Maximum Temperature Gradient Research Articles

Self-adaptive heat management of solid oxide electrolyzer cell under fluctuating power supply

Solid oxide electrolyzer cell (SOEC) can efficiently reduce CO2/H2O into CO/H2 using renewable powers. But the fluctuating nature of renewable energy can significantly change the temperature field and cause thermal fatigue even mechanical failure. Herein, we propose a self-adaptive heat management method of SOEC by coupling SOEC with an in-situ thermochemical energy storage (TES) section. Co3O4/CoO redox pair is selected as the TES material for heat management during the exothermic and endothermic operating conditions. 2D dynamic models are developed to study the effects of TES section on the SOEC performances with a special attention on the temperature fluctuation. Results show that the addition of TES section can reduce temperature fluctuation by 73 %, from 119.2 K to 31.7 K. Besides, the maximum temperature gradient and the surface maximum temperature difference at 1.5 V are reduced to 2.62 K/mm and 30 K, respectively, which are 65 % and 82 % lower than those without TES section. An inlet temperature of 1123 K is found to be the best operating condition for the Co3O4/CoO pair in inhibiting the temperature fluctuation of the cell, where the standard deviation is 8.51. This study provides a novel strategy for efficient heat management and safe operation of SOEC under fluctuating working conditions.

Optimising integrated heat spreaders with distributed heat transfer coefficients: A case study for CPU cooling

Increasing power densities of modern CPUs has led to regions of high temperature on the semiconductor die which can lead to performance and reliability problems. In this case study, the effect of imposing a non-uniform heat transfer coefficient profile across the convective surface the CPU's integrated heat spreader was investigated as a potential enhanced cooling concept. A finite element model of a copper heat spreader of 40 × 40 mm2 area and 2.5 mm thickness with a centred 13 × 13 mm2 heat source at 100 W/cm2 heat flux was considered to approximate typical modern high-powered CPUs. Both uniform and Gaussian distributions of the heat transfer coefficient were then considered. For the latter, both single and multi-objective Genetic Algorithm optimisation were carried out for three source temperature objectives; average temperature, maximum temperature and maximum temperature difference. The analysis showed that the multi-objective optimisation strategy produced the best overall heat transfer coefficient distribution, with almost 5 K reduction in both the maximum temperature and temperature gradient across the heat source compared with a uniform heat transfer coefficient distribution.

Investigation of thermal effect on solidification in Sn/Cu interconnects during self-propagating exothermic reaction bonding

Self-propagating exothermic reaction (SPER) of alternating metal nanolayers provides intense localised heat that allows bonding of metals or alloys under ambient temperature. However, the formation of the bonds through the rapid heating and cooling confined at the bonding interfaces is a non-equilibrium process, and the thermal effect on solidification and manufacturing reliability is yet to be understood. In this work, the Cu/Sn-nanofoil-Sn/Cu interconnects (where Sn is a solder layer) prepared via SPER of Ni/Al nanofoil are studied by numerical simulations and experiments to understand the thermal transfer and its effect on the solidification. It has been found that the SPER completes within a few milliseconds, the temperature at solder/Cu interface can be higher than the melting point of solder, and the cooling rate can be as high as 1.5 × 107 °C/s, the maximum temperature gradient can reach 5.40 × 107 °C/m. The microstructure predicted by simulation agrees well to the experimental results: the columnar dendrites are formed in the solder during the cooling stage, and the columnar structures prefer to form and grow in the solder region due to the high cooling rate.

Numerical analysis for solid-liquid interface shape at various temperature gradient in electromagnetic cold crucible directional solidification

The straight solid-liquid (S-L) interface is necessary for obtaining a directional solidification ingot with industrial size and well directional solidification in electromagnetic cold crucible directional solidification (CCDS). Overheating and lateral heat dissipation are the significant parameters for the straight S-L interface in CCDS. In this paper, Nb-16Si-22Ti as an example was used for analyzing the influence of temperature gradient and boundary conditions on the shape of S-L interface by Comsol Multiphysics software. A 3-D parametric geometry as original proportional model was established and the accuracy of the model was verified by measuring magnetic flux density norm with small coil method. The simulation results exhibit that the shape of S-L interface formed by 50kHz-2400A is closer to the plane and beneficial to gain directional grain. The heat supplement meets the requirement of heat loss with 50kHz, and there is little difference for temperature gradient in both solid and liquid interface. The axial and radial maximum temperature gradient of 50 kHz-2400 A is 61.46 K/mm and 63.84 K/mm, respectively.

Mini-channel liquid cooling system for large-sized lithium-ion battery packs by integrating step-allocated coolant scheme

• Three types of liquid cooling systems are explored for large-sized batteries. • The fully-covered cold plate enables a more even temperature distribution. • The cooling performance is seriously deteriorated for the battery packs. • The optimized approach employing the step-allocated coolant scheme is verified. To regulate the temperature spikes and temperature gradients of large-sized lithium-ion battery packs, the mini-channel liquid cooling systems are developed and numerically investigated in this study. Three design schemes are firstly analyzed and compared at the cell level based on a three-dimensional transient thermal model. It shows that design scheme 2 using the fully-covered cold plate and segmented centralized minichannels performs best. However, the cooling performance is seriously deteriorated at the module level. At the same flow rate of 2 × 10 −5 kg/s, the maximum surface temperature and temperature gradient increase from 34.79 °C and 4.12 °C to 49.61 °C and 14.34 °C when the cell number increases from N = 1 to N = 3. Finally, an optimized approach employing the step-allocated coolant scheme is conceived, with which the maximum surface temperature and the largest temperature difference of the 3S1P pack can be controlled at 33.38 °C and 4.56 °C over the 5C discharge process. The research results suggest that the mini-channel liquid cooling system integrating the step-allocated coolant scheme can be a new approach for the thermal management of large-sized battery packs.

Comparative study on the microstructure, mechanical properties and fracture mechanism of wire arc additive manufactured Inconel 718 alloy under the assistance of alternating magnetic field

In this study, the microstructure, mechanical properties and fracture mechanism of wire arc additive manufactured Inconel 718 alloy fabricated by cold metal transfer process under the action of the alternating magnetic field (AMF) are studied by changing the excitation current. The results show that the AMF deflects the droplet and changes the direction of the molten pool maximum temperature gradient, which inhibits the growth of large columnar crystals and refines the grains so that the index of {100}<001> texture decreases significantly. The microstructure of the 0 A and 40 A samples is composed of γ(Ni) + (TiN) [nucleus]/(NbC + TiC)[shell] + NbC + Laves. The length of γʹʹ-Ni3Nb of the 0 A sample (98 nm) is greater than that of the 40 A sample (84 nm). The AMF suppresses the large columnar crystals, and the average grain size is reduced to 161 μm. The volume fraction of the Laves phases is significantly reduced from 2.4% to 1.3%, and the Laves phases morphology changes from long stripe to granular under the action of the AMF. AMF increases the ultimate tensile strength and decreases the anisotropy.

Temperature Gradient Analyses of a Tubular Solid Oxide Fuel Cell Fueled by Methanol

Thermal management in solid oxide fuel cells (SOFC) is a critical issue due to non-uniform electrochemical reactions and convective flows within the cells. Therefore, a 2D mathematical model is established herein to investigate the thermal responses of a tubular methanol-fueled SOFC. Results show that unlike the low-temperature condition of 873 K, where the peak temperature gradient occurs at the cell center, it appears near the fuel inlet at 1073 K because of the rapid temperature rise induced by the elevated current density. Despite the large heat convection capacity, excessive air could not effectively eliminate the harmful temperature gradient caused by the large current density. Thus, optimal control of the current density by properly selecting the operating potential could generate a local thermal neutral state. Interestingly, the maximum axial temperature gradient could be reduced by about 18% at 973 K and 20% at 1073 K when the air with a 5 K higher temperature is supplied. Additionally, despite the higher electrochemical performance observed, the cell with a counter-flow arrangement featured by a larger hot area and higher maximum temperature gradients is not preferable for a ceramic SOFC system considering thermal durability. Overall, this study could provide insightful thermal information for the operating condition selection, structure design, and stability assessment of realistic SOFCs combined with their internal reforming process.

A study on topology optimization of heat dissipation structures with different objective functions based on an explicit moving morphable components method

This article investigates two different objective functions (minimizing heat dissipation weakness and temperature variance) to realize topology design optimization of heat dissipation problems based on the explicit topology optimization method of moving morphable components (MMC). The advantages of explicit and clear geometric profile descriptions in dealing with heat dissipation are explored. Sensitivity derivation with respect to the explicit topological geometric variables of the MMC-based method is established for two objective functions. Numerical examples are presented, with extensive discussion and comparisons of the key factors of maximum temperature gradient, temperature variance and maximum temperature based on the two objective functions. These discussions demonstrate the scope of application of the objective functions. Compared with density-based topology design optimization, the present MMC-based method describes the geometric profile of the heat dissipation structure accurately and achieves a more accurate and efficient heat dissipation performance of the structure.

Curling of Cast-in-Situ Short Slabs on Lean Concrete Base: Measured Versus Theoretical Analysis

Cast-in-situ short paneled concrete pavements (CiSPCP) are a class of innovative concrete pavements, which are being considered as a sustainable replacement for jointed plain concrete pavement. However, there is a lack of understanding of various aspects of CiSPCP such as joint spacing, long-term joint performance, dominant stresses, failure criteria, and curling behavior. In this study, the curling behavior of CiSPCP test sections with different slab sizes and thicknesses on National Highway (NH)-18 (old NH-33) were investigated during the summer of 2019 and the winter of 2020. The vertical displacements at mid-slab (longitudinally and diagonally to the slab), the effect of slab size and thickness on curling with seasonal variation were considered, along with a comparison of measured curling using theoretical analysis. The measured displacements at the edge of slabs were smaller compared with those at the center of the slab. Interestingly, the occurrence of maximum slab curl was not in tandem with the maximum temperature gradient (TG). The time lag for the response was around 2 to 4.5 h of the occurrence of a maximum TG. This observation was very significant because temperature stresses have a profound effect on stresses in concrete pavement. However, this field observation has indicated that the lag in the development of maximum TG may also lead to a lag in the development of stresses. Further, it was found that the theoretical method overestimates the curling compared with the field-measured displacements, which can be mainly attributed to the lag.

The Relationship of the Spatial Structure of the Total Suspended Matter Concentration and Hydrological Parameters in the Northern Black Sea According to Contact Measurements

Here we describe the features of the horizontal and vertical distribution of total suspended matter in the northern part of the Black Sea and their relationships with the water temperature, salinity, and density fields measured at the identical grid during hydro-optical surveys from 2016 to 2020. The results show that the primary sources of increased total suspended matter concen trations in the northern part of the Black Sea are low-salinity and turbid waters of the Kerch Strait; runoffs of the Rioni, Enguri, and other rivers in the east of the survey area; together with freshened waters of the Dnieper, Dniester, and Danube runoff from the northwestern shelf. Higher turbidity was observed in the deep-water part of the sea, associated with the cyclonic gyres and meanders of the Rim Current effects. The total suspended matter vertical structure features an upper mixed layer, which usually coincides in thickness with the upper thermohaline upper mixed layer. Significant negative correlations were found for this layer comparing total suspended matter concentration versus temperature and salinity, while the correlation appears positive with density values. Below, a total suspended matter subsurface maximum was observed in the seasonal thermocline and pycnocline layer. The high turbidity layer appeared almost an order of magnitude thinner in the regions of maximum temperature gradients versus the areas where the temperature gradient was weak. A local total suspended matter minimum occurred below the cold intermediate core, corresponding to the main thermocline, halocline, and pycnocline layer. Beneath this minimum, there was a local increase of total suspended matter coinciding with the upper boundary of the hydrogen sulfide zone.

Experimental investigation on a floating multi-effect solar still with rising seawater film

In this paper, a floating multi-effect solar still using parabolic concentrators to directly heat rising seawater film is investigated. The novel desalination device integrates solar still and two concentrators as a whole, which avoids the installation of a heat exchange pipeline and can float on the ocean to produce freshwater. The floating still consists of a front parabolic concentrator, a rear parabolic concentrator, and several embedded distillation cells. The distillation cell is composed of a hydrophilic wick, a condensing plate, and a narrow space in between. The parabolic concentrator greatly increases the solar heat to improve the temperature gradient and enhance the phase transition and diffusion process of water vapor. During desalination, the rising seawater film for evaporation is formed in the hydrophilic wick by capillary force. Through indoor steady-state experiments, some key parameters such as solar irradiance and incident angle on the temperature, water yield and gain output ratio (GOR) of the still were studied. Results indicate that the maximum temperature gradient in the 5-effect still can reach 48.5 °C. Under a 900 W/m2 irradiation, the water productivity and GOR are 2.7 kg/m2/h and 2.2, respectively. Additionally, outdoor experiments show that the daily freshwater reaches 4.7 kg/m2 with an average irradiation of 543 W/m2.

Analysis of the Thermal Characteristics and Energy performance of Electro Chromic Glazing window

Windows and shading devices occupy an essential part between inside and outside environment of buildings, for providing interior air quality and optimization of lighting and HVAC energy consumption. This paper aims to perform the thermal performance of double pane Electrochromic window (ECW) using Finite Element Method and the energy performance using the Building Information Modelling (BIM) tool. The thermal model of the ECW is simulated in COMSOL Multiphysics. Double pane glass with and without electrochromic (EC) layer is analyzed to obtain the average and maximum surface temperature between the top and bottom layers of the glazing. It is observed that the maximum temperature gradient is observed with EC layer. The energy performance with a double glazing and ECW for warm and humid climate is evaluated using eQUEST DOE tool. A 30 % reduction is observed in the annual energy consumption with an ECW compared to that with a double-glazing window. In addition, during the monthly evaluation of energy consumption, there is 10% reduction with the ECW compared to baseline. The appreciable thermal characteristics and the energy performance of the EC glazing proves it to be an alternative solution for normal window glazing in automated buildings for thermal comfort and lesser cooling load demand.

Cooling High-Speed Railway Slab Tracks with Solar Reflective Coatings: A Feasibility Study

The slab track temperature is significant with respect to the safety of the vehicle. The objective of this study was to investigate the cooling effects of solar reflective coatings (SRCs) on slab tracks. Two types of coatings were applied in the outdoor environment, and a model considering reflective coatings was subsequently established. The coatings decreased the maximum temperature and maximum temperature gradient by 8°C-12°C and 20°C/m-30°C/m, respectively. The albedo of an SRC on a slab track was suggested to be greater than 0.6. The coatings exhibited superior cooling effects in case the wind scale was lower than Level 2.

Lattice Boltzmann method for simulation of solid–liquid conjugate boiling heat transfer surface with mixed wettability structures

Based on the one-component multiphase lattice Boltzmann method, a novel solid–liquid conjugate boiling heat transfer pseudo-potential lattice Boltzmann (LB) model is tentatively proposed in this paper. By respectively introducing the physical property parameters of solids and liquids into the relaxation time τT of the temperature distribution equation, different energy transfer rates in solid, liquid, and vapor regions can be successfully predicted. After verifying the accuracy, stability, and reasonability of this model, the bubble detaching behavior and boiling heat transfer performance on the rectangular cavity structure are analyzed through setting different contact angles of the cavity surface and plane heating surface. The results show that the hydrophobic cavity surface can initialize bubble nucleation earlier and obviously increase the bubble detaching frequency because of its gas-bounding character, while the hydrophilic plane heating surface can restrict the expansion of bubbles and delay the appearance of film boiling. Moreover, for uniform wettability surfaces, the bubble detaching period varies in the quadratic equation with the surface contact angle due to the interaction of surface tension and buoyancy, and there is a minimum detaching period. While for the mixed wettability surfaces, the bubble detaching period also has a minimum value with the decrease in the contact angle the cavity surface, but the average bubble detaching diameter basically does not change with the cavity surface contact angle; moreover, the cavity surface contact angle corresponding to the minimum detaching period also increases with the increase in the plane heating surface contact angle. In addition, for the boiling heat transfer surface with cavity structure, the maximum heat flux and temperature gradient occur on the cavity surface, and the local heat flux of the hydrophobic cavity surface is higher than that of the hydrophilic cavity surface. This work will provide useful help for the further development of the conjugate boiling heat transfer LB model and clarify the mechanism of enhanced boiling heat transfer on a mixed wettability surface.

Experimental investigation of temperature gradients in a three-cell concrete box-girder

To study the temperature field of a three-cell concrete box girder, a box girder model was poured, and 258 temperature sensors were embedded in the model. Environmental parameters, including air temperature, air humidity, wind speed, wind direction and solar radiation, were recorded by a weather station nearby the model. Data receiving frequency was once every 30 mins, and a wireless acquisition module for data collection was used. After a year of temperature observation, the temperature field of a three-cell concrete girder was obtained. Temperature prediction equations for a three-cell box girder were established for the first time, which used air temperature, solar radiation, and wind speed at a moment, rather than temperature prediction equations of previous studies, which used the maximum single-day temperature difference, the total single-day solar radiation and the average wind speed. The lateral temperature difference of the sunny side web was more obvious in winter. The lateral temperature difference with a 98% exceeded probability was 19.49 °C, which was larger than the recommended value of the European standard (15 °C). The negative temperature gradient influenced by cold wave was considered. The maximum lateral temperature gradient of the top plate and bottom plate in winter was larger than that in summer. The vertical and lateral temperature difference calculated by the present equations agreed well with the experimental values recorded by a five-tower six-span cable-stayed bridge.

Multiscale collaborative optimization for the thermochemical and thermomechanical cure process during composite manufacture

To reconcile the contradiction between the improvement of carbon fiber reinforced resin matrix (CFRP) composite performance and the increase of manufacturing cost, this paper proposes a collaborative optimization strategy for the cure process during the composite manufacture to reduce both the process-induced defects and the process time. Considering the multiscale characteristics of the composites, the temperature gradient is calculated by the macroscale laminate model through the nonlinear heat transfer thermochemical analysis, and the residual stresses are obtained by the representative volume element (RVE) microscale model, which involves the viscoelasticity, thermal expansion and cure shrinkage of the constituents during the thermomechanical analysis. The multi-objective optimization is implemented by an interface which combines the finite element based cure process analysis with the non-dominated sorting genetic algorithm-II (NSGA-II). The results show the proposed optimization strategy can significantly reduce the maximum temperature gradient, the maximum residual stress and the process time simultaneously. Besides, the self-organizing map (SOM) obtained from the Pareto front clarifies the relationship between the design variables and the objectives.

Coupling deep learning and multi-objective genetic algorithms to achieve high performance and durability of direct internal reforming solid oxide fuel cell

Direct internal reforming (DIR) operation of solid oxide fuel cell (SOFC) reduces system complexity, improves system efficiency but increases the risk of carbon deposition which can reduce the system performance and durability. In this study, a novel framework that combines a multi-physics model, deep learning, and multi-objective optimization algorithms is proposed for improving SOFC performance and minimizing carbon deposition. The sensitive operating parameters are identified by performing a global sensitivity analysis. The results of parameter analysis highlight the effects of overall temperature distribution and methane flux on carbon deposition. It is also found that the reduction of carbon deposition is accompanied by a decrease in cell performance. Besides, it is found that the coupling effects of electrochemical and chemical reactions cause a higher temperature gradient. Based on the parametric simulations, multi-objective optimization is conducted by applying a deep learning-based surrogate model as the fitness function. The optimization results are presented by the Pareto fronts under different temperature gradient constraints. The Pareto optimal solution set of operating points allows a significant reduction in carbon deposition while maintaining a high power density and a safe maximum temperature gradient, increasing cell durability. This novel approach is demonstrated to be powerful for the optimization of SOFC and other energy conversion devices.

Thermal optics of a collimator radiatively cooled under vacuum

Infrared optoelectronic equipment with cooled optics operating in a background limited mode is tested in a vacuum and a low radiation background. The latter is ensured by cooling the optical elements of the collimator and preventing direct illumination of the entrance pupil of the equipment by warm elements of the vacuum chamber. Subject of study. The thermal optics of a two-mirror collimator are investigated in this study. The mirrors of this collimator are cooled by heat transfer through infrared emission to the cooled cylindrical shields of the thermostat, which was specifically designed for collimator cooling. Method. The collimator cooling modes are calculated considering both thermophysical material properties and structural features of the elements comprised in the thermostat and collimator. The thermophysical model of thermal equilibrium in an isolated system of solid bodies is used in the calculations. The issue of selecting a particular material for the collimator mirrors is considered provisionally. The thermal stability of the mirror material calculated as a ratio of the coefficient of thermal expansion β to its heat conduction coefficient λ is used as a parameter determining the choice. Sitall, silicon, and silicon carbide were considered in this study as materials for infrared mirrors. Main results. The magnitude of thermal deformations is determined by not only the occurring temperature gradients in a plane mirror but also the variation in the curvature of the mirror surface under general cooling of the nonplanar mirrors. The maximum temperature gradient over the surface is observed for the mirrors composed of sitall. The temperature gradient in the mirror composed of silicon carbide is significantly smaller. This is related to the heat conduction coefficient of silicon carbide being 2 orders of magnitude higher than that of sitall. Consequently, the thermal deformations of the mirror surface are also smaller in the plane mirror composed of silicon carbide. These results correspond to the criterial parameter of thermal stability β/λ for each of the discussed materials. However, in the case of cooling of the nonplanar (spherical or aspherical) mirrors, the calculations show that their thermal deformations result from not only the nonuniformity of heat flow distribution over the mirror surface but also the general reduction in mirror temperature. Practical significance. When cooled infrared mirrors are used in optical systems, the appearance of thermal deformation of their mirror surface should be considered. This thermal deformation is determined by not only the occurring temperature gradients in the volume of the mirror material, but also the change in the curvature of the mirror surface. In this regard, the mirrors composed of sitall are preferable for use under thermal vacuum conditions over mirrors composed of silicon carbide.

QUBIC VI: Cryogenic half wave plate rotator, design and performance

Setting an upper limit or detection of B-mode polarization imprinted by gravitational waves from Inflation is one goal of modern large angular scale cosmic microwave background (CMB) experiments around the world. A great effort is being made in the deployment of many ground-based, balloon-borne and satellite experiments, using different methods to separate this faint polarized component from the incoming radiation. QUBIC exploits one of the most widely-used techniques to extract the input Stokes parameters, consisting in a rotating half-wave plate (HWP) and a linear polarizer to separate and modulate polarization components. QUBIC uses a step-by-step rotating HWP, with 15° steps, combined with a 0.4°s-1 azimuth sky scan speed. The rotation is driven by a stepper motor mounted on the cryostat outer shell to avoid heat load at internal cryogenic stages. The design of this optical element is an engineering challenge due to its large 370 mm diameter and the 8 K operation temperature that are unique features of the QUBIC experiment. We present the design for a modulator mechanism for up to 370 mm, and the first optical tests by using the prototype of QUBIC HWP (180 mm diameter). The tests and results presented in this work show that the QUBIC HWP rotator can achieve a precision of 0.15° in position by using the stepper motor and custom-made optical encoder. The rotation induces <5.0 mW (95% C.L) of power load on the 4 K stage, resulting in no thermal issues on this stage during measurements. We measure a temperature settle-down characteristic time of 28 s after a rotation through a 15° step, compatible with the scanning strategy, and we estimate a maximum temperature gradient within the HWP of ≤ 10 mK. This was calculated by setting up finite element thermal simulations that include the temperature profiles measured during the rotator operations. We report polarization modulation measurements performed at 150 GHz, showing a polarization efficiency >99% (68% C.L.) and a median cross-polarization χPol of 0.12%, with 71% of detectors showing a χPol + 2σ upper limit <1%, measured using selected detectors that had the best signal-to-noise ratio.

Design and test of shape memory alloy fins for self-adaptive liquid cooling device

• Self-adaptive cooling fins based on Shape Memory Alloys (SMA). • The set of conditions for proper operation are defined analytically. • The impact of an array of SMA fins on thermal resistance is experimentally studied. • Nearly constant wall temperature is achieved for varying heat flux scenarios. Thermal management complexity increases in high-performance chips, where the heat loads vary spatially and temporally, while liquid cooling systems are usually designed for most stringent stationary conditions. Several works developed heat transfer enhancement techniques to increase the cooling capacity of liquid cooled heat sinks, but pumping power is increased in a permanent way due to the addition of elements within the channels. Here, a liquid cooling self-adaptive heat sink that can efficiently adapt the distribution of its heat extraction capacity to time dependent and non-uniform heat load scenarios is proposed. Numerical design of the mesoscale cooling device with bimorph metal/SMA fins, definition of the fabrication and training procedure of the SMA fins to reach the desired behavior and experimental assessment is presented. The capacity of the self-adaptive fins to locally boost the heat transfer is numerically and experimentally demonstrated. Results obtained show that the self-adaptive fins can improve the temperature uniformity by 63% with respect to plain channel. The reduction in thermal resistance using bimorph metal/SMA fins sample allows the surface maximum temperature gradient to remain almost constant although heat flux increases. Energy savings are maximized in applications where partial load intervals contributes significantly to the overall operating period.