Centrifugally generated free convection in a rotating porous box

doi:10.1016/0017-9310(94)90281-X

International Journal of Heat and Mass Transfer

Volume 37, Issue 16, November 1994, Pages 2399-2404

https://doi.org/10.1016/0017-9310(94)90281-X Get rights and content

Abstract

An analytical method of solution to the non-linear problem of centrifugally generated free convection in a rotating porous box is presented. The free convection results from differential heating of the horizontal walls leading to temperature gradients perpendicular to the centrifugal body force. The validity of the solution was found to be restricted to small values of the centrifugal Rayleigh number, although this restriction was not explicitly imposed. The results are compared to an asymptotic solution of the corresponding problem for a long rotating porous box. A direct extraction and substitution of the dependent variables was found to be useful in this case for de-coupling the non-linear partial differential equations, resulting in a set of independent non-linear ordinary differential equations which was solved analytically. The solution results, their significance and their validity domain are discussed in their physical context.

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Cited by (27)

Destabilizing convection using vibration in a rotating porous layer with a stabilizing temperature gradient
2019, International Journal of Heat and Mass Transfer
Citation Excerpt :
Thermo-flow in porous media saturated by a pure fluid and involving rotation has been extensively studied by numerous authors and subject to various boundary conditions. Pioneering work by Vadasz [1–9], presents analytical results for fluid flow and heat transfer in a vertical porous layer subjected to centrifugal acceleration only various locations from the axis of rotation. Vadasz and Govender [10] later included the effects of gravity and discovered that gravity plays a fairly passive role in the stability criteria describing the convection threshold.
An analytical investigation in a vertical fluid saturated porous layer distant from the axis of rotation is presented when vibration occurs in the presence of a stable temperature gradient. A linear stability analysis is used to determine the convection threshold in terms of the critical Rayleigh number for variation within the porous layer and for the offset distance from the axis of rotation. The results indicate that the presence of vibration in a stable system serves to reduce the Rayleigh numbers (both within the porous layer and due to offset from the axis of rotation), thus destabilizing the system when a stabilizing temperature gradient exists.
Vibration effects on convection in a rotating fluid saturated porous layer distant from the axis of rotation
2019, International Journal of Heat and Mass Transfer
Citation Excerpt :
Fluid flow and heat transfer in porous media saturated by a pure fluid and involving rotation has been extensively studied by numerous authors in various configurations. The pioneering work by Vadasz [1–9], presents analytical results for fluid flow and heat transfer in a vertical porous layer subjected to centrifugal acceleration only, for the porous layer placed at the axis of rotation, distant from the axis of rotation, and far away from axis of rotation. Vadasz and Govender [10] then included the effects of gravity and discovered that gravity plays a fairly passive role in the stability criteria describing the convection threshold.
An analytical investigation for the onset of convection in a vertical saturated porous layer distant from the axis of rotation is presented when vibration is present. A linear stability analysis is used to determine the convection threshold in terms of the critical Rayleigh number for variation within the porous layer and for the offset distance from the axis of rotation. The results indicate that the presence of vibration stabilizes the convection across the range of offset distances. The effect of decreasing the offset distance (from very large to almost zero) serves to destabilize the critical Rayleigh number due to offset distance and to stabilize the Rayleigh number for variations within the porous layer.
Effects of centrifugal buoyancy on developing convective laminar flow in a square channel occupied with a high porosity fibrous medium
2015, International Journal of Heat and Mass Transfer
Citation Excerpt :
The data has confirmed the ability of inducing a mainstream flow along the channel by means of the secondary circulation resulting from the locally varying permeability. The natural convection induced by the centrifugal acceleration in a narrow porous layer subjected to rotation was examined analytically by Vadasz [18], Vadasz [19], and Vadasz [20] for an axis of rotation attached to the porous layer, distant from the porous layer, and located within the porous layer, respectively. The results indicated that displacing the porous layer away from the axis of rotation has a destabilizing effect, while placing the rotation axis within the porous layer produces a stabilising influence in the part of the layer located to the left of the axis of rotation and conversely a destabilising effect to the right part of it.
The development of three-dimensional heat transfer and fluid flow in a square channel rotating in a parallel-mode has been investigated numerically. The duct is occupied by a foam material of high porosity (ɛ ⩾ 0.9) and subjected to a uniform wall heat flux. In regards to the influence of rotation, both the centrifugal buoyancy effect and Coriolis forces are considered in the current study. The generalised model is used to mathematically simulate the momentum equations employing the Boussinesq approximation for the density variation. Moreover, both the fluid and solid phases are considered to be in local thermal non-equilibrium. The governing equations are discretised according to the finite volume method employing the hybrid differencing scheme to calculate the fluxes across the faces of each control volume in the transverse plane. Computations are performed for a wide range of dimensionless parameters including the medium porosity (0.9 ⩽ ε ⩽ 0.97), rotation number (0 ⩽ Ro ⩽ 1.0), Darcy–Rayleigh rotational number (1.1 × 10³ ⩽ ${Ra}_{Ω}^{*}$ ⩽ 6.2 × 10⁵), and solid to fluid-phase thermal conductivity ratio (10² ⩽ κ ⩽ 10³), while the values of Reynolds and Prandtl numbers are maintained constant at Re = 2000 and Pr = 0.7, respectively. The results reveal that the rotation seems to have a dominant role in enhancing heat transfer at high levels of porosity and low conductivity ratios. However, this role is reduced gradually with decreasing the medium porosity or increasing thermal conductivity ratio, but does not completely vanish. Eventually, the worth of using high porosity fibrous media in enhancing the heat transported through rotating channels has been inspected. An overall enhancement parameter was compared for the current study with a previous work regarding turbulent flow in a rotating clear channel, where it has been confirmed that the current proposal is practically justified and efficient.
Developing convective flow in a square channel partially filled with a high porosity metal foam and rotating in a parallel-mode
2015, International Journal of Heat and Mass Transfer
Citation Excerpt :
The data has confirmed the ability to induce a mainstream flow along the channel by means of the secondary circulation resulting from a locally varying permeability. Natural convection induced by centrifugal acceleration in a narrow porous layer subjected to rotation was examined analytically by Vadasz [25–27] for an axis of rotation attached to, distant from, and located within the porous layer, respectively. The results indicated that displacing the porous layer away from the axis of rotation has a destabilizing effect that enhances the centrifugal buoyancy.
The development of three-dimensional heat transfer and fluid flow in a square channel rotating in a parallel-mode has been investigated numerically. The duct is partially occupied by a foam material of high porosity ε ⩾ 0.89 and subjected to a uniform wall heat flux. In regards to the influence of rotation, both the centrifugal buoyancy and Coriolis forces are considered in the current study. The generalized model is used to mathematically simulate the momentum equations employing the Boussinesq approximation for the density variation. Moreover, thermal dispersion has been taken into account with considering that fluid and solid phases are in a local thermal non-equilibrium. The governing equations are discretized according to the finite volume method with employing a hybrid differencing scheme. Computations are performed for a wide range of parameters including the hollow ratio (0 ⩽ S ⩽ 1), foam porosity (0.89 ⩽ ε ⩽ 0.97), pore density (5PPI ⩽ ω ⩽ 40PPI), solid to fluid thermal conductivity ratio (250 ⩽ κ ⩽ 4000), Reynolds number (250 ⩽ Re ⩽ 2000), and rotation number (0 ⩽ Ro ⩽ 1), while the values of characteristic temperature difference and Prandtl numbers are maintained constant at ΔT_c = 1000 °C and Pr = 0.7, respectively. Results reveal that flow resistance and heat transport are augmented with either decreasing the hollow ratio and foam porosity or increasing Reynolds and rotation numbers, while two contradictory trends are found for the impact of increasing pore density on heat transfer; either enhancing or suppressing depending on the size of hollow zone. In addition, both rotation and thermal dispersion have dominant roles in enhancing heat transfer at the higher levels of porosity or the lower values of conductivity ratios. However, these roles are reduced gradually with decreasing the foam porosity or increasing thermal conductivity ratio, but do not completely vanish. Eventually, the worth of using high porosity fibrous media in enhancing the heat transported through rotating channels has been inspected. An overall enhancement parameter is compared for the current study with a previous work regarding turbulent flow in a rotating clear channel, where it has been confirmed that the current proposal is practically justified and efficient.
Hydrodynamically and thermally developing flow in a rectangular channel filled with a high porosity fiber and rotating about a parallel axis
2015, International Communications in Heat and Mass Transfer
Citation Excerpt :
The data have confirmed the ability to induce a mainstream flow along the channel by means of the secondary circulation resulting from a locally varying permeability. Natural convection induced by centrifugal acceleration in a narrow porous layer subjected to rotation was examined analytically by Vadasz [12–14] for an axis of rotation attached to, distant from, and located within the porous layer, respectively. The results indicated that displacing the porous layer away from the axis of rotation has a destabilizing effect that enhances the centrifugal buoyancy.
Rotating machineries operating at extreme temperature conditions usually need to be cooled internally by involving cooling passages inside them. A potential way to improve heat dissipated by these channels is by filling them with high porosity metal foams ε ≥ 0.89. This proposal is examined numerically by studying developing convective flow across a porous rectangular channel subjected to a uniform wall heat flux and rotating in a parallel mode. In regards to the influence of rotation, both centrifugal buoyancy and Coriolis forces are considered. The generalized model is used to mathematically simulate the momentum equations employing the Boussinesq approximation for the density variation. Moreover, thermal dispersion has been taken into account with considering that fluid and solid phases are in a local thermal non-equilibrium. Computations are performed for a wide range of dimensionless parameters including the aspect ratio, medium porosity, fiber size, rotation number, and solid- to fluid-phase thermal conductivity ratio, while the values of Reynolds and Prandtl numbers are maintained constant. The results reveal that both rotation and thermal dispersion have significant roles in enhancing heat transfer at high levels of porosity and low conductivity ratios. However, these roles are reduced gradually with decreasing the medium porosity or increasing thermal conductivity ratio, but do not completely vanish. In addition, overall performance is improved with either decreasing the aspect ratio for A_r < 1 or increasing it for A_r > 1. Eventually, the worth of using high porosity fibers in enhancing the heat transported through rotating channels has been inspected. An overall enhancement parameter was compared for the current study with a previous study regarding turbulent flow in a rotating clear channel, where it has been confirmed that the current proposal is practically justified and efficient.
Heat transfer and fluid flow in rotating porous media
2002, Developments in Water Science
The fundamental theory of flow and thermal convection in porous media is reviewed and a systematic classification and identification of the relevant problems is introduced. An initial distinction between rotating flows in isothermal heterogeneous porous systems and free convection in homogeneous non-isothermal porous systems provides the two major classes of problems to be considered. The properties of flow in rotating porous media are being demonstrated theoretically as well as experimentally and compared to the corresponding properties of flow in rotating pure fluids (i.e. in non-porous domains). Application of the latter to non-isothermal problems of thermal convection in rotating porous layers raises a wide range of distinct problems that are being reviewed in light of their theoretical, experimental as well as their applied impact. These include the effects of centrifugal as well gravity induced buoyancy on convection as well as the impact of the offset distance of the fluid saturated porous layer from the axis of rotation on the resulting heat transfer. Other important effects include the Coriolis effect on gravity driven convection in a porous layer heated from below. Examples of solutions to selected problems are presented, highlighting the significant impact of rotation on the flow in porous media.

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Centrifugally generated free convection in a rotating porous box

Abstract

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Fluid flow through heterogeneous porous media in a rotating square channel

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On setting up of convection currents in a rotating porous medium under the influence of variable viscosity

Int. J. Engng Sci.