Magneto-double diffusive convection in a viscoelastic fluid saturated porous layer with internal heat source

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.

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Linear and nonlinear double-diffusive convection in a saturated anisotropic porous layer with Soret effect and internal heat source

International Journal of Heat and Mass Transfer ◽

10.1016/j.ijheatmasstransfer.2012.12.005 ◽

2013 ◽

Vol 59 ◽

pp. 103-111 ◽

Cited By ~ 24

Author(s):

A.A. Altawallbeh ◽

B.S. Bhadauria ◽

I. Hashim

Keyword(s):

Heat Source ◽

Porous Layer ◽

Soret Effect ◽

Internal Heat ◽

Internal Heat Source ◽

Double Diffusive Convection ◽

Diffusive Convection ◽

Linear And Nonlinear ◽

Double Diffusive

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

Proceedings of The Royal Society A Mathematical Physical and Engineering Sciences ◽

10.1098/rspa.2004.1328 ◽

2005 ◽

Vol 461 (2054) ◽

pp. 561-574 ◽

Cited By ~ 43

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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