R.J. Goldstein

FLOW AND HEAT TRANSFER IN THE BOUNDARY LAYER ON A CONTINUOUS MOVING SURFACE

Abstract A combined analytical and experimental study of the flow and temperature fields in the boundary layer on a continuous moving surface has been carried out. The investigation includes both laminar and turbulent flow conditions. The analytical solutions provide results for the boundary-layer veolcity and temperature distributions and for the surface-friction and heat-transfer coefficients. Measurements of the laminar velocity field are in excellent agreement with the analytical predictions, thereby verifying that a mathematically describable boundary layer on a continuous moving surface is a physically realizable flow. Experimentally determined turbulent velocity profiles are also in very good accord with those of analysis. Similar agreement is found to exist for friction coefficients deduced from the data by application of the Clauser-plot technique. Temperature distribution measurements, carried out for the turbulent boundary layer, show satisfactory correspondence with analysis.

An experimental and theoretical study of natural convection in the annulus between horizontal concentric cylinders

An experimental and theoretical-numerical investigation has been carried out to extend existing knowledge of velocity and temperature distributions and local heat-transfer coefficients for naturel convection within a horizontal annulus. A Mach—Zehnder interferometer was used to determine temperature distributions and local heat-transfer coefficients experimentally. Results were obtained using water and air at atmospheric pressure with a ratio of gap width to inner-cylinder diameter of 0·8. The Rayleigh number based on the gap width varied from 2·11 × 10 4 to 9·76 × 10 5 . A finite-difference method was used to solve the governing constant-property equations numerically. The Rayleigh number was changed from 10 2 to 10 5 with the influence of Prandtl number and diameter ratio obtained near a Rayleigh number of 10 4 . Comparisons between the present experimental and numerical results under similar conditions show good agreement.

Thermal instability in a horizontal fluid layer: Effect of boundary conditions and non-linear temperature profile

An investigation is carried out to determine the conditions marking the onset of convective motion in a horizontal fluid layer in which a negative temperature gradient occurs somewhere within the layer. In such cases, fluid of greater density is situated above fluid of lesser density. Consideration is given to a variety of thermal and hydrodynamic boundary conditions at the surfaces which bound the fluid layer. The thermal conditions include fixed temperature and fixed heat flux at the lower bounding surface, and a general convective-radiative exchange at the upper surface which includes fixed temperature and fixed heat flux as special cases. The hydrodynamic boundary conditions include both rigid and free upper surfaces with a rigid lower bounding surface. It is found that the Rayleigh number marking the onset of motion is greatest for the boundary condition of fixed temperature and decreases monotonically as the condition of fixed heat flux is approached. Non-linear temperature distributions in the fluid layer may result from internal heat generation. With increasing departures from the linear temperature profile, it is found that the fluid layer becomes more prone to instability, that is, the critical Rayleigh number decreases.

A review of mass transfer measurements using naphthalene sublimation

Abstract The naphthalene sublimation method can be used to study mass and heat transfer with confidence for a variety of applications, but with certain restrictions. This method is particularly useful in complex flows and geometries and for flows with large gradients in wall transport rate. Mass transfer boundary conditions analogous to isothermal and adiabatic walls in convective heat transfer can be easily imposed. Furthermore, the nature of mass transfer allows one to impose these boundary conditions such that errors analogous to conductive losses in a wall are not present. The test specimen can be easily prepared by several methods, including dipping, machining spraying, and casting. The local transfer coefficients can be determined with high accuracy and in detail by automated measurement systems that eliminate most human errors and reduce extraneous sublimation losses during the measurement process. The heat transfer coefficient, which is often desired, can be readily determined from the measured mass transfer results with good confidence via a heat/mass transfer analogy. However this method cannot generally be used in certain flow situations such as high-velocity flows because of recovery temperature effects and natural convection due to the thermal buoyancy effects of sublimation latent heat.

Numerical solution to the Navier-Stokes equations for laminar natural convection about a horizontal isothermal circular cylinder

Abstract Laminar natural-convection heat transfer from a horizontal isothermal cylinder is studied by solving the Navier-Stokes and energy equations using an elliptic numerical procedure. Results are obtained for 100 ≤ Ra ≤ 107. The flow approaches natural convection from a line heat source as Ra → 0 and laminar boundary-layer flow as Ra → ∞. Boundary-layer solutions do not adequately describe the flow and heat transfer at low or moderate values of Ra because of the neglect of curvature effects and the breakdown of the boundary-layer assumptions in the region of the plume. Good agreement with experimental results is achieved.

Turbulent convection in a horizontal layer of water

Overall heat transfer and mean temperature distribution measurements have been made of turbulent thermal convection in horizontal water layers heated from below. The Nusselt number is found to be proportional to Ra 0·278 in the range 2·76 × 10 5 Ra 8 . Eight discrete heat flux transitions are found in this Rayleigh number range. An interferometric method is used to measure the mean temperature distribution for Rayleigh numbers between 3·11 × 10 5 and 1·86 × 10 7 . Direct visual and photographic observations of the fluctuating interferogram patterns show that the main heat transfer mechanism is the release of thermals from the boundary layers. For relatively low Rayleigh numbers (up to 5 × 10 5 ) many of the thermals reach the opposite surface and coalesce to form large masses of relatively warm fluid near the cold surface and masses of cold fluid near the warm surface, resulting in a temperature-gradient reversal. With increasing Rayleigh numbers, fewer and fewer thermals reach the opposite bounding surface and the thermals show persistent horizontal movements near the bounding surfaces. The central region of the layer becomes an isothermal core. The mean temperature distributions for the high Rayleigh number range are found to follow a Z −2 power law over a considerable range, where Z is the distance from the bounding surface. A very limited agreement with the theoretically predicted Z −1 power law is also found.

Natural convection mass transfer adjacent to horizontal plates

Abstract Experiments on natural convection adjacent to horizontal plane surfaces were performed using the naphthalene sublimation technique. By analogy, the present mass transfer experiments correspond to heat transfer at a heated isothermal upward-facing plate or at a cooled downward-facing plate. Circular, square and 7:1 rectangular planforms were employed in the tests. Overall mass transfer coefficients and Sherwood numbers were determined and correlated as a function of the Rayleigh number. A common correlation for all three planforms was attained by using characteristic lengths equal to the ratio of the surface area to the perimeter. The transfer coefficients predicted by laminar boundary layer theory fell well below the experimental data and exhibited a different dependence on the Rayleigh number. The oft-quoted empirical correlation of Fishenden and Saunders was found to be a less satisfactory representation of the present data than that of Mikheyev. In the range of lower Rayleigh numbers, the results given by a numerical finite-difference solution were very much lower than the experimental data.

Observations and other characteristics of thermals

Experiments have been performed to explore the qualitative and quantitative characteristics of thermals which ascend through the fluid environment above a heated horizontal surface. With water as the participating fluid, an electrochemical technique was employed which made the flow field visible and facilitated the direct observation of thermals. Measurements were also made of the fluid temperature above an active site of thermal generation. As seen in flow field photographs, a thermal has a mushroom-like appearance, with a blunted nearly hemispherical cap. At a given heating rate, thermals are generated at fixed sites which are spaced more or less regularly along the span of the heated surface. At these sites, the generation of thermals is periodic in time, thereby validating a prediction of Howard. Both the spatial frequency of the sites and the rate of thermal production increase with increases in heating rate. The break-up Rayleigh number of the conduction layer is shown to be a constant (within the uncertainties of the experiment), which is in accord with Howards phenomenological model.

Correlating equations for natural convection heat transfer between horizontal circular cylinders

Abstract Correlating equations for heat transfer by natural convection from horizontal cylinders to a cylindrical enclosure are obtained using a conduction boundary-layer model. The correlation is valid for heat transfer by conduction, laminar flow and turbulent flow. The results approach the correlation for heat transfer from a free horizontal cylinder as the outer cylinder diameter becomes infinite and for quasi-steady heat transfer to fluid within a horizontal cylinder as the inner cylinder diameter approaches zero. Horizontal concentric, eccentric and arrays of cylinders within the outer cylinder are geometries included in the correlation.

Impingement of a circular jet with and without cross flow

Abstract Measurements are reported for the local heat transfer to an impinging air jet with and without a cross flow of air. At large jet-to-plate spacing the cross flow diminishes the peak heat transfer coefficient ; at a smaller spacing cross flow can increase the peak heat transfer coefficient. A correlation is obtained for the average heat transfer in the absence of cross flow.