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• 1. [Article] The design, construction and calibration of an instrumented surface for convective heat transfer studies

  The purpose of this thesis work has been the design, construction and calibration of an instrumented surface for convective heat transfer studies. The surface is in the form of a flat plate roughly 24 ...

  Citation × Citation Citation Abstract Copy Title: The design, construction and calibration of an instrumented surface for convective heat transfer studies Author: Meyers, Stanley Kent The purpose of this thesis work has been the design, construction and calibration of an instrumented surface for convective heat transfer studies. The surface is in the form of a flat plate roughly 24 inches wide by 48 inches long. It is made up of 48 individual cells, laminated side-by-side and insulated from each other, which can be individually heated or cooled with water. This results in the ability to impose arbitrary boundary conditions with respect to surface temperature along the plate. The individual cells were laminated together in three layers. The upper surface facing the fluid stream is a copper strip which incorporates a thermocouple to measure surface temperature. The center section includes a 3/32 inch micarta thermal resistance with a thermopile wrapped around it and a thermocouple installed on one side to measure temperature. This was then cast into one piece with epoxy resin. The bottom of the sandwich is an aluminum tube which provides a hot or cold water supply to the instrumented plate. The thermopiles, which are included in 28 of the cells, were then calibrated to indicate heat flux between the aluminum tube and the copper surface. An average value for the thermopile response of 0.0528 mv/Btu/hr-ft² was found for all the calibration runs. Included in the body of the thesis are the construction details and calibration data which were obtained during the calibration of the instrument. Title: The design, construction and calibration of an instrumented surface for convective heat transfer studies Author: Meyers, Stanley Kent The purpose of this thesis work has been the design, construction and calibration of an instrumented surface for convective heat transfer studies. The surface is in the form of a flat plate roughly 24 inches wide by 48 inches long. It is made up of 48 individual cells, laminated side-by-side and insulated from each other, which can be individually heated or cooled with water. This results in the ability to impose arbitrary boundary conditions with respect to surface temperature along the plate. The individual cells were laminated together in three layers. The upper surface facing the fluid stream is a copper strip which incorporates a thermocouple to measure surface temperature. The center section includes a 3/32 inch micarta thermal resistance with a thermopile wrapped around it and a thermocouple installed on one side to measure temperature. This was then cast into one piece with epoxy resin. The bottom of the sandwich is an aluminum tube which provides a hot or cold water supply to the instrumented plate. The thermopiles, which are included in 28 of the cells, were then calibrated to indicate heat flux between the aluminum tube and the copper surface. An average value for the thermopile response of 0.0528 mv/Btu/hr-ft² was found for all the calibration runs. Included in the body of the thesis are the construction details and calibration data which were obtained during the calibration of the instrument. Close

• 2. [Article] An experimental study of natural convection in air between a vertical isothermal flat plate and a parallel insulated flat plate

  Natural convection heat transfer in air between two vertical plates 38 by 24 inches was investigated in this work with spacings between the plates of 0.625, 1.0 and 1.75 inches. One plate was isothermal and ...

  Citation × Citation Citation Abstract Copy Title: An experimental study of natural convection in air between a vertical isothermal flat plate and a parallel insulated flat plate Author: Kim, Sung-Soo Natural convection heat transfer in air between two vertical plates 38 by 24 inches was investigated in this work with spacings between the plates of 0.625, 1.0 and 1.75 inches. One plate was isothermal and the other adiabatic. To measure the point velocities in the air layer a very thin quartz fiber 0.0005 in. in diameter was used. An iron- constantan thermocouple 0.001 in. in diameter was used for local temperature measurement. Velocity and temperature profiles were obtained at several positions along the plate for each spacing between the plates. An equation in the form Nu[subscript x] = 0. 348 (Gr[subscript x] (x/W))⁰[superscript .]²⁴¹ best describes the local heat transfer characteristics for this study. Title: An experimental study of natural convection in air between a vertical isothermal flat plate and a parallel insulated flat plate Author: Kim, Sung-Soo Natural convection heat transfer in air between two vertical plates 38 by 24 inches was investigated in this work with spacings between the plates of 0.625, 1.0 and 1.75 inches. One plate was isothermal and the other adiabatic. To measure the point velocities in the air layer a very thin quartz fiber 0.0005 in. in diameter was used. An iron- constantan thermocouple 0.001 in. in diameter was used for local temperature measurement. Velocity and temperature profiles were obtained at several positions along the plate for each spacing between the plates. An equation in the form Nu[subscript x] = 0. 348 (Gr[subscript x] (x/W))⁰[superscript .]²⁴¹ best describes the local heat transfer characteristics for this study. Close

• 3. [Article] An experimental study of natural convection in air between a vertical isothermal flat plate and a parallel insulted flat plate

  The free convective heat transfer phenomena in air between two vertical plates 24 by 38 inches spaced 15.895 mm apart, was investigated in this experimental study. One plate was isothermal and, the other ...

  Citation × Citation Citation Abstract Copy Title: An experimental study of natural convection in air between a vertical isothermal flat plate and a parallel insulted flat plate Author: Lee, Soon Mo The free convective heat transfer phenomena in air between two vertical plates 24 by 38 inches spaced 15.895 mm apart, was investigated in this experimental study. One plate was isothermal and, the other adiabatic. A quartz fiber anomometer was used for measuring local velocities in the air between the vertical plates. A very fine iron-constantan thermocouple was used for local temperature measurements. Velocity and temperature profiles were obtained at several vertical positions along the plates. With the data obtained, local and mean convective heat transfer coefficients were determined at each vertical position. Title: An experimental study of natural convection in air between a vertical isothermal flat plate and a parallel insulted flat plate Author: Lee, Soon Mo The free convective heat transfer phenomena in air between two vertical plates 24 by 38 inches spaced 15.895 mm apart, was investigated in this experimental study. One plate was isothermal and, the other adiabatic. A quartz fiber anomometer was used for measuring local velocities in the air between the vertical plates. A very fine iron-constantan thermocouple was used for local temperature measurements. Velocity and temperature profiles were obtained at several vertical positions along the plates. With the data obtained, local and mean convective heat transfer coefficients were determined at each vertical position. Close

• 4. [Article] Numerical study of mass transfer enhanced by theromocapillary convection in a 2-D microscale channel

  The effect of unsteady thermocapillary convection on the mass transfer rate of a solute between two immiscible liquids within a rectangular microscale channel with differentially heated sidewalls was numerically ...

  Citation × Citation Citation Abstract Copy Title: Numerical study of mass transfer enhanced by theromocapillary convection in a 2-D microscale channel Author: Kittidacha, Witoon The effect of unsteady thermocapillary convection on the mass transfer rate of a solute between two immiscible liquids within a rectangular microscale channel with differentially heated sidewalls was numerically investigated. A computational fluid dynamic code in Fortran77 was developed using the finite volume method with Marker and Cell (MAC) technique to solve the governing equations. The discrete surface tracking technique was used to capture the location of the moving liquid-liquid interface. The code produced results consistent with those reported in published literature. The effect of the temperature gradients, the aspect ratio, the viscosity of liquid, and the deformation of the interface on the mass transfer rate of a solute were studied. The mass transfer rate increases with increasing temperature gradient. The improvement of the mass transfer rate by the thermocapillary convection was found to be a function of the Peclet number (Pe). At small Pe, the improvement of the mass transfer rate increases with increasing Pe. At high Pe, increasing the Pe has no significant effect on increasing the mass transfer rate. Increasing the aspect ratio of the cavity up to 1 increases the mass transfer rate. When the aspect ratio is higher than 1, the vortex moves only near the interface, resulting in decreasing the mass transfer rate. By increasing the viscosity of the liquid in top phase, the maximum tangential velocity at the interface decreases. As a result, the improvement of the mass transfer rate decreases. The deformation of the interface has no significant effect on the improvement of the mass transfer rate. By placing the heating source at the middle of the cavity, two steady vortices can be induced in a cavity. As a result, the mass transfer rate is slightly enhanced than that in the system with one vortex. By reversing the direction of the temperature gradient, the mass transfer rate decreases due to the decrease in the velocity of bulk fluid. The thermocapillary convection also promotes the overall reaction process when the top wall of the cavity is served as a catalyst. Title: Numerical study of mass transfer enhanced by theromocapillary convection in a 2-D microscale channel Author: Kittidacha, Witoon The effect of unsteady thermocapillary convection on the mass transfer rate of a solute between two immiscible liquids within a rectangular microscale channel with differentially heated sidewalls was numerically investigated. A computational fluid dynamic code in Fortran77 was developed using the finite volume method with Marker and Cell (MAC) technique to solve the governing equations. The discrete surface tracking technique was used to capture the location of the moving liquid-liquid interface. The code produced results consistent with those reported in published literature. The effect of the temperature gradients, the aspect ratio, the viscosity of liquid, and the deformation of the interface on the mass transfer rate of a solute were studied. The mass transfer rate increases with increasing temperature gradient. The improvement of the mass transfer rate by the thermocapillary convection was found to be a function of the Peclet number (Pe). At small Pe, the improvement of the mass transfer rate increases with increasing Pe. At high Pe, increasing the Pe has no significant effect on increasing the mass transfer rate. Increasing the aspect ratio of the cavity up to 1 increases the mass transfer rate. When the aspect ratio is higher than 1, the vortex moves only near the interface, resulting in decreasing the mass transfer rate. By increasing the viscosity of the liquid in top phase, the maximum tangential velocity at the interface decreases. As a result, the improvement of the mass transfer rate decreases. The deformation of the interface has no significant effect on the improvement of the mass transfer rate. By placing the heating source at the middle of the cavity, two steady vortices can be induced in a cavity. As a result, the mass transfer rate is slightly enhanced than that in the system with one vortex. By reversing the direction of the temperature gradient, the mass transfer rate decreases due to the decrease in the velocity of bulk fluid. The thermocapillary convection also promotes the overall reaction process when the top wall of the cavity is served as a catalyst. Close

• 5. [Article] An experimental investigation of natural convection heat transfer from vertical flat plates in mercury

  Heat transfer from a vertical flat plate in an infinite pool of mercury was investigated. Velocity profiles were measured with a hot-film anemometer and simultaneous temperature profiles measured with ...

  Citation × Citation Citation Abstract Copy Title: An experimental investigation of natural convection heat transfer from vertical flat plates in mercury Author: White, Donald Henry Heat transfer from a vertical flat plate in an infinite pool of mercury was investigated. Velocity profiles were measured with a hot-film anemometer and simultaneous temperature profiles measured with thermocouples in this low Prandtl number liquid metal. Constant heat flux plates at Grashof numbers of 9 x 10⁸ and 4 x 10⁷ were investigated. Pseudo-constant temperature plates at Grashof numbers of 8 x 10⁷ and 2 x 10⁷ were investigated. The velocity profiles, the first known natural convection experimental profiles reported for liquid metals, were found to be a function of both plate position and Grashof number. This relationship was predicted by available perturbation solutions for the flat plate in an infinite, low Prandtl number fluid, but not by the similarity or integral solutions. Indications are that the best analytical solutions do a poor job of predicting profiles and that natural convection heat transfer rates in liquid metals are higher than originally believed. The use of a hot-film anemometer to measure low velocities in mercury is possible, but the existence of a thermo-barrier film causes serious experimental problems which have been only partially solved. Title: An experimental investigation of natural convection heat transfer from vertical flat plates in mercury Author: White, Donald Henry Heat transfer from a vertical flat plate in an infinite pool of mercury was investigated. Velocity profiles were measured with a hot-film anemometer and simultaneous temperature profiles measured with thermocouples in this low Prandtl number liquid metal. Constant heat flux plates at Grashof numbers of 9 x 10⁸ and 4 x 10⁷ were investigated. Pseudo-constant temperature plates at Grashof numbers of 8 x 10⁷ and 2 x 10⁷ were investigated. The velocity profiles, the first known natural convection experimental profiles reported for liquid metals, were found to be a function of both plate position and Grashof number. This relationship was predicted by available perturbation solutions for the flat plate in an infinite, low Prandtl number fluid, but not by the similarity or integral solutions. Indications are that the best analytical solutions do a poor job of predicting profiles and that natural convection heat transfer rates in liquid metals are higher than originally believed. The use of a hot-film anemometer to measure low velocities in mercury is possible, but the existence of a thermo-barrier film causes serious experimental problems which have been only partially solved. Close

• 6. [Article] Experimental study of subcooled water spray cooling using flow symmetric micro-structured surfaces

  Spray impingement cooling has been shown to be a leading candidate for future high heat flux cooling applications. In general, spray cooling curves consist of three heat flux regimes; single-phase, two-phase ...

  Citation × Citation Citation Abstract Copy Title: Experimental study of subcooled water spray cooling using flow symmetric micro-structured surfaces Author: Tulchinsky, Alex M. Spray impingement cooling has been shown to be a leading candidate for future high heat flux cooling applications. In general, spray cooling curves consist of three heat flux regimes; single-phase, two-phase and critical heat flux (CHF). CHF is considered the design limit for almost all two-phase cooling applications, as a rapid increase in temperature and decrease in heat flux occurs beyond this point. Recent studies have shown that the addition of micro-structures on the impingement surface can enhance heat transfer relative to a smooth surface. In the present study, spray cooling curves are obtained for two micro-structured surfaces and are compared to smooth surface results. Micro-structured surfaces consisted of bio-inspired fractal-like geometries, denoted as grooves and fins, extending in a radial direction from the center to the periphery of a 37.8 mm circular disc. Depending on the location on the surface, dimensions of groove widths and heights varied from 100 to 500 μm, and 30 to 60 μm, respectively. Fin width and height dimension remained constant throughout the surface at 127 and 60 μm, respectively. Heat flux and wall temperature at the impingement surface were calculated from temperature data measured at multiple locations below the impingement surface. Results are presented as heat flux, q" , versus the wall-to-spray temperature difference, ΔT[subscript w], at each of 5 volume flux, Q", conditions ranging from 0.54 to 2.04 x 10⁻³ m³/m²s. Convection coefficients, h[subscript cv], and spray efficiencies, η, are also presented for each case as a function of q" and ΔT[subscript w] , respectively. Results of the study indicate that at low and high volume fluxes, an improvement in heat transfer occurs in the single-phase regime for the fin geometry. Enhancement in the single-phase regime did not occur at the intermediate volume flux condition of 1.37 x 10⁻³ m³/m²s. At all volume flux states tested, significant enhancements, as high as 50% in some cases, were observed in the two-phase regime for the fin structure, whereas the groove structure performed identically to the flat surface in the single-phase regime and exhibited a large degradation in the two-phase and critical heat flux regimes (~50%). Critical heat flux for the fin surface compared to the flat surface was slightly lower at low volume flux conditions, equivalent at the intermediate volume flux, and slightly greater at high volume flux conditions. Further investigations into the underlying mechanisms responsible for these results are needed. Title: Experimental study of subcooled water spray cooling using flow symmetric micro-structured surfaces Author: Tulchinsky, Alex M. Spray impingement cooling has been shown to be a leading candidate for future high heat flux cooling applications. In general, spray cooling curves consist of three heat flux regimes; single-phase, two-phase and critical heat flux (CHF). CHF is considered the design limit for almost all two-phase cooling applications, as a rapid increase in temperature and decrease in heat flux occurs beyond this point. Recent studies have shown that the addition of micro-structures on the impingement surface can enhance heat transfer relative to a smooth surface. In the present study, spray cooling curves are obtained for two micro-structured surfaces and are compared to smooth surface results. Micro-structured surfaces consisted of bio-inspired fractal-like geometries, denoted as grooves and fins, extending in a radial direction from the center to the periphery of a 37.8 mm circular disc. Depending on the location on the surface, dimensions of groove widths and heights varied from 100 to 500 μm, and 30 to 60 μm, respectively. Fin width and height dimension remained constant throughout the surface at 127 and 60 μm, respectively. Heat flux and wall temperature at the impingement surface were calculated from temperature data measured at multiple locations below the impingement surface. Results are presented as heat flux, q" , versus the wall-to-spray temperature difference, ΔT[subscript w], at each of 5 volume flux, Q", conditions ranging from 0.54 to 2.04 x 10⁻³ m³/m²s. Convection coefficients, h[subscript cv], and spray efficiencies, η, are also presented for each case as a function of q" and ΔT[subscript w] , respectively. Results of the study indicate that at low and high volume fluxes, an improvement in heat transfer occurs in the single-phase regime for the fin geometry. Enhancement in the single-phase regime did not occur at the intermediate volume flux condition of 1.37 x 10⁻³ m³/m²s. At all volume flux states tested, significant enhancements, as high as 50% in some cases, were observed in the two-phase regime for the fin structure, whereas the groove structure performed identically to the flat surface in the single-phase regime and exhibited a large degradation in the two-phase and critical heat flux regimes (~50%). Critical heat flux for the fin surface compared to the flat surface was slightly lower at low volume flux conditions, equivalent at the intermediate volume flux, and slightly greater at high volume flux conditions. Further investigations into the underlying mechanisms responsible for these results are needed. Close

• 7. [Article] Experimental investigation of natural convection of mercury in an open, uniformly heated, vertical channel

  An experimental investigation was conducted to determine characteristics of natural convection of mercury in a vertical channel, which was open at both ends. Two cases were investigated separately: 1) ...

  Citation × Citation Citation Abstract Copy Title: Experimental investigation of natural convection of mercury in an open, uniformly heated, vertical channel Author: Colwell, Robert G. An experimental investigation was conducted to determine characteristics of natural convection of mercury in a vertical channel, which was open at both ends. Two cases were investigated separately: 1) both walls uniformly and symmetrically heated, and 2) one wall heated with the other insulated. Heat transfer correlations in laminar flow were obtained for several aspect ratios (channel height/width ratio), using streamwise distance from the leading edge as the characteristic dimension. These were generalized into one correlation which contains aspect ratio, parametrically, for each set of boundary conditions. The influence of flow in from the open sides of the channel was investigated by installing insulating plates along the vertical edges. It was observed that the average velocity of a low Prandtl number fluid in buoyant flow increases as the channel width is reduced. This results in a reduction of average wall temperature until the channel is sufficiently narrow that viscous forces begin to play an important role in the integral momentum balance across the channel. The channel was thus observed to be more thermally efficient than a single heated plate for aspect ratios less than 20. Velocity profiles were obtained in the region of laminar flow for each set of boundary conditions and several channel aspect ratios. Integration of the profiles gave mass flux predictions for various conditions. A hot film anemometer was used, and has proven to be very accurate for velocity measurement in the 5-100 in/min range. The documentation of laminar instability in buoyant channel flow was also an integral facet of this experiment. The criterion used was Grashof modulus based on the streamwise coordinate where the first "observable" velocity disturbance waves were determined. Channel width decrease initially had a destabilizing influence on the flow. The transition criterion displayed a minimum value at a particular aspect ratio. It was also observed that, in narrow channel cases at the highest heat flux used, flow underwent transition then relaminarized as the boundary layers met and fully-developed conditions were established. The thesis also discusses the apparatus and unique aspects of the experimental program. Data reduction methods, property determination and some anomalies of hot film anemometry in a liquid metal are also discussed. Title: Experimental investigation of natural convection of mercury in an open, uniformly heated, vertical channel Author: Colwell, Robert G. An experimental investigation was conducted to determine characteristics of natural convection of mercury in a vertical channel, which was open at both ends. Two cases were investigated separately: 1) both walls uniformly and symmetrically heated, and 2) one wall heated with the other insulated. Heat transfer correlations in laminar flow were obtained for several aspect ratios (channel height/width ratio), using streamwise distance from the leading edge as the characteristic dimension. These were generalized into one correlation which contains aspect ratio, parametrically, for each set of boundary conditions. The influence of flow in from the open sides of the channel was investigated by installing insulating plates along the vertical edges. It was observed that the average velocity of a low Prandtl number fluid in buoyant flow increases as the channel width is reduced. This results in a reduction of average wall temperature until the channel is sufficiently narrow that viscous forces begin to play an important role in the integral momentum balance across the channel. The channel was thus observed to be more thermally efficient than a single heated plate for aspect ratios less than 20. Velocity profiles were obtained in the region of laminar flow for each set of boundary conditions and several channel aspect ratios. Integration of the profiles gave mass flux predictions for various conditions. A hot film anemometer was used, and has proven to be very accurate for velocity measurement in the 5-100 in/min range. The documentation of laminar instability in buoyant channel flow was also an integral facet of this experiment. The criterion used was Grashof modulus based on the streamwise coordinate where the first "observable" velocity disturbance waves were determined. Channel width decrease initially had a destabilizing influence on the flow. The transition criterion displayed a minimum value at a particular aspect ratio. It was also observed that, in narrow channel cases at the highest heat flux used, flow underwent transition then relaminarized as the boundary layers met and fully-developed conditions were established. The thesis also discusses the apparatus and unique aspects of the experimental program. Data reduction methods, property determination and some anomalies of hot film anemometry in a liquid metal are also discussed. Close

• 8. [Article] Effect of vibration on forced convection to water from a cylinder at Reynolds numbers in the range of stable vortex shedding

  An experimental investigation has been made of the effect of vibration on heat transfer from a cylinder in crossflow. The cylinder used was 3/16-inch in diameter and was sinusoidally oscillated in the ...

  Citation × Citation Citation Abstract Copy Title: Effect of vibration on forced convection to water from a cylinder at Reynolds numbers in the range of stable vortex shedding Author: Graves, Donald Larry An experimental investigation has been made of the effect of vibration on heat transfer from a cylinder in crossflow. The cylinder used was 3/16-inch in diameter and was sinusoidally oscillated in the vertical direction by a mechanical drive mechanism while immersed in an open water channel. Nominal amplitude ratios, a/d, varied from 0.125 to 1.43 while frequency varied from 0 to 6.5 cycles per second. Data was taken at three flow Reynolds numbers: 64; 103 and 144. Temperature difference between the cylinder and the water was held at approximately 10°F. A hydrogen bubble technique was used in conjunction with dye studies to observe the flow near the cylinder. It was found that the heat transfer could be increased or decreased by vibration, depending on the amplitude ratio and the vibrational Reynolds number, (N[subscript Re])[subscript v] = awρ d/√2μ. Below a critical vibrational Reynolds number, which increased with the flow Reynolds number, oscillation had no effect on the heat transfer. After this critical point was passed, the data for the amplitude ratios 0.125, 0.250, and 0.500 showed a decrease in the heat transfer while the data for higher amplitude ratios (a/d = 1.00; 1.43) gave a steady increase. After reaching a minimum, the data for a/d = 0.500 increased to converge with the data of higher amplitudes; this trend was also suggested by the lower amplitude ratios but was not completely substantiated because of the frequency limitation of the drive mechanism. The maximum decrease in the heat transfer below stationary conditions was about 20 percent; the maximum increase in the heat transfer was 180, 125, and 90 percent for flow Reynolds numbers of 64; 103 and 144 respectively. The vortex shedding frequencies were in the range of frequency used for mechanical oscillation; noting this, an attempt was made to oscillate the cylinder through the immediate frequency range of vortex shedding to see if any special heat transfer effects would result. No change occurred other than the general increase due to increasing the vibrational intensity. The increases in heat transfer are attributed to vibrationally induced turbulence. An adequate explanation of the decreases in heat transfer was not provided by this investigation; however, it is thought that the phenomenon occurring may be similar to the observations of Kubanskii (11) who imposed acoustical vibrations on a cylinder in crossflow. By appropriately locating the cylinder with respect to the nodes of the sound field he found that the point of flow separation shifted toward the upstream side of the cylinder resulting in lower heat transfer rates. A critical (N[subscript Re])[subscript v]/(N[subscript Re])[subscript f] required to alter the heat transfer was established for this investigation and although it had a weak dependence on the amplitude ratio, a value of 0.35 serves as a good approximation for the data of this experiment. Title: Effect of vibration on forced convection to water from a cylinder at Reynolds numbers in the range of stable vortex shedding Author: Graves, Donald Larry An experimental investigation has been made of the effect of vibration on heat transfer from a cylinder in crossflow. The cylinder used was 3/16-inch in diameter and was sinusoidally oscillated in the vertical direction by a mechanical drive mechanism while immersed in an open water channel. Nominal amplitude ratios, a/d, varied from 0.125 to 1.43 while frequency varied from 0 to 6.5 cycles per second. Data was taken at three flow Reynolds numbers: 64; 103 and 144. Temperature difference between the cylinder and the water was held at approximately 10°F. A hydrogen bubble technique was used in conjunction with dye studies to observe the flow near the cylinder. It was found that the heat transfer could be increased or decreased by vibration, depending on the amplitude ratio and the vibrational Reynolds number, (N[subscript Re])[subscript v] = awρ d/√2μ. Below a critical vibrational Reynolds number, which increased with the flow Reynolds number, oscillation had no effect on the heat transfer. After this critical point was passed, the data for the amplitude ratios 0.125, 0.250, and 0.500 showed a decrease in the heat transfer while the data for higher amplitude ratios (a/d = 1.00; 1.43) gave a steady increase. After reaching a minimum, the data for a/d = 0.500 increased to converge with the data of higher amplitudes; this trend was also suggested by the lower amplitude ratios but was not completely substantiated because of the frequency limitation of the drive mechanism. The maximum decrease in the heat transfer below stationary conditions was about 20 percent; the maximum increase in the heat transfer was 180, 125, and 90 percent for flow Reynolds numbers of 64; 103 and 144 respectively. The vortex shedding frequencies were in the range of frequency used for mechanical oscillation; noting this, an attempt was made to oscillate the cylinder through the immediate frequency range of vortex shedding to see if any special heat transfer effects would result. No change occurred other than the general increase due to increasing the vibrational intensity. The increases in heat transfer are attributed to vibrationally induced turbulence. An adequate explanation of the decreases in heat transfer was not provided by this investigation; however, it is thought that the phenomenon occurring may be similar to the observations of Kubanskii (11) who imposed acoustical vibrations on a cylinder in crossflow. By appropriately locating the cylinder with respect to the nodes of the sound field he found that the point of flow separation shifted toward the upstream side of the cylinder resulting in lower heat transfer rates. A critical (N[subscript Re])[subscript v]/(N[subscript Re])[subscript f] required to alter the heat transfer was established for this investigation and although it had a weak dependence on the amplitude ratio, a value of 0.35 serves as a good approximation for the data of this experiment. Close

• 9. [Article] An approach to thermal convection problems in geophysics with application to the earth's mantle and ground water systems

  Two thermal convection problems of geophysical interest are examined, theoretically. First, convection in the earth's mantle is treated on the basis of a one-dimensional 'strip model'. This model results ...

  Citation × Citation Citation Abstract Copy Title: An approach to thermal convection problems in geophysics with application to the earth's mantle and ground water systems Author: Lowell, Robert P. Two thermal convection problems of geophysical interest are examined, theoretically. First, convection in the earth's mantle is treated on the basis of a one-dimensional 'strip model'. This model results from further simplification of the well known 'Rayleigh model'. For homogeneous, Newtonian fluids, the strip model yields results similar to those obtained by the Rayleigh method. The strip model is used to determine the critical Rayleigh number for convection in an internally heated two-phase fluid. The critical number depends on the parameters of the phase transition, the physical properties of the fluid, and the depth of the fluid layer. Depending on these factors, a univariant phase transformation may either enhance or hinder convective instability. For the olivine-spinel and spinel-oxides transitions in (MgFe)₂SiO₄ which are thought to take place in the upper mantle, it is shown that the critical Rayleigh number is altered only slightly from the critical number for convection in a fluid with one phase. This result holds both for convection in the entire mantle or convection restricted to the upper mantle. Hence the phase changes are of minor importance regarding the existence of mantle convection in general. A method for estimating the order of magnitude of the displacement of the phase surface as a function of Rayleigh number is outlined for a fluid with only one phase transition. The strip model is also used to treat convection in non-Newtonian fluids obeying a power law rheological equation. If the mantle is governed by a flow law of this type, it appears that convection can take place. Lastly, the procedure for applying the strip model to fluids with variable viscosity and thermal conductivity is outlined. The second convection problem concerns some aspects of convection of fluids in thin vertical fractures in the crust. A steady state model is developed to estimate the magnitude of the mass flow as a function of fracture thickness. It is shown that fractures of the order of a millimeter thick or greater can carry a measurable convective flow. A time dependent model is used to estimate the rate of decay of the mass flow with time. The results indicate that in fractures of the order of a centimeter thick, a measurable decrease of the mass flow takes place after a period of the order of a day. This rapid decay rate suggests that the principal effect of sea water convection in extensive fracture systems which are expected on mid-ocean ridge crests is to cool a volume of crustal rock in the vicinity of the fractures. Circulation of sea water in vertical fractures in the upper crust may provide an explanation of 1) the relatively low conductive heat flow measured at some locations on ocean ridge axes and 2) the very 'noisy' data obtained in the axial zone. Title: An approach to thermal convection problems in geophysics with application to the earth's mantle and ground water systems Author: Lowell, Robert P. Two thermal convection problems of geophysical interest are examined, theoretically. First, convection in the earth's mantle is treated on the basis of a one-dimensional 'strip model'. This model results from further simplification of the well known 'Rayleigh model'. For homogeneous, Newtonian fluids, the strip model yields results similar to those obtained by the Rayleigh method. The strip model is used to determine the critical Rayleigh number for convection in an internally heated two-phase fluid. The critical number depends on the parameters of the phase transition, the physical properties of the fluid, and the depth of the fluid layer. Depending on these factors, a univariant phase transformation may either enhance or hinder convective instability. For the olivine-spinel and spinel-oxides transitions in (MgFe)₂SiO₄ which are thought to take place in the upper mantle, it is shown that the critical Rayleigh number is altered only slightly from the critical number for convection in a fluid with one phase. This result holds both for convection in the entire mantle or convection restricted to the upper mantle. Hence the phase changes are of minor importance regarding the existence of mantle convection in general. A method for estimating the order of magnitude of the displacement of the phase surface as a function of Rayleigh number is outlined for a fluid with only one phase transition. The strip model is also used to treat convection in non-Newtonian fluids obeying a power law rheological equation. If the mantle is governed by a flow law of this type, it appears that convection can take place. Lastly, the procedure for applying the strip model to fluids with variable viscosity and thermal conductivity is outlined. The second convection problem concerns some aspects of convection of fluids in thin vertical fractures in the crust. A steady state model is developed to estimate the magnitude of the mass flow as a function of fracture thickness. It is shown that fractures of the order of a millimeter thick or greater can carry a measurable convective flow. A time dependent model is used to estimate the rate of decay of the mass flow with time. The results indicate that in fractures of the order of a centimeter thick, a measurable decrease of the mass flow takes place after a period of the order of a day. This rapid decay rate suggests that the principal effect of sea water convection in extensive fracture systems which are expected on mid-ocean ridge crests is to cool a volume of crustal rock in the vicinity of the fractures. Circulation of sea water in vertical fractures in the upper crust may provide an explanation of 1) the relatively low conductive heat flow measured at some locations on ocean ridge axes and 2) the very 'noisy' data obtained in the axial zone. Close