Triple diffusive convection in water is modelled with properties like density, specific heat, thermal conductivity, thermal diffusivity and thermal expansion, modified in the presence of salts. The Ginzburg-Landau equation is derived to study heat and mass transports of different combinations of salts in water. A table is prepared documenting the actual values of thermophysical properties of water with different salts and the critical Rayleigh number is calculated. This information is used in the estimation of Nusselt and Sherwood numbers and their relative magnitudes are commented upon. A detailed study on different single, double and triple diffusive systems is done and comparison is made of the results. The local nonlinear stability analysis made via a Ginzburg-Landau model mimics many properties of the original governing equations, namely, Hamiltonian character and a bounded solution.
The influence of sinusoidal (trigonometric cosine [TC]) and nonsinusoidal waveforms (square, sawtooth, and triangular) of internal heat source modulation on triple diffusive convection in viscoelastic liquids is investigated. An Oldroyd-B type model is taken into account for viscoelastic liquids. Nonlinear analysis is carried out using a truncated representation of the Fourier series. To analyze the heat and mass transfer over a triply diffusive liquid layer, expressions for average Nusselt and average Sherwood numbers are derived using 8-mode generalized Lorenz equations. The transient behavior of Nusselt and Sherwood numbers is analyzed on different parameters of the problem. From the results, it is found that the internal heat source enhances the heat transfer and diminishes the mass transfer while the heat sink diminishes the heat transfer and enhances the mass transfer. The results for respective waveforms are obtained for each parameter and it is found that the maximum heat and mass transfer occurs due to TC waveform. The limiting cases of viscoelastic liquids (Newtonian, Oldroyd-B, Maxwell, and Rivlin-Ericksen) have been tabulated and corresponding results for each of the waveforms on heat and mass transfer have been shown.
A linear stability analysis is carried out for triple diffusive convection in Oldroyd-B liquid. The expressions of Rayleigh number for stationary and oscillatory convection has been obtained. The neutral curves for oscillatory mode for different values of stress relaxation parameter, strain retardation parameter, solute Rayleigh numbers, ratio of diffusivity of solutes and heat diffusivity and Prandtl number has been examined. It is found that the oscillatory triple diffusive convection sets in earlier in system with Oldroyd-B liquid as compared to Newtonian liquid system.
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