Flows Between Rotating Cylinders With a Porous Lining

2008 ◽  
Vol 130 (10) ◽  
Author(s):  
M. Subotic ◽  
F. C. Lai
Keyword(s):  
Porous Layer ◽  
Stokes Equations ◽  
Fluid Layer ◽  
Outer Cylinder ◽  
Tangential Velocity ◽  
Darcy Number ◽  
Temperature Fields ◽  
Rotating Cylinders ◽  
Press Fit ◽  
Porous Sleeve

Flow and temperature fields in an annulus between two rotating cylinders have been examined in this study. While the outer cylinder is stationary, the inner cylinder is rotating with a constant angular speed. A homogeneous and isotropic porous layer is press fit to the inner surface of the outer cylinder. The porous sleeve is saturated with the fluid that fills the annulus. The Brinkman-extended Darcy equations are used to model the flow in the porous layer while the Navier–Stokes equations are used for the fluid layer. The conditions applied at the interface between the porous and fluid layers are the continuity of temperature, heat flux, tangential velocity, and shear stress. Analytical solutions have been attempted. Through these solutions, the effects of Darcy number, Brinkman number, and porous sleeve thickness on the velocity profile and temperature distribution are studied.

Flows in Rotating Cylinders With a Porous Lining

2007 ◽  
Author(s):  
M. Subotic ◽  
F. C. Lai
Keyword(s):  
Porous Layer ◽  
Stokes Equations ◽  
Fluid Layer ◽  
Outer Cylinder ◽  
Tangential Velocity ◽  
Darcy Number ◽  
Temperature Fields ◽  
Rotating Cylinders ◽  
Press Fit ◽  
Porous Sleeve

Flow and temperature fields in an annulus between two rotating cylinders have been examined in this study. While the outer cylinder is stationary, the inner cylinder is rotating with a constant angular speed. A homogeneous and isotropic porous layer is press-fit to the inner surface of the outer cylinder. The porous sleeve is saturated with the fluid that fills the annulus. The Brinkman-extended Darcy equations are used to model the flow in the porous layer while Navier-Stokes equations are used for the fluid layer. The conditions applied at the interface between the porous and fluid layers are the continuity of temperature, heat flux, tangential velocity and shear stress. Analytical solutions have been attempted. Through these solutions, the effects of Darcy number, Brinkman number, and porous sleeve thickness on the velocity profile and temperature distribution are studied.

Natural Convection From a Buried Pipe With a Superimposed Fluid Layer

2007 ◽  
Author(s):  
C. C. Ngo ◽  
F. C. Lai
Keyword(s):  
Heat Transfer ◽  
Porous Medium ◽  
Rayleigh Number ◽  
Layer Thickness ◽  
Stokes Equations ◽  
Fluid Layer ◽  
Tangential Velocity ◽  
Darcy Number ◽  
Velocity Shear ◽  
Buried Pipe

Heat transfer induced by buoyancy from a pipe buried in a semi-infinite porous medium with a superimposed fluid layer has been numerically examined in this study. Due to the complexity involved, finite difference method along with body-fitted coordinate systems has been employed. The Brinkman-extended Darcy equations are used to model flow in the porous medium while Navier-Stokes equations are used for the fluid layer. The conditions applied at the interface between the fluid and porous layers are the continuity of temperature, heat flux, normal and tangential velocity, shear stress and pressure. A parametric study has been performed to investigate the effects of Rayleigh number, Prandtl number, Darcy number, and fluid layer thickness on the flow patterns and heat transfer rates. The results show that heat transfer increases with the Rayleigh number, but the convective strength decreases with the Darcy number. The heat transfer rate is smaller when the superimposed fluid is air instead of water. For a porous layer with Da ≤ 0.0005 and an overlaying fluid layer thickness of L/ri ≥ 1, convection is initiated in the fluid layer and it may develop into multiple recirculating cells at a moderate Rayleigh number (i.e., Ra ≤ 104), and may further develop into a single cell at a higher Rayleigh number of 105.

Flows and Their Stability in Rotating Cylinders With a Porous Lining

2010 ◽  
Vol 132 (5) ◽  
Author(s):  
M. Subotic ◽  
F. C. Lai
Keyword(s):  
Outer Cylinder ◽  
Three Dimensional ◽  
Angular Speed ◽  
Rotating Cylinders ◽  
Press Fit ◽  
Wide Range ◽  
Fluid Layers ◽  
Inner Surface ◽  
Porous Sleeve ◽  
Porous Lining

Flow fields in an annulus between two rotating cylinders with a porous lining have been numerically examined in this study. While the outer cylinder is stationary, the inner cylinder is rotating with a constant angular speed. A homogeneous and isotropic porous layer is press-fit to the inner surface of the outer cylinder. The porous sleeve is saturated with the fluid that fills the annulus. The effects of porous sleeve thickness and its properties on the flows and their stability in the annulus are numerically investigated. Three-dimensional momentum equations for the porous and fluid layers are formulated separately and solved simultaneously in terms of velocity and vorticity. The solutions have covered a wide range of the governing parameters (10−5≤Da≤10−2,  2000≤Ta≤5000,  0.8≤b¯≤0.95). The results obtained show that the presence of a porous sleeve generally has a stabilizing effect on the flows in the annulus.

Mixed Convection in Rotating Concentric Annulus With a Porous Sleeve

2003 ◽  
Author(s):  
J. C. Leong ◽  
F. C. Lai
Keyword(s):  
Heat Transfer ◽  
Mixed Convection ◽  
Numerical Solutions ◽  
Outer Cylinder ◽  
Darcy Number ◽  
Thermal Buoyancy ◽  
Concentric Annulus ◽  
Concentric Cylinders ◽  
Inner Surface ◽  
Porous Sleeve

Numerical solutions are presented for mixed convection in rotating concentric cylinders with a porous sleeve. The porous sleeve is press-fitted to the inner surface of the outer cylinder. While the inner cylinder is rotating at a constant speed, the outer cylinder remains stationary. The main objective of the present study is to numerically investigate the flow pattern and temperature distribution as affected by the presence of the porous layer, the centrifugal force, and thermal buoyancy. A parametric study has been performed to investigate the effects of Peclet number, Rayleigh number, and Darcy number on the heat transfer results.

Thermal Stability of Horizontally Superposed Porous and Fluid Layers

1989 ◽  
Vol 111 (2) ◽  
pp. 357-362 ◽  
Author(s):  
M. E. Taslim ◽  
U. Narusawa
Keyword(s):  
Porous Layer ◽  
Fluid Layer ◽  
Critical Rayleigh Number ◽  
Convective Motion ◽  
Darcy Number ◽  
Wave Number ◽  
Thermal Conductivity Ratio ◽  
Porous Layers ◽  
Fluid Layers ◽  
Comprehensive Picture

The results of stability analyses for the onset of convective motion are reported for the following three horizontally superposed systems of porous and fluid layers: (a) a porous layer sandwiched between two fluid layers with rigid top and bottom boundaries, (b) a fluid layer overlying a layer of porous medium, and (c) a fluid layer sandwiched between two porous layers. By changing the depth ratio dˆ from zero to infinity, a set of stability criteria (i.e., the critical Rayleigh number Rac and the critical wave number ac) is obtained, ranging from the case of a fluid layer between two rigid boundaries to the case of a porous layer between two impermeable boundaries. The effects of k/km (the thermal conductivity ratio), δ (the square root of the Darcy number), and α (the nondimensional proportionality constant in the slip condition) on Rac and ac are also examined in detail. The results in this paper, combined with those reported previously for Case (a) (Pillatsis et al., 1987), will provide a comprehensive picture of the interaction between a porous and a fluid layer.

Analysis of Surface Enhancement by a Porous Substrate

1990 ◽  
Vol 112 (3) ◽  
pp. 700-706 ◽  
Author(s):  
Kambiz Vafai ◽  
Sung-Jin Kim
Keyword(s):  
Heat Transfer ◽  
Boundary Layer ◽  
Fluid Layer ◽  
Composite Layer ◽  
Darcy Number ◽  
Temperature Fields ◽  
External Boundary ◽  
Porous Substrate ◽  
Frictional Drag ◽  
Practical Applications

Convective flow and heat transfer through a composite porous/fluid system have been studied numerically. The composite medium consists of a fluid layer overlaying a porous substrate, which is attached to the surface of the plate. The numerical simulations focus primarily on flows that have the boundary layer characteristics. However, the boundary layer approximation was not used. A general flow model that accounts for the effects of the impermeable boundary and inertia is used to describe the flow inside the porous region. Several important characteristics of the flow and temperature fields in the composite layer are reported. The dependence of these characteristics on the governing parameters such as the Darcy number, the inertia parameter, the Prandtl number, and the ratio of the conductivity of the porous material to that of the fluid is also documented. The results of this investigation point out a number of interesting practical applications such as in frictional drag reduction, and heat transfer retardation or enhancement of an external boundary.

Stability of Poiseuille flow of a Bingham fluid overlying an anisotropic and inhomogeneous porous layer

2019 ◽  
Vol 874 ◽  
pp. 573-605 ◽  
Author(s):  
Sourav Sengupta ◽  
Sirshendu De
Keyword(s):  
Modal Analysis ◽  
Layer Thickness ◽  
Porous Layer ◽  
Poiseuille Flow ◽  
Initial Conditions ◽  
Fluid Layer ◽  
Darcy Number ◽  
Flow Stability ◽  
Bingham Fluid ◽  
Bingham Number

Modal and non-modal stability analyses are performed for Poiseuille flow of a Bingham fluid overlying an anisotropic and inhomogeneous porous layer saturated with the same fluid. In the case of modal analysis, the resultant Orr–Sommerfeld type eigenvalue problem is formulated and solved via the Chebyshev collocation method, using QZ decomposition. It is found that no unstable eigenvalues are present for the problem, indicating that the flow is linearly stable. Therefore, non-modal analysis is attempted in order to observe the short-time response. For non-modal analysis, the initial value problem is solved, and the response of the system to initial conditions is assessed. The aim is to evaluate the effects on the flow stability of porous layer parameters in terms of depth ratio (ratio of the fluid layer thickness $d$ to the porous layer thickness $d_{m}$), Bingham number, Darcy number and slip coefficient. The effects of anisotropy and inhomogeneity of the porous layer on flow transition are also investigated. In addition, the shapes of the optimal perturbations are constructed. The mechanism of transient growth is explored to comprehend the complex interplay of various factors that lead to intermediate amplifications. The present analysis is perhaps the first attempt at analysing flow stability of viscoplastic fluids over a porous medium, and would possibly lead to better and efficient designing of flow environments involving such flow.

scholarly journals Stokes drift through corals

2021 ◽  
Author(s):  
Joseph J. Webber ◽  
Herbert E. Huppert
Keyword(s):  
Coral Reef ◽  
Coral Reefs ◽  
Porous Layer ◽  
Large Scale ◽  
Fluid Layer ◽  
Ocean Waves ◽  
Stokes Drift ◽  
Inviscid Fluid ◽  
Porous Bed ◽  
Vertical Drift

AbstractMotivated by shallow ocean waves propagating over coral reefs, we investigate the drift velocities due to surface wave motion in an effectively inviscid fluid that overlies a saturated porous bed of finite depth. Previous work in this area either neglects the large-scale flow between layers (Phillips in Flow and reactions in permeable rocks, Cambridge University Press, Cambridge, 1991) or only considers the drift above the porous layer (Monismith in Ann Rev Fluid Mech 39:37–55, 2007). Overcoming these limitations, we propose a model where flow is described by a velocity potential above the porous layer and by Darcy’s law in the porous bed, with derived matching conditions at the interface between the two layers. Both a horizontal and a novel vertical drift effect arise from the damping of the porous bed, which requires the use of a complex wavenumber k. This is in contrast to the purely horizontal second-order drift first derived by Stokes (Trans Camb Philos Soc 8:441–455, 1847) when working with solely a pure fluid layer. Our work provides a physical model for coral reefs in shallow seas, where fluid drift both above and within the reef is vitally important for maintaining a healthy reef ecosystem (Koehl et al. In: Proceedings of the 8th International Coral Reef Symposium, vol 2, pp 1087–1092, 1997; Monismith in Ann Rev Fluid Mech 39:37–55, 2007). We compare our model with field measurements by Koehl and Hadfield (J Mar Syst 49:75–88, 2004) and also explain the vertical drift effects as documented by Koehl et al. (Mar Ecol Prog Ser 335:1–18, 2007), who measured the exchange between a coral reef layer and the (relatively shallow) sea above.

Development of Convective Heat Transfer Near Suddenly Heated, Vertically Aligned Horizontal Wires

1987 ◽  
Vol 109 (4) ◽  
pp. 912-918 ◽  
Author(s):  
J. R. Parsons ◽  
M. L. Arey
Keyword(s):  
Heat Transfer ◽  
Heat Source ◽  
Fluid Layer ◽  
Convective Motion ◽  
Transient Behavior ◽  
Temperature Fields ◽  
Heat Sources ◽  
Transfer Coefficients ◽  
Vertically Aligned ◽  
The Wire

Experiments have been performed which describe the transient development of natural convective flow from both a single and two vertically aligned horizontal cylindrical heat sources. The temperature of the wire heat sources was monitored with a resistance bridge arrangement while the development of the flow field was observed optically with a Mach–Zehnder interferometer. Results for the single wire show that after an initial regime where the wire temperature follows pure conductive response to a motionless fluid, two types of fluid motion will begin. The first is characterized as a local buoyancy, wherein the heated fluid adjacent to the wire begins to rise. The second is the onset of global convective motion, this being governed by the thermal stability of the fluid layer immediately above the cylinder. The interaction of these two motions is dependent on the heating rate and relative heat capacities of the cylinder and fluid, and governs whether the temperature response will exceed the steady value during the transient (overshoot). The two heat source experiments show that the merging of the two developing temperature fields is hydrodynamically stabilizing and thermally insulating. For small spacing-to-diameter ratios, the development of convective motion is delayed and the heat transfer coefficients degraded by the proximity of another heat source. For larger spacings, the transient behavior approaches that of a single isolated cylinder.

Heat Transfer Investigation of a Tube Partially Wrapped by Metal Porous Layer as a Potential Novel Tube for Air Cooled Heat Exchangers

2018 ◽  
Vol 141 (1) ◽  
Author(s):  
M. Mohammadpour-Ghadikolaie ◽  
M. Saffar-Avval ◽  
Z. Mansoori ◽  
N. Alvandifar ◽  
N. Rahmati
Keyword(s):  
Heat Transfer ◽  
Reynolds Number ◽  
Nusselt Number ◽  
Heat Transfer Rate ◽  
Porous Layer ◽  
Transfer Rate ◽  
Metal Foam ◽  
Convection Heat Transfer ◽  
Darcy Number ◽  
High Heat Transfer

Laminar forced convection heat transfer from a constant temperature tube wrapped fully or partially by a metal porous layer and subjected to a uniform air cross-flow is studied numerically. The main aim of this study is to consider the thermal performance of some innovative arrangements in which only certain parts of the tube are covered by metal foam. The combination of Navier–Stokes and Darcy–Brinkman–Forchheimer equations is applied to evaluate the flow field. Governing equations are solved using the finite volume SIMPLEC algorithm and the effects of key parameters such as Reynolds number, metal foam thermophysical properties, and porous layer thickness on the Nusselt number are investigated. The results show that using a tube which is fully wrapped by an external porous layer with high thermal conductivity, high Darcy number, and low drag coefficient, can provide a high heat transfer rate in the high Reynolds number laminar flow, increasing the Nusselt number almost as high as 16 times compared to a bare tube. The most important result of thisstudy is that by using some novel arrangements in which the tube is partially covered by the foam layer, the heat transfer rate can be increased at least 20% in comparison to the fully wrapped tube, while the weight and material usage can be considerably reduced.

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