Maximum Temperature Constraint Research Articles

Comparison of Maximum Heat Transfer Rate of Thin Vapor Chambers with Different Wicks under Multiple Heat Sources and Sinks

In this paper, we present a new analytical model to investigate the maximum heat transfer rate of a thin vapor chamber (TVC) with multiple heat sources and sinks. The model can specifically consider different heat flux conditions for each heat source. Both capillary limitations and allowable maximum temperature constraints were employed to determine the maximum heat transfer rate. The liquid and vapor pressure distributions within the TVC were analytically derived using the Brinkman-extended Darcy equation and the Hagen–Poiseuille equation, respectively. Additionally, the theoretical wall temperature distribution was calculated based on the 3D energy equation, considering different heat flux conditions for multiple heat sources with a weighting factor. Our results demonstrate that the heat flux conditions applied to the heat sources significantly impact the internal flow pattern of the TVC. These changes in flow patterns influence the pressure distributions of the liquid and vapor, thereby affecting the maximum heat transfer rate. Furthermore, the effects of wick parameters on the maximum heat transfer rate under various heat flux conditions were examined.

Hot-spot aware thermoelectric array based cooling for multicore processors

In this paper, we propose a hot-spot aware Thermoelectric Cooler (TEC)-based active cooling technique, called TEC-Array, which can perform targeted cooling of the spatially and temporally changing on-chip hot spots in any multi-core processor. It is in contrast to many existing works, where TECs were used for spatially homogeneous cooling, which leads to high energy costs. The proposed cooling system involves a 2D array of TEC modules where each TEC module is individually controllable. This enables the ability to spatially vary the cooling for hot spots across the chip’s surface while the processor is under load. This way, the areas of the chip consuming more power, and consequently generating more heat, can be cooled more intensely than the areas that are consuming very little power. To dynamically control the TEC-Array, the proposed approach applies machine learning predicted full-chip power-density maps to generate discrete voltage maps which are in turn used to dynamically configure the voltage settings of the TEC-Array. In addition, we also propose a numerical simulation framework, which employs an accurate 3D coupled multi-physics model for TEC devices to consider Peltier, heat transfer, Joule heating and complex electro-thermal coupling effects by solving the coupled heat conduction and current continuity equations. The numerical results on an Intel quad-core chip shows that the proposed TEC-Array cooling can substantially reduce the peak temperatures compared to the traditional passive heat sink cooling method. Furthermore, compared to the existing single TEC module based cooling method, the proposed method can reduce both TEC power and temperature gradients across chips under the same maximum temperature constraints, which can further reduce spatial temperature induced stress such as thermal cycling, thermo-migration and unbalanced aging etc. As a result, the new TEC-Array cooling can enable more aggressive chip performance with increased thermal design power (TDP) while maintaining the chip design lifetime.

Two-channel time-optimal control of induction heating process with maximum temperature constraint

The formulation and method of solution of the problem of time-optimal control of induction heating process of an unlimited plate with two control actions on the value of internal heat sources with technological constraint in relation to a one-dimensional model of the temperature field are proposed. The problem is solved under the conditions of a given accuracy of uniform approximation of the final temperature distribution over the thickness of the plate to the required. The method of finite integral transformations is used to search for the input-output characteristics of an object with distributed parameters with two control actions. The preliminary parameterization of control actions based on analytical optimality conditions in the form of the Pontryagin maximum principle is used. At the next stage reduction is performed to the problem of semi-infinite optimization, the solution of which is found using the alternance method. The alternance properties of the final resulting temperature state at the end of the optimal process lead to a basic system of relations, which, if there is additional information about the shape of the temperature distribution curve, is reduced to a system of equations that can be solved. An example of solving the problem of time-optimal control of temperature field of an unlimited plate with two offices is carried out in two stages. At first stage the case of induction heating without maximum temperature constraints is considered, at the second stage is carried out on the basis of the results of the first stage to obtain the solution subject to the limitation on the maximum temperature of the heated billet.

Application of a novel approach to assess the thermal evolution processes associated with the disposal of high-heat-generating waste in a geological disposal facility

The widely accepted solution for the long-term management of higher activity radioactive waste is disposal in a suitably engineered facility, located deep underground. A geological disposal facility (GDF) consists of a series of engineered and natural barriers preventing or inhibiting the release of radioactivity. These barriers include: the radioactive wasteform, the waste disposal container, the buffer material to protect the container and the natural barrier provided by the rocks in which the facility is constructed. This multi-barrier system aims to isolate the waste and contain the harmful effects of the radioactivity on humans and biota in the surface environment.The engineered barrier system (EBS) used in a GDF can include buffers based on cement and clay-based materials. The choice of buffer can have significant implications for the disposal system; the heat must be managed such that the properties of the buffer are not compromised to the extent that it cannot deliver the required level of safety. One of these materials is bentonite, usually rich in sodium montmorillonite, selected for its swelling properties and low hydraulic conductivity when saturated. In the presence of significantly elevated temperatures sodium montmorillonite can undergo mineral alteration, reducing the swelling properties of this material. This paper describes an efficient approach to assess strategies for meeting a maximum temperature constraint placed on either the buffer or geosphere surrounding the waste container. In preparation for designing and building a GDF, it is important, for the purpose of robust planning, to understand the important factors, and uncertainties, affecting the maximum temperature. The objective of this work is to inform the future emplacement strategy to enable: appropriate decay storage times; acceptable waste package loading and spatial configurations of the packages to be determined, to thus enable high-heat-generating waste to be safely disposed in a GDF.

Structural topology optimization considering connectivity constraint

Topology optimization has been regarded as a powerful design approach for determining optimal topology of a structure to obtain desired functional performances within a defined design domain. Considering manufacturing process constraints in topology optimization becomes increasingly important due to its potential practical applications. In this paper, we propose a novel topology optimization model with manufacturing process related connectivity constraints. A generalized method, named as virtual scalar field method (VSFM), is developed for describing and enforcing desired connectivity constraint. As an illustrative example, the connectivity constraint can be converted to an equivalent maximum temperature constraint when temperature is chosen as the scalar field. The temperature constraint is then easily integrated and implemented in routine topology optimization. The simply-connected constraint, which excludes interior closed cavities and is representative of many advanced manufacturing techniques, e.g. additive manufacturing (AM) or casting, is used as an example to demonstrate the key ideas and the efficiency of the VSF method. Some numerical examples, which consider the connectivity constraint in topology optimization, are presented to show the validity of this method.

An identification method for enclosed voids restriction in manufacturability design for additive manufacturing structures

Additive manufacturing (AM) technologies, such as selective laser sintering (SLS) and fused deposition modeling (FDM), have become the powerful tools for direct manufacturing of complex parts. This breakthrough in manufacturing technology makes the fabrication of new geometrical features and multiple materials possible. Past researches on designs and design methods often focused on how to obtain desired functional performance of the structures or parts, specific manufacturing capabilities as well as manufacturing constraints of AM were neglected. However, the inherent constraints in AM processes should be taken into account in design process. In this paper, the enclosed voids, one type of manufacturing constraints of AM, are investigated. In mathematics, enclosed voids restriction expressed as the solid structure is simplyconnected. We propose an equivalent description of simply-connected constraint for avoiding enclosed voids in structures, named as virtual temperature method (VTM). In this method, suppose that the voids in structure are filled with a virtual heating material with high heat conductivity and solid areas are filled with another virtual material with low heat conductivity. Once the enclosed voids exist in structure, the maximum temperature value of structure will be very high. Based upon this method, the simplyconnected constraint is equivalent to maximum temperature constraint. And this method can be easily used to formulate the simply-connected constraint in topology optimization. The effectiveness of this description method is illustrated by several examples. Based upon topology optimization, an example of 3D cantilever beam is used to illustrate the trade-off between manufacturability and functionality. Moreover, the three optimized structures are fabricated by FDM technology to indicate further the necessity of considering the simply-connected constraint in design phase for AM.

A numerical investigation of the entropy generation in and thermodynamic optimization of a combustion chamber

In this study, we are simulating the turbulent combustion of a mixed bluff-body swirl stabilized flame in a gas turbine combustion chamber and investigating the effects of different parameters, including the swirl number, distance between the air and fuel nozzle which is called bluff size, equivalence ratio, inlet fuel flow rate, and the inlet air velocity, on the entropy generation. We perform the process of the design of the combustion chamber by proposing the optimal value of each parameter based on the EGM (entropy generation minimization) method under the two maximum allowable temperature and size constraints. Two common methods of entropy generation calculation, one based on the overall entropy balance on a system and the other based on the local entropy generation rate calculation, are used and compared in this study. Our results show that the deviation between the total entropy generations calculated by the two methods is 6.4% in average which is an acceptable error in turbulent combustion simulations. Also, the two opposing factors, namely chemical reaction and heat transfer, have the main contribution to the total entropy generation.

Targeting and design of CWNs (cooling water networks)

CWNs (cooling water networks) are targeted and designed in this work by an analytical approach requiring no graphical procedures. The key basis for the approach is the conversion of the cooling duties to equivalent inlet–outlet (demand–source) pairs. The UTA (Unified Targeting Algorithm) is first used to establish the minimum CW (cooling water) flowrate and identify the pinch temperature. The Enhanced NNA (Nearest-Neighbors Algorithm) is then utilized to systematically synthesize CWNs by giving priority to LR (local-recycle) matches. The flowrate of the LR match is maximized wherever possible by choosing the neighbor source as the cleanest available source rather than the nearest neighbor. This is advantageous because LR matches can be eliminated for fixed load operations to yield relatively simple network designs that not only meet the minimum CW flow target but also minimize the flowrate through the coolers resulting in reduced network cost. Two case studies are presented to illustrate the versatility of the approach in generating multiple optimum network designs for maximum reuse, temperature constraints and debottlenecking. Importantly, it is demonstrated that superior practical networks can be designed for temperature constrained CWNs with pinch migration as well as without pinch recognition.

Optimal design of dispersive tubular reactors at steady-state using optimal control theory

This paper studies the design of optimal temperature profiles for a class of exothermic, jacketed dispersive tubular reactors under steady-state conditions and subject to maximum temperature constraints. The studied class ranges from perfectly mixed continuous stirred tank reactors to plug flow reactors. The aim is to derive the Pareto optimal set of temperature profiles for conflicting conversion and energy costs, while extracting generic features from the obtained solutions. Hereto, a four step procedure which is based on a weighted sum of both costs and which combines indirect, analytical and direct, numerical optimal control techniques, is employed. The generic features are studied (i) along the Pareto set by varying the weights and (ii) along the reactor class by adapting the dispersion level.

Solar Sail Near-Optimal Circular Transfers with Plane Change

DOI: 10.2514/1.38079 Near-minimum time interplanetary trajectories between circular orbits with different orbital planes are investigated. By assumption, the mission is carried out with a solar sail spacecraft, whose performance takes into account the optical characteristics of the sail film and the maximum temperature constraint. In an effort to obtain a general, albeit approximate, solution, the problem is tackled by dividing the mission in two or three phases, depending on the value of the inclination change between the initial and target orbit. Each phase is analyzed by solvingaminimumtimeproblemwithanindirectapproach,andthewholemissiontimeisestimatedasthesumofthe contributions of the elementary phases. The obtained results are then collected through graphs and fitting functions that can be used effectively to get a good and quick estimate of the main mission parameters, as well as to quantify their effect on the mission flight time. A comparison of the proposed approach with the optimal results available for the Solar Polar Imager mission confirms the effectiveness of the developed methodology.

GOP-Level Dynamic Thermal Management in MPEG-2 Decoding

In this paper, we present a dynamic thermal management (DTM) algorithm based on: 1) accurate estimation of the workload of frames in a group of pictures (GOP) in an MPEG-2 video stream and 2) slack borrowing across the GOP frames in order to achieve a thermally safe state of operation in microprocessors during the video decoding process. The proposed DTM algorithm employs dynamic voltage and frequency scaling (DVFS) while considering the frame-rate-dependent GOP deadline, variance of the frame decoding times within the GOP, and a maximum chip temperature constraint. If it becomes necessary to sacrifice video quality or violate the GOP deadline due to a low temperature bound, then the (intra-frame) spatial quality degradation and the (inter-frame) temporal quality degradation will be applied to the GOP. Experimental results demonstrate the competence and efficiency of the proposed online DTM algorithm.

Linear Programming Approach for Optimization of Radionuclide Loading in Vitrified HLW

A linear programming approach has been developed to determine maximum mass loading of radionuclides in vitrified high-level waste (HLW). Linear approximation for the centerline temperature of vertically stacked cylindrical HLW canisters has been developed by assuming constant heat flux from a canister, steady-state heat transfer, natural convection, and by neglecting radiation effects. With the linear formula for the centerline temperature, it has been demonstrated that maximum radionuclide mass loading can be determined by the linear programming model conservatively. A numerical result for vitrification of HLW from PUREX reprocessing of pressurized water reactor spent fuel indicates that the maximum temperature constraint is one of the essential constraints in determining the feasible solution space for optimization if the heat emission from the waste is in a certain range (between 11.2 and 24.5 W/kg in this example).The linear programming model can be utilized to link various fuel cycle models and repository performance models in a consistent and quantitative manner.

Thermal-Safe Test Scheduling for Core-Based System-on-Chip Integrated Circuits

Overheating has been acknowledged as a major problem during the testing of complex system-on-chip integrated circuits. Several power-constrained test-scheduling solutions have been recently proposed to tackle this problem during system integration. However, we show that these approaches cannot guarantee hot-spot-free test schedules because they do not take into account the nonuniform distribution of heat dissipation across the die and the physical adjacency of simultaneously active cores. This paper proposes a new test-scheduling approach that is able to produce short test schedules and guarantee thermal safety at the same time. Two thermal-safe test-scheduling algorithms are proposed. The first algorithm computes an exact (shortest) test schedule that is guaranteed to satisfy a given maximum temperature constraint. The second algorithm is a heuristic intended for complex systems with a large number of embedded cores, for which the exact thermal-safe test-scheduling algorithm may not be feasible. Based on a low-complexity test-session thermal-cost model, this algorithm produces near-optimal length test schedules with significantly less computational effort compared to the optimal algorithm

The application of the CFD and Kriging method to an optimization of heat sink

The shape optimization of the plate-fin type heat sink with an air deflector is numerically performed to minimize the pressure loss subjected to the desired maximum temperature and geometrical constraints. A function evaluation using the FVM, in general, is required much computational costs in fluid/thermal systems. Thus, global approximate optimization techniques have been introduced into the optimization of fluid/thermal systems. In this study, the Kriging method, which is one of the metamodels, associated with the computational fluid dynamics (CFD) is used to obtain the optimal solutions. The Kriging method can dramatically reduce a computational cost by 1/6 times compared to that of the SQP method so that its efficiency can be validated. The results also show that when the temperature rise is less than 40 K, the optimal design variables are B 1 = 2.44 mm, B 2 = 2.09 mm, and t = 7.58 mm.

Optimal curing for thermoset matrix composites: Thermochemical considerations

AbstractA design sensitivity analysis is used to optimize the applied wall temperature vs. time in autoclave curing for thermoset matrix composites. The calculation minimizes the cure time and obeys a maximum temperature constraint in the composite. The transient, coupled thermal and cure problem is solved by a finite element method. Design sensitivity information is extracted efficiently from this primal analysis, based on an analytical, direct differentiation approach. The sensitivities are then used with gradient‐based optimization techniques to systematically improve the curing process. The optimal cure cycles for different numbers of temperature dwells may be similar (for a 2 mm thick part) or very different (for a 4 cm thick part), depending on the nature of the problem. In the latter case a large reduction of cure time is obtained when a three‐dwell cure cycle is used, and the optimizer has more flexibility to adjust the cure cycle. This systematic optimization approach provides a powerful and practical means of optimizing composite manufacturing processes.

Electronic Desorption of Surface Species Using Short-Pulse Lasers

New methods of removing surface contaminants from microelectronic and microelectromechanical systems (MEMS) devices are needed since the decreasing size of their components is reducing the allowable contamination levels. By choosing the pulse duration and fluence to optimize electronic rather than thermal desorption in short-pulse laser processing, surface species can be removed without exceeding maximum temperature constraints. A two-temperature model for short-pulse laser heating of, and subsequent desorption from, metal surfaces is presented. A scaling analysis indicates the material properties and laser parameters on which the ratio of electronic to thermal desorption depends. Regimes of predominantly electronic and thermal desorption are identified, and predicted desorption yields from gold films show that electronic desorption is the primary desorption mechanism in certain short-pulse laser processes.

Start-up and safeguarding of an industrial adiabatic tubular reactor

The safeguarding methodology currently used in the chemical industry is based on controlling the instantaneous values of the process state variables within a certain operating window, the process being brought to shut-down when the operating constraints are exceeded. It is concluded from an analysis of runaways which occurred in industrial reactors that this safeguarding methodology does not necessarily prevent reactor systems suffering from a runaway because (a) excessive amounts of unreacted chemicals can still accumulate in the process, and (b) no means are provided to the operating personnel of identifying such hazardous process deviations during dynamic operations. A model-based start-up and safeguarding procedure is developed for an industrial adiabatic tubular reactor to improve process safety during start-up operations. The trajectories of the manipulated variables are optimized by minimizing the breakthrough of one of the main reactants in the reactor effluent. A maximum reactor temperature constraint is also taken into account. It is concluded that a proper control of the initial reactor temperature profile is critical for a safe reactor start-up while the impact of the other manipulated variables is relatively small in comparison to the effect of the initial reactor temperature profile.

Optimum Choice of Robot Actuators

The object of this paper is to present a method for the optimum choice of robot actuators. The modelling of the system takes into account the inertia of the links and actuators, and viscous and Coulomb friction effects. The thermal model of the actuators is included in the model. The optimum actuators set is that corresponding to the minimization of the global mass of all the actuators with respect to the maximum pulse torque and maximum temperature constraints for each one. Under specified conditions, the solution of this problem is obtained by exploring a manufacturer’s data base of actuators which contains the inertial, electrical, and thermal characteristics. An application of our approach on a SCARA robot type is given in the paper.

Optimal temperature control for batch beer fermentation

Optimal control theory was applied to the process of batch beer fermentation. The performance functional considered was a weighted sum of maximum ethanol production and minimum time. Calculations were based on the model of Engasser et al. modified to include temperature effects. Model parameters were determined from isothermal batch fermentations. The fermentor cooling duty was the single available control. Temperature state variable constraints as well as control variable constraints were considered. The optimal control law is shown to be bang-bang control with the existence of a singular arc corresponding to isothermal operation at the maximum temperature constraint. An iterative algorithm is presented for computing appropriate switching times using a penalty-function-augmented performance functional.