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Research Papers: Porous Media

# Combined Effect of Temperature Modulation and Magnetic Field on the Onset of Convection in an Electrically Conducting-Fluid-Saturated Porous Medium

[+] Author and Article Information

Department of Mathematics, Faculty of Science, Banaras Hindu University, Varanasi 321005, Indiadrbsbhadauria@yahoo.com

J. Heat Transfer 130(5), 052601 (Apr 10, 2008) (9 pages) doi:10.1115/1.2885871 History: Received December 11, 2006; Revised September 18, 2007; Published April 10, 2008

## Abstract

The effect of temperature modulation on the onset of thermal convection in an electrically conducting fluid-saturated-porous medium, heated from below, has been studied using linear stability analysis. The amplitudes of temperature modulation at the lower and upper surfaces are considered to be very small. The porous medium is confined between two horizontal walls and subjected to a vertical magnetic field; flow in porous medium is characterized by Brinkman–Darcy model. Considering only infinitesimal disturbances, and using perturbation procedure, the combined effect of temperature modulation and vertical magnetic field on thermal instability has been studied. The correction in the critical Rayleigh number is calculated as a function of frequency of modulation, Darcy number, Darcy Chandrasekhar number, magnetic Prandtl number, and the nondimensional group number $χ$. The influence of the magnetic field is found to be stabilizing. Furthermore, it is also found that the onset of convection can be advanced or delayed by proper tuning of the frequency of modulation. The results of the present model have been compared with that of Darcy model.

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## Figures

Figure 1

(a) The curves representing the marginal stability limit for Q=10.0, Prm=0.1, and Da=0.1; (b) As in (a) but for Q=100.0

Figure 2

(a) The curves representing the marginal stability limit for Q=10.0, Prm=0.1, and χ=1.0; (b) As in (a) but for Q=100.0

Figure 3

The stability map showing the division of the (Q, χ) plane into the zones of stationary and overstable

Figure 4

(a). Variation of R2c with ω; χ=1.0, Prm=1.0, and Da=0.1 and (b) variation of R2c with ω; χ=1.0, Prm=1.0, and Da=0.1

Figure 5

Variation of R2c with ω; χ=1.0, Prm=1.0, and Q=25.0

Figure 6

Variation of R2c with ω; Q=25.0, Prm=1.0, and Da=0.1

Figure 7

(a). Variation of R2c with ω; χ=1.0, Prm=1.0, and Da=0.1; (b) Variation of R2c with ω; χ=1.0, Prm=1.0, and Da=0.1

Figure 8

Variation of R2c with ω; χ=1.0, Prm=1.0, and Q=25.0

Figure 9

Variation of R2c with ω; Q=25.0, Prm=1.0, and Da=0.1

Figure 10

(a) Variation of R2c with ω; χ=1.0, Prm=1.0, and Q=25.0; (b) variation of R2c with ω; χ=1.0, Prm=1.0, and Q=25.0; and (c) variation of R2c with ω; χ=1.0, Prm=1.0, and Q=25.0

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