equation. Results from the basic physical model show excellent agreement with the scaling of the experimental data but exhibit about 80% relative error when compared with experimental data on the decantation time. Consequently, a physicochemical model of electrodecantation was developed to include electrical conductivity variations that develop as ions transport during electrodecantation. Results show markedly better agreement (about 10% relative error) with experimental data concerning the decantation rate. Additionally, the physicochemical model is able to predict the pH and electrical conductivity stratification that was measured experimentally by Belongia (1999). A problem concerning the electrohydrodynamic deformation of miscible fluids, with differing electromechanical properties (electrical conductivity and dielectric constant), was also investigated. Numerical results predicting the sense and extent of deformation for various values of the two fluids’ electrical conductivity ratio compare well (less than 10% relative error) with measurements by Rhodes, et al. (1989). The role of dielectric constant differences in electrohydrodynamic deformations was also investigated. It was determined that an O(1) difference in the fluids’ dielectric constants is necessary to produce electrohydrodynamic deformations on the time scales reported by Rhodes, et al. (1989) and Trau, et al. (1995).

The effects of gravity modulation on the instability of double-diffusive convections in a horizontal tank with aspect ratio (width/height) of 11 have been investigated by experiments and numerical simulations. The stably stratified fluid layer is set up with ethanol-water solution of 0.0 and 2.0% (by weight). The tank is fixed on a platform that can oscillate in the vertical direction. A constant temperature difference is maintained across the tank at thermal Rayleigh number . The fluid layer becomes unstable as the initially stable solute gradient slowly decreases due to the non-diffusive boundary conditions. The experiments determine that the instability onset under steady gravity is at with onset vortices of wavelength and oscillatory frequency . When the tank is oscillated at modulation frequency and amplitude , the fluid layer is destabilized slightly with a critical and onset vortices of and . A two-dimensional numerical simulation has accurately reproduced the experimental results of steady gravity, and demonstrated that the slight destability effect of gravity modulation is contributed by the asymmetry of the actual gravity modulation.Further simulations have yielded following results: (1) Under steady gravity, the kinetic energy and mechanical work components oscillate synchronously with . Under modulated gravity, they only oscillate synchronously with when is low, whereas not only synchronously with locally but also synchronously with globally when is high; (2) The resonance phenomenon predicted by Chen (2001) also exists under the present lab conditions. Such instability is in the sub-harmonic mode and the destability effect increases as increases. (3) The double-diffusive fluid layer may experience density-mode instability before the double-diffusive instability onset at certain and . Such density-mode instability is generally in the sub-harmonic mode, although it may be in the synchronous mode when is low and is large. This instability accelerates the mixing of the density gradient across the fluid layer and thus affects the succeeding double-diffusive instability; (4) When the background gravity is absent, the purely modulated gravity destabilizes the fluid layer when is low. On the contrary, it stabilizes the fluid layer when is high and the instability onset is in the synchronous mode.

Numerical simulations were used to investigate natural convection and radiation interactions in small enclosures of both two and three-dimensional geometries. The objectives of the research were to (1) determine the relative importance of natural convection and radiation, and to (2) estimate the natural convection heat transfer coefficients. Models are generated using Gambit, while numerical computations were conducted using the CFD code FLUENT. Dimensions for the two-dimensional enclosure were a height of 2.54 cm (1 inch), and a width that varied between 5.08 cm and 10.16 cm (2 inches and 4 inches). The three-dimensional model had a depth of 5.08 cm (2 inches) with the same height and widths as the two-dimensional model. The obstruction is located at the centroid of the enclosure and is represented as a circle in the two-dimensional geometry and a cylinder in the three-dimensional geometry. Obstruction diameters varied between .51 cm and 1.52 cm (0.2 inches and 0.6 inches). Model parameters used in the investigation were average surface temperatures, net total heat flux, and net radiation heat flux. These parameters were used to define percent temperature differences, percent heat flux contributions, convective heat transfer coefficients, Nusselt numbers, and Rayleigh numbers. The Rayleigh numbers varied between 0.005 and 300, and the convective heat transfer coefficients ranged between 2 and 25 W/m2K depending on the point in the simulation. The simulations were conducted with temperatures ranging between 310 K and 1275 K on the right boundary. For right boundary temperatures above 800 K, the estimated error on the obstruction temperature is less than 6.1% for neglecting natural convection and conduction from the heat transfer analysis. Lower right boundary temperatures such as 310 K had significant contributions, over 50%, from heat transfer modes other than radiation. For lower right boundary temperatures, a means of including natural convection should be included. When a bulk fluid temperature and average surface temperature values are available, a time average heat transfer coefficient of 6.73 W/m2K is proposed for simplifying the numerical calculations. In the transient right boundary temperature analysis, all modes of heat transfer other than radiation can be neglected to have an error below 8.1%.

In this dissertation we investigate free convective heat and mass transfer in micropolar fluid flow past a moving semi-infinite vertical porous plate in the presence of a magnetic field. The aim of this study was to use recent semi-numerical methods such as the successive linearisation method and the spectral-homotopy analysis method to study the effects of viscous heating and the effects of different fluid parameters. The governing boundary layer equations for linear momentum, angular momentum (microrotation), temperature and concentration profiles are transformed to a system of ordinary differential equations and solved using the successive linearisation method and the spectral-homotopy analysis method. The accuracy of the solutions was determined by comparison with numerical approximations obtained using the Matlab bvp4c solver. The influences of the micropolar parameter, Darcy number, Prandtl number, Schmidt number, magnetic parameter, heat absorption parameter, Soret and Dufour numbers, local Reynolds number and Grashof number on velocity, microrotation, temperature and concentration profiles were determined. The results obtained are presented graphically and in tabular form. / Thesis (M.Sc.)-University of KwaZulu-Natal, Pietermaritzburg, 2012.

A steady state two-dimensional mixed convection problem in an air filled square unit cavity has been numerically investigated. Two different cases of heating are investigated and compared. In the first case, the bottom wall was uniformly heated, the side walls were linearly heated and the top moving wall was heated sinusoidally. The second case differed from the first in that the side walls were instead uniformly cooled. This investigation is an extension of the work by Basak et al. [6, 7] who investigated mixed convection in a square cavity with similar boundary conditions to the cases listed above with the exception of the top wall which was well insulated. In this dissertation, their work is extended to include a sinusoidally heated top wall. The nonlinear coupled equations are solved using the Penalty Galerkin Finite Element Method. Stream function and isotherm results are found for various values of the Reynolds number and the Grashof number. The strength of the circulation is seen to increase with increasing Grashof number and to decrease with increasing Reynolds number for both cases of heating. A comparison is made between the stream function and isotherm results for the two cases. The results for the rate of heat transfer in terms of the Nusselt number are discussed. Both local and average Nusselt number results are presented and discussed. The average Nusselt number is found using Simpson's 1/3rd rule. The rate of heat transfer is found to be higher at all four walls for the case of cooled side walls than that of linearly heated side walls. / Thesis (M.Sc.)-University of KwaZulu-Natal, Pietermaritzburg, 2010.

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