Showing papers on "Combined forced and natural convection published in 1989"

Forced Convection in a Channel Filled With a Porous Medium: An Exact Solution

Abstract: In this paper fully developed forced convection in a porous channel bounded by parallel plates is considered based on the general flow model. Exact solutions are obtained and presented for both the velocity and the temperature fields. From these results the Nusselt number can be expressed in terms of the Darcy number and the inertia parameter. Finally, comparisons are made with the limiting case of no inertia and/or boundary effects. These results provide an in-depth insight into the underlying relationships between all of the pertinent variables. Furthermore, they can be used as strong candidates for bench marking of many numerical schemes.

A reassessment of the heat transport by variable viscosity convection with plates and lids

Abstract: The heat transport by a viscous fluid with temperature dependent viscosity has been studied numerically. As opposed to previous models, the top surface of the fluid clearly defines a tectonic plate with horizontally uniform velocity and subduction. Past studies failed to incorporate plates resulting in inefficient heat transport. With tectonic plates, the heat transport is as efficient as Rayleigh-Benard convection with constant viscosity; there is a strong buffering between internal temperature and heat loss. Past studies of parameterized convection which incorporated parameters indicative of a strong buffering between internal temperature and total heat output still provide the most physically plausible representation of the Earth's thermal evolution.

Mixed Convection Along a Wavy Surface

Abstract: The results of a study of mixed-convection flow along a wavy surface are presented. The forced-convection component of the heat transfer contains two harmonics. The amplitude of the first harmonic is proportional to the amplitude of the wavy surface; the second harmonic is proportional to the square of this amplitude. Thus, for a slightly wavy surface, only the influence of the first harmonic can be detected. The natural-convection component is a second harmonic, with a frequency twice that of the wavy surface. Since natural convection has a cumulative effect, the second harmonic eventually becomes the dominant component far downstream from the leading edge where forced convection is the dominant heat transfer mode. The results also demonstrate that the total mixed-convection heat flux along a wavy surface is smaller than that of a flat surface.

Mixed convection boundary layer similarity solutions: prescribed wall heat flux

Abstract: The similarity solutions for mixed convection boundary-layer flow when the wall heat flux is prescribed are analysed in detail in terms of a buoyancy parameterα andm the exponent of the free stream flow. It is shown that forα〉0 the solution approaches the free convection limit, and forα〈0, there is a range ofα,αs〈α〈0, over which dual solutions exist. The nature of the bifurcation atα=αs, and how the lower branch of solutions behaves asα→0− are also considered. It is established that the solution becomes singular asm→1/5 and the nature of this singularity is also discussed, where it is shown that two separate cases have to be treated, namely whenα is of 0(1) and whenα is small. Finally it is shown that form large the solution approaches that corresponding to exponential forms for the free stream and prescribed wall heat flux. Taken all together this information enables a complete description of how the solution behaves over all possible ranges of the parametersα andm to be deduced.

Laminar and Turbulent Natural Convection-Radiation Interactions in a Square Enclosure Filled with a Nongray Gas

Abstract: A numerical investigation of interactions oflaminar and turbulent natural convection and radiation in a differentially heated square enclosure was performed. Songray gas radiation was analyzed with the P^-approximation method for the radiative transfer equation and the weighted sum of gray gases model, A desirable compatibility was achieved in the resultant formulation for radiative transfer with the governing equations for natural convection flows. The Favre-averaged formulation was employed for analyzing turbulent flows together with a k-e model. In the analysis, a two-dimensional enclosure filled with carbon dioxide gas was considered. Solutions were obtained for a range of Grashof numbers and Prandtl numbers varying from 104 to 1010 Characteristics of flow and temperature fields were compared with predictions in the literature and were found to be in good agreement in general.

Dynamical influences from thermal‐chemical instabilities at the core‐mantle boundary

Abstract: Two-dimensional, time-dependent calculations show that the thermal and flow structures can be influenced by the lower-mantle thermal-chemical instabilities. The style of the core-mantle boundary (CMB) deformation in thermal-chemical convection is different from that obtained in thermal convection. The amplitude of CMB hills is reduced greatly from the depth-dependence of thermal expansivity, found in recent high-pressure experiments.

The brinkman model for natural convection in a shallow porous cavity with uniform heat flux

Abstract: The Brinkman model is used to study steady-stale natural convection in a shallow porous cavity with uniform heating and cooling through opposite walls. The horizontal boundaries are considered rigid-rigid, rigid-free, or free-free, and heating is through the bottom or the side wall. An approximate solution is obtained by assuming parallel flow in the core region of the cavity and a numerical solution by solving the complete governing equations. The flow and heat transfer variables are obtained in terms of the Darcy-Rayleigh number R and the Darcy number Da. The critical Darcy-Raleigh number for the onset of convection in a bottom-heated cavity is predicted. The results for a viscous fluid (Da → ∞) and the Darcy porous medium (Da → 0) emerge from the present analysis as limiting cases.

Thermosolutal Convection during Dendritic Solidification of Alloys: Part II. Nonlinear Convection

Abstract: A mathematical model of thermosolutal convection in directionally solidified dendritic alloys has been developed that includes a mushy zone underlying an all-liquid region. The model assumes a nonconvective initial state with planar and horizontal isotherms and isoconcentrates that move upward at a constant solidification velocity. The initial state is perturbed, nonlinear calculations are performed to model convection of the liquid when the system is unstable, and the results are compared with the predictions of a linear stability analysis. The mushy zone is modeled as a porous medium of variable porosity consistent with the volume fraction of, interdendritic liquid that satisfies the conservation equations for energy and solute concentrations. Results are presented for systems involving lead-tin alloys (Pb-10 wt pct Sn and Pb-20 wt pct Sn) and show significant differences with results of plane-front solidification. The calculations show that convection in the mushy zone is mainly driven by convection in the all-liquid region, and convection of the interdendritic liquid is only significant in the upper 20 pct of the mushy zone if it is significant at all. The calculated results also show that the systems are stable at reduced gravity levels of the order of 10−4 g 0 (g 0=980 cm·s−1) or when the lateral dimensions of the container are small enough, for stable temperature gradients between 2.5≤G l≤100 K·cm−1 at solidification velocities of 2 to 8 cm·h−1.

Recirculating Combined Convection in Laminar Pipe Flow

Abstract: Investigations are conducted into situations where flow recirculation occurs in laminar combined convection flows in vertical circular tubes. Particular attention is given to flows in which finite sections of the tube wall are maintained at constant temperatures, which may be either hotter or colder than the temperature of the fluid at the entrance of the tube. A numerical study is carried out in which the governing elliptic partial differential equations are expressed in finite difference form and solved using a relaxation technique. The values of the governing parameters, namely the Reynolds, Prandtl, and Grashof numbers, and the thermal and viscous boundary conditions are chosen to correspond as closely as possible to an experimental investigation that involves water being forced along a perspex vertical circular tube, which is heated and/or cooled over finite sections. It is found that the numerical model is able to predict quite accurately the location, shape, and size of the recirculation regions observed in the experiments.

Compressible convection with constant and variable viscosity: The effect on slab formation, geoid, and Topography

Abstract: Two-dimensional, Cartesian finite difference models of compressible convection with constant and variable viscosity and fixed bottom temperature are presented. Density variations according to the Adams Williamson equation of state are included. In the case of constant viscosity convection, viscous and adiabatic heating damp the flow. Compressible density variations hardly influence geoid undulations; however, the lower thermal boundary layer becomes thinner, and the mean cell temperature increases. In the case of variable viscosity, the nonlinear coupling between compression, adiabatic and viscous heating, and a temperature-, pressure-, and stress-dependent rheology leads to important consequences: The upwelling flow broadens and plumes are retarded. The flow strongly concentrates toward the downwelling region and becomes mechanically decoupled from the interior of the cell by a low-viscosity region. This mechanism seems to be important for the formation of subducting slabs. Extrapolated to mantle conditions, two low-viscosity regions are predicted flanking the slab on either side and inhibiting an early dispersal and mixing of slab material into the mantle. This process might be aided by an increase of negative buoyancy forces with depth as observed in the models. Further results are as follows: Increasing the dissipation number in variable viscosity convection may either damp or speed up convection, depending on the rheology. Models with internal heating and a fixed bottom temperature show that the threshold to time-dependent variable viscosity convection is drastically reduced if the anelastic liquid approximation is applied instead of the extended Boussinesq approximation.

The evolution of the double-diffusive instability: Salt fingers

Abstract: The finite‐amplitude growth of finger convection at an interface of two uniform solutions is studied to determine the processes that govern the scale and amplitude of the convection, the growth of the fingering interface, and the transition of the convection to turbulence. A conceptual model of fingering processes is provided and details are studied by means of direct numerical simulation. The simulations obtain full finger convection and turbulence for ratios of viscosity to diffusivities in the range between 1 and 10. The study shows that the evolution of finger convection in its entirety is characterized by the scale and amplitude of the fastest growing finger mode. In the parameter range studied, the growth of the fingering interface is found to be controlled mostly by molecular diffusion. Convective flux divergence only plays a secondary role. The growth of the interface is shown to have the effect of increasing the horizontal scale of the convection while decreasing the buoyancy flux. However, the kinetic and potential energies remain statistically stationary for fully developed finger convection. Density inversion developed within finger convection is shown to play an important role in the breakup of finger structures into turbulence. The significance of ‘‘collective’’ instability in determining this transition is not substantiated by the simulation for the parameter values studied here.