Transient, laminar, free-convection heat and mass transfer in closed, partially filled, liquid containers
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A general analysis is presented of the steady nondissipative constant-property laminar boundary layer flow over a two-dimensional body of uniform surface heat flux situated in an infinite ambient fluid of undisturbed temperature. The analysis is then applied to a long horizontal circular cylinder. Numerical solutions to the universal functions associated with the first two terms in the derived series are given for Prandtl numbers 0.7, 1, 3, 5, 7, and 10. The results are compared with those obtained by Koh (1964) whose method is patterned after the Blasius-Frossling procedure for forced convection flow. The study reveals that Wilks' (1972) analysis concerning the external natural convection about two-dimensional bodies with constant heat flux is in error.
Sodium chlorate crystals growing from unstirred aqueous solutions were observed by Schlieren techniques. Growth rate data were best correlated by a Sherwood number with finite interface kinetics and a characteristic length equal to the crystal height plus the inverse reciprocal sum of the horizontal dimensions. The growth rate was slightly higher when the plume was laminar than when it was irregular. The horizontal growth rate was greater than the vertical growth rate, with the ratio tending to decrease with increasing plume instability. The threshold Grashof number for plume instability was greatly decreased with decreasing height for crystals with the same horizontal dimensions. The velocity of the eddies approached a constant value with increasing distance above the crystal surface, the terminal value being roughly proportional to the ratio of the square root of the Rayleigh number to the crystal characteristic length.
A transformation of the laminar boundary layer equations, similar to the transformation of Kao et al. (1977), is presented which allows arbitrary distributions of both wall temperature and blowing. The procedure yields constant boundary conditions, but variable coefficients appear in the differential equations. The proposed transformation is applicable to the problem of downward burning of vertical pieces of condensed-phase combustibles.
An experimental and analytical investigation of heat transfer from a horizontal, thin, square plate inside of an enclosure was carried out. Experimental results were obtained from both the upward-facing and the downward-facing sides of the heated plate. Starting with the integrated momentum and energy equations, approximate solutions were obtained for heat transfer in the laminar and the turbulent regime that correlate well with experimental data. Radiative heat transfer correction was given special attention. Effects of the enclosure-related recirculation of the test fluid, as well as effects of simultaneous heat transfer on both sides of the plate, caused an early transition, and indicated a high level of internal turbulence.
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Explore the source record for details and available documents.
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Explore the source record for details and available documents.
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An apparatus was built to verify an analysis of combined forced and free convection in a vertical tube with uniform wall heat flux and to determine the limits of the analysis. The test section was electrically heated by resistance heating of the tube wall and was instrumented with thermocouples in such a way that detailed thermal entrance heat-transfer coefficients could be obtained for both upflow and downflow and any asymmetry in wall temperature could be detected. The experiments showed that fully developed heat-transfer results, predicted by a previous analysis, were confirmed over the range of Rayleigh numbers investigated. The concept of "locally fully developed" heat transfer was established. This concept involves the assumption that the fully developed heat-transfer analysis can be applied locally even though the Rayleigh number is varying along the tube because of physical-property variations with temperature. Thermal entrance region data were obtained for pure forced convection and for combined forced and free convection. The analysis of laminar pure forced convection in the thermal entrance region conducted by Siegel, Sparrow, and Hallman was experimentally confirmed. A transition to an eddy motion, indicated by a fluctuation in wall temperature was found in many of the upflow runs. A stability correlation was found. The fully developed Nusselt numbers in downflow were below those for pure forced convection but fell about 10 percent above the analytical curve. Quite large circumferential variations in wall temperature were observed in downflow as compaired with those encountered in upflow, and the fully developed Nussalt numbers reported are based on average wall temperatures determined by averaging the readings of two diametrically opposite wall thermocouples at each axial position. With larger heating rates in downflow the wall temperature distributions strongly suggested a cell flow near the bottom. At still larger heating rates the wall temperatures varied in a periodic way.
Structural performance and resizing of the finite-element thermal analysis computer program was used in the reentry heat transfer analysis of the space shuttle orbiter. One midfuselage cross section and one midspan wing segment were selected to study the effects of internal convection and internal radiation on the structural temperatures. The effect of internal convection was found to be more prominent than that of internal radiation in the orbiter thermal analysis. Without these two effects, the calculated structural temperatures at certain stations could be as much as 45 to 90 percent higher than the measured values. By considering internal convection as free convection, the correlation between the predicted and measured structural temperatures could be improved greatly.
The Solar Dynamic Power Module being developed for Space Station Freedom uses a eutectic mixture of LiF-CaF2 phase change material (PCM) contained in toroidal canisters for thermal energy storage. Presented are the results from heat transfer analyses of a PCM containment canister. One and two dimensional finite difference computer models are developed to analyze heat transfer in the canister walls, PCM, void, and heat engine working fluid coolant. The modes of heat transfer considered include conduction in canister walls and solid PCM, conduction and pseudo-free convection in liquid PCM, conduction and radiation across PCM vapor filled void regions, and forced convection in the heat engine working fluid. Void shape, location, growth or shrinkage (due to density difference between the solid and liquid PCM phases) are prescribed based on engineering judgment. The PCM phase change process is analyzed using the enthalpy method. The discussion of the results focuses on how canister thermal performance is affected by free convection in the liquid PCM and void heat transfer. Characterizing these effects is important for interpreting the relationship between ground-based canister performance (in 1-g) and expected on-orbit performance (in micro-g). Void regions accentuate canister hot spots and temperature gradients due to their large thermal resistance. Free convection reduces the extent of PCM superheating and lowers canister temperatures during a portion of the PCM thermal charge period. Surprisingly small differences in canister thermal performance result from operation on the ground and operation on-orbit. This lack of a strong gravity dependency is attributed to the large contribution of container walls in overall canister energy redistribution by conduction.
Electrocrystallization under microgravity conditions is proposed as a potential method of crystallization that would be almost completely free of fluid convection. Such crystallization may result in purer, more perfect, and larger crystals than is possible under normal gravity conditions. Observations made and data collected during the crystallization process under convection-free conditions should add to our knowledge of the crystallization process. The proposed method would allow easy comparison of crystals growth in space with those grown under normal gravity conditions. Nine types of electrocrystallization are presented: an example of each is discussed. Electrocrystallization is compared with the compartmental crystallization method used by 3M Corporation in recent shuttle experiments.
The structure and kinetic energy budget of turbulence in the convective marine atmospheric boundary layer as observed by aircraft during a cold air outbreak have been studied using mixed layer scaling. The results are significantly different from those of previous studies under conditions closer to free convection. The normalized turbulent kinetic energy and turbulent transport are about twice those found during the Air Mass Transformation Experiment (AMTEX). This implies that for a given surface heating the present case is dynamically more active. The difference is mainly due to the greater importance of wind shear in the present case. This case is closer to the roll vortex regime, whereas AMTEX observed mesoscale cellular convection which is closer to free convection. Shear generation is found to provide a significant energy source, in addition to buoyancy production, to maintain a larger normalized turbulent kinetic energy and to balance a larger normalized dissipation. The interaction between turbulent pressure and divergence (i.e., pressure scrambling) is also found to transfer energy from the vertical to the horizontal components, and is expected to be stronger in roll vortices than in m esoscale cells. The sensible heat flux is found to fit well with a linear vertical profile in a clear or subcloud planetary boundary layer (PBL), in good agreement with the results of Lenschow et al., (1980). The heat flux ratio between the PBL top and the surface, derived from the linear fitted curve, is approximately -0.14, in good agreement with that derived from the lidar data for the same case. Near the PBL top, the heat flux profiles are consistent with those of Deardoff (1979) and Deardorff et al. (1980).
Observations of solar cosmic rays between 0.1 MeV and 1 GeV are more consistent with scatter-free than diffusive propagation near 1 AU. Since these particles also are constrained to interplanetary magnetic field lines, the parallel and transverse flow are decoupled by collimated convection. Local propagation is therefore more appropriately described by Liouville's equation, and transport properties can be examined from the exact zeroeth and first moments of the equation averaged over all directions in momentum space. Observational results which may be explained directly without invoking local scattering include the decay of solar flare events as well as the radial gradient, diurnal and semidiurnal variation of galactic cosmic rays.