E.M. Sparrow

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.

Condensation heat transfer in the presence of noncondensables, interfacial resistance, superheating, variable properties, and diffusion

Abstract A wide-ranging analytical investigation of laminar film condensation is presented. The situation under study is an isothermal vertical plate with steam as the condensing vapor and air as the noncondensable gas. In addition to the noncondensable gas, the analytical model includes interfacial resistance, superheating, free convection due to both temperature and concentration gradients, mass diffusion and thermal diffusion, and variable properties in both the liquid and the gas-vapor regions. Heat-transfer results are obtained for a wide range of parameters including bulk concentration of the noncondensable gas, system pressure level, wall-to-bulk temperature difference, and degree of superheating. It is demonstrated that small bulk concentrations of the noncondensable gas can have a decisive effect on the heat-transfer rate. For instance, for a bulk mass fraction of air equal to 0.5 per cent, reductions in heat transfer of 50 per cent or more are sustained. The influence of the noncondensable gas is accentuated at lower pressure levels. It is shown that the aforementioned reductions in heat transfer are due entirely to the diffusional resistance of the gas-vapor boundary layer. The interfacial resistance is shown to be a second order effect. A similar finding applies to thermal diffusion and diffusion thermo. The effect of superheating, which is very small in the case of a pure vapor, becomes much more significant in the presence of a noncondensable gas. A reference temperature rule is deduced for extending the Nusselt model to variable-property conditions.

Analysis of Melting in the Presence of Natural Convection in the Melt Region

An analysis of multidimensional melting is performed which takes account of natural convection induced by temperature differences in the liquid melt. Consideration is given to the melt region created by a heated vertical tube embedded in a solid which is at its fusion temperature. Solutions were obtained by an implicit finite-difference scheme tailored to take account of the movement of the liquid-solid interface as melting progresses. The results differed decisively from those corresponding to a conventional pure-conduction model of the melting problem. The calculated heat transfer rate at the tube wall decreased at early times and attained a minimum, then increased and achieved a maximum, and subsequently decreased. This is in contrast to the pure conduction solution whereby the heat transfer rate decreases monotonically with time. The thickness of the melt region was found to vary along the length of the tube, with the greatest thickness near the top. This contrasts with the uniform thickness predicted by the conduction solution. These findings indicate that natural convection effects, although unaccounted for in most phase change analyses, are of importance and have to be considered.

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.

The two phase boundary layer in laminar film condensation

Abstract Consideration is given to the two-phase flow problem in laminar film condensation which arises when induced motions of the vapor are included. The shear forces at the liquid-vapour interface, heretofore neglected, have been fully taken into account. It is shown that the problem can be formulated as an exact boundary layer solution. From numerical solutions of the governing equations, it is found that the effects of the interfacial shear on heat transfer are negligible for Prandtl numbers of ten or greater and are quite small even for a Prandtl number of one. For the liquid metal range, the interfacial shear was found to cause substantial reductions in heat transfer.

The Inverse Problem in Transient Heat Conduction

A general theory is devised for determining the temperature and heat flux at the surface of a solid when the temperature at an interior location is a prescribed function of time. The theory is able to accommodate an initial temperature distribution which varies arbitrarily with position throughout the solid. Detailed analytical treatment is extended to the sphere, the plane slab, and the long cylinder; and it is additionally shown that the semi-infinite solid is a particular case of the general formulation. The accuracy of the method is demonstrated by a numerical example. In addition, a numerical calculation procedure is devised which appears to provide smooth, nonoscillatory results.

Buoyancy effects on horizontal boundary-layer flow and heat transfer

Abstract The conditions have been determined under which there are significant effects of buoyancy on a forced-convection, boundary-layer flow along a flat plate. It is found that lowPrandtl number fluids are more sensitive to buoyancy effects.

Enhanced and local heat transfer, pressure drop, and flow visualization for arrays of block-like electronic components

Abstract Experiments were performed to investigate the heat transfer and fluid flow characteristics of arrays of heat-generating, block-like modules affixed to one wall of a parallel-plate channel and cooled by forced convection airflow. Heat transfer enhancements exceeding a factor of two were achieved by the use of multiple fence-like barriers, with the interbarrier spacing and the barrier height being varied parametrically along with the Reynolds number. The barrier-related pressure drop for a multi-barrier system was found-to be less than the corresponding multiple of the pressure drop for a single-barrier system when the interbarrier spacing is small. When the barriers are separated by six or more rows of modules, the direct multiple is applicable. The heat transfer coefficients at individual surfaces of the various modules were measured in fully populated arrays without barriers, in arrays with barriers, and in arrays in which there was a missing module. Perspectives on the heat transfer and pressure drop results were provided by flow visualizations performed using the oillampblack technique.

Vertical-channel natural convection spanning between the fully-developed limit and the single-plate boundary-layer limit

The effect of interplate spacing on natural convection in an open-ended vertical channel bounded by an isothermal and an unheated wall was studied both experimentally and computationally. The investigation encompassed the full range of operating conditions of the channel, i.e. from the limit of the fully-developed channel flow to the limit of the single vertical plate. Overall, a 50-fold variation in the spacing between the channel walls was investigated, and the vertical plate was employed in order to achieve the limit of infinite spacing. The experiments were performed in water (Pr ≊ 5) with the aforementioned parametric variation of the interplate spacing and for an order of magnitude range of the wall-to-ambient temperature difference. The numerical solutions were carried out for the experimentally investigated operating conditions and took account of both natural convection in the channel and conduction in the wall. It was found that the flat plate heat transfer does not form an upper bound for the channel heat transfer. The channel heat transfer is particularly sensitive to changes in interplate spacing for narrow channels and at small temperature differences. The results for all operating conditions were brought tightly together in terms of the groups Nus and (S/H)Ras, and a highly accurate correlation encompassing eight decades of (S/H)Ras, was developed. Excellent agreement between the experimental results and the computational predictions was obtained.

Experiments on hydrodynamically developing flow in rectangular ducts of arbitrary aspect ratio

Abstract A comprehensive experimental investigation of laminar flow development in rectangular ducts is performed employing an apparatus which permits study of any cross sectional aspect ratio. The primary concern of the research is the determination of the pressure field associated with the hydrodynamic development of the flow. Experimental results are presented in terms of both the local pressure defect and the incremental pressure drop due to flow development. Comparisons are made with the available predictions of analysis and with prior experimental information. Hydrodynamic development lengths are deduced and the threshold of significant effects of the viscous normal stress is identified.