Abstract

The nonlinear analysis using the finite volume method is carried in a thin rectangular domain filled with liquid gallium having stress-free horizontal isothermal boundaries for stationary convection. The length of the front horizontal faces is 60 mm and the lateral faces have a small thickness of 0.5 mm with the depth of 15 mm. The results are simulated for the range of Rayleigh numbers (Ra), starting from critical Rac (threshold) to 10Rac to analyze the flow structure of the convective system. At the onset, Ra=Rac, the mean temperature profile is linear and nonlinear for Ra>Rac. The Nusselt number (Nu) values obtained using direct numerical simulations coincide with the analytical results until 5Rac. For further higher values of Ra>5Rac the deviation between the theoretical and computational results are observed. In the range of 2Rac <= Ra <= 5Rac, the wavelength of a cell varies from 2.6 to 3 and accordingly the wavenumber decreases from 2.41 to 1.57. With the augmenting Ra the isotherms show the mushroom-like spreading of cold-descending and warm-ascending currents. The synergy (coordination) between velocity vector and temperature gradient at 5Rac showed the presence of two sets of anchor shaped profiles of the synergy coefficient. Each set is occupied by the positive and negative synergy coefficients (angle between the velocity and the temperature gradient). These anchor shaped profiles become thinner as Ra increases. The positive and negative regions of the synergy coefficient profiles get interchanged between 9Rac and 10Rac.