Double Convection of a Binary Viscoelastic Fluid under Helical Force Effect: Linear and Weakly Nonlinear Analysis

Kpossa Gbedode Mathieu¹ and Monwanou Vincent Adjimon^1,

¹Institut de Mathématiques et de Sciences Physiques (IMSP), Laboratoire de la Mécanique des Fluides, de la Dynamique Non linéaire et de la Modélisation des Systèmes Biologiques (LMFDNMSB), Porto-Novo, Bénin

Cite this paper:
Kpossa Gbedode Mathieu and Monwanou Vincent Adjimon. Double Convection of a Binary Viscoelastic Fluid under Helical Force Effect: Linear and Weakly Nonlinear Analysis. International Journal of Physics. 2022; 10(4):193-203. doi: 10.12691/ijp-10-4-2

Abstract

We used linear stability theory based on the normal mode decomposition technique to study the criterion of appearance of the stationary convection and the oscillatory convection in a binary viscoelastic fluid mixture in a porous medium under the effect of helical force. Nonlinear stability theory based on the minimum representation of double Fourier series is used to study the rate of heat and mass transfer. We have determined the analytical expression of the Rayleigh number of the system as a function of the dimensionless parameters. Expressions for heat and mass transfer rates are determined as a function of Nusselt and Sherwood number, respectively. The transient behaviors of the Nusselt number and the Sherwood number are studied by solving the finite amplitude equations using the Runge - Kutta method. Then, the effect of each dimensionless parameter on the system is studied pointed out interesting results.

Keywords:
helical force stationary convection oscillatory convection viscoelastic fluid porous medium stability theory

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