Synchronous and asynchronous boundary temperature modulations of Bénard–Darcy convection

Siddheshwar, P. G.; Bhadauria, B. S.; Suthar, Om P.

doi:10.1016/j.ijnonlinmec.2012.09.006

Cited by 31 publications

(19 citation statements)

References 28 publications

(32 reference statements)

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“…We also can observe our results in Fig. 9 are the results which are similar to Siddheshwar et al [49] for the Newtonian fluid case. It is clear that for temperature modulation the boundary temperatures should not be in in-phase modulation (synchronized), where the effect of modulation is negligible on heat transport.…”

Section: Nonlinear Throughflow Effects Under Modulationsupporting

confidence: 91%

“…(21) and (22) are obtained by Lapwood [47], Siddheshwar et al [48,49], Bhadauria et al [28] for Pe ¼ 0 and isotropic porous medium.…”

Section: Amplitude Equation For Stationary Instabilitymentioning

confidence: 77%

“…We also have presented our results (according to Siddheshwar et al [49]) on mean Nusselt number (Nu), which depends on both the phase difference h and frequency x of modulation than only on the choice of the small amplitude modulation. Fig.…”

Section: Nonlinear Throughflow Effects Under Modulationmentioning

confidence: 99%

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Nonlinear throughflow effects on thermally modulated porous medium

Kiran

Bhadauria

2016

Ain Shams Engineering Journal

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Effect of vertical throughflow on Darcy convection has been investigated subject to timeperiodic temperature modulation of the boundaries. The amplitudes of temperature modulation at the lower and upper surfaces are considered to be very small, and the disturbances are expanded in terms of power series of amplitude of convection. A weak nonlinear stability analysis has been performed for the stationary mode of convection, and heat transport in terms of the Nusselt number, which is governed by the non-autonomous Ginzburg-Landau equation, is calculated. The effect of vertical throughflow is found to be either to destabilize or stabilize the system for downward or upward throughflows in the case of impermeable boundary conditions. The effect of amplitude and frequency of modulation, Prandtl-Darcy number on heat transport has been analyzed and depicted graphically. Further, the study establishes that the heat transport can be controlled effectively by a mechanism that is external to the system. Ó 2015 Faculty of Engineering, Ain Shams University. Production and hosting by Elsevier B.V. This is an open access article under the CC BY-NC-ND license (http://creativecommons.org/licenses/by-nc-nd/4.0/).

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Section: Nonlinear Throughflow Effects Under Modulationsupporting

confidence: 91%

“…(21) and (22) are obtained by Lapwood [47], Siddheshwar et al [48,49], Bhadauria et al [28] for Pe ¼ 0 and isotropic porous medium.…”

Section: Amplitude Equation For Stationary Instabilitymentioning

confidence: 77%

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Nonlinear throughflow effects on thermally modulated porous medium

Kiran

Bhadauria

2016

Ain Shams Engineering Journal

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“…Siddheshwar et al [53] show the effect of temperature modulation on mean Nusselt number Eq. (41) depends on both the phase difference / and frequency X of modulation than only on the choice of the small amplitude (d) modulation.…”

Section: Only Lower Boundary Modulated (Lbmo) ð/ ¼ àI1þmentioning

confidence: 99%

Throughflow and non-uniform heating effects on double diffusive oscillatory convection in a porous medium

Kiran

2016

Ain Shams Engineering Journal

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A weak nonlinear oscillatory mode of thermal instability is investigated while deriving a non autonomous complex Ginzburg-Landau equation. Darcy porous medium is considered in the presence of vertical throughflow and time periodic thermal boundaries. Only infinitesimal disturbances are considered. The disturbances in velocity, temperature and solutal fields are treated by a perturbation expansion in powers of amplitude of applied temperature field. The effect of throughflow has either to stabilize or to destabilize the system for stress free and isothermal boundary conditions. Nusselt and Sherwood numbers are obtained numerically and presented the results on heat and mass transfer. It is found that, throughflow and thermal modulation can be used alternatively to control the heat and mass transfer. Further, it is also found that oscillatory flow enhances the heat and mass transfer than stationary flow. Effect of modulation frequency and phase angle on mean Nusselt number is also discussed. Ó 2015 Faculty of Engineering, Ain Shams University. Production and hosting by Elsevier B.V. This is an open access article under the CC BY-NC-ND license (http://creativecommons.org/licenses/by-nc-nd/4.0/).

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“…(35), we use the standard Fredholm solvability condition, which requires that the right-hand side lie in the kernel of the operator. Applying the solvability condition [18,21,22] to the second-order system (35), the correction Rayleigh number Ra (2) c can be, on rearrangement, obtained in the form…”

Section: Linear Stability Analysismentioning

confidence: 99%

A study on the onset of thermally modulated Darcy–Bénard convection

2016

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A stability analysis of linearized Rayleigh-Bénard convection in a densely packed porous layer was performed using a matrix differential operator theory. The boundary temperatures were assumed to vary periodically with time in a sinusoidal manner. The correction in the critical Darcy-Rayleigh number was computed and depicted graphically. It was shown that the phase difference between the boundary temperatures rather than the frequency of modulated temperatures decides the nature of influence of modulation on the onset of convection. Conclusions were drawn regarding the possible transitions from harmonic to subharmonic solutions. The results on the onset of thermally modulated convection in a rectangular porous enclosure were obtained using those on the modulated Darcy-Bénard convection.

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Synchronous and asynchronous boundary temperature modulations of Bénard–Darcy convection

Cited by 31 publications

References 28 publications

Nonlinear throughflow effects on thermally modulated porous medium

Nonlinear throughflow effects on thermally modulated porous medium

Throughflow and non-uniform heating effects on double diffusive oscillatory convection in a porous medium

A study on the onset of thermally modulated Darcy–Bénard convection

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