Showing papers on "Combined forced and natural convection published in 1985"
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TL;DR: In this paper, the authors performed two-dimensional numerical calculations of convection in a domain containing a divariant phase change and found that the critical value of the negative Clapeyron slope, which must be surpassed in order to induce layered convection, decreases in magnitude with increasing Rayleigh number Ra in the range 104 ≤ Ra ≤ 2×106.
Abstract: We report a systematic study on the conditions under which an endothermic phase transition can enforce layered convection. Two-dimensional numerical calculations of convection in a domain containing a divariant phase change were performed in the framework of the “extended Boussinesq approximation,” i.e., considering the effects of adiabatic gradient, latent heat, and frictional heating in the energy equation. We find that the critical value of the negative Clapeyron slope, which must be surpassed in order to induce layered convection, decreases in magnitude with increasing Rayleigh number Ra in the range 104 ≤ Ra ≤ 2×106. Near the critical Clapeyron slope, vacillations between double- and single-layer convection or strongly leaking double-layer convection are possible. The breakdown into layers is influenced very little by the latent heat release but depends solely on the phase boundary deflection caused by lateral temperature differences. The value of the critical Clapeyron slope also seems little affected by the width of the transition zone or by its depth. A possible superplastic rheology within the transition zone would tend to favor layered convection. Scaling the model results to the 670-km discontinuity in the earth's mantle as a possible endothermic phase boundary, we estimate the critical Clapeyron slope to be in the range of −4 to −8 MPa/K (−40 to −80 bar/K). The possibility that the spinel → perovskite + periclase transition is within this range appears to be remote but certainly cannot be neglected.
628 citations
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TL;DR: In this paper, the authors reported a fundamental study of the phenomenon of natural convection heat and mass transfer near a vertical surface embedded in a fluid-saturated porous medium, which is due to the variation of temperature and concentration across the boundary layer.
357 citations
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TL;DR: In this paper, Laminar steady-state natural convection in a two-dimensional rectangular open cavity is investigated numerically, and is shown that outgoing flow patterns and the heat transfer results are governed by strong characteristics of the heated cavity.
186 citations
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TL;DR: In this paper, the authors present the papers given at a conference on free convection in porous materials, including heat transfer, nonlinear temperature profiles and magnetic fields, boundary conditions, concentrated heat sources in stratified porous media, free convective flow in a cavity, heat flux, laminar mixed convection flow, and the onset of convection.
Abstract: This book presents the papers given at a conference on free convection in porous materials. Topics considered at the conference included heat transfer, nonlinear temperature profiles and magnetic fields, boundary conditions, concentrated heat sources in stratified porous media, free convective flow in a cavity, heat flux, laminar mixed convection flow, and the onset of convection in a porous medium with internal heat generation and downward flow.
166 citations
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TL;DR: In this article, numerical simulations of giant-cell solar convection and magnetic field generation are presented for a stratified, rotating, spherical shell of ionized gas, and the velocity, magnetic field, and thermodynamic variables are solved simultaneously and self-consistently with full nonlinear feedback.
Abstract: We describe numerical simulations of giant-cell solar convection and magnetic field generation. Nonlinear, three-dimensional, time-dependent solutions of the anelastic magnetohydrodynamic equations are presented for a stratified, rotating, spherical shell of ionized gas. The velocity, magnetic field, and thermodynamic variables are solved simultaneously and self-consistently with full nonlinear feedback. Convection, driven in the outer part of this shell by a superadiabatic gradient, penetrates into the inner, subadiabatic part. Previous dynamic dynamo sjmulations have demonstrated that, when the dynamo operates in the convection zone, the magnetic fields propagate away from the equator in the opposite direction inferred from the solar butterfly diagram. Our simulations suggest that the solar dynamo may be operating at the base of the convection zone in the transition region between the stable interior and the turbulent convective region. There our simulated angular velocity decreases with depth, as it does in the convection zone; but the simulated helicity has the opposite sign compared to its convection zone value. As a result, our simulated magnetic fields in this transition region initially propagated toward the equator. However, due to our limited numerical resolution of the small amplitude helical fluid motions in this dense, stable region, only the initial phase propagation could be simulated, not a complete magnetic cycle.
137 citations
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TL;DR: In this article, a two-dimensional numerical method is presented which permits the observation of deformation within convecting fluids at high Prandtl number, from which it is concluded that deformation is achieved by simple shear, when considered over long time-scales.
Abstract: Summary. A two-dimensional numerical method is presented which permits the observation of deformation within convecting fluids at high Prandtl number. This method is applied to steady state convection, from which it is concluded that deformation is achieved by simple shear, when considered over long time-scales. In numerical examples over a wide range of Rayleigh numbers and heat sources this shear is shown usually to be prograde, with the periphery of the convection cell rotating slower than the core. Occasionally retrograde shear occurs, in which the reverse is true.
When the method is applied to time-dependent convection, the deformation of discrete bodies occurs by lateral eddy diffusion of mass, and exponential increase of surface area. The rates of these two processes are coupled and vary as Ra0.5 over a wide range of Rayleigh numbers. It is shown that an eddy diffusive approximation is only appropriate for horizontal scales greater than about 3 times the depth of a convecting layer and for time-scales of at least 300 Myr in the upper mantle. The effects of variable viscosity and three-dimensionality are discussed, and the results of the experiments applied to the Earth's mantle. It is concluded that any convecting layer within the mantle must be well mixed on a lateral scale of at least 2000 km after a time of 0.5–1 Gyr, depending on the processes of magma extraction from a streaky parental material. The deformation rate depends only upon the layer depth and the fluid viscosity. Hence whole mantle convection is 5 times more effective in dispersing geochemical heterogeneities than is convection confined to the upper mantle. Various models for the spatial distribution of geochemical reservoirs are discussed and the only viable models are those in which geochemical reservoirs are identified with separate fluid layers. Whole mantle convection is not favoured by these conclusions. On other grounds, some layered models are discarded and we support a conventional model with separate convection in the upper and lower mantle with a boundary at about 700 km depth. Isotopic anomalies erupted at the surface must be relatively recent additions to the otherwise homogeneous upper mantle.
129 citations
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119 citations
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TL;DR: In this paper, an experimental study has been conducted to determine hydrodynamic and thermal conditions in laminar water flow between horizontal parallel plates with uniform, asymmetric heat fluxes.
91 citations
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TL;DR: In this paper, numerical and experimental results for buoyancy-induced flow in a two-dimensional, fluid-filled enclosure were presented and discussed, and good agreement has been obtained between the measured and the predicted temperatures in both the solid wall and in the fluid using the mathematical model.
Abstract: This paper presents numerical and experimental results for buoyancy-induced flow in a two-dimensional, fluid-filled enclosure. Rectangular cavities formed by finite conductance walls of different void fractions and aspect ratios are considered. Parametric heat transfer calculations have been performed and results are presented and discussed. Local and average Nusselt numbers along the cavity walls are reported for a range of parameters of physical interest. The temperatures in the walls were measured with thermocouples, and the temperature distributions in the air-filled cavity were determined using a Mach-Zehnder interferometer. Good agreement has been obtained between the measured and the predicted temperatures in both the solid wall and in the fluid using the mathematical model. Wall heat conduction reduces the average temperature differences across the cavity, partially stabilizes the flow, and decreases natural convection heat transfer.
84 citations
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TL;DR: In this paper, a laminar, three-dimensional, steady-state model has been solved to determine the nature and effect of thermally driven secondary flows in, a horizontal channel with heated top and bottom surfaces and insulated side walls.
Abstract: A laminar, three-dimensional, steady-state model has been solved to determine the nature and effect of thermally driven secondary flows in, a horizontal channel with heated top and bottom surfaces and insulated side walls. The secondary flow is characterized by ascending and descending thermals that form longitudinal vortex rolls and enhance the bottom surface heat transfer and channel friction factor by as much as 400 and 30%, respectively. Parametric calculations have been performed to determine the effect on hydrodynamic and thermal conditions of Reynolds number (100 ≤ Re ≤. 1000), Grashof number (2.5 × 105 ≤ Gr∗ ≤ 6.5 × 104), Prandtl number (Pr = 6.5 and 0.7), top-to-bottom surface heat flux ratio (−1.0 ≤ q1/qb ≤ 5.0), aspect ratio (1 ≤ A ≤ 10), and entrance velocity profile. Conditions near the bottom surface are characterized by mixed convection and are unaffected by heating at the top surface. Conversely, conditions at the top surface are dominated by forced convection and are unaffected by heating...
78 citations
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TL;DR: In this paper, the boundary and inertia effects have a significant influence on the velocity profiles and surface heat transfer rate of convection from a vertical plate embedded in a high-porosity medium.
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TL;DR: In this paper, the analysis of mixed convection about inclined surfaces in a saturated porous media incorporating the variation of permeability and thermal conductivity due to packing of particles was carried out for convective flow in a liquid dominated geothermal reservoir.
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TL;DR: The natural convection of a homogeneous incompressible fluid of grade three between two infinite parallel vertical plates was investigated in this article, where the effect of non-Newtonian nature of fluid on the skin friction and heat transfer was studied.
Abstract: The natural convection of a homogeneous incompressible fluid of grade three is investigated between two infinite parallel vertical plates. The effect of the non-Newtonian nature of fluid on the skin friction and heat transfer are studied.
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TL;DR: In this paper, the effects of free convection on the laminar flow of water through a circular duct having essentially constant wall heat transfer rate per unit length of the duct and circumferentially uniform wall temperature were investigated.
Abstract: This investigation considers the effects of free convection on the laminar flow of water through a circular duct having essentially constant wall heat transfer rate per unit length of the duct and circumferentially uniform wall temperature. The effect of the Reynolds and Rayleigh number variations on heat transfer results has been analysed for both horizontal and inclined pipe. The experiment has covered the range of the inlet Reynolds number from 200 to 2300, and of the Rayleigh number from 6,000 to 70,000. The effect of pipe inclination has been investigated for slope angle values up to 60°, with laminar ascending flow.
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TL;DR: In this paper, the problems of mixed convection about a nonisothermai horizontal cytiner and sphere embedded in a porous medium are analyzed based on a curvilinear orthogonal coordinate system together with boundary-layer simplifications.
Abstract: The problems of mixed convection about a nonisothermai horizontal cytiner and sphere embedded in a porous medium are analyzed based on a curvilinear orthogonal coordinate system together with boundary-layer simplifications. Different transformations were performed for the horizontal cylinder and the sphere, and the resulting equations are identical for the two geometries. Approximate solutions for the problems are obtained based on the nonlocal similarity method. Numerical computations for the temperature distribution and heat flux were carried out up to the third level of truncation. The effects of buoyancy and wall temperature variations on heat transfer characteristics about a heated horizontal cylinder and sphere in a porous medium are examined.
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TL;DR: In this paper, a fundamental study of laminar natural convection in a rectangular enclosure with heat and mass transfer from the side, when the bouyancy effect is due to density variations caused by either temperature or concentration variations, is presented.
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TL;DR: In this paper, the heat transport properties of convection with Newtonian temperature-dependent viscosity were investigated and it was shown that the Nusselt number only weakly depends on the Rayleigh number defined with the viscosities at the mean internal temperature (Ra T ) when the temperature at the top boundary is fixed.
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TL;DR: In this article, the effect of buoyancy on the flow and heat transfer in shrouded arrays of rectangular blocks is studied numerically, and the results show that buoyancy leads to a significant enhancement in heat transfer along with a smaller increase in pressure drop, with the greatest enhancement found when the heated blocks face upward.
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TL;DR: In this paper, the effect of buoyancy on convection heat transfer for transitional and turbulent water flow between horizontal parallel plates was investigated. But the results for the top plate were attributed to boundary-layer laminarization, while those for the bottom plate are attributed to heat transfer enhancement by free convection.
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TL;DR: In this paper, the mixed convection flow over a horizontal plate is investigated and the boundary-layer equations, modified to account for the hydrostatic pressure variation across the boundary layer, are solved numerically by a finite-difference scheme.
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TL;DR: In this paper, the effects of fin thickness and free-stream turbulence on the flow and heat transfer characteristics of a two-dimensional system with a staggered array of vertical flat plates used in the free-forced mixed convection regime at low Reynolds number are discussed.
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TL;DR: In this paper, the effects of inertia on convection in a fluid-saturated porous medium are considered, and it is shown that the effect of quadratic drag is physically significant for natural convection, at realistic values of the Rayleigh number.
Abstract: The effects of inertia (involving a drag which is quadratic in the velocity) on convection in a fluid‐saturated porous medium are considered. It is shown that the effect of quadratic drag is physically significant for natural convection, at realistic values of the Rayleigh number, in a thin layer of a medium whose overall Prandtl number is small. The qualitative effect of quadratic drag on the global stability of the conduction regime, and on bifurcation into the convection regime, is reported. Convection in an inclined slab of material is also discussed.
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TL;DR: In this paper, the fully developed laminar mixed-convection flow in horizontal ducts of rectangular, circular and semicircular cross-sections has been studied using a numerical model of the governing equations of motion, subject to the Boussinesq approximation and an axially uniform heat-flux condition.
Abstract: The fully developed laminar mixed-convection flow in horizontal ducts of rectangular, circular and semicircular cross-sections has been studied using a numerical model of the governing equations of motion, subject to the Boussinesq approximation and an axially uniform heat-flux condition. Dual solutions with a two- and a four-vortex flow pattern have been observed in all cases. The rectangular geometry, with its aspect ratio and Grashof number as parameters, is posed as a two-parameter problem. In this parameter-space, the critical points where the transition between the two- and the four-vortex pattern occur, follow a tilted cusp. This is akin to the phenomenon in the Taylor problem which has been thoroughly investigated by Benjamin and co-workers in a general study of bifurcation phenomena for viscous flow problems. The bifurcation phenomenon in circular ducts, which is essentially a one-parameter problem, has features similar to that observed for the Dean problem, by Nandakumar and Masliyah.
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TL;DR: In this paper, the authors investigated the thermal conditions along the partition are not known beforehand; rather, they are an outcome of the coupling of the natural convection systems on either side of the enclosure partition.
Abstract: Natural convection in an inclined enclosure with a centrally located, complete partition has been investigated by a finite-difference procedure. The thermal conditions along the partition are not known beforehand; rather, they are an outcome of the coupling of the natural convection systems on either side of the enclosure partition. To resolve this coupling, a consecutive calculation procedure is used in which the natural convection on either side of the enclosure is successively solved (until convergence) with information exchange in each cycle of solution. Results have been obtained for enclosures with overall aspect ratios of 1 and 2 for Rayleigh numbers up to 107 and for inclination angles of 30, 45, 60, and 90 degrees. Results indicate that the strength of the convective motion and the average Nusselt number are both considerably reduced owing to the presence of the partition. The partition temperature increases monotonically along its length. For a vertical enclosure, the non-uniformity in the parti...
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TL;DR: In this paper, the effects of phase change between water vapor and ice on heat transfer were modeled and quantified as linear functions of Ra/Racr, where Ra is the Rayleigh number and Racr refers to the critical value for the onset of Benard convection.
Abstract: Buoyancy-driven flows of air in show are modeled including the effects of phase change and inclination. Phase change between water vapor and ice is important because of latent heat terms in the energy equation. Upper boundaries of the snow are taken as either permeable or impermeable, with temperature or heat flux specified at the lower boundary. When the ratio of thermal to mass diffusivity is greater than 1, phase change intensifies convection. When this ratio is less than 1, phase change damps convection. The effects of permeable top and uniform heat flux bottom boundary conditions on heat transfer are quantified and described as linear functions of Ra/Racr, where Ra is the Rayleigh number and Racr refers to the critical value for the onset of Benard convection. The slope of each function depends only on the thermal boundary condition at the lower boundary. If a snow cover is inclined, Rayleigh convection occurs for any nonzero Rayleigh number. Velocity profiles for flows in inclined layers with permeable tops are derived, and it is found that velocity is proportional to Ra sin Φ, where Φ is the angle of inclination from the horizontal. The numerical results for different boundary conditions compare reasonably well with experimental results from the literature.
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TL;DR: In this article, a finite-difference procedure was used to investigate the effect of conduction on Laminar natural convection between finitely conducting vertical plates, and the results indicated that conduction has a significant influence on the heat transfer rate.