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• 1. [Article] Fully developed laminar natural convection in a vertical parallel plate channel with symmetric uniform wall temperature

  Described in this thesis is an investigation of the fully developed natural convection heat transfer in a vertical channel formed by two infinitely wide parallel plates maintained at a uniform wall temperature. ...

  Citation × Citation Citation Abstract Copy Title: Fully developed laminar natural convection in a vertical parallel plate channel with symmetric uniform wall temperature Author: Willie, Robert H. Described in this thesis is an investigation of the fully developed natural convection heat transfer in a vertical channel formed by two infinitely wide parallel plates maintained at a uniform wall temperature. Closed-form solutions for the velocity and temperature profiles are developed along with local and averaged Nusselt numbers. The local Nusselt number based on bulk temperature is found to be 3.77. This result is an analog corresponding to 7.60 for fully developed laminar forced convection in a parallel plate channel with uniform wall temperature boundary condition. The local Nusselt number based on the ambient temperature is deduced as a function of flowwise location. Results are compared with existing numerical and experimental data to find good agreement. Title: Fully developed laminar natural convection in a vertical parallel plate channel with symmetric uniform wall temperature Author: Willie, Robert H. Described in this thesis is an investigation of the fully developed natural convection heat transfer in a vertical channel formed by two infinitely wide parallel plates maintained at a uniform wall temperature. Closed-form solutions for the velocity and temperature profiles are developed along with local and averaged Nusselt numbers. The local Nusselt number based on bulk temperature is found to be 3.77. This result is an analog corresponding to 7.60 for fully developed laminar forced convection in a parallel plate channel with uniform wall temperature boundary condition. The local Nusselt number based on the ambient temperature is deduced as a function of flowwise location. Results are compared with existing numerical and experimental data to find good agreement. Close

• 2. [Article] Fully developed laminar natural convection in a vertical parallel-plate duct with constant wall heat flux

  The problem of heat transfer due to free convection in a channel formed by two parallel, isoflux, vertical plates is of considerable importance in electronic cooling applications, thermosiphons, the optimum ...

  Citation × Citation Citation Abstract Copy Title: Fully developed laminar natural convection in a vertical parallel-plate duct with constant wall heat flux Author: Aktan, Gülçin The problem of heat transfer due to free convection in a channel formed by two parallel, isoflux, vertical plates is of considerable importance in electronic cooling applications, thermosiphons, the optimum spacing of plates or components, industrial stacks, heat exchangers, nuclear power plants and combustion involving vertical walls. Although in each implementation other physical considerations are necessary, fully developed flow with symmetric isoflux boundary condition offers a fundamental heat transfer problem. Thus, here, the fully developed laminar natural convective flow of a viscous fluid in a channel formed by heated infinitely long vertical plates is investigated. Using boundary layer approximations, the basic governing equations of continuity, momentum and energy are combined into a single equation and solved analytically for a symmetric uniform heat flux boundary condition to find the velocity and temperature profiles and heat transfer coefficients for the flow. The closed-form solutions that are presented are strightforward and simple compared to previous solutions existing in the literature. For Rayleigh numbers sufficiently small to ensure a fully developed flow, it is found that the local Nusselt number based on local wall to bulk temperature difference is 4.118. Furthermore the pressure and mass flow rates for this particular geometry are also investigated. Title: Fully developed laminar natural convection in a vertical parallel-plate duct with constant wall heat flux Author: Aktan, Gülçin The problem of heat transfer due to free convection in a channel formed by two parallel, isoflux, vertical plates is of considerable importance in electronic cooling applications, thermosiphons, the optimum spacing of plates or components, industrial stacks, heat exchangers, nuclear power plants and combustion involving vertical walls. Although in each implementation other physical considerations are necessary, fully developed flow with symmetric isoflux boundary condition offers a fundamental heat transfer problem. Thus, here, the fully developed laminar natural convective flow of a viscous fluid in a channel formed by heated infinitely long vertical plates is investigated. Using boundary layer approximations, the basic governing equations of continuity, momentum and energy are combined into a single equation and solved analytically for a symmetric uniform heat flux boundary condition to find the velocity and temperature profiles and heat transfer coefficients for the flow. The closed-form solutions that are presented are strightforward and simple compared to previous solutions existing in the literature. For Rayleigh numbers sufficiently small to ensure a fully developed flow, it is found that the local Nusselt number based on local wall to bulk temperature difference is 4.118. Furthermore the pressure and mass flow rates for this particular geometry are also investigated. Close

• 3. [Article] Natural Convection Heat Transfer and Boundary Layer Transition for Vertical Heated Cylinders

  In recent years, the global nuclear industry has placed a greater emphasis on passively safe reactor designs. In particular, much attention and design work has been applied to engineered systems for passive ...

  Citation × Citation Citation Abstract Copy Title: Natural Convection Heat Transfer and Boundary Layer Transition for Vertical Heated Cylinders Author: Goodrich, Sam S. In recent years, the global nuclear industry has placed a greater emphasis on passively safe reactor designs. In particular, much attention and design work has been applied to engineered systems for passive cooling of nuclear fuel, whether it be loaded in a core or stored in spent fuel pools. The most common nuclear fuel geometry takes the shape of vertically oriented cylindrical rods. Given the emphasis on passive cooling and the prevalence of cylindrical nuclear fuel, one would anticipate a rather full and developed body of knowledge regarding natural convection heat transfer phenomena from vertical cylinders. However, the current body of knowledge centered on this topic is lacking a comprehensive understanding of several key phenomena that would facilitate more accurate modeling and design of passive heat exchange systems of this geometry. These phenomena include the relationship between heat transfer rate and cylinder diameter in both the laminar and turbulent regimes, as well as the relationship between boundary layer regime transition and diameter. Given that turbulent heat transfer rates are nearly an order of magnitude greater than the laminar regime, characterizing and being able to predict regime transition is essential to understanding heat transfer from a heated cylinder as a whole. The importance of this point is further underscored by considering how, due to the disparity in heat transfer rate between regimes, the cylinder temperature at the location just prior to transition may be the highest of the whole cylinder – directly feeding into the thermal design limits of the reactor fuel. One of the many difficulties in empirically deriving a heat transfer correlation is determining the bounds of the correlation. With respect to natural convection heat transfer from vertical cylinders, there are several interdependent phenomena that need to be considered simultaneously. The current experimental study addresses these phenomena using five heated cylinders with a range of diameters. Data from these heated cylinders is obtained through a combination of thermocouples, distributed temperature sensors, and particle image velocimetry. The results of this study are dimensionless, diameter-dependent, natural convection heat transfer correlations for the laminar, transition, and turbulent regimes. Additionally, the dimensionless bounds of applicability for these correlations (the regime transition points) as a function of diameter have also been experimentally determined using boundary layer theory and empirical data. Title: Natural Convection Heat Transfer and Boundary Layer Transition for Vertical Heated Cylinders Author: Goodrich, Sam S. In recent years, the global nuclear industry has placed a greater emphasis on passively safe reactor designs. In particular, much attention and design work has been applied to engineered systems for passive cooling of nuclear fuel, whether it be loaded in a core or stored in spent fuel pools. The most common nuclear fuel geometry takes the shape of vertically oriented cylindrical rods. Given the emphasis on passive cooling and the prevalence of cylindrical nuclear fuel, one would anticipate a rather full and developed body of knowledge regarding natural convection heat transfer phenomena from vertical cylinders. However, the current body of knowledge centered on this topic is lacking a comprehensive understanding of several key phenomena that would facilitate more accurate modeling and design of passive heat exchange systems of this geometry. These phenomena include the relationship between heat transfer rate and cylinder diameter in both the laminar and turbulent regimes, as well as the relationship between boundary layer regime transition and diameter. Given that turbulent heat transfer rates are nearly an order of magnitude greater than the laminar regime, characterizing and being able to predict regime transition is essential to understanding heat transfer from a heated cylinder as a whole. The importance of this point is further underscored by considering how, due to the disparity in heat transfer rate between regimes, the cylinder temperature at the location just prior to transition may be the highest of the whole cylinder – directly feeding into the thermal design limits of the reactor fuel. One of the many difficulties in empirically deriving a heat transfer correlation is determining the bounds of the correlation. With respect to natural convection heat transfer from vertical cylinders, there are several interdependent phenomena that need to be considered simultaneously. The current experimental study addresses these phenomena using five heated cylinders with a range of diameters. Data from these heated cylinders is obtained through a combination of thermocouples, distributed temperature sensors, and particle image velocimetry. The results of this study are dimensionless, diameter-dependent, natural convection heat transfer correlations for the laminar, transition, and turbulent regimes. Additionally, the dimensionless bounds of applicability for these correlations (the regime transition points) as a function of diameter have also been experimentally determined using boundary layer theory and empirical data. Close

• 4. [Article] Stability analysis on single-phase natural circulation in Argonne Lead Loop Facility

  Natural convection provides a means for circulating fluids without the use of pumps. This type of system is of great interest for a wide variety of applications, including solar heaters, process industry, ...

  Citation × Citation Citation Abstract Copy Title: Stability analysis on single-phase natural circulation in Argonne Lead Loop Facility Author: Tang, Hong Natural convection provides a means for circulating fluids without the use of pumps. This type of system is of great interest for a wide variety of applications, including solar heaters, process industry, and nuclear reactors. Natural convection will play a vital role in the area of passive safety and reliability, particularly for the development of Generation IV nuclear energy systems. This study mainly focuses on the linear stability analysis of asymmetrically heated/cooled natural convection loops with large temperature variations across the heated core. The study targets the Argonne Lead Loop Facility (ALLF), a concept for an experiment loop to support the development of the Secure Transportable Autonomous Reactor-Liquid Metal (STAR-LM) at Argonne National Laboratory, using lead-bismuth eutectic (LBE) as the primary reactor coolant. A one-dimensional linear stability analysis is performed and the Nyquist criterion is employed to find the linear stability boundary of both forward and backward circulations. It was found that the natural circulations could be linearly unstable in a high Reynolds number region. Increasing loop friction makes a forward circulation more stable, but destabilizes the corresponding backward circulation under the same heating/cooling conditions. The preliminary results suggest that as the Peclet number decreases, the forward circulation is prone to become unstable while the backward circulation is prone to remain stable. Title: Stability analysis on single-phase natural circulation in Argonne Lead Loop Facility Author: Tang, Hong Natural convection provides a means for circulating fluids without the use of pumps. This type of system is of great interest for a wide variety of applications, including solar heaters, process industry, and nuclear reactors. Natural convection will play a vital role in the area of passive safety and reliability, particularly for the development of Generation IV nuclear energy systems. This study mainly focuses on the linear stability analysis of asymmetrically heated/cooled natural convection loops with large temperature variations across the heated core. The study targets the Argonne Lead Loop Facility (ALLF), a concept for an experiment loop to support the development of the Secure Transportable Autonomous Reactor-Liquid Metal (STAR-LM) at Argonne National Laboratory, using lead-bismuth eutectic (LBE) as the primary reactor coolant. A one-dimensional linear stability analysis is performed and the Nyquist criterion is employed to find the linear stability boundary of both forward and backward circulations. It was found that the natural circulations could be linearly unstable in a high Reynolds number region. Increasing loop friction makes a forward circulation more stable, but destabilizes the corresponding backward circulation under the same heating/cooling conditions. The preliminary results suggest that as the Peclet number decreases, the forward circulation is prone to become unstable while the backward circulation is prone to remain stable. Close

• 5. [Article] An experimental study of natural convection heat transfer from a horizontal cylinder array vertically aligned to and confined by a single wall and two walls

  Convection heat transfer was experimentally investigated for two different geometries. One case had three horizontal cylinders in a vertical plane placed between two vertical walls. The second case had ...

  Citation × Citation Citation Abstract Copy Title: An experimental study of natural convection heat transfer from a horizontal cylinder array vertically aligned to and confined by a single wall and two walls Author: Al-Alusi, Thamir R. Convection heat transfer was experimentally investigated for two different geometries. One case had three horizontal cylinders in a vertical plane placed between two vertical walls. The second case had three horizontal cylinders in a vertical plane with only one vertical wall. Several different cylinder center-tocenter spacings were investigated. The wall spacings for the two wall and single wall cases were also varied. The cylinders were placed in a still air medium at atmospheric pressure and were maintained at a constant heat flux. The modified Rayleigh number, based on the diameter of the cylinders, ranged from 6.2 x 10⁴ to 1.2 x 10⁶. A scale analysis was performed to predict the relationship between the Nusselt number and the modified Rayleigh number. A standard finite-difference code was employed to show the temperature distribution and velocity vectors distribution around the cylinders. The results showed that there was a maximum heat transfer from each cylinder at a specific wall-array spacing and a specific center-to-center spacing. Comparisons of heat transfer results with a single free cylinder and a free array of horizontal cylinders were made and discussed. Empirical equations were proposed to predict the effects of the experimental parameters on the heat transfer as expressed by the average Nusselt number of each cylinder or the average Nusselt number of the whole array. Flow visualization was accomplished using laser sheets. The resulting studies showed that the presence of a single wall or the asymmetrical placement of the array between the two walls eliminated the presence of the vortices in the spaces between the cylinders and displaced the stagnation points. The asymmetrical placement of the array between two walls created a reversed current between the two walls. Title: An experimental study of natural convection heat transfer from a horizontal cylinder array vertically aligned to and confined by a single wall and two walls Author: Al-Alusi, Thamir R. Convection heat transfer was experimentally investigated for two different geometries. One case had three horizontal cylinders in a vertical plane placed between two vertical walls. The second case had three horizontal cylinders in a vertical plane with only one vertical wall. Several different cylinder center-tocenter spacings were investigated. The wall spacings for the two wall and single wall cases were also varied. The cylinders were placed in a still air medium at atmospheric pressure and were maintained at a constant heat flux. The modified Rayleigh number, based on the diameter of the cylinders, ranged from 6.2 x 10⁴ to 1.2 x 10⁶. A scale analysis was performed to predict the relationship between the Nusselt number and the modified Rayleigh number. A standard finite-difference code was employed to show the temperature distribution and velocity vectors distribution around the cylinders. The results showed that there was a maximum heat transfer from each cylinder at a specific wall-array spacing and a specific center-to-center spacing. Comparisons of heat transfer results with a single free cylinder and a free array of horizontal cylinders were made and discussed. Empirical equations were proposed to predict the effects of the experimental parameters on the heat transfer as expressed by the average Nusselt number of each cylinder or the average Nusselt number of the whole array. Flow visualization was accomplished using laser sheets. The resulting studies showed that the presence of a single wall or the asymmetrical placement of the array between the two walls eliminated the presence of the vortices in the spaces between the cylinders and displaced the stagnation points. The asymmetrical placement of the array between two walls created a reversed current between the two walls. Close