Dissertationen zum Thema „Convective mixers“

Comprendre le comportement d'écoulement des poudres lors de l'agitation mécanique est crucial pour optimiser les processus de mélange dans les applications industrielles. Cette étude introduit la rhéologie μ(I), une loi rhéologique développée pour analyser la rhéologie des poudres dans les écoulements denses au sein d'un dispositif de mélange en laboratoire. Le cadre se concentre sur les interactions entre les pales et le lit de poudre, en abordant les défis de mesure de paramètres complexes des poudres tels que le coefficient de friction effectif µeff. La rhéologie μ(I), développée grâce à l'analyse dimensionnelle et à la visualisation des bandes de cisaillement, démontre de fortes capacités prédictives pour différentes configurations de poudres ayant des formes de particules similaires mais des tailles variées. Le cadre de la rhéologie μ(I) s'est révélé applicable à diverses configurations de systèmes agités et a posé les bases des premières études de mise à l'échelle incluant les caractéristiques des poudres. Les comparaisons avec l'équation de Hatano confirment la robustesse de la rhéologie μ(I), notamment pour les lits de poudre profonds. Les améliorations futures se concentreront sur le raffinement de l'évaluation de la largeur des bandes de cisaillement et la réévaluation des hypothèses de contrainte normale pour améliorer la précision du modèle. Cette recherche contribue à une compréhension approfondie de la dynamique des poudres dans les systèmes de mélange et soutient l'efficacité de la mise à l'échelle des processus industriels
Understanding powder flow behaviour during mechanical agitation is crucial for optimising mixing processes in industrial applications. This study introduces μ(I)-rheology, a novel rheological law developed to analyse powder rheology in dense flows within a laboratory mixing setup. The framework focuses on the interactions between paddles and the powder bed, addressing the challenges of measuring complex powder parameters such as the effective friction coefficient µeff. μ(I)-rheology, developed through dimensional analysis and shear band visualisation, demonstrates strong predictive capabilities across different powder configurations with similar particle shapes but varying sizes. The μ(I)-rheology framework proved applicable across various agitated system configurations and has laid the groundwork for initial scale-up studies that includes powder characteristics. Comparisons with Hatano's equation confirm the robustness of μ(I)-rheology, particularly for deep powder beds. Future improvements will focus on refining shear band width evaluation and reassessing normal stress assumptions to enhance model accuracy. This research contributes to a deeper understanding of powder dynamics in mixing systems and supports efficient scaling-up of industrial processes

Turbulent mixed convection is a complicated flow where the buoyancy and shear forces compete with each other in affecting the flow dynamics. This thesis deals with the near wall dynamics in a turbulent mixed convection flow over an isothermal horizontal heated plate. We distinguish between two types of mixed convection ; low-speed mixed convection (LSM) and high-speed mixed convection (HSM). In LSM the entire boundary layer, including the near-wall region, is dominated by buoyancy; in HSM the near-wall region, is dominated by shear and the outer region by buoyancy. We show that the value of the parameter (* = ^ determines whether the flow is LSM or HSM. Here yr is the friction length scale and L is the Monin-Obukhov length scale. In the present thesis we proposed a model for the near-wall dynamics in LSM. We assume the coherent structure near-wall for low-speed mixed convection to be streamwise aligned periodic array of laminar plumes and give a 2d model for the near wall dynamics, Here the equation to solve for the streamwise velocity is linear with the vertical and spanwise velocities given by the free convection model of Theerthan and Arakeri [1]. We determine the profiles of streamwise velocity, Reynolds shear stress and RMS of the fluctuations of the three components of velocity. From the model we obtain the scaling for wall shear stress rw as rw oc (UooAT*), where Uoo is the free-stream velocity and AT is the temperature difference between the free-stream and the horizontal surface.A similar scaling for rw was obtained in the experiments of Ingersoll [5] and by Narasimha et al [11] in the atmospheric boundary layer under low wind speed conditions. We also derive a formula for boundary layer thickness 5(x) which predicts the boundary layer growth for the combination free-stream velocity Uoo and AT in the low-speed mixed convection regime.

Turbulent mixed convection is a complicated flow where the buoyancy and shear forces compete with each other in affecting the flow dynamics. This thesis deals with the near wall dynamics in a turbulent mixed convection flow over an isothermal horizontal heated plate. We distinguish between two types of mixed convection ; low-speed mixed convection (LSM) and high-speed mixed convection (HSM). In LSM the entire boundary layer, including the near-wall region, is dominated by buoyancy; in HSM the near-wall region, is dominated by shear and the outer region by buoyancy. We show that the value of the parameter (* = ^ determines whether the flow is LSM or HSM. Here yr is the friction length scale and L is the Monin-Obukhov length scale. In the present thesis we proposed a model for the near-wall dynamics in LSM. We assume the coherent structure near-wall for low-speed mixed convection to be streamwise aligned periodic array of laminar plumes and give a 2d model for the near wall dynamics, Here the equation to solve for the streamwise velocity is linear with the vertical and spanwise velocities given by the free convection model of Theerthan and Arakeri [1]. We determine the profiles of streamwise velocity, Reynolds shear stress and RMS of the fluctuations of the three components of velocity. From the model we obtain the scaling for wall shear stress rw as rw oc (UooAT*), where Uoo is the free-stream velocity and AT is the temperature difference between the free-stream and the horizontal surface.A similar scaling for rw was obtained in the experiments of Ingersoll [5] and by Narasimha et al [11] in the atmospheric boundary layer under low wind speed conditions. We also derive a formula for boundary layer thickness 5(x) which predicts the boundary layer growth for the combination free-stream velocity Uoo and AT in the low-speed mixed convection regime.

An experimental apparatus was designed and constructed for the study of laminar mixed convection heat transfer in vertical, horizontal and inclined tubes. The working fluid was distilled water, with bulk temperatures in the range of 8$ sp circ$C to 31$ sp circ$C.
An innovative design allows, for the first time, flow visualization over the entire heated portion of the test section. The key element of this design is a thin, electrically conductive gold-film heater suitably attached to the outside surface of a plexiglas pipe: the gold film is approximately 80% transparent to electromagnetic radiation in the visible wavelength band. This test section was mounted inside a transparent vacuum chamber to insulate it from the environment. A dye injection technique was used to visualize the mixed-convection flow patterns. The apparatus was also designed and instrumented to allow the measurement of both circumferential and axial temperature variations over the heated tube.
The flow-visualization results revealed the following: (i) a steady recirculating flow pattern, followed by laminar flow instability in vertical tubes; (ii) steady spiralling flow patterns in inclined and horizontal tubes, that confirmed earlier numerical predictions. The temperature results agreed qualitatively with earlier published experimental and numerical data. Local and overall Nusselt numbers can be calculated using the data presented, but this is not within the scope of this thesis.

Thesis (S.B.)--Massachusetts Institute of Technology, Dept. of Mechanical Engineering, 2007.
Includes bibliographical references (leaves 28-29).
The Mars Gravity Biosatellite will house fifteen mice in a low Earth orbit satellite spinning about its longitudinal axis. The satellite's payload thermal control system will reject heat through the base of the payload module and provide air circulation vital to maintaining a habitable environment for the mice. The centripetal acceleration due to rotation creates the tendency for heated air to move by free convection toward the axis of rotation. Dominance of forced convection throughout the payload module will ensure nearly isothermal air and effective heat rejection from the payload to the bus module via fan/heatsink/thermoelectric cooler units. Circulation effectiveness is measured by the Richardson number, which expresses the ratio of the influence of free convection to the influence of forced convection in a mixed-convection flow. Experiments were executed with the current circulation system to determine the forced convection flow velocity. The free convection flow parameter was determined theoretically. Cross-flow fan/heatsink units mounted on the baseplate rim created low Reynolds number (88-985) flow throughout the enclosure. The calculated Richardson number for the worst-case 19°C difference between heated components and cooled air is between 0.78 and 2.34.
(cont.) For a realistic steady 3°C-80C temperature difference, the calculated Richardson number for the overall flow field is between 0.22 and 0.37. It was found that the flow capacity of the fan/heatsink assemblies must be increased from 1CFM to 5CFM to achieve the desired dominance of forced convection (a Richardson number of 0.1) in the worst-case on-orbit scenario. Increasing the capacity of the circulation system would allow for recovery from worst-case thermal scenarios under spaceflight conditions and allow a fraction of the cooler units to be powered during normal spaceflight conditions. The methods used here are scalable to analysis for the design of rotating human habitation vehicles.
by Jesse B. Marsh.
S.B.

This work focuses on magnetohydrodynamic (MHD) mixed convection flow of electrically conducting fluids enclosed in simple 1D and 2D geometries in steady periodic regime. In particular, in Chapter one a short overview is given about the history of MHD, with reference to papers available in literature, and a listing of some of its most common technological applications, whereas Chapter two deals with the analytical formulation of the MHD problem, starting from the fluid dynamic and energy equations and adding the effects of an external imposed magnetic field using the Ohm's law and the definition of the Lorentz force. Moreover a description of the various kinds of boundary conditions is given, with particular emphasis given to their practical realization. Chapter three, four and five describe the solution procedure of mixed convective flows with MHD effects. In all cases a uniform parallel magnetic field is supposed to be present in the whole fluid domain transverse with respect to the velocity field. The steady-periodic regime will be analyzed, where the periodicity is induced by wall temperature boundary conditions, which vary in time with a sinusoidal law. Local balance equations of momentum, energy and charge will be solved analytically and numerically using as parameters either geometrical ratios or material properties. In particular, in Chapter three the solution method for the mixed convective flow in a 1D vertical parallel channel with MHD effects is illustrated. The influence of a transverse magnetic field will be studied in the steady periodic regime induced by an oscillating wall temperature. Analytical and numerical solutions will be provided in terms of velocity and temperature profiles, wall friction factors and average heat fluxes for several values of the governing parameters. In Chapter four the 2D problem of the mixed convective flow in a vertical round pipe with MHD effects is analyzed. Again, a transverse magnetic field influences the steady periodic regime induced by the oscillating wall temperature of the wall. A numerical solution is presented, obtained using a finite element approach, and as a result velocity and temperature profiles, wall friction factors and average heat fluxes are derived for several values of the Hartmann and Prandtl numbers. In Chapter five the 2D problem of the mixed convective flow in a vertical rectangular duct with MHD effects is discussed. As seen in the previous chapters, a transverse magnetic field influences the steady periodic regime induced by the oscillating wall temperature of the four walls. The numerical solution obtained using a finite element approach is presented, and a collection of results, including velocity and temperature profiles, wall friction factors and average heat fluxes, is provided for several values of, among other parameters, the duct aspect ratio. A comparison with analytical solutions is also provided, as a proof of the validity of the numerical method. Chapter six is the concluding chapter, where some reflections on the MHD effects on mixed convection flow will be made, in agreement with the experience and the results gathered in the analyses presented in the previous chapters. In the appendices special auxiliary functions and FORTRAN program listings are reported, to support the formulations used in the solution chapters.

This work focuses on magnetohydrodynamic (MHD) mixed convection flow of electrically conducting fluids enclosed in simple 1D and 2D geometries in steady periodic regime. In particular, in Chapter one a short overview is given about the history of MHD, with reference to papers available in literature, and a listing of some of its most common technological applications, whereas Chapter two deals with the analytical formulation of the MHD problem, starting from the fluid dynamic and energy equations and adding the effects of an external imposed magnetic field using the Ohm's law and the definition of the Lorentz force. Moreover a description of the various kinds of boundary conditions is given, with particular emphasis given to their practical realization. Chapter three, four and five describe the solution procedure of mixed convective flows with MHD effects. In all cases a uniform parallel magnetic field is supposed to be present in the whole fluid domain transverse with respect to the velocity field. The steady-periodic regime will be analyzed, where the periodicity is induced by wall temperature boundary conditions, which vary in time with a sinusoidal law. Local balance equations of momentum, energy and charge will be solved analytically and numerically using as parameters either geometrical ratios or material properties. In particular, in Chapter three the solution method for the mixed convective flow in a 1D vertical parallel channel with MHD effects is illustrated. The influence of a transverse magnetic field will be studied in the steady periodic regime induced by an oscillating wall temperature. Analytical and numerical solutions will be provided in terms of velocity and temperature profiles, wall friction factors and average heat fluxes for several values of the governing parameters. In Chapter four the 2D problem of the mixed convective flow in a vertical round pipe with MHD effects is analyzed. Again, a transverse magnetic field influences the steady periodic regime induced by the oscillating wall temperature of the wall. A numerical solution is presented, obtained using a finite element approach, and as a result velocity and temperature profiles, wall friction factors and average heat fluxes are derived for several values of the Hartmann and Prandtl numbers. In Chapter five the 2D problem of the mixed convective flow in a vertical rectangular duct with MHD effects is discussed. As seen in the previous chapters, a transverse magnetic field influences the steady periodic regime induced by the oscillating wall temperature of the four walls. The numerical solution obtained using a finite element approach is presented, and a collection of results, including velocity and temperature profiles, wall friction factors and average heat fluxes, is provided for several values of, among other parameters, the duct aspect ratio. A comparison with analytical solutions is also provided, as a proof of the validity of the numerical method. Chapter six is the concluding chapter, where some reflections on the MHD effects on mixed convection flow will be made, in agreement with the experience and the results gathered in the analyses presented in the previous chapters. In the appendices special auxiliary functions and FORTRAN program listings are reported, to support the formulations used in the solution chapters.

On etudie les conditions dans lesquelles un ecoulement de convection peut penetrer un milieu poreux et les consequences que cette circulation engendre sur les transferts thermiques. Etude theorique a partir d'une approche de type couche limite. Mesure de la vitesse, des temperatures et des flux thermiques dans une cavite rectangulaire partiellement occupee par un isolant fibreux

Thesis (Ph. D.)--Massachusetts Institute of Technology, Dept. of Nuclear Engineering, 1986.
MICROFICHE COPY AVAILABLE IN ARCHIVES AND SCIENCE.
Bibliography: leaves 322-326.
by Tae Sun Ro.
Ph.D.

Mixed convection heat transfer in enclosures has been studied in order to enhance the associated heat transfer performance through the use of either different convective fluid types, domain configurations, boundary conditions, or combinations thereof. Analysing the enhancement in heat transfer has been accomplished through the isotherm and streamline contours, temperature isosurfaces, flow vectors, mean and root mean square velocity profiles, turbulence kinetic energy profiles and Nusselt number profiles. Firstly, laminar mixed convection in a lid-driven trapezoidal cavity using different nanoparticle types and various parameters other than configuration parameters has been investigated. It was found that any nanofluid types can provide greater heat transfer than water, especially, at high nanoparticle volume fraction and low diameter. Heat convection can be affected by changing either rotational and inclination angles, aspect ratio, or flow direction. Secondly, turbulent mixed convection due to the moving sidewalls of a lid-driven cuboid has been analysed. Remarkable enhancement in heat transfer has been achieved by either increasing the turbulent flow circulation or using nanofluids. Thirdly, turbulent mixed convection in a top wall lid-driven cuboid containing a clockwise- or anticlockwise-rotating cylinder has been studied. Significant enhancement in heat convection was noticed with the use of the rotating cylinder, especially when the direction of rotation can enhance the top wall movement. In addition, the Reynolds number and nanofluids have a positive impact on the heat transfer in the presence of the rotating cylinder. Finally, the study has been extended by artificially roughening the heated wall in order to increase the heat transfer rate. A noteworthy enhancement has been found due to the use of two rib shapes, particularly in combination with the rotating cylinder. Overall, in terms of the comparison between the URANS and LES predictions, even though both methods have performed well, the LES approach is more successful in capturing more detail of the secondary eddies.

Thesis (Sc. D.)--Massachusetts Institute of Technology, Dept. of Nuclear Engineering, 1986.
MICROFICHE COPY AVAILABLE IN ARCHIVES AND SCIENCE
Bibliography: v.1, leaves 287-292.
by Victor Iannello.
Sc.D.

Thesis (S.M.)--Massachusetts Institute of Technology, Dept. of Nuclear Engineering, 2005.
Includes bibliographical references (p. 79-84).
For decay heat removal systems in the conceptual Gas-cooled Fast Reactor (GFR) currently under development, passive emergency cooling using natural circulation of a gas at an elevated pressure is being considered. Since GFR cores have high power density and low thermal inertia, relative to the high temperature gas-cooled thermal reactor (HTGR), the decay heat removal (DHR) in depressurization accidents is a major challenge to be overcome. This is due to (1) a gas has inherently inferior heat transport capabilities compared to a liquid and (2) the high surface heat flux of the GFR strongly affects the gas flow under natural circulation. The high heat flux places the flow into a mixed convection regime, which is not yet fully understood. One of the issues of mixed convection is that the transition from laminar to turbulent flow is not clearly defined in the existing literature. Review of previous work on heat transfer mechanisms and flow characteristics of the mixed convection transitional regime shows that two transitional zones exist between laminar or laminar-like flow and fully turbulent flow for the upward heated case. Previous work has focused on liquids and thus is not applicable to gas mixed convection.
(cont.) An experimental facility is designed to obtain the data in the regions not covered in previous work, using nitrogen, helium and carbon dioxide. The facility is expected to operate with heat fluxes up to 10kW/m2 and gas velocities up to 2.5m/s by natural circulation only. A velocity calibration method is designed in addition to the hotwire probe for velocity and temperature profiles measurement. Finally, computational simulations, using the commercial code FLUENT, are performed to select an appropriate turbulence model for investigating mixed convection transitional flow regimes. It was concluded that the basic models in FLUENT were not capable of predicting the transitional flow as the Launder-Sharma turbulence model does. Nevertheless, the advanced numerical algorithm and convenient post processor of FLUENT can still be utilized by using UDF to incorporate other turbulence models into the code.
by Jeongik Lee.
S.M.

A FORTRAN code was developed to numerically simulate the mixed convective flow over a three-dimensional horizontal backward-facing step. The momentum and energy equations under the assumption of the Boussinesq approximation were discretized by means of a finite volume technique. The SIMPLE algorithm scheme was applied to link the pressure and velocity fields inside the domain while an OpenMP parallel implementation was proposed to improve the numerical performance and to accelerate the numerical solution. The heating process corresponds to a channel heated from below at constant temperature keeping insulated all the other channel walls. In addition, the back-step was considered as a thermally conducting block and its influence in the heating process was explored by holding different solid to fluid thermal conductivity ratios. The effects over the velocity and temperature distribution of buoyancy forces, acting perpendicular to the mainstream flow, are studied for three different Richardson numbers Ri=3, 2, and 1 and the results are compared against those of pure forced convection Ri=0. In these simulations the Reynolds number is fixed at 200 while the bottom wall temperature is adjusted to fulfill the conditions for the different Ri. Under this assumption, as Ri increases the buoyancy effects are the dominant effects in the mixed convective process. The numerical results indicate that the velocity field and the temperature distribution for pure forced convection are highly distorted if compared with the mixed convective flow. If the Ri parameter is increased, then the primary re-circulation zone is reduced. Similarly, as the buoyancy forces become predominant in the flow, the convective rolls, in the form of spiral-flow structures, become curlier and then higher velocity components are found inside the domain. The temperature field distribution showed that as the Ri is increased a thicker layer of high temperature flow is located at the channel??s top wall as a result of the higher rates of low-density flow moving to the top wall. The flow is ascending by the channel sidewalls, while descending by the channel span-wise central plane. The parallel numerical strategy is presented and some results for the performance of the OpenMP implementation are included. In this sense, linear speedup was obtained when using 16 possessors in parallel.

Cooling of electronic components is one of the most important issues concerned in the electronic industry for design of equipment. Maintaining the temperature of an electronic device within its safe operating temperature limits is essential to operate the equipment safely with proper functionality. According to the Arrhenious law of failure rate, for a device with activation energy 0.65eV, every 10°C increase in temperature doubles the failure rate. Recent miniaturisation of components and high device heat dissipation rates lead to high heat fluxes, which cause temperature rise. Hence, there is an increasing need for research to achieve high heat removal rates and optimal design. Several cooling techniques are used for cooling of electronics based on the application and cooling rate requirements. Air-cooling of electronics has a wide range of applications due to its greater reliability, simplicity, easy maintenance, low cost, easy availability of coolant (air), and light weight. Air-cooling is also free from boiling and dripping problems. Air-cooling is used in applications such as avionics, cooling of personal computers, cooling of data centers, and in automobile electronics. In a typical electronic cooling application, cooling fluid is driven by the combination of external pressure forces and buoyancy forces. Based on the relative contribution of these forces towards the total driving force, the cooling techniques can be categorized as forced, natural or mixed convection cooling. However, in many of the electronic cooling situations, such as in the applications with very high heat fluxes, tall Printed Circuits Boards (PCBs) with low forced convection velocity, and in large scale applications such as data centers, the contributions of the buoyancy forces and external pressure forces for the total driving force are comparable, which results in a mixed convection situation. In the present study, mixed convection in vertical channels heated with five heating configurations, which represent typical electronic cooling applications, is studied numerically. The five different heating configurations are channels with flush-mounted continuous heater, flush-mounted strip heaters, flush-mounted square block heaters, protruding rib heaters and protruding square heaters. The first three configurations are categorised as flush-mounted heating configurations and the latter two configurations are categorised as protruded heating configurations. One of the channel walls represents the substrate on which the heaters are mounted and the heat sources represent the heat generating electronic components. Heat transfer under steady state conditions is considered in the study. The study includes laminar as well as turbulent heat transfer. For a systematic study of mixed convection, an analytical or semi-analytical formulation is desirable for a simplified model, as it can highlight the effect of relevant non-dimensional parameters on the heat transfer characteristics of a system. The results of a simplified model can be used for benchmarking the results of practical situations. Hence, before numerically solving the governing equations for mixed convection in channels, mixed convection boundary layer flows over a heated vertical plate is considered for study. Perturbation technique is used to solve the boundary layer equations with non-isothermal boundary conditions. The perturbation analysis is carried out for an arbitrarily variation of wall temperature or heat flux. Subsequently, the results are extended to find heat transfer rates in the cases of power-law variation of temperature and heat flux, as special cases. It is always required to design a cooling system to remove maximum possible amount of heat, keeping the device temperature within its safe operating limits. Hence, optimization of heat transfer in boundary layers is attempted, whose results can be used as guidelines to achieve optimal heat transfer in practical situations of channels with continuous as well as discrete heating. Similarity analysis is used for the optimization of heat distribution in boundary layer flows. In the similarity analysis, in the search of optimal heat transfer from the plate, the boundary layer equations are solved for various power-law heat flux variations and the appropriate power-law variation of optimal heat transfer is found. Similarly, the heat flux variation for optimal heat transfer is found for the cases of natural and forced convection, as they are the limiting cases of mixed convection. In the numerical part of the study, the generalised three-dimensional governing equations for the five heating configurations considered for the study are solved numerically with appropriate boundary conditions. Separation of natural, forced and mixed convection regimes is carried out in all the heating configurations using a criterion based on individual contributions of pressure force and buoyancy force towards the total driving force for the fluid movement. Heat transfer characteristics are studied in laminar as well as turbulent regimes in terms of parameters such as Grashof number, Reynolds number, Nusselt number, maximum temperature of heaters, pressure drop across the channel, and so on. The influence of conjugate effects on the heat transfer characteristics is studied by varying the substrate thermal conductivity. A systematic comparison of various effects such as the effect of discrete heating in plain channels, effect of discrete heating in channels with heated ribs, and the effect of three-dimensional protrusions on heat transfer, is achieved. The parameters in the individual configurations, which affect heat transfer, are explored for better cooling solutions. Optimal heat distribution among the heaters to minimise the temperature of the hottest heater for a given total amount of heat generation in the channel is found for all the channel configurations, which are heated either continuously or discretely. In the process of finding the optimal heat distribution among heaters, guidelines are taken from the optimal heat distribution in boundary layer flows. Compared to usual optimization approaches such as genetic algorithm, the present physics based optimisation procedure requires fewer runs to arrive at the optimal distribution. The fluid flow characteristics in all the three configurations with flush-mounted heaters are found to be similar. However, heat transfer characteristics in channels with flush-mounted square heaters differ from those in the other two flush-mounted channel configurations. Hot spots with higher temperatures are found at heater locations in channels with flush-mounted square heaters. The effect of substrate follows the same trend in all the flush-mounted configurations. At lower thermal conductivities, the maximum temperature decreases sharply with increasing thermal conductivity. However, at higher conductivities, the influence reduces. In all the flush-mounted configurations, heat transfer will not be influenced by substrate thermal conductivity increment at conductivities more than 150 times the fluid thermal conductivity. The fluid flow and heat transfer characteristics in channels with protruded heaters differ significantly from those in channels with flush-mounted heaters. The protrusions in the channels interact with the fluid flow and make it different from that of smooth channels. In turn, the protrusions affect heat transfer characteristics in the channels. The influence of the protrusions on the heat transfer and locations of hot spots in the domain is examined. Effect of thermal conductivity in channels with protruded square heaters is similar to that in channels with flush-mounted heaters. However, conductivity in channels with protruded rib heaters affects the heat transfer in a wider range of conductivities than in the other heating configurations. Unlike in the other configurations, at low thermal conductivities, maximum temperature does not drop sharply with increase of conductivity. In channels with protruded square heaters, staggering arrangement of heaters results in higher heat transfer rates than those with in-line heater arrangement. In all the configurations, pressure drop is found to be independent of Grashof number in the range of heat dissipation rates considered in the study. Heat transfer rates in turbulent region are much higher than the heat transfer rates in laminar regime. However, the pressure drops encountered are also high in the turbulent regime. Turbulent heat transfer results in a more uniform temperature distribution in channels. The cooling performances of the individual configurations are compared. For a given pressure drop the cooling performances decreases in the order of flush-mounted strip heating, protruded square heating, flush-mounted square heating, protruded rib heating. For a given inlet fluid flow rate, the cooling performances decreases in the order of protruded rib heating, protruded square heating, flush-mounted square heating, flush-mounted strip heating. However, for a given inlet fluid flow rate, the pressure drop increases in the order of increasing cooling performance.

Cooling of electronic components is one of the most important issues concerned in the electronic industry for design of equipment. Maintaining the temperature of an electronic device within its safe operating temperature limits is essential to operate the equipment safely with proper functionality. According to the Arrhenious law of failure rate, for a device with activation energy 0.65eV, every 10°C increase in temperature doubles the failure rate. Recent miniaturisation of components and high device heat dissipation rates lead to high heat fluxes, which cause temperature rise. Hence, there is an increasing need for research to achieve high heat removal rates and optimal design. Several cooling techniques are used for cooling of electronics based on the application and cooling rate requirements. Air-cooling of electronics has a wide range of applications due to its greater reliability, simplicity, easy maintenance, low cost, easy availability of coolant (air), and light weight. Air-cooling is also free from boiling and dripping problems. Air-cooling is used in applications such as avionics, cooling of personal computers, cooling of data centers, and in automobile electronics. In a typical electronic cooling application, cooling fluid is driven by the combination of external pressure forces and buoyancy forces. Based on the relative contribution of these forces towards the total driving force, the cooling techniques can be categorized as forced, natural or mixed convection cooling. However, in many of the electronic cooling situations, such as in the applications with very high heat fluxes, tall Printed Circuits Boards (PCBs) with low forced convection velocity, and in large scale applications such as data centers, the contributions of the buoyancy forces and external pressure forces for the total driving force are comparable, which results in a mixed convection situation. In the present study, mixed convection in vertical channels heated with five heating configurations, which represent typical electronic cooling applications, is studied numerically. The five different heating configurations are channels with flush-mounted continuous heater, flush-mounted strip heaters, flush-mounted square block heaters, protruding rib heaters and protruding square heaters. The first three configurations are categorised as flush-mounted heating configurations and the latter two configurations are categorised as protruded heating configurations. One of the channel walls represents the substrate on which the heaters are mounted and the heat sources represent the heat generating electronic components. Heat transfer under steady state conditions is considered in the study. The study includes laminar as well as turbulent heat transfer. For a systematic study of mixed convection, an analytical or semi-analytical formulation is desirable for a simplified model, as it can highlight the effect of relevant non-dimensional parameters on the heat transfer characteristics of a system. The results of a simplified model can be used for benchmarking the results of practical situations. Hence, before numerically solving the governing equations for mixed convection in channels, mixed convection boundary layer flows over a heated vertical plate is considered for study. Perturbation technique is used to solve the boundary layer equations with non-isothermal boundary conditions. The perturbation analysis is carried out for an arbitrarily variation of wall temperature or heat flux. Subsequently, the results are extended to find heat transfer rates in the cases of power-law variation of temperature and heat flux, as special cases. It is always required to design a cooling system to remove maximum possible amount of heat, keeping the device temperature within its safe operating limits. Hence, optimization of heat transfer in boundary layers is attempted, whose results can be used as guidelines to achieve optimal heat transfer in practical situations of channels with continuous as well as discrete heating. Similarity analysis is used for the optimization of heat distribution in boundary layer flows. In the similarity analysis, in the search of optimal heat transfer from the plate, the boundary layer equations are solved for various power-law heat flux variations and the appropriate power-law variation of optimal heat transfer is found. Similarly, the heat flux variation for optimal heat transfer is found for the cases of natural and forced convection, as they are the limiting cases of mixed convection. In the numerical part of the study, the generalised three-dimensional governing equations for the five heating configurations considered for the study are solved numerically with appropriate boundary conditions. Separation of natural, forced and mixed convection regimes is carried out in all the heating configurations using a criterion based on individual contributions of pressure force and buoyancy force towards the total driving force for the fluid movement. Heat transfer characteristics are studied in laminar as well as turbulent regimes in terms of parameters such as Grashof number, Reynolds number, Nusselt number, maximum temperature of heaters, pressure drop across the channel, and so on. The influence of conjugate effects on the heat transfer characteristics is studied by varying the substrate thermal conductivity. A systematic comparison of various effects such as the effect of discrete heating in plain channels, effect of discrete heating in channels with heated ribs, and the effect of three-dimensional protrusions on heat transfer, is achieved. The parameters in the individual configurations, which affect heat transfer, are explored for better cooling solutions. Optimal heat distribution among the heaters to minimise the temperature of the hottest heater for a given total amount of heat generation in the channel is found for all the channel configurations, which are heated either continuously or discretely. In the process of finding the optimal heat distribution among heaters, guidelines are taken from the optimal heat distribution in boundary layer flows. Compared to usual optimization approaches such as genetic algorithm, the present physics based optimisation procedure requires fewer runs to arrive at the optimal distribution. The fluid flow characteristics in all the three configurations with flush-mounted heaters are found to be similar. However, heat transfer characteristics in channels with flush-mounted square heaters differ from those in the other two flush-mounted channel configurations. Hot spots with higher temperatures are found at heater locations in channels with flush-mounted square heaters. The effect of substrate follows the same trend in all the flush-mounted configurations. At lower thermal conductivities, the maximum temperature decreases sharply with increasing thermal conductivity. However, at higher conductivities, the influence reduces. In all the flush-mounted configurations, heat transfer will not be influenced by substrate thermal conductivity increment at conductivities more than 150 times the fluid thermal conductivity. The fluid flow and heat transfer characteristics in channels with protruded heaters differ significantly from those in channels with flush-mounted heaters. The protrusions in the channels interact with the fluid flow and make it different from that of smooth channels. In turn, the protrusions affect heat transfer characteristics in the channels. The influence of the protrusions on the heat transfer and locations of hot spots in the domain is examined. Effect of thermal conductivity in channels with protruded square heaters is similar to that in channels with flush-mounted heaters. However, conductivity in channels with protruded rib heaters affects the heat transfer in a wider range of conductivities than in the other heating configurations. Unlike in the other configurations, at low thermal conductivities, maximum temperature does not drop sharply with increase of conductivity. In channels with protruded square heaters, staggering arrangement of heaters results in higher heat transfer rates than those with in-line heater arrangement. In all the configurations, pressure drop is found to be independent of Grashof number in the range of heat dissipation rates considered in the study. Heat transfer rates in turbulent region are much higher than the heat transfer rates in laminar regime. However, the pressure drops encountered are also high in the turbulent regime. Turbulent heat transfer results in a more uniform temperature distribution in channels. The cooling performances of the individual configurations are compared. For a given pressure drop the cooling performances decreases in the order of flush-mounted strip heating, protruded square heating, flush-mounted square heating, protruded rib heating. For a given inlet fluid flow rate, the cooling performances decreases in the order of protruded rib heating, protruded square heating, flush-mounted square heating, flush-mounted strip heating. However, for a given inlet fluid flow rate, the pressure drop increases in the order of increasing cooling performance.

碩士
國立虎尾科技大學
機械與機電工程研究所
98
This study is aimed to treat the problem of convective heat transfer introduced by combined electrokinetic and pressure forces in microchannels. Analytical solution are presented for a slit microchannel with constant surface temperature, taking into account the effect of joule heating and viscous dissipation for different Peclet number. First , the Poisson-Boltzmann equation is solved to obtain the electrokinetic potential. Next, the fluid velocity distribution across the channel is determined form the momentum equation. Finally, we solve the energy equation by using the integral transformation method to obtain the temperature distribution for the thermally developing flow within the microchannel. Governing parameters include the velocity scale ratio Γ ( the ratio of the pressure-driven velocity scale for Poiseuille flow to Helmhlotz - Smoluchowski velocity for electroosmotic flow i.e. ) , Joule heating parameter , Peclet number and Brinkman number . Representative results for the results for the mean fluid temperature and the local Nusselt number are presented at selected governing parameters. The mean fluid temperature attains the fully - developed value at a smaller distance as Peclet number increases . The similar behavior is observed for the local Nusselt number. For pure electroosmotic flow (Γ=0) , the effect viscous dissipation on the thermal transport is not important. However, for mixed electro-osmotic and pressure-driven flow , viscous dissipation plays a role in the heat transfer. When viscous dissipation is neglected (Br=0) , the local Nusselt number decreases monotonously with streamwise location to the fully developed value . On the other hand, for Br≠0 the local Nusselt number occurs a rise in the fully developed value . As compared to the effect of joule heating , the effect viscous dissipation on the thermal transport is of less importance.

碩士
國立中央大學
化學工程學系
84
This paper studied laminar mixed convection from combined heat and mass transfer. The investigated system are vertical and horizontal plates which are maintained with uniform temperature and concentration. The case of plates maintained with uniform fluxes of heat and spesies are also included. By introducing some proper dimensionless variables and parameters from scale analysis, the governing equations can be transformed and solved efficiently by a finite-difference method. Very accurate numerical results have been obtained for dilute gaseous solutions (Pr=0.7,0.3