Stability of Magneto Double Diffusive Convection in Couple Stress Liquid with Chemical Reaction

Document Type : Full Length Research Article

Authors

1 Department of Mathematics, Central University of Jharkhand, Ranchi, 835222, India

2 Department of Mathematics, Sarala Birla University, Ranchi, 835103, India

Abstract

The effect of chemical reaction and external vertical magnetic field on the onset of the double diffusive convection in couple stress fluid between infinite horizontal parallel plates  has been studied.  The effectiveness of vertical magnetic field and chemical reaction were gauged by determining the values of  Chandrashekhar number (Q) and Damk hler number  in terms of other controlling parameters and shown their effect on stability of system through graphs. The entire investigation is performed in two parts: linear and weakly non-linear stability analysis. A comparative study is presented in stationary case of linear stability analysis for four types of bounding surfaces: (a) Realistic bounding surfaces i.e. Rigid-Rigid, Rigid-Free and Free-Rigid (R/R, R/F and F/R) (b) Non Realistic bounding surface i.e. Free-Free (F/F). However, oscillatory case and weakly non-linear stability analysis are restricted for Free-Free (F/F) boundary surfaces. Graphical representations are used to illustrate how different parameters affect stationary, oscillatory, finite-amplitude states and  the amount of heat and mass transfer. By analysing the linear stability analysis, it is observed that the onset of convection is more dominant in oscillatory case than stationary. The stability criteria for Q came out as (in decreasing order) F/F>F/R>R/R>R/F which is different from the criteria came out for rest of the controlling parameters i.e F/R>R/R>F/F>R/F in stationary case. It is also reported that the Q, Couple stress parameter (C) and ratio of heat capacities on heat transfer  is responsible for the delay of the onset of convection while  (impact of chemical reaction) enhances the onset of convection. Non-linear stability analysis using the truncated representation of Fourier series method predicts the occurrence of sub-critical instability in the form of finite amplitude motion. The effect of Q, Lewis number Le, and solute Rayleigh number RaS, increased the amount of heat and mass transfer while C decreased. We also draw streamlines, isotherms, isohalines and magnetic streamlines for different time intervals (unsteady) i.e. for (0.01, 0.03, 0.009, 0.006) and showed the pattern of the onset of convection.

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References

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  • Receive Date: 22 March 2023
  • Revise Date: 01 November 2023
  • Accept Date: 02 November 2023

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