Numerical Study of High Rayleigh Number Convection in a Vertical Porous Enclosure

Shiralkar, G.S.; Haajizadeh, Masoud; Tien, C. L.

doi:10.1080/01495728308963084

Cited by 36 publications

(10 citation statements)

References 9 publications

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“…The results of Weber [2] and Shiralkar et al [8] were obtained using the pure Darcy model, while Tong and Subramanian [I71 performed a boundary-layer analysis using the Brinkman-extended Darcy model. Klarsfeld's results [I21 are actual experimental data.…”

Section: Numerical Proceduresmentioning

confidence: 98%

A Numerical Study of Non-Darcian Natural Convection in a Vertical Enclosure Filled With a Porous Medium

Beckermann

Viskanta

Ramadhyani

1986

Numerical Heat Transfer

135

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A numerical study of n o n -J I i a n natuml convection in a vertieal enclosure f l e d with a porous medium is performed. The flow is modeled using the Brinkman-Forchheimerextended Darcy equations. The governing equations are solved with the SIMPLER a l p rirhm and good agreement with previously reported numerical and experimental results is found. An order of magnitude analysis and the numerical results demonshute the impor tance of m n -J I i a n effects. For high M y numbers (Da > lo-'), both extensions are of the same order of magnitude and must be used simultaneously. I n oddirion, Forchheimer's extension must be included for Pr s 1.0 and all J I y numbers. FEnaly, Nusselt number comlclrions an presented for three dijjcrent mnges of the DMy number covering wide mnges of the governing pornmeters.

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Section: Numerical Proceduresmentioning

confidence: 98%

A Numerical Study of Non-Darcian Natural Convection in a Vertical Enclosure Filled With a Porous Medium

Beckermann

Viskanta

Ramadhyani

1986

Numerical Heat Transfer

135

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“…Values of the Nusselt num ber obtained by other authors (Lauriat & Prasad 1987;Shiralkar et al 1983;Prasad & Kulacki 1984a, b) by full numerical simulations of the cavity flow a t various D arcy-R ayleigh num bers in the range 20 ^ 1000 and for an aspect ratio h = 5 are also shown in figure 5. These results agree well w ith present theory and even closer agreem ent m ight be expected for som ew hat larger values of h. The results confirm the existence of the universal N usselt-num ber curve Nu(l) predicted here and are also consistent w ith the prediction of the m inim um of the N usselt num ber a t l « 4.25.…”

Section: Resultsmentioning

confidence: 92%

“…This reduces the system to an infinite coupled set of nonlinear ordinary differential equations in the horizontal direction, a truncated form of which is then solved by a finite difference m ethod outlined in §4. The results are described in §5 and are compared with heat transfer predictions obtained from full numerical simulations of the eavity flow by Shiralkar et al (1983), Kulacki (1984a, b) andL auriat &Prasad (1987). The solution of the main core problem does not satisfy the full boundary conditions at the horizontal walls, and there is an adjustm ent within a two-tier boundary-layer structure near the top and bottom of the cavity.…”

Section: Introductionmentioning

confidence: 99%

Thermally driven tall cavity flows in porous media: the convective régime

Ansari

Daniels

1994

Proc. R. Soc. Lond. A

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Thermally driven flows in a two-dimensional rectangular cavity filled with a fluid-saturated porous medium are considered when the applied temperature difference is perpendicular to the gravity vector. The flow depends on two non-dimensional parameters, the Darcy-Rayleigh number, A , and the cavity aspect ratio, h (height / width). Steady motion is generated by maintaining the vertical sidewalls at different constant temperatures and the horizontal boundaries are assumed to be thermally insulating. The present study is concerned with the limit of large aspect ratio, h → ∞. and Darcy-Rayleigh numbers A of order h , such that convection is important throughout the cavity. The main properties of the flow and heat transfer are obtained by considering a vertical boundary-layer approximation to the motion in the main body of the cavity. This leads, in particular, to the prediction of a position of minimum heat transfer across the cavity, of interest in the thermal insulation of buildings and other areas of technology.

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“…A representative Nusselt num ber for the overall cavity flow is defined by the heat transfer out of the cold wall rn N u = (7.1) Jo 0* This integral, taken down the entire cold wall, m ust be subdivided into three parts, corresponding to contributions arising from the core region and from the two end zones a t the top and bottom of the cavity. Thus where a 0 k, -0.012 and /?0 « 0.076, with formula (7.3) formally valid provided th a t A h. Practically speaking, the correction term in (7.3) is less th an the leading-order term provided A ^ 15 h,giving an indication of the actual range of v H eat transfer predictions obtained from full numerical simulations (Lauriat & Prasad 1987;Shiralkar et al 1983;Prasad & Kulacki 1984a, b) are shown in table 3 and are seen to be in excellent agreement with the formula (7.3) over the range A < 15 h.…”

Section: Discussionmentioning

confidence: 99%

“…(1978), while numerical simulations have been carried out for tall cavities by Chan et at. (1970), Shiralkar et at. (1983), Prasad & Kulacki (1984a, b) and L auriat & Prasad (1987).…”

Section: Introductionmentioning

confidence: 99%

Thermally driven tall cavity flows in porous media

Ansari

Daniels

1993

Proc. R. Soc. Lond. A

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Thermally driven flows in a two-dimensional rectangular cavity filled with a fluid-saturated porous medium are considered when the applied temperature difference is perpendicular to the gravity vector. The flow depends on two non-dimensional parameters, the Darcy–Rayleigh number A and the cavity aspect ratio h (height/length). Steady motion is generated by maintaining the vertical sidewalls at different constant temperatures and the present study is concerned with the limit of large aspect ratio, h –> ∞, where nonlinear convective flow occurs near each end of the cavity. This flow is analysed by asymptotic methods for small and large values of A and is computed numerically for other values of A . Predictions of the heat transfer across the cavity are obtained and are compared with the results of full numerical simulations.

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Numerical Study of High Rayleigh Number Convection in a Vertical Porous Enclosure

Cited by 36 publications

References 9 publications

A Numerical Study of Non-Darcian Natural Convection in a Vertical Enclosure Filled With a Porous Medium

A Numerical Study of Non-Darcian Natural Convection in a Vertical Enclosure Filled With a Porous Medium

Thermally driven tall cavity flows in porous media: the convective régime

Thermally driven tall cavity flows in porous media

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