Showing papers on "Combined forced and natural convection published in 1994"

On large-scale circulations in convecting atmospheres

Abstract: The dominant thinking about the interaction between large-scale atmospheric circulations and moist convection holds that convection acts as a heat source for the large-scale circulations, while the latter supply water vapour to the convection. We show that this idea has led to fundamental misconceptions about this interaction, and offer an alternative paradigm, based on the idea that convection is nearly in statistical equilibrium with its environment. According to the alternative paradigm, the vertical temperature profile itself, rather than the heating, is controlled by the convection, which ties the temperature directly to the subcloud-layer entropy. The understanding of large-scale circulations in convecting atmospheres can, therefore, be regarded as a problem of understanding the distribution in space and time of the subcloud-layer entropy. We show that the subcloud-layer entropy is controlled by the sea surface temperature, the surface wind speed, and the large-scale vertical velocity in the convecting layer, and demonstrate how the recognition of this control leads to a simple, physically consistent view of large-scale flows, ranging from the Hadley and Walker circulations to the 30–50-day oscillation. In particular, we argue that the direct effect of convection on large-scale circulations is to reduce by roughly an order of magnitude the effective static stability felt by such circulations, and to damp all of them.

Convection enhanced diffusion for periodic flow

Abstract: This paper studies the influence of convection by periodic or cellular flows on the effective diffusivity of a passive scalar transported by the fluid when the molecular diffusivity is small. The flows are generated by two-dimensional, steady, divergence-free, periodic velocity fields.

Onset of thermal convection in fluids with temperature‐dependent viscosity: Application to the oceanic mantle

Abstract: Heat flow measurements through old seafloor demonstrate that the oceanic lithosphere is heated from below away from hot spot tracks. We reevaluate the hypothesis of small-scale convection beneath the lithosphere with laboratory experiments in fluids whose viscosity depends strongly on temperature. Rayleigh numbers were between 106 and 108 and viscosity contrasts were up to 106. A layer of fluid was impulsively cooled from above, and a cold boundary layer grew at the top of the fluid layer. After a finite time, convective instabilities developed in the lowermost part of the boundary layer, while the upper part remained stagnant. The variation of surface heat flow as a function of time reflects the three-dimensional nature of the flow and the presence of a thick lid. At viscosity contrasts greater than 103, this variation is very similar to what is observed on the oceanic lithosphere. For small times, heat flow follows the behavior of a half-space cooled from above by conduction. Some time after the onset of convection, it deviates from the conductive evolution and settles to a value which seems almost constant over a length of time equal to a few multiples of the onset time. The occurrence of small-scale convection is difficult to detect in global data sets of seafloor depths. The onset of convection is marked by a small “trough” in the local subsidence curve but does not occur at the same time everywhere because of the probabilistic nature of the instability process. Later instabilities occur independently of each other and, at any given age, involve a region of small horizontal extent below a thick lid. The characteristics of the instability depend on the function describing the variation of viscosity with temperature. Scaling laws are derived for the onset time and for the surface heat flow. The requirement that small-scale convection supplies 45 mW m−2 to the oceanic lithosphere provides a relationship between the activation enthalpy for creep and the asthenosphere viscosity. For a range of activation enthalpy of 250 to 600 kJ mol−1, the asthenosphere viscosity must be between 3×1018 and 4×1017 Pa s. The thickness of the stagnant lid and the temperature difference driving small-scale convection are predicted to be about 80 km and 200°C, respectively.

A comparison of two dynamic subgrid closure methods for turbulent thermal convection

Abstract: Two dynamic subgrid‐scale (SGS) closure methods for turbulent thermal convection are described. The first method assumes the dissipation rate equals the SGS energy production rate that includes a troublesome buoyancy term, while the second method avoids this complication with a simplifying scale analysis. Tests with large‐eddy simulations (LES) of thermal convection reveal that the second method is computationally efficient, and produces results agreeing with direct numerical simulation (DNS) data, as well as values predicted by the inertial subrange theory. Within the LES, the SGS representation is locally and dynamically adjusted to match the statistical structure of the smallest resolvable eddies.

On coupling between the Poincare equation and the heat equation

Abstract: It has been suggested that in a rapidly rotating fluid sphere, convection would be in the form of slowly drifting columnar rolls with small azimuthal scale (Roberts 1968; Busse 1970). The results in this paper show that there are two alternative convection modes which are preferred at small Prandtl numbers. The two new convection modes are, at leading order, essentially those inertial oscillation modes of the Poincare equation with the simplest structure along the axis of rotation and equatorial symmetry: one propagates in the eastward direction and the other propagates in the westward direction; both are trapped in the equatorial region. Buoyancy forces appear at next order to drive the oscillation against the weak effects of viscous damping. On the basis of the perturbation of solutions of the Poincare equation, and taking into account the effects of the Ekman boundary layer, complete analytical convection solutions are obtained for the first time in rotating spherical fluid systems. The condition of an inner sphere exerts an insignificant influence on equatorially trapped convection. Full numerical analysis of the problem demonstrates a quantitative agreement between the analytical and numerical analyses.

Mixed Convection From Simulated Electronic Components at Varying Relative Positions in a Cavity

Abstract: A numerical study of the combined forced and natural convective cooling of heat-dissipating electronic components, located in a rectangular enclosure, and cooled by an external through flow of air is carried out. A conjugate problem is solved, describing the flow and thermal fields in air, as well as the thermal field within the walls of the enclosure and the electronic components themselves. The interaction between the components is of interest here, depending on their relative placement in the enclosure, and different configurations are considered. For Re=100 laminar, steady flow is predicted for up to Gr/Re 2 =10, but R single-frequency oscillatory behavior is observed for most of the configurations studied, at Gr/R 2 =50

Temperature effects in capillary electrophoresis 2: Some theoretical calculations and predictions

Abstract: The dependence of the temperature excess, θ, in the capillary bore on the applied power, EI, is considered for both natural and forced convective cooling, using classical heat equations. The dependence of θ on EI is found to be linear for forced convection but not for natural convection. Use of forced convective cooling and capillaries of large outer diameter reduces θ. Direct comparison of the performance of different systems can be achieved by consideration of θ. Column performance is ultimately limited by thermal gradients across the capillary bore.

Strongly nonlinear convection cells in a rapidly rotating fluid layer

Abstract: We investigate the properties of some strongly nonlinear convection cells which may occur in a rapidly rotating fluid layer. Although the stability properties of such layers have been extensively studied, most of the theoretical work concerned with this topic has been based upon either linear or weakly nonlinear analyses. However, it is well known that weakly nonlinear theory has a limited domain of validity for if the amplitude of the convection cells becomes too large then the mean temperature profile within the layer is dramatically perturbed away from its undisturbed state and the assumptions underpinning weakly nonlinear theory break down. It is the case for most fluid stability problems that when the stage is reached that the mean flow is significantly altered by the presence of instability modes, then analytical progress becomes impossible. The problem can then only be resolved by a numerical solution of the full governing equations but we show that for the case of convection rolls within a rapidly rotating layer this sequence of events does not arise. Instead, the properties of large amplitude convection rolls (which are sufficiently strong so as to completely restructure the mean temperature profile) can be determined by analytical methods. In particular, the whole flow structure can be deduced once a single, very simple eigenproblem has been solved. This solution enables us to discuss how large amplitude cells can significantly affect the characteristics of the flow leading to greatly enhanced heat transfer across the layer.

State space approach to unsteady two-dimensional free convection flow through a porous medium

Abstract: The equations of magnetohydrodynamic unsteady two-dimensional free convection flow through a porous medium bounded by an infinite vertical porous plate are cast into matrix form using the state space and Laplace-transform techniques. The results obtained can be used to generate solutions in the Laplace-transform domain to a broad class of problems in magnetohydrodynamic free convection flow. The technique is applied to a heated vertical plate problem and to a problem pertaining to a plate under uniform heating. The inversion of the Laplace-transforms is carried out using a numerical approach. Numerical results for the temperature, velocity, and skin friction distributions are given and illustrated graphically for both problems.

Heat convection in a 180-deg turning duct with different turn configurations

Abstract: The numerical results for secondary flow patterns and heat transfer distribution in a two-pass, square duct with a 180-deg sharp turn are presented to examine the effects of three different turning configurations: 1) straight-corner turn, 2) rounded-corner turn, and 3) circular turn. The simulation employs a nonstaggered grid, pressure-based, finite difference method and solves for three-dimensional transport equations in curvilinear coordinates. Modeling of turbulence uses an extended version of k-? model. The computed results reveal that secondary flow in the post-turn region displays combined features of a bend-induced, Dean-type circulation and a form-induced separation behind the partition wall. The detailed flow structure as well as its effect on the local heat transfer varies significantly with different turn configurations. At the turn, the straight-corner case has the strongest turn-induced heat transfer enhancement, while the circular turn has the weakest. In the post-turn region heat transfer with circular turn surpasses those of the other two configurations by almost the same difference in the turning region. Average heat transfer results from the present numerical modeling agree favorably with experimental data.

Natural Convection Over a Rotating Cylindrical Heat Source in a Rectangular Enclosure

Abstract: A numerical study of laminar two-dimensional natural convection heat transfer from a uniformly heated horizontal cylinder rotating about its center, and placed in an isothermal rectangular enclosure, is performed using a spectral element method. The physical aspects of the flow and its thermal behavior are studied for a wide range of pure natural convection to mixed convection at low and high rotational speeds of the cylinder. The computer program has been validated against experimental correlations available on pure natural convection of heated bodies in enclosures. The rotation of the cylinder has been found to enhance the heat transfer. At low ratios of Rayleigh number to the square of the rotational Reynolds number, Ra / Reω 2, the maximum temperature on the cylinder surface is decreased by as much as 25–35% from similar cases with fixed cylinders. At moderate values of Ra/ Reω 2, the thermal plume rising above the cylinder is shifted in the rotation direction and the angular shift decreases as Ra / R...

Enhancement of Heat Transfer by Thermocapillary Convection around Bubbles -a Numerical Study

Abstract: For a gas bubble floating in a liquid-filled rectangular enclosure, the effect of thermocapU-lary convection on fluid flow and heat transfer is studied in a cross section with a two-dimensional model. A transient finite difference scheme is applied for the numerical calculations. For a fluid with Pr = 1.93, the overall heat transfer in the liquid is presented for selected configurations in terms of the dimensionless numbers Nu and Ma. Contrary to the common view that an enclosed gas volume would reduce the heat transfer due to its insulating behavior, the energy transport is rather augmented by the thermocapillary convection acting on the free surface. For higher Marangoni numbers, oscillatory flow behavior occurs.

Convection with internal heat sources and thermal turbulence in the Earth's mantle

Abstract: SUMMARY The influence of internal heat sources on mantle convection is investigated using numerical calculations of 2-D thermal convection in an infinite Prandtl number, incompressible fluid. The geometry is a cylindrical annulus with inner and outer radii in proportion to the whole mantle. Time-dependent calculations are made starting from random initial conditions, with Rayleigh numbers RaT (based on boundary-temperature difference) and Ra, (based on internal-heat production) in the range 1dsRaTs lo7 and OsRa,524RaT. At fixed RaT, increasing Ra, results in transitions in flow structure from steady cells, to a pattern of stationary cells with time-variable amplitude, and finally to thermally turbulent convection with a non-stationary cell count. For RaT 10' and Ra, >RaT approximately, the travelling plumes disrupt the large-scale circulation, producing turbulent convection. At Ra, = lo7 the flow is fully developed thermal turbulence, and for Ra, > 0, consists of a rapidly fluctuating, irregular flow driven by transient rising and sinking sheets of buoyant fluid. Large fluctuations in total kinetic energy occur in this regime, with periodicities ranging from 40 to 1400Myr. The transition to thermal turbulence occurs in these calculations at Rayleigh numbers well below the value estimated for subsolidus convection in the mantle, suggesting thermally turbulent convection may occur in the mantle, a consequence of internal heat sources. Thermal turbulence offers an explanation for long-term fluctuations in the rate of subduction, sea-floor spreading and global volcanic activity.

A saline laboratory model of the planetary convective boundary layer

Abstract: A laboratory water-analog of clear-air penetrative convection in the atmosphere has been constructed to continue studies of the turbulent dispersion of buoyant plumes in the convective boundary layer (CBL). A unique feature is the utilization of saline rather than thermal convection, which has been made possible by the development of a reliable method for delivering a controllable buoyancy flux through a porous membrane. It has been shown in an earlier paper that at typical laboratory scales, a saline convection tank is well suited to modelling buoyant plume dipersion under strongly convective (light wind) conditions. A range of experiments has clearly demonstrated the validity of the model. Results for density and velocity variances show much less scatter than most comparable measurements because of the greatly improved sampling that is possible in the tank. The results are generally in good agreement with field data and other laboratory simulations but the improved accuracy of the data has highlighted the anomalously low values for the horizontal velocity variances produced by large-eddy simulations of the CBL. The cause of this apparent underprediction remains unresolved.

Multicellular natural convection of a low prandtl number fluid between horizontal concentric cylinders

Abstract: Two-dimensional natural convection of a fluid of low Prandtl number (Pr = 0.02) in an annulus between two concentric horizontal cylinders is numerically investigated in a wide range of gap widths. For low Grashof numbers, a steady unicellular convection is obtained. Above a transition Grashof number that depends on the gap width, a steady bicellular flow occurs. With further increase of the Grashof number, steady or time-periodic multicellular convection occurs, and finally, complex unsteady convective flow appears. A plot is presented that predicts the type of flow patterns for various combinations of gap widths and Grashof numbers.

Oscillatory buoyant thermocapillary flow

Abstract: A computational study of the character and stability of two‐dimensional buoyant thermocapillary flows, valid to leading order in capillary number (Ca), is conducted in the Grashof number (Gr), Reynolds number (Re), aspect ratio, and Prandtl number (Pr) parameter space Calculations of thermocapillary convection for low Pr fluids have generally produced steady results Calculations of pure buoyant convection (Re=0) exhibit a Hopf bifurcation at Grcr (no thermocapillarity) that is well understood Thus, the combined thermocapillary buoyant problem is studied to investigate the onset of oscillatory convection in the limit Gr→0 The unsteady natural convection pattern at fixed Gr≳Grcr is modified only slightly for low values of Re When thermocapillarity acts in conjunction with buoyancy (Re≳0) it is stabilizing, in that the transition to unsteady flow occurs at Gr≳Grcr, as defined for the strictly buoyant problem When thermocapillarity acts in opposition to buoyancy (Re<0), it is destabilizing for relativel

Theoretical analysis on mixed convection boundary layer flow over a wedge with uniform suction or injection

Abstract: Forced and free mixed convection boundary layer flow over a wedge with uniform suction or injection is theoretically investigated. Nonsimilar partial differential equations are transformed into ordinary differential equations by means of difference-differential method. The solutions of the resulting equations are obtained in integral forms and are calculated by iterative numerical procedures. The results were given for velocity profiles, temperature profiles, friction and heat transfer parameters for various values of suction/injection parameter, pressure gradient parameter and buoyancy parameter.