Stability of an Anisotropic Porous Layer With Internal Heat Source and Brinkman Effects

Mahajan, Amit; Nandal, Reena

doi:10.1615/specialtopicsrevporousmedia.2018025396

Cited by 5 publications

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“…Although an internal heat source is capable of producing heat, a heat sink which is a negative heat source is capable of absorbing the excessive heat from a physical system. Many researchers [40][41][42][43][44][45][46][47][48] investigated the influence of heat sources in convection processes. Internal heat source modulation by considering a sine wave in natural convection is examined by Bazylak et al 49 where a layer of heat sources are distributed and the results show a good indication of heat transfer when a slight decrease in the temperature is noticed.…”

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confidence: 99%

Heat and mass transfer of triple diffusive convection in viscoelastic liquids under internal heat source modulations

2021

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The influence of sinusoidal (trigonometric cosine [TC]) and nonsinusoidal waveforms (square, sawtooth, and triangular) of internal heat source modulation on triple diffusive convection in viscoelastic liquids is investigated. An Oldroyd-B type model is taken into account for viscoelastic liquids. Nonlinear analysis is carried out using a truncated representation of the Fourier series. To analyze the heat and mass transfer over a triply diffusive liquid layer, expressions for average Nusselt and average Sherwood numbers are derived using 8-mode generalized Lorenz equations. The transient behavior of Nusselt and Sherwood numbers is analyzed on different parameters of the problem. From the results, it is found that the internal heat source enhances the heat transfer and diminishes the mass transfer while the heat sink diminishes the heat transfer and enhances the mass transfer. The results for respective waveforms are obtained for each parameter and it is found that the maximum heat and mass transfer occurs due to TC waveform. The limiting cases of viscoelastic liquids (Newtonian, Oldroyd-B, Maxwell, and Rivlin-Ericksen) have been tabulated and corresponding results for each of the waveforms on heat and mass transfer have been shown.

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confidence: 99%

Heat and mass transfer of triple diffusive convection in viscoelastic liquids under internal heat source modulations

2021

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“…Other works including internal heat generation in porous media with anisotropy are presented in [25,26]. Research specifically involving the effects of gravity modulation and internal heat generation in porous media are presented in [25][26][27][28]. Readers are also referred to two important books [29,30] for further review/reading.…”

Section: Introductionmentioning

confidence: 99%

Vadasz Number Effects on Convection in a Horizontal Porous Layer Subjected to Internal Heat Generation and G-Jitter

Govender

2020

Fluids

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Flow and heat transfer in a horizontal porous layer subjected to internal heat generation and g-jitter is considered for the Dirichlet thermal boundary condition. A linear stability analysis is used to determine the convection threshold in terms of the critical Rayleigh number. For the low amplitude, high frequency approximation, the results show that vibration has a stabilizing effect on the onset of convection when the porous layer is heated from below. When the porous layer is cooled from below and heated from above, the vibration has a destabilizing effect in the presence of internal heat generation. It is also demonstrated that when the top and bottoms walls are cooled and rigid/impermeable, the critical Rayleigh number is infinitely large and conduction is the only possible mode of heat transfer. The impact of increasing the Vadasz number is to stabilize the convection, in addition to reducing the transition point from synchronous to subharmonic solutions.

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“…Nouri-Borujerdi et al [14] relaxed the assumption of local thermal equilibrium between the phases. In addition Mahajan and Nandal [19] considered how anisotropy and Brinkman effects alter the stability criteria, while Yadav et al [20] consider the combined effects of rotation and the Brinkman terms. We also mention some works which include anisotropy but with heating from below: Malashetty and Swamy [21] and Yavogan et al [22] both analysed the effect of a viscoelastic fluid and obtained an analytical expression for the critical Darcy-Rayleigh number, Raghunatha et al [23] considered the case when the porous medium is saturated by an Oldroyd-B fluid, Abdelhafez and Tsybulin [24] who considered the presence of a binary fluid, Yadav and Kim [25] who studied the instability of a time-evolving boundary layer flow and Storesletten and Rees [26] on the instability of a boundary layer induced by uniform surface suction.…”

Section: Introductionmentioning

confidence: 99%

“…This work, then, represents the combined effects of internal heating, anisotropy and inclination. It may be regarded as being an extension (i) of the works of Rees and Postelnicu [27] and Storesletten and Tveitereid [29] by having the presence of internal heating, (ii) of the work of Barletta et al [11] by the inclusion of the effect of anisotropy and (iii) of the works of Mahajan and Nandal [19] and Capone et al [30] by inclining the layer. We concentrate first on two-dimensional convection (transverse rolls) which will always arise whenever the porous layer is sufficiently narrow in the spanwise direction.…”

Section: Introductionmentioning

confidence: 99%

Onset of Convection in an Inclined Anisotropic Porous Layer with Internal Heat Generation

Storesletten

Rees

2019

Fluids

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The onset of convection in an inclined porous layer which is heated internally by a uniform distribution of heat sources is considered. We investigate the combined effects of inclination, anisotropy and internal heat generation on the linear instability of the basic parallel flow. When the Rayleigh number is sufficiently large, instability occurs and a convective motion is set up. It turns out that the preferred motion at convection onset depends quite strongly on the anisotropy ratio, ξ , and the inclination angle. When ξ < 1 the preferred motion is in the form of longitudinal rolls for all inclinations. When ξ > 1 transverse rolls are preferred for small inclinations but, at high inclinations, longitudinal rolls are preferred. At intermediate inclinations the preferred roll orientation varies smoothly between these two extremes.

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Stability of an Anisotropic Porous Layer With Internal Heat Source and Brinkman Effects

Cited by 5 publications

References 0 publications

Heat and mass transfer of triple diffusive convection in viscoelastic liquids under internal heat source modulations

Heat and mass transfer of triple diffusive convection in viscoelastic liquids under internal heat source modulations

Vadasz Number Effects on Convection in a Horizontal Porous Layer Subjected to Internal Heat Generation and G-Jitter

Onset of Convection in an Inclined Anisotropic Porous Layer with Internal Heat Generation

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