Dynamics of Newtonian Liquids with Distinct Concentrations Due to Time-Varying Gravitational Acceleration and Triple Diffusive Convection: Weakly Non-Linear Stability of Heat and Mass Transfer

Pervinder Singh, Vinod K. Gupta, Isaac Lare Animasaun (), Taseer Muhammad and Qasem M. Al-Mdallal
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Pervinder Singh: Department of Mathematics, School of Physical Sciences, DIT University, Dehradun 248009, India
Vinod K. Gupta: Department of Mathematics, School of Physical Sciences, DIT University, Dehradun 248009, India
Isaac Lare Animasaun: Fluid Dynamics and Survey Research Group, Department of Mathematical Sciences, Federal University of Technology, Akure PMB 704, Nigeria
Taseer Muhammad: Department of Mathematics, College of Science, King Khalid University, Abha 61413, Saudi Arabia
Qasem M. Al-Mdallal: Department of Mathematical Sciences, United Arab Emirates University, Al Ain PMB 15551, United Arab Emirates

Mathematics, 2023, vol. 11, issue 13, 1-20

Abstract: One of the practical methods for examining the stability and dynamical behaviour of non-linear systems is weakly non-linear stability analysis. Time-varying gravitational acceleration and triple-diffusive convection play a significant role in the formation of acceleration, inducing some dynamics in the industry. With an emphasis on the natural Rayleigh–Bernard convection, more is needed on the significance of a modulated gravitational field on the heat and mass transfer due to triple convection focusing on weakly non-linear stability analysis. The Newtonian fluid layers were heated, salted and saturated from below, causing the bottom plate’s temperature and concentration to be greater than the top plate’s. In this study, the acceleration due to gravity was assumed to be time-dependent and comprised of a constant gravity term and a time-dependent gravitational oscillation. More so, the amplitude of the modulated gravitational field was considered infinitesimal. The case in which the fluid layer is infinitely expanded in the x -direction and between two concurrent plates at z = 0 and z = d was considered. The asymptotic expansion technique was used to retrieve the solution of the Ginzburg–Landau differential equation (i.e., a system of non-autonomous partial differential equations) using the software MATHEMATICA 12. Decreasing the amplitude of modulation, Lewis number, Rayleigh number and frequency of modulation has no significant effect on the Nusselt number proportional to heat-transfer rates ( N u ), Sherwood number proportional to mass transfer of solute 1 ( S h 1 ) and Sherwood number proportional to mass transfer of solute 2 ( S h 2 ) at the initial time. The crucial Rayleigh number rises in value in the presence of a third diffusive component. The third diffusive component is essential in delaying the onset of convection.

Keywords: triple-diffusive convection; gravitational modulation; thermal Rayleigh number; Lewis number; solute Rayleigh number (search for similar items in EconPapers)
JEL-codes: C (search for similar items in EconPapers)
Date: 2023
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