Unsteady Conjugate Natural Convection in a Vertical Cylinder Containing a Horizontal Porous Layer: Darcy Model and Brinkman-Extended Darcy Model

Sheremet, Mikhail А.; Trifonova, T A

doi:10.1007/s11242-013-0253-8

Cited by 36 publications

(20 citation statements)

References 35 publications

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“…In addition, the flow and heat transfer are transient, laminar and two-dimensional. The governing conservation equations for the fluid and porous layers and also for the solid shell have been formulated in dimensionless form using stream function, vorticity and temperature variables [7], [8]:  for the pure fluid layer:…”

Section: Governing Equations and Numerical Methodsmentioning

confidence: 99%

“…1-Eq. 6 with corresponding initial and boundary conditions were solved by finite difference method [7], [8], [24], [25] using the uniform grid. For an approximation of the convective terms we used the monotonic Samarskii scheme of the second order, allowing considering a sign of velocity and for an approximation of the diffusion terms we used the central differences.…”

Section: Governing Equations and Numerical Methodsmentioning

confidence: 99%

“…Optimum value of the relaxation parameter was chosen on the basis of computing experiments. The accuracy of the numerical code developed by the author was checked by preparing the benchmark solutions both for non-conjugate and conjugate natural convection in porous and pure media [7], [8]. In the case of non-conjugate problem we have analyzed laminar natural convection in a square cavity containing a fluid layer overlying a porous layer saturated with the same fluid [6].…”

Section: Governing Equations and Numerical Methodsmentioning

confidence: 99%

“…It has been found that for moderate to small Darcy numbers the results obtained on the basis of the Darcy model with the Beavers-Joseph empirical condition at the fluid-porous interface are similar to the results obtained by the Brinkman and Brinkman-Forchheimer models. Sheremet and Trifonova [7], [8] vertical cylinder containing horizontal pure fluid and porous layers. It has been shown that at small values of the thermal conductivity ratio the linear Darcy model is valid for the conjugate natural convection problems.…”

Section: Introductionmentioning

confidence: 99%

See 3 more Smart Citations

Numerical Simulation of Conjugate Free Convection in a Vertical Cylinder Having Porous Layer

Sheremet¹

2017

IJMMM

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Section: Governing Equations and Numerical Methodsmentioning

confidence: 99%

Section: Governing Equations and Numerical Methodsmentioning

confidence: 99%

Section: Governing Equations and Numerical Methodsmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

See 2 more Smart Citations

Numerical Simulation of Conjugate Free Convection in a Vertical Cylinder Having Porous Layer

Sheremet¹

2017

IJMMM

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“…One of the advantages of Darcy-Brinkman model is that the dynamic viscosities is taken the same in both layers (μ eff = μ f ) [25]. Hence, the porous-fluid interface conditions can be written as; (10a) where is the thermal conductivity ratio.…”

Section: Mathematical Modellingmentioning

confidence: 99%

Double Diffusive Natural Convection in a Partially Layered Cavity with inner Solid Conductive Body

Ismael

Ghalib

2017

Scientia Iranica

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Conjugate natural convection in a fluid‐saturated porous enclosure with two solid vertical partitions

Chordiya

Sharma

2018

Heat Trans. Asian Res.

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Conjugate natural convection in a fluid‐saturated square porous enclosure with two solid vertical partitions of finite and equal thickness equispaced from center of enclosure is investigated in this paper. The primary objective is to attenuate the Nusselt number (Nu) and hence the heat transfer rate across a differentially heated enclosure. Darcy's model is considered. Numerical computation is performed using successive accelerated replacement and explicit scheme. Partition ratio, partition length, thermal conductivity ratio, and modified Rayleigh number are the parameters under study. Fluid flow is analyzed by observing transient changes of streamlines and isotherms for partition length 0.3‐1, thermal conductivity ratio 0.5‐2, partition ratio 0.1‐0.3 and modified Rayleigh number 100 and 1000 where partition ratio is the ratio of distance between center of enclosure and either of the partition center to the total length of the enclosure; while Nusselt number is calculated to estimate the heat transfer rate for each configuration. It is found that, employing a solid partition within the enclosure most definitely reduces the Nusselt number. The drop in Nusselt number is more for partition length 0‐0.6 after which it does show a drop in Nu but only very subtle. Further, Nu is the least for partition ratio 0.2. Also, Nusselt number is proportional to thermal conductivity ratio which is the ratio of thermal conductivity of solid to porous medium.

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Unsteady Conjugate Natural Convection in a Vertical Cylinder Containing a Horizontal Porous Layer: Darcy Model and Brinkman-Extended Darcy Model

Cited by 36 publications

References 35 publications

Numerical Simulation of Conjugate Free Convection in a Vertical Cylinder Having Porous Layer

Numerical Simulation of Conjugate Free Convection in a Vertical Cylinder Having Porous Layer

Double Diffusive Natural Convection in a Partially Layered Cavity with inner Solid Conductive Body

Conjugate natural convection in a fluid‐saturated porous enclosure with two solid vertical partitions

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