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 ((Formula presented.)), starting from critical (Formula presented.) (threshold) to 10 (Formula presented.) to analyze the flow structure of the convective system. At the onset, (Formula presented.) the mean temperature profile is linear and nonlinear for (Formula presented.) The Nusselt number (Nu) values obtained using direct numerical simulations coincide with the analytical results until 5 (Formula presented.) For further higher values of (Formula presented.) the deviation between the theoretical and computational results are observed. In the range of 2 (Formula presented.) Ra (Formula presented.) 5 (Formula presented.) 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 (Formula presented.) the isotherms show the mushroom-like spreading of cold-descending and warm-ascending currents. The synergy (coordination) between velocity vector and temperature gradient at 5 (Formula presented.) 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 (Formula presented.) increases. The positive and negative regions of the synergy coefficient profiles get interchanged between 9 (Formula presented.) and 10 (Formula presented.). © 2024 Taylor & Francis Group, LLC.