Showing papers on "Combined forced and natural convection published in 2000"

Realistic Solar Convection Simulations

Abstract: We report on realistic simulations of solar surface convection that are essentially parameter-free, but include detailed physics in the equation of state and radiative energy exchange. The simulation results are compared quantitatively with observations. Excellent agreement is obtained for the distribution of the emergent continuum intensity, the profiles of weak photospheric lines, the p-mode frequencies, the asymmetrical shape of the mode velocity and intensity spectra, the p-mode excitation rate, and the depth of the convection zone. We describe how solar convection is non-local. It is driven from a thin surface thermal boundary layer where radiative cooling produces low entropy gas which forms the cores of the downdrafts in which most of the buoyancy work occurs. Turbulence and vorticity are mostly confined to the intergranular lanes and underlying downdrafts. Finally, we present some preliminary results on magneto-convection.

Similarity solutions for hydromagnetic mixed convection heat and mass transfer for Hiemenz flow through porous media

Abstract: The problem of coupled heat and mass transfer by mixed convection in a linearly stratified stagnation flow (Hiemenz flow) in the presence of an externally applied magnetic field and internal heat generation or absorption effects is formulated. The plate surface is embedded in a uniform Darcian porous medium and is permeable in order to allow for possible fluid wall suction or blowing and has a power‐law variation of both the wall temperature and concentration. The resulting governing equations are transformed into similarity equations for the case of linearly varying wall temperature and concentration with the vertical distance using an appropriate similarity transformation. These ordinary differential equations are then solved numerically by an implicit, iterative, finite‐difference scheme. Comparisons with previously published work are performed and excellent agreement between the results is obtained. A parametric study of all involved parameters is conducted and a representative set of numerical results for the velocity and temperature profiles as well as the skin‐friction parameter, local Nusselt number, and the local Sherwood number is illustrated graphically to elucidate interesting features of the solutions.

Hydromagnetic combined heat and mass transfer by natural convection from a permeable surface embedded in a fluid‐saturated porous medium

Abstract: The problem of coupled heat and mass transfer by natural convection from a vertical, semi‐infinite flat plate embedded in a porous medium in the presence of an external magnetic field and internal heat generation or absorption effects is formulated. The plate surface is maintained at either constant temperature or constant heat flux and is permeable to allow for possible fluid wall suction or blowing. The resulting governing equations are non‐dimensionalized and transformed using a non‐similarity transformation and then solved numerically by an implicit, iterative, finite‐difference scheme. Comparisons with previously published work are performed and excellent agreement is obtained. Useful correlations containing the various physical parameters for both isothermal and isoflux wall conditions are reported. A parametric study of all involved parameters is conducted and a representative set of numerical results for the velocity, temperature and concentration profiles as well as the skin‐friction parameter, Nusselt number, and the Sherwood number is illustrated graphically to show typical trends of the solutions.

Forced Convection Heat Transfer to Phase Change Material Slurries in Circular Ducts

Abstract: Conclusions Expressions for the analytical temperature distribution and efŽ ciency of a heat pipe Ž n were derived and compared with experimental data. Two heat pipe Ž n cases were studied,  ush mounted and inserted into the object. The derived expressions are useful as a design tool. They allow the designer to compare heat pipe Ž ns to standard Ž ns before doing a detailed heat pipe design. Further researchcould focus on variations in heat pipe design and geometry.Thesecouldincludenonconstantpropertiesandboundary conditions.For this work, the wall cross-sectionalarea, the internal convectioncoefŽ cient, and the external convectioncoefŽ cient were assumed constant. The impact of these assumptions on accuracy should be investigated. It would also be interesting to extend the analysis to Ž ns in radiation environments.

Combined heat and mass transfer along a vertical moving cylinder with a free stream

Abstract: The mixed convection flow over a continuous moving vertical slender cylinder under the combined buoyancy effect of thermal and mass diffusion has been studied. Both uniform wall temperature (concentration) and uniform heat (mass) flux cases are included in the analysis. The problem is formulated in such a manner that when the ratio λ(= u w/(u w + u ∞), where u w and u ∞ are the wall and free stream velocities, is zero, the problem reduces to the flow over a stationary cylinder, and when λ = 1 it reduces to the flow over a moving cylinder in an ambient fluid. The partial differential equations governing the flow have been solved numerically using an implicit finite-difference scheme. We have also obtained the solution using a perturbation technique with Shanks transformation. This transformation has been used to increase the range of the validity of the solution. For some particular cases closed form solutions are obtained. The surface skin friction, heat transfer and mass transfer increase with the buoyancy forces. The buoyancy forces cause considerable overshoot in the velocity profiles. The Prandtl number and the Schmidt number strongly affect the surface heat transfer and the mass transfer, respectively. The surface skin friction decreases as the relative velocity between the surface and free stream decreases.

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, , and accurately predicts the experimental results to within an RMS difference of 2.1%.

effects of driving mechanisms in geodynamo models

Abstract: We compare the influence of different mechanisms for driving convection in the Earth's core on the structure of the magnetic and velocity fields using a 3D numerical dynamo model. We find dynamos with a dipolar magnetic field in cases of chemical convection or convection driven by an imposed temperature contrast. With purely internal heating we obtain only dynamos with a quadrupolar or more complex field. The relative strength of convection and magnetic field generation in the regions close to the poles depends on whether a condition of fixed composition or of fixed chemical flux is specified on the inner core boundary. If applicable to the geodynamo, our results favor the dominance of chemical convection during the past 3 Gyr.

Experiments to simulate effect of Marangoni convection on weld pool shape

Abstract: Stationary welds of sodium nitrate (NaNO 3 , a high-Prandtl-number material) and gallium (Ga, a low-melting-point, low-Prandtl-number material) were made with a defocused CO 2 laser beam to simulate the effect of Marangoni convection on the shape of arc weld pools without a surface-active agent. A Peclet number representing the ratio of (heat transport by convection)/(heat transport by conduction) was defined as Pe = LV/a, where L is the pool surface radius, V the maximum outward surface velocity and a the thermal diffusivity. The Ga and NaNO 3 pools represented the low and high extremes of Pe, respectively, with commonly welded metals such as aluminum, steel and stainless steel falling in between. By going to these extremes, the effect of convection on the pool shape could be much more easily understood. For Ga, Pe was low because low V (weak Marangoni convection) and high a promoted conduction down into the pool, and the resultant pool bottom was concave. For NaNO 3 , however, Pe became high easily because high V (strong Marangoni convection) and very low a promoted outward convective heat transport, and the resultant pool bottom was shallow and flat. Reducing the beam diameter further increased V (even stronger Marangoni convection) and Pe. The fast outward surface flow turned and penetrated downward at the pool edge, resulting in a convex pool bottom. Both the flat and convex pool bottoms are a clear indication Marangoni convection dominated over gravity-induced buoyancy convection. It is proposed that, in the absence of both a surface-active agent and a significant electromagnetic force, the pool bottom convexity increases with increasing Pe. It was shown that, for a given material composition and welding process, the weld shape often reveals a good deal about the nature of weld pool convection.

Mixed convection cooling of a heated, continuously stretching surface

Abstract: An numerical study of the flow and heat transfer characteristics associated with a heated, continuously stretching surface being cooled by a mixed convection flow has been carried out. The relevant heat transfer mechanisms are of interest in a wide variety of practical applications, such as hot rolling, continuous casting, extrusion, and drawing. The surface velocity of the continuously stretching sheet was assumed to vary according to a power-law form, that is, u w (x)=Cx p . Two conditions of surface heating were considered, a variable wall temperature (VWT) in the form T w (x)−T ∞=Ax n and a variable surface heat flux (VHF) in the form q w (x)=Bx m . The governing differential equations are transformed by introducing proper nonsimilarity variables and solved numerically using a procedure based on finite difference approximations. Results for the local Nusselt number and the local friction coefficient are obtained for a wide range of governing parameters, such as the surface velocity parameter p, the wall temperature exponent n, the surface heat flux exponent m, the buoyancy force parameters (ξ for the VWT case and χ for the VHF case), and Prandtl number of the fluid. It is found that the local Nusselt number is increased with increasing the velocity exponent parameter p for the VWT case, while the opposite trend is observed for the VHF case. The local friction coefficient is increased for a decelerated stretching surface, while it is decreased for an accelerated stretching surface. Also, appreciable effects of the buoyancy force on the local Nusselt number and the local friction coefficient are observed for both VWT and VHF cases, as expected.

A study of free convection induced by a vertical wavy surface with heat flux in a porous enclosure

Abstract: Free convection induced by a vertical wavy surface with uniform heat flux in a porous enclosure has been analyzed numerically using the finite element method (FEM). The flow and the convection process in the cavity is found to be sensitive to the flow parameter Rayleigh number (Ra), and geometrical parameters like wave amplitude (a), wave phase (φ), and number of waves (N) in the vertical dimension of the cavity. The study reveals that small sinusoidal drifts from the smoothness of a vertical wall with a phase angle of 60o and high frequency enhances the free convection from a vertical wall with uniform heat flux.

Mixed convection in a rectangular enclosure with discrete heat sources

Abstract: A numerical study is carried out on mixed convective heat transfer in an enclosure. The discrete heat sources are embedded on a vertical board, which is situated on the bottom wall of an enclosure. An external airflow enters the enclosure through an opening in one vertical wall and exits from another opening in the opposite wall. This study simulates a practical system, such as air-cooled electronic devices with heated elements. Emphasis is placed on the influence of the governing parameters, such as Reynolds number, Re, buoyancy parameter, Gr/Re2, location of the heat sources, and the conductivity ratio, rk, on the thermal phenomenon in the enclosure. The coupled equations of the simulated model are solved numerically using the cubic spline collocation method. The computational results indicate that both the thermal field and the average Nusselt number (Nu) depend strongly on the governing parameters, position of the heat sources, as well as the property of the heat-source-embedded board.

Mixed convection in cavities with a locally heated lower wall and moving sidewalls

Abstract: A numerical study is conducted to investigate the transport mechanism of laminar mixed convection in a shear - and buoyancy-driven cavity having a locally heated lower wall and moving cooled sidewalls. Effort is focused on the interaction of forced convection with natural convection. Localized heating is simulated by a centrally located heat source on the bottom wall, and four different values of the dimensionless heat source length, epsilon, 1 / 5, 2 / 5, 3 / 5, and 4 / 5 of the nondimensional length of the bottom wall, are considered. Parametric studies on the effect of mixed convection parameter, Gr Re2 (also referred to as Richardson number, Ri), in the range 0.1 ? 10, on the fluid flow and heat transfer are performed for each epsilon. Local results are presented in the form of streamline and isotherm plots as well as the variation of local Nusselt number on the heated wall. Three different regimes are observed with increasing Gr Re2: forced convection (with negligible natural convection), mixed conve...

Route to chaos for moderate Prandtl number convection in a porous layer heated from below

Abstract: The route to chaos for moderate Prandtl number gravity driven convection in porous media is analysed by using Adomian's decomposition method which provides an accurate analytical solution in terms of infinite power series. The practical need to evaluate numerical values from the infinite power series, the consequent series truncation, and the practical procedure to accomplish this task, transform the otherwise analytical results into a computational solution achieved up to a desired but finite accuracy. The solution shows a transition to chaos via a period doubling sequence of bifurcations at a Rayleigh number value far beyond the critical value associated with the loss of stability of the convection steady solution. This result is extremely distinct from the sequence of events leading to chaos in low Prandtl number convection in porous media, where a sudden transition from steady convection to chaos associated with an homoclinic explosion occurs in the neighbourhood of the critical Rayleigh number (unless mentioned otherwise by 'the critical Rayleigh number' we mean the value associated with the loss of stability of the convection steady solution). In the present case of moderate Prandtl number convection the homoclinic explosion leads to a transition from steady convection to a period-2 periodic solution in the neighbourhood of the critical Rayleigh number. This occurs at a slightly sub-critical value of Rayleigh number via a transition associated with a period-1 limit cycle which seem to belong to the sub-critical Hopf bifurcation around the point where the convection steady solution looses its stability. The different regimes are analysed and periodic windows within the chaotic regime are identified. The significance of including a time derivative term in Darcy's equation when wave phenomena are being investigated becomes evident from the results.

Convective rolls and heat transfer in finite-length rayleigh-Benard convection: A two-dimensional numerical study

Abstract: A two-dimensional (2D) numerical study using a single-point algebraic k-straight theta;(2)-varepsilon-varepsilon(straight theta) turbulence closure was performed to detect the existence, origin, creation and behavior of convective rolls and associated wall Nusselt (Nu) number variation in thermal convection in 2D horizontal slender enclosures heated from below. The study covered the Rayleigh (Ra) numbers from 10(5) to 10(12) and aspect ratios from 4:1 to 32:1. The time evolution of the convective rolls and the formation of the corner vortices were analyzed using numerical flow visualization, and the correlation between roll structures and heat transfer established. A major consequence of the imposed two dimensionality appeared in the persistence of regular roll structures at higher Ra numbers that approach a steady state for all configurations considered. This finding contradicts the full three-dimensional direct numerical simulations (DNS), large eddy simulations (LES), and three-dimensional transient Reynolds-averaged Navier-Stokes (TRANS) computations, which all show continuously changing unsteady patterns. However, the final-stage roll structures, long-term averaged mean temperature and turbulence moments, and the Nusselt number (both local and integral), are all reproduced in good agreement with the ensemble-averaged 3D DNS, TRANS, and several recent experimental results. These findings justified the 2D approach as an acceptable method for ensemble average analysis of fully 3D flows with at least one homogeneous direction. Based on our 2D computations and adopting the low and high Ra number asymptotic power laws of Grossmann and Lohse [J. Fluid Mech. 407, 27 (2000)], new prefactors in the Nu-Ra correlation for Pr=O(1) were proposed that fit better several sets of data over a wide range of Ra numbers and aspect ratios: Nu=0.1Ra(1/4)+0.05Ra(1/3). Even better agreement of our computations was achieved with the new correlation Nu=0.124 Ra0.309 proposed recently by Niemela et al. [Nature (London) 404, 837 (2000)] for 10(6)

Numerical study of heat transfer in a non-Newtonian Carreau-fluid between rotating concentric vertical cylinders

Abstract: Centrifugally forced convection, mixed and natural convection are numerically studied in a short vertical annulus with a heated and rotating inner cylinder. The cooled outer cylinder is at rest and the hortizontal endplates are assumed adiabatic. The effect of a non-Newtonian shear thinning viscosity modeled by the Carreau-shifted constitutive equation is examined. Computations were performed for different values of the flow index and Weissenberg number with the Prandtl number based on the zero-shear-rate viscosity, the radius ratio and the ratio of height to gap spacing are kept fixed. The results show that the shear thinning effect decreases the friction factor at the rotating cylinder and increases the heat transfer through the annular gap. It is also shown that the reduction in apparent viscosity may produce oscillatory flows, especially for centrifugally forced convection.

Thermal convection in fluidized granular systems

Abstract: Thermal convection is observed in molecular dynamic simulations of a fluidized granular system of nearly elastic hard disks moving under gravity, inside a square box. Boundaries introduce no shearing or time dependence, but the energy injection comes from a slip (shear-free) thermalizing base. The top wall is perfectly elastic and lateral boundaries are either elastic or periodic. The spontaneous temperature gradient appearing in the system due to the inelastic collisions, combined with gravity, produces a buoyancy force that, when dissipation is large enough, triggers convection.

Linear stability analysis of mixed-convection flow in a vertical pipe

Abstract: A comprehensive numerical study on the linear stability of mixed-convection flow in a vertical pipe with constant heat flux is presented with particular emphasis on the instability mechanism and the Prandtl number effect. Three Prandtl numbers representative of different regimes in the Prandtl number spectrum are employed to simulate the stability characteristics of liquid mercury, water and oil. The results suggest that mixed-convection flow in a vertical pipe can become unstable at low Reynolds number and Rayleigh numbers irrespective of the Prandtl number, in contrast to the isothermal case. For water, the calculation predicts critical Rayleigh numbers of 80 and −120 for assisted and opposed flows, which agree very well with experimental values of Rac = 76 and −118 (Scheele & Hanratty 1962). It is found that the first azimuthal mode is always the most unstable, which also agrees with the experimental observation that the unstable pattern is a double spiral flow. Scheele & Hanratty's speculation that the instability in assisted and opposed flows can be attributed to the appearance of inflection points and separation is true only for fluids with O(1) Prandtl number. Our study on the effect of the Prandtl number discloses that it plays an active role in buoyancy-assisted flow and is an indication of the viability of kinematic or thermal disturbances. It profoundly affects the stability of assisted flow and changes the instability mechanism as well. For assisted flow with Prandtl numbers less than 0.3, the thermal–shear instability is dominant. With Prandtl numbers higher than 0.3, the assisted-thermal–buoyant instability becomes responsible. In buoyancy-opposed flow, the effect of the Prandtl number is less significant since the flow is unstably stratified. There are three distinct instability mechanisms at work independent of the Prandtl number. The Rayleigh–Taylor instability is operative when the Reynolds number is extremely low. The opposed-thermal–buoyant instability takes over when the Reynolds number becomes higher. A still higher Reynolds number eventually leads the thermal–shear instability to dominate. While the thermal–buoyant instability is present in both assisted and opposed flows, the mechanism by which it destabilizes the flow is completely different.

Effect of Double Dispersion on Mixed Convection Heat and Mass Transfer in Non-Darcy Porous Medium

Abstract: Similarity solution for the problem of hydrodynamic dispersion in mixed convection heat and mass transfer from vertical surface embedded in porous media has been presented. The flow induced by the density variations is comparable with the freestream flow. The heat and mass transfer in the boundary layer region for aiding and opposing buoyancies in both aiding and opposing flows has been analyzed. The structure of the flow, temperature, and concentration fields in the Darcy and non-Darcy porous media are governed by complex interactions among the diffusion rate (Le) and buoyancy ratio (N) in addition to the flow driving parameter (Ra/Pe). The flow, temperature, and concentration fields are analyzed and the variation of heat and mass transfer coefficients with the governing parameters are presented

Convectively Generated Internal Gravity Waves in the Lower Atmosphere of Venus. Part II: Mean Wind Shear and Wave–Mean Flow Interaction

Abstract: This paper is the second of a two-part study that numerically investigates internal gravity wave generation by convection in the lower atmosphere of Venus. Part I of this study considers gravity wave generation and propagation in the absence of mean wind shear. In Part II, the Venus westward superrotation is included, and wave–mean flow interaction is assessed. Both lower-atmosphere convection and cloud-level convection play active roles in the dynamics of the stable layer from 31- to 47-km altitude when mean wind shear is present. This result contrasts with the simulation without mean wind shear presented in Part I where cloud-level convection was primarily responsible for gravity wave generation in the stable layer. In the presence of mean wind shear, upward entrainment from lower-atmosphere convection and downward penetration from cloud-level convection are comparable in magnitude. Convectively generated internal gravity waves have horizontal wavelengths (∼25–30 km) comparable to horizontal sc...

Mixed convection in a square cavity due to heat generating rectangular body

Abstract: Flow in the cavity with heat generating body finds wide domestic and industrial applications The heat transfer characteristics and the irreversibility generated in the cavity depend on mainly the cavity size, aspect ratio of the heat generating body, and inlet/exit port locations In the present study, effect of exit port locations on the heat transfer characteristics and irreversibility generation in a square cavity with heat generating body is investigated A numerical simulation is carried out to predict the velocity and temperature fields in the cavity To examine the effect of solid body aspect ratio on the heat transfer characteristics two extreme aspect ratios (025 and 40) are considered in the analysis Fifteen different locations of exit port are introduced while air is used as an environment in the cavity It is found that non‐uniform cooling of the solid body occurs for exit port location numbers of 13 and beyond In this case, heat transfer reduces while irreversibility increases in the cavity These findings are valid for both aspect ratios of the solid body