Convection in a horizontal layer of water with three diffusing components
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Convection in a horizontal layer of water with three diffusing components S. Pranesh1 · P. G. Siddheshwar2 · Sameena Tarannum1 · Vasudha Yekasi1 Received: 21 November 2019 / Accepted: 10 March 2020 © Springer Nature Switzerland AG 2020
Abstract 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. Keywords Three component convection · Aqueous salt solutions · Thermophysical properties · Nusselt and Sherwood number · Ginzburg–Landau equation Mathematics Subject Classification 76E06
1 Introduction Double diffusive convection is a well-studied topic when compared to systems with more than two components. Turner [1] was the first person to consider the two-component convection problem by considering heat and solute as two components having their influence on density and which lead to the instability of the system. Huppert and Turner [2] studied experimentally the influence of heat and salinity in Lake Vanda and concluded that the obtained experimental results are applicable to large scale motions. Double diffusive convection and its applications are well documented in the book by Turner [3]. Rudraiah and Siddheshwar [4] and Mokhtar and Khalidah [5] investigated the effects of cross-diffusion coefficients in a double diffusive system and they concluded that diffusive and finger
instabilities are possible by choosing suitable sign and magnitude of cross-diffusion coefficients. Motivated by the above works, Malashetty and Kollur [6], Malashetty et al. [7] and Narayana et al. [8] studied the effect of external constraints like magnetic field and rotation on the stability of a double diffusive system and concluded that these external constraints stabilize the system and reduce the heat and mass transports. The competing influences of various diffusing components on the onset of convection in a three-component system make it a very interesting problem. Griffiths [9] pioneered the study of the linear stability of a triple diffusive system in a horizontal fluid layer of infinite horizontal extent. Griffiths [10] and Griffiths [11] reported an experimental investigation of a three-component system and measured simultaneous fluxes of many dissolved solutes through the diffusive
* S. Pranesh,
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