Erratum: “Free Convection From a Vertical Cone at High Prandtl Numbers” (Journal of Heat Transfer, 1974, 96, pp. 115–117)

1974 ◽  
Vol 96 (2) ◽  
pp. 144-144
Author(s):  
S. Roy
Keyword(s):  
Heat Transfer ◽  
Free Convection ◽  
Vertical Cone ◽  
Prandtl Numbers

Free-convection effects in the boundary layer along a vertically stretching flat surface

1992 ◽  
Vol 70 (12) ◽  
pp. 1253-1260 ◽  
Author(s):  
John E. Daskalakis
Keyword(s):  
Heat Transfer ◽  
Boundary Layer ◽  
Free Convection ◽  
Skin Friction ◽  
Flat Surface ◽  
Relaxation Method ◽  
Boussinesq Approximation ◽  
Axial Coordinate ◽  
Prandtl Numbers ◽  
Energy Equations

We assess the effects of free convection on the boundary layer formed along a flat surface stretching vertically in a quiescent fluid. The flow is laminar and incompressible, the buoyancy forces conform to the Boussinesq approximation and the surface temperature is variable. The two-point boundary value problem of the coupled momentum and energy equations is solved using a simple and accurate relaxation method that provides the general nonsimilar solution to the flow. The effect of free-convection currents on velocity and temperature profiles, skin friction, and heat transfer is studied by varying the flow Grashof and Prandtl numbers. Zero shear stress and heat-transfer rate are predicted at some axial coordinate on a surface with decreasing wall temperature. Also the skin friction is markedly modified by the buoyancy while the heat transfer at the surface is correspondingly only moderately influenced.

scholarly journals Heat Transfer and Flow Visualization in Natural Convection in Rapidly Spinning Systems

1986 ◽  
Vol 108 (3) ◽  
pp. 547-553 ◽  
Author(s):  
L. Sobel ◽  
M. El-Masri ◽  
J. L. Smith
Keyword(s):  
Heat Transfer ◽  
Free Convection ◽  
Flow Visualization ◽  
Fluid Viscosity ◽  
Two Dimensional ◽  
Thermal Plumes ◽  
Buoyant Plumes ◽  
Thermal Transients ◽  
Wide Range ◽  
Prandtl Numbers

The design of airborne superconducting generators for intermittent duty requires the understanding of some unique free-convection processes in the spinning helium bath. Toward that end, some fundamental experiments on steady and transient free convection in rotating containers of representative geometries have been performed. Heat transfer data from heaters of various geometries mounted on the outer container surface to several fluids are reported. A correlation for steady-state Nusselt number is presented for a wide range of Rayleigh and Prandtl numbers. The heat transfer coefficient was found to be independent of heater size, geometry, and fluid viscosity. Heat transfer measurements during simultaneous thermal transients and sudden increases in rotational speed were also made. They show an enhancement of heat transfer due to the relative counterrotation of the fluid following the acceleration of the container. This persists for a period well below that for fluid spinup. A model based upon the submergence of the thermal boundary layer by the diffusive wave from the wall was successful in correlating this period. Quasi-steady flow visualization experiments indicate that the thermal plumes generate two-dimensional, axially invariant flow fields. Their trajectories are radial relative to the spinning container. Those observations are shown to be consistent with the fact that weak buoyant plumes in containers rotating at small Ekman numbers result in low Rossby number motions. Those are two dimensional according to the Taylor–Proudman theorem. It is shown that the Coriolis and pressure forces on such a thermal column are in azimuthal equilibrium, hence the radial trajectory. Flow visualization following impulsive acceleration in an off-axis, nonaxisymmetric container shows that the flow field is dominated by vortices expelled from corners. The fluid spinup time, however, was found to be the same as that for an on-axis circular cylinder of the same characteristic diameter.

Heat Transfer Across Vertical Layers

1965 ◽  
Vol 87 (1) ◽  
pp. 110-114 ◽  
Author(s):  
A. Emery ◽  
N. C. Chu
Keyword(s):  
Heat Transfer ◽  
Free Convection ◽  
Integral Equations ◽  
Temperature Difference ◽  
Vertical Plane ◽  
Measured Data ◽  
Transfer Coefficients ◽  
Heat Transfer Coefficients ◽  
Prandtl Numbers

The heat transferred through vertical plane layers by free convection was measured as a function of the temperature difference across the layer, the height of the layer, and its thickness. Heat transfer coefficients are reported for fluids having Prandtl numbers from 3 to 30,000. An analysis of the problem by means of integral equations yielded results which differed by no more than 12 percent from the measured data in the range in which the equations were applicable.

Vortex Instability of Free Convection Flow Over Horizontal and Inclined Surfaces

1982 ◽  
Vol 104 (4) ◽  
pp. 637-643 ◽  
Author(s):  
T. S. Chen ◽  
K. L. Tzuoo
Keyword(s):  
Heat Transfer ◽  
Free Convection ◽  
Surface Heat ◽  
Convection Flow ◽  
Neutral Stability ◽  
Free Convection Flow ◽  
Vortex Instability ◽  
Surface Heat Transfer ◽  
Wide Range ◽  
Prandtl Numbers

The vortex instability characteristics of laminar free convection flow over horizontal and inclined isothermal surfaces are studied analytically by linear theory. As a prelude to the analysis, the effects of the angle of inclination on the main flow and thermal fields are re-examined by a new approach. Numerical results are presented for wall shear stress, surface heat transfer, neutral stability curve, and critical Grashof number for Prandtl numbers of 0.7 and 7 over a wide range of angles of inclination, φ, from the horizontal. It is found that as the angle of inclination increases the rate of surface heat transfer increases, whereas the susceptibility of the flow to the vortex mode of instability decreases. The present study provides new vortex instability results for small angles of inclination (φ≤30 deg) and more accurate results for large angles of inclination (φ ≥ 30 deg) than previous studies. The present results are also compared with available wave instability results.

Local Nonsimilarity Solution of Free Convection Flow and Heat Transfer from an Inclined Isothermal Plate

1979 ◽  
Vol 101 (4) ◽  
pp. 642-647 ◽  
Author(s):  
M. M. Hasan ◽  
R. Eichhorn
Keyword(s):  
Heat Transfer ◽  
Temperature Field ◽  
Free Convection ◽  
Prandtl Number ◽  
Numerical Solutions ◽  
Convection Flow ◽  
Appreciable Effect ◽  
Free Convection Flow ◽  
Flow And Heat Transfer ◽  
Prandtl Numbers

The effect of the angle of inclination on free convection flow and heat transfer from an isothermal surface is analyzed by the local nonsimilarity method of solution. An inclination parameter ξ as obtained from the analysis is tan γ/4 (Grx/4)1/4, where γ is the angle of inclination measured from the vertical and Grx is the local Grashof number, based on the component of the gravity vector along the surface. Numerical solutions of the equations are obtained for Prandtl numbers of 0.1, 0.7, 6 and 275. Results show an appreciable effect of ξ on the velocity field, and practically none on the temperature field, except for very large angles of inclination from the vertical or for very small values of the Prandtl number. In the limiting case of very large Prandtl number, ξ has no effect either on the velocity or the temperature field.

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