Showing papers on "Natural convection published in 1999"

Streaming potential in porous media: 2. Theory and application to geothermal systems

Abstract: Self-potential electric and magnetic anomalies are increasingly being observed associated with hydrothermal fields, volcanic activity, and subsurface water flow. Until now a formal theoretical basis for predicting streaming potential of porous materials has not been available. We develop here a model giving both the macroscopic constitutive equations and the material properties entering these equations. The material properties, like the streaming potential coupling coefficient, depend on pore fluid salinity, temperature, water and gas saturations, mean grain diameter, and porosity. Some aspects of the model are directly tested with success against laboratory data. The streaming potential increases with temperature, grain size, and gas saturation, and decreases with salinity. At the scale of geological structures the model provides an explanation for the presence of kilometer-scale dipolar self-potential anomalies in geothermal systems and volcanoes. Positive self-potential anomalies are associated with fluid discharge areas, whereas negative self-potential anomalies are associated with fluid recharge areas. Self-potential anomaly maps determined at the surface of active hydrothermal fields appear to be a powerful way of mapping the fluid recharge and discharge areas. In the case of free convection the vorticities of the convection pattern generate a magnetic field. The greater these vorticities, the greater the associated magnetic field. It follows that hydrothermal systems act as natural geobatteries because of the flow of pore fluids in the subsurface of these systems.

Liquid Cooling of Electronic Devices by Single-Phase Convection

Abstract: Fundamentals of Heat Transfer and Fluid Flow. Natural Convection. Channel Flows. Jet Impingement Cooling. Heat Transfer Enhancement. Appendices. References. Indexes.

Analytical forced convection modeling of plate fin heat sinks

Abstract: An analytical model is presented that predicts the average heat transfer rate for forced convection air cooled plate fin heat sinks for use in the design and selection of heat sinks for electronics applications. Using a composite solution based on the limiting cases of fully-developed and developing flow between isothermal parallel plates, the average Nusselt number can be calculated as a function of the heat sink geometry and fluid velocity. The resulting model is applicable for the full range of Reynolds number, 0.1

Heat transport in stagnant lid convection with temperature‐ and pressure‐dependent Newtonian or non‐Newtonian rheology

Abstract: A numerical model of two-dimensional Rayleigh-Benard convection is used to study the relationship between the surface heat flow (or Nusselt number) and the viscosity at the base of the lithosphere. Newtonian or non-Newtonian, temperature- and pressure-dependent rheologies are considered. In the high Rayleigh number time-dependent regime, calculations yield Nu ∝ RaBL1/3beff−4/3 where beff is the effective dependence of viscosity with temperature at the base of the upper thermal boundary layer and RaBL is the Rayleigh number calculated with the viscosity νBL (or the effective viscosity) at the base of the upper thermal boundary layer. The heat flow is the same for Newtonian and non-Newtonian rheologies if the activation energy in the non-Newtonian case is twice the activation energy in the Newtonian case. In this chaotic regime the heat transfer appears to be controlled by secondary instabilities developing in thermal boundary layers. These thermals are advected along the large-scale flow. The above relationship is not valid at low heat flow where a stationary regime prevails and for simulations forced into steady state. In these cases the Nusselt number follows a trend Nu ∝ RaBL1/5beff−1 for a Newtonian rheology, as predicted by the boundary layer theory. We argue that the equilibrium lithospheric thickness beneath old oceans or continents is controlled by the development of thermals detaching from the thermal boundary layers. Assuming this, we can estimate the viscosity at the base of the stable oceanic lithosphere. If the contribution of secondary convection to the surface heat flux amounts to 40 to 50 mW m−2, the asthenospheric viscosity is predicted to be between 1018 and 2×l019 Pa s.

Electrohydrodynamic behaviour of a drop subjected to a steady uniform electric field at finite electric Reynolds number

Abstract: The electrohydrodynamic flow associated with a fluid drop in an electric field is a consequence of the tangential electric stress at the fluid interface. The tangential viscous stress due to the electrohydrodynamic flow arises to just balance the tangential electric stress at the fluid interface so that the traction boundary condition is satisfied. Influenced by both the local electric stress and viscous stress, the drop interface may exhibit various shapes. The presence of fluid flow also leads to charge convection phenomena. The relative significance of the charge convection effect is usually measured in terms of the electric Reynolds number, Re E , defined as the ratio of the timescales of charge convection by flow and that for charge relaxation by ohmic conduction. This work presents a quantitative analysis of the charge convection effects in a framework of the leaky dielectric model at finite Re E , which has not been considered in previous investigations. Axisymmetric steady flows driven by an applied uniform electric field about a deformable fluid drop suspended in an immiscible fluid are studied by computational means of the Galerkin finite–element method with supplementary asymptotic analysis. The results of finite–element computations are in general agreement with the prediction by the asymptotic analysis for spherical drops at vanishingly small Re E . A common effect of charge convection is found to reduce the intensity of electrohydrodynamic flow. As a consequence, oblate drops are predicted to be less deformed in an electric field when charge convection is taken into account. The prolate drops are often associated with an equator–to–pole flow, which convects charges toward the poles to form a charge distribution resembling that in a highly conducting drop immersed in an insulating medium. Therefore, charge convection tends to enhance the prolate drop deformation. In many cases, charge convection effects are found to be significant even at apparently small Re E , corresponding to the charge relaxation time–scale about 10 −3 s, suggesting that many experimental results reported in the previous publications could have been influenced by charge convection effects.

Combined heat and mass transfer in natural convection flow from a vertical wavy surface

Abstract: In the present paper, effects of combined buoyancy forces from mass and thermal diffusion by natural convection flow from a vertical wavy surface have been investigated using the implicit finite difference method. Here we have focused our attention on the evolution of the surface shear stress,f″(0), rate of heat transfer,g′(0), and surface concentration gradient,h′(0) with effect of different values of the governing parameters, such as the Schmidt number Sc ranging from 7 to 1500 which are appropriate for different species concentration in water (Pr=7.0), the amplitude of the waviness of the surface ranging from 0.0 to 0.4 and the buoyancy parameter,w, ranging from 0.0 to 1.

Effect of Surface Radiation on Natural Convection in a Square Enclosure

Abstract: Results of an experimental study of heat transfer by natural convection and surface radiation in an air-e lled squareenclosureusingadifferentialinterferometerarereported.Theenclosurecomprisestwodifferentiallyheated vertical walls and two horizontal adiabatic walls. The suppression of natural convection in the presence of surface radiation has been demonstrated experimentally. For the case of an enclosure with highly emissive walls, mean Nusselt number correlations for convection and radiation, as well as combined convection and radiation, are also presented in terms of Grashof number in the laminar range. Nomenclature d = width of the enclosure, m Gr = Grashof number, gb (Th i Tc)d 3 /m 2 h = local heat transfer coefe cient along the hot wall, W/m 2 K N h = average heat transfer coefe cient along the hot wall, W/m 2 K km = thermal conductivity of air at Tm, W/m K N Nuc = Nusselt number (mean) due to convection, [(qcd)]/[(Th i Tc)km] N Nur = Nusselt number (mean) due to radiation, [(qrd)]/[(Th i Tc)km] N Nur qc = convective heat e ux entering the enclosure from the hot wall, W/m 2 qr = radiative heat e ux entering the enclosure from the hot wall, W/m 2 qt = total heat e ux entering the enclosure, (qc C qr), W/m 2

Mixing and compositional stratification produced by natural convection: 1. Experiments and their application to Earth's core and mantle

Abstract: An extensive series of laboratory experiments is used to quantify the circumstances under which fluids can be mixed by natural convection at high flux Rayleigh number. A compositionally buoyant fluid was injected at a fixed rate into an overlying layer of ambient fluid from a planar, horizontally uniform source. The nature of the resulting compositional convection was found to depend on two key dimensionless parameters: a Reynolds number Re and the ratio U of the ambient fluid viscosity to the input fluid viscosity. Increasing the Reynolds number corresponded to increasing the vigor of the convection, while the viscosity ratio was found to determine the spacing between plumes and whether buoyant fluid rose as sheets (U 1). From measurements of the final density profile in the fluid after the experiments we quantified the extent to which buoyant liquid was mixed in terms of a thermodynamic mixing efficiency E. The mixing efficiency was found to be high (E > 0.9) when either the Reynolds number was large (Re > 100) or the viscosity ratio was small (U 200. The amount of mixing was related to whether ascending plumes generated a large-scale circulation in the ambient fluid. When our results are applied to the differentiation of the Earth's core, we suggest that the convection resulting from the release of buoyant residual liquid into the liquid outer core due to crystallization at the boundary between the inner and the outer core will probably lead to nearly complete mixing. In the dynamically very different context of the mantle, mantle plumes are predicted to ascend through the mantle and pond beneath the lithosphere, whereas convection driven by the subduction of oceanic lithosphere is expected to produce moderate to extensive mixing of the mantle. When the competing plate and plume modes of mantle convection are considered together, we find that owing to a larger driving buoyancy flux, the plate-scale flow will destroy any stratification at the top of the mantle produced by mantle plumes. Applying our results to the “stagnant lid” style of thermal convection predicted to occur in the mantles of the Moon, Mercury, Mars, Venus, and pre-Archean Earth, we expect the respective flows to produce minor thermal stratification at the respective core-mantle boundaries. In part 2 of this study [Jellinek and Kerr, this issue] we apply our results to the differentiation of magma chambers and komatiite lava flows.

Coupled heat and mass transfer by free convection over a truncated cone in porous media: VWT/VWC or VHF/VMF

Abstract: The heat and mass transfer characteristics of natural convection about a truncated cone embedded in a saturated porous medium subjected to the coupled effects of thermal and mass diffusion is numerically analyzed. The surface is maintained at variable wall temperature/concentration (VWT/VWC) or variable heat/mass flux (VHF/VMF). The transformed governing equations are solved by Keller box method. Numerical data for the dimensionless temperature profiles, the dimensionless concentration profiles, the local Nusselt number and the local Sherwood number are presented for wide range of dimensionless distance ξ, the Lewis number Le, the exponent λ, and buoyancy ratioN (orN*). In general, it has been found that when the buoyancy ratio is increasing both the local Nusselt number and the local Sherwood number increase. Increasing the value of λ and ξ increases the local surface heat and mass transfer rates. The local Nusselt (Sherwood) number increases (decreases) with decreasing the Lewis number. Furthermore, it is shown that the local Nusselt number and the local Sherwood number of the truncated cone approach those of inclined plate (full cone) for the case of ξ=0 (ξ→∞).

Weak turbulence and chaos for low Prandtl number gravity driven convection in porous media

Abstract: Low Prandtl number convection in porous media is relevant to modern applications of transport phenomena in porous media such as the process of solidification of binary alloys. The transition from steady convection to chaos is analysed by using Adomian's decomposition method to obtain an analytical solution in terms of infinite power series. The practical need to evaluate the solution and obtain numerical values from the infinite power series, the consequent series truncation, and the practical procedure to accomplish this task, transform the analytical results into a computational solution evaluated up to a finite accuracy. The solution shows a transition from steady convection to chaos via a Hopf bifurcation producing a 'solitary limit cycle’ which may be associated with an homoclinic explosion. This occurs at a slightly subcritical value of Rayleigh number, the critical value being associated with the loss of linear stability of the steady convection solution. Periodic windows within the broad band of parameter regime where the chaotic solution persists are identified and analysed. It is evident that the further transition from chaos to a high Rayleigh number periodic convection occurs via a period halving sequence of bifurcations.