Showing papers on "Combined forced and natural convection published in 1969"

The Anelastic Approximation for Thermal Convection

Abstract: A formal scale analysis of the equations of motion in a plane parallel atmosphere is made, assuming conditions to be such that relative fluctuations in density and temperature are small. It is found that an energetically consistent set of approximate equations can be derived which preclude the existence of acoustic motions. Such equations can be used to describe subsonic convection or internal gravity waves. Under certain conditions the analysis can be generalized to include vertical pulsations of the atmosphere.

Effect of modulation on the onset of thermal convection

Abstract: The stability of a horizontal layer of fluid heated from below is examined when, in addition to a steady temperature difference between the walls of the layer, a time-dependent sinusoidal perturbation is applied to the wall temperatures. Only infinitesimal disturbances are considered. The effects of the oscillating temperature field are treated by a perturbation expansion in powers of the amplitude of the applied field. The shift in the critical Rayleigh number is calculated as a function of frequency, and it is found that it is possible to advance or delay the onset of convection by time modulation of the wall temperatures.

Thermocapillary convection in a horizontal layer of liquid

Abstract: An exact solution is found for the equations for free convection in a planar horizontal layer of liquid with a constant temperature gradient at the boundaries. Two cases of boundary conditions for the velocity are considered: 1) the liquid is bounded by two solid planes, 2) the upper surface of the liquid is free, and the surface tension is a function of temperature.

Stability of natural convection in a vertical slot

Abstract: The stability of natural convection of a viscous fluid in a vertical slot having isothermal side walls of different temperatures is investigated analytically. Both the conduction and boundary-layer regimes are found to be unstable with respect to stationary disturbances in the form of multicellular secondary flows. Theoretical predictions of the critical Rayleigh number and of the form of the secondary flow are verified by experimental measurements.

Natural convection above unconfined horizontal surfaces

Abstract: The paper discusses free convective flows above a horizontal plate, both theoretically and on the basis of experiments which yield quantitative data. The theory is applicable to the semi-infinite plate and is extended to cover the complete range of Prandtl number values including Pr → 0 and Pr → ∞. Experiments were carried out to demonstrate the existence of a laminar boundary layer above a horizontal plate at intermediate Grashof (respectively Rayleigh) numbers, and its extent along the plate. This layer breaks down into large-eddy instability some distance from the leading edge. The value of the critical Rayleigh number for this to occur, obtained experimentally using semi-focusing colour-Schlieren photography is in reasonable qualitative agreement with previously known data (Tritton 1963a,b).

Viscous dissipation in external natural convection flows

Abstract: The effects of viscous dissipation are considered for external natural convection flow over a surface. A class of similar boundary-layer solutions is given and numerical results are presented for a wide range of the dissipation and Prandtl numbers. Several general aspects of similarity conditions for flow over surfaces and in convection plumes are discussed and their special characteristics considered. The general equations including the dissipation effect are given for the non-similar power law surface condition.

Numerical study of natural convection in an enclosure with localized heating from below—creeping flow to the onset of laminar instability

Abstract: An analytical study was made of the natural convection induced in an enclosure by a small hot spot centrally located on the floor. The enclosure was a circular cylinder, vertically oriented, with height equal to radius. A Prandtl number of 0.7 (air) was assumed; the Grashof number (Gr) was based on cylinder height and hot spot temperature. The equations of fluid flow in axisymmetric cylindrical co-ordinates were simplified with the Boussinesq approximation. The equations were solved numerically with a computationally stable, explicit method. The computation, starting from quiescent conditions, proceeded through the initial transient to the fully developed flow. Solutions were obtained for Gr from 4 × 104 to 4 × 1010. The theoretical flows are in excellent agreement with experimentally observed laminar flows (Gr [lsim ] 1.2 × 109) which are discussed in a companion paper, Torrance, Orloff & Rockett (1969). Turbulence was observed experimentally for Gr [gsim ] 1.2 × 109. When the theoretical calculations were extended to Gr = 4 × 1010, a periodic vortex shedding developed, suggestive of the onset of laminar instability. The theoretical results reveal a √Gr scaling for the initial flow transients and, at large Gr, the velocities and heat transfer rates.

Longitudinal vortices in natural convection flow on inclined plates

Abstract: Experiments are performed to demonstrate the occurrence and explore the characteristics of a secondary flow superposed upon the natural convection main flow on an inclined plate A flow visualization technique is employed whereby the flow pattern is made visible by local changes of colour of the fluid itself, the colour change being brought about by a change in pH The secondary flow consists of longitudinal vortices or rolls distributed more or less periodically across the width of the plate The number of such vortices increases with the temperature difference between the surface and the ambient fluid, but appears to be relatively insensitive to the inclination angle of the plate The secondary flow results from the destabilizing effect of the buoyancy force component, which acts normal to the plate surface The longitudinal vortices are the first stage of the laminarturbulent transition process This is in contrast to the case of natural convection on a vertical plate, where the first stage of transition is Tollmien-Schlichting waves

Convection Heat Transfer in Rotating Systems

Abstract: Publisher Summary Because the convective heat transfer phenomena in rotating systems are intimately related to the flow characteristics, they too are quite complex and offer challenges to theoreticians as well as experimenters. Heat transfer by convection to or from bodies of revolution spinning about their axes of symmetry in an otherwise undisturbed fluid has been studied analytically and experimentally by numerous authors. This chapter summarizes results of more recent investigations. The flow and heat transfer characteristics of spinning bodies of revolution in a forced flow field are important for projectiles or re-entry missiles with spin as well as for certain other engineering problems. The fluid-mechanical phenomena of enclosed rotating disks and of parallel corotating disks are distinctly different from those of disks rotating in an infinite environment. In general, the results for convection heat transfer of a disk rotating in an infinite environment can, therefore, not be applied to shrouded or corotating disks. When a quiescent horizontal layer of fluid is heated from below, the fluid at the bottom becomes lighter than the fluid at the top and convection currents are set into motion. The chapter deals with convection in fluids that are set in motion principally by rotating bounding surfaces, but that do not have an independent axial flow. It also deals with heat transfer by convection in systems in which the fluids also have an independent axial motion superimposed on the rotating motion.

Centrifugally driven thermal convection in a rotating cylinder

Abstract: Thermally induced convection in a rotating cylinder of fluid heated from above and strongly influenced by centrifugal accelerations is treated using boundary-layer methods. As in the theory of homogeneous rotating fluids, the horizontal Ekman layers control the inviscid axial flow. The solution also largely depends upon the thermal conditions assumed at the side wall, and if these be insulated, consideration of the side-wall boundary layers is necessary for complete specification of the problem. For perfectly conducting side walls, the side layers do not influence the zeroth-order flow, but contribute a second-order correction, which would be absent if the lateral boundaries were ignored. The critical parameters governing the solutions in both cases are found to be γ and the group σβe−½, where γ is the aspect ratio, σ the Prandtl number, e the Ekman number, and β the thermal Rossby number for the flow. Boundary-layer solutions are given for a wide range of parameters, and gravity is seen to have at most only a local effect on the flow near the side walls.

Onset of Manifest Convection in a Layer of Fluid with a Time‐Dependent Surface Temperature

Abstract: Experiments have been performed in deep layers of fluid in which the bottom surface temperature was increased at a constant rate. It was found that when the thermal boundary layer was only a small fraction of the total depth of the fluid layer, the onset of manifest convection was independent of the layer depth. The predictions of linear time‐dependent theory that the time of onset of manifest convection should vary with the ‐ 25 power of the rate of bottom surface temperature increase and that the horizontal spacing of the convection cells should vary with the ‐ 15 power of the rate of bottom surface temperature increase were verified within reasonable limits.

Experiments on natural convection in enclosures with localized heating from below

Abstract: An experimental study was made of the steady-state natural convection induced in enclosures by a small hot spot centrally located on the floor. Enclosures of rectangular and circular floor plan were employed, with height equal to one-half the major dimension of the floor plan. The movement of air within the chambers was made visible by adding metaldehyde dust particles and illuminating them with an intense light beam. The Grashof number (Gr) based on hot-spot temperature and enclosure height ranged from 8 × 105 to 1 × 1010. Laminar flows were observed for Gr [lsim ] 1.2 × 109. The experimental flows in the circular chamber are compared in a companion paper with theoretically calculated flows (Torrance & Rockett 1969). In the region of laminar flows the agreement was excellent. The present paper notes certain similarities in the flows in rectangular and circular geometries. The disturbing effect of a slight heating of one wall of the rectangular enclosure was also investigated. Measurements were made of heat transfer from the hot spot to the air in the chamber.

Mixed convection from a sphere at small Reynolds and Grashof numbers

Abstract: Consideration is given to the effects of gravity which arise when a heated sphere, maintained at a steady uniform temperature, is located in a vertical uniform stream. Restricting analysis to a medium of unit Prandtl number (σ), the method of matched asymptotic expansions is employed in obtaining solutions for the velocity, temperature and pressure fields in the limit: G = o(R2), R ↓ 0 (G and R being, respectively, the Grashof and Reynolds numbers). Based on these results, conjectures are formed about the corresponding pure natural convection problem.

Free convection at low Prandtl numbers

Abstract: In this paper it is shown that the free convection boundary layer approaches a singular character if the Prandtl number tends to zero. The method of matched asymptotic expansions is used to integrate the equations for this extreme case. An expression is derived for the Nusselt—Grashof relation and the results are compared with those of previous investigations which attack the problem in a different way.

Numerical Study of Natural Convection in a Vertical Rectangular Enclosure

Abstract: The steady‐state natural convection of a fluid in a vertical rectangular cavity with isothermal side walls and adiabatic top and bottom walls is considered for 6 × 104 ≤ Ra ≤ 3.6 × 105 with Pr = 1, 6, 2000, and at an aspect ratio of 5.0. The governing nonlinear fourth‐order equation in the stream function and the coupled second‐order energy equation are solved numerically by a stable and rapidly converging iteration scheme. The computed flow distributions, including the appearance of multicellular flows, the temperature profiles, and the heat transfer predictions compare favorably with experimental results and with other numerical studies.

Combined Free and Forced Convection Heat Transfer From a Heated Tube to a Transverse Air Stream

Abstract: Heat transfer by combined free and forced convection from a heated tube to a transverse air stream has been experimentally studied over a wide range of Grashof and Reynolds numbers. The data obtained have been correlated with Gr/Re2.5 as the correlating parameter. Criteria for transition from free convection to combined convection and from combined convection to forced convection have also been obtained.

Convection in a variable viscosity fluid heated from within

Abstract: A time-dependent theoretical model of finite amplitude thermal convection in a layer of fluid that has a variable viscosity and that is heated from within is developed. Numerical results are presented for the case where the viscosity increases exponentially with depth for a range of rates of increase with depth and a range of Rayleigh numbers that may be appropriate for the earth's mantle. It is found that convection is confined largely to the low-viscosity zone and that the cells are shortened in horizontal extent. A steady state was not reached in any case considered. Initial thermal structure is found to drastically affect the history and pattern of convection, and thus the theory cannot, provide much constraint to speculations about mantle convection.

Stability of a horizontal fluid layer with zero shear boundaries

Abstract: The onset of thermal convection in a horizontal fluid layer heated from below and bounded, above and below, by zero shear boundaries is studied experimentally. The measured value of the critical Rayleigh number is in reasonable agreement with the closed form solution obtained by Rayleigh and is in good agreement with that expected for the actual thermal boundary conditions experienced in the laboratory.