Linear and Nonlinear Double Diffusive Convection in a Couple Stress Fluid Saturated Anisotropic Porous Layer with Soret Effect and Internal Heat Source

2019 ◽  
pp. 429-448
Author(s):  
Kanchan Shakya
Keyword(s):  
Heat Source ◽  
Porous Layer ◽  
Couple Stress ◽  
Soret Effect ◽  
Internal Heat ◽  
Internal Heat Source ◽  
Double Diffusive Convection ◽  
Diffusive Convection ◽  
Linear And Nonlinear ◽  
Double Diffusive

Double Diffusive Convection in a Couple Stress Fluid Saturated Rotating Anisotropic Porous Layer with Internal Heating and Soret Effect.

2018 ◽  
Vol 10 (02) ◽  
pp. 121-136
Author(s):  
Ajay Singh ◽  
Kanchan Shakya
Keyword(s):  
Heat Source ◽  
Couple Stress ◽  
Soret Effect ◽  
Time Derivative ◽  
Internal Heat ◽  
Internal Heat Source ◽  
Mechanical Anisotropy ◽  
Double Diffusive Convection ◽  
Diffusive Convection ◽  
Double Diffusive

In this paper, the effect of internal heat source and Soret effect has been investigated on double diffusive convection in a rotating anisotropic porous medium saturated with a couple stress fluids, heated and salted from below. Linear stability analysis has been performed by using Normal mode technique and for nonlinear analysis, minimal representation of Fourier series up to two terms has been considered. The modified Darcy model, which includes the time derivative term and Coriolis term, has been employed in the momentum equation. The effect of Taylor number, couple stress parameter, solute Rayleigh number, internal heat source parameter, Lewis number, Darcy-Prandtl number, thermal and mechanical anisotropy parameter on the stationary and oscillatory modes of convection has been obtained and shown graphically, Also the heat and mass transports are obtained in terms of the Nusselt number and Sherwood number respectively, and shown graphically.

scholarly journals Linear and Nonlinear Stability Analysis of Double Diffusive Convection in a Maxwell Fluid Saturated Porous Layer with Internal Heat Source

2014 ◽  
Vol 2014 ◽  
pp. 1-12 ◽  
Author(s):  
Moli Zhao ◽  
Qiangyong Zhang ◽  
Shaowei Wang
Keyword(s):  
Rayleigh Number ◽  
Heat Source ◽  
Internal Heat ◽  
Internal Heat Source ◽  
Maxwell Fluid ◽  
Double Diffusive Convection ◽  
Diffusive Convection ◽  
Saturated Porous Layer ◽  
Linear And Nonlinear ◽  
Double Diffusive

The onset of double diffusive convection is investigated in a Maxwell fluid saturated porous layer with internal heat source. The modified Darcy law for the Maxwell fluid is used to model the momentum equation of the system, and the criterion for the onset of the convection is established through the linear and nonlinear stability analyses. The linear analysis is obtained using the normal mode technique, and the nonlinear analysis of the system is studied with the help of truncated representation of Fourier series. The effects of internal Rayleigh number, stress relaxation parameter, normalized porosity, Lewis number, Vadasz number and solute Rayleigh number on the stationary, and oscillatory and weak nonlinear convection of the system are shown numerically and graphically. The effects of various parameters on transient heat and mass transfer are also discussed and presented analytically and graphically.

Double–diffusive convection in a porous medium with a concentration based internal heat source

2005 ◽  
Vol 461 (2054) ◽  
pp. 561-574 ◽  
Author(s):  
Antony A. Hill
Keyword(s):  
Heat Source ◽  
Linear Theory ◽  
Internal Heat ◽  
Internal Heat Source ◽  
Boussinesq Approximation ◽  
Double Diffusive Convection ◽  
Diffusive Convection ◽  
Saturated Porous Layer ◽  
Linear And Nonlinear ◽  
Double Diffusive

Linear and nonlinear stability analyses of double–diffusive convection in a fluid–saturated porous layer with a concentration based internal heat source are studied. Darcy's law and the Boussinesq approximation are employed, with the equation of state taken to be linear with respect to temperature and concentration. Both the numerical and analytical analysis for the linear theory strongly suggest the presence of a critical value γ c , where γ is essentially a measure of the internal heat source, for which no oscillatory convection occurs when γ c ⩽ γ . This, in the present literature, appears to be an unobserved phenomenon. A nonlinear energy stability analysis demonstrates more comparable linear and nonlinear thresholds when the linear theory predicts the onset of fully stationary convection. However, irrespective of the γ value, the agreement of the thresholds does deteriorate as the solute Rayleigh number R c increases.

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