Search results for: numerical quadrature

Authors: Amritpal Singh Nafria, Rohit Sharma, Md. Shami Ansari

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Up to now only five different equations of motion can be derived from velocity time graph without needing to know the normal and frictional forces acting at the point of contact. In this paper we obtained all possible requisite conditions to be considering an equation as an equation of motion. After that we classified equations of motion by considering two equations as fundamental kinematical equations of motion and other three as additional kinematical equations of motion. After deriving these five equations of motion, we examine the easiest way of solving a wide variety of useful numerical problems. At the end of the paper, we discussed the importance and educational benefits of classification of equations of motion.

Keywords: velocity-time graph, fundamental equations, additional equations, requisite conditions, importance and educational benefits

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Authors: Engin Metin Kaplan, Kemal Yaman

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In this study, the crash of a medium heavy vehicle onto a designed Road blocker (vehicle barrier) is studied numerically. Structural integrity of the Road blocker is studied by nonlinear dynamic methods under the loading conditions which are defined in the standards. NASTRAN® and LS-DYNA® which are commercial software are used to solve the problem. Outer geometry determination, alignment of the inner part and material properties of the road blocker are studied linearly to yield design parameters. Best design parameters are determined to achieve the most structurally optimized road blocker. Strain and stress values of the vehicle barrier are obtained by solving the partial differential equations.

Keywords: vehicle barrier, truck collision, road blocker, crash analysis

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Authors: Farhat Hajer, Khir Tahar, Ammar Ben Brahim

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This work presents a study on the influence of the main operating variables on the gas turbine cycle. A numerical simulation of a gas turbine cycle is performed for a real net power of 100 MW. A calculation code is developed using EES software. The operating variables are taken in conformity with the local environmental conditions adopted by the Tunisian Society of Electricity and Gas. Results show that the increase of ambient temperature leads to an increase of Tpz and NO_x emissions rate and a decrease of cycle efficiency and UHC emissions. The CO emissions decrease with the raise of residence time, while NO_x emissions rate increases and UHC emissions rate decreases. Furthermore, both of cycle efficiency and NOx emissions increase with the increase of the pressure ratio.

Keywords: Carbon monoxide, Efficiency, Emissions, Gas Turbine, Nox, UHC

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Authors: Yildiray Keskin, Omer Acan, Murat Akkus

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In this paper, the solution of fractional diffusion equations is presented by means of the reduced differential transform method. Fractional partial differential equations have special importance in engineering and sciences. Application of reduced differential transform method to this problem shows the rapid convergence of the sequence constructed by this method to the exact solution. The numerical results show that the approach is easy to implement and accurate when applied to fractional diffusion equations. The method introduces a promising tool for solving many fractional partial differential equations.

Keywords: fractional diffusion equations, Caputo fractional derivative, reduced differential transform method, partial

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Authors: M. Bouinoun, M. Bouhadef

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The present study is concerned with the problem of determining the shape of the free surface flow in a hydraulic channel which has an uneven bottom. For the mathematical formulation of the problem, the fluid of the two-dimensional irrotational steady flow in water is assumed inviscid and incompressible. The solutions of the nonlinear problem are obtained by using the usual conformal mapping theory and Hilbert’s technique. An experimental study, for comparing the obtained results, has been conducted in a hydraulic channel (subcritical regime and supercritical regime).

Keywords: free-surface flow, experiments, numerical method, uneven bottom, supercritical regime, subcritical regime

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Authors: B. Mahfoud, A. Bendjaghlouli

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Natural convection is simulated in a truncated cone filled with nanofluid. Inclined and top walls have constant temperature where the heat source is located on the bottom wall of the conical container which is thermally insulated. A finite volume approach is used to solve the governing equations using the SIMPLE algorithm for different parameters such as Rayleigh number, inclination angle of inclined walls of the enclosure and heat source length. The results showed an enhancement in cooling system by using a nanofluid, when conduction regime is assisted. The inclination angle of inclined sidewall and heat source length affect the heat transfer rate and the maximum temperature.

Keywords: heat source, truncated cone, nanofluid, natural convection

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Authors: Mackenzie Leake, Liyu Xia, Kamil Rocki, Wayne Imaino

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In the Hierarchical Temporal Memory (HTM) paradigm the effect of overlap between inputs on the activation of columns in the spatial pooler is studied. Numerical results suggest that similar inputs are represented by similar sets of columns and dissimilar inputs are represented by dissimilar sets of columns. It is shown that the spatial pooler produces these results under certain conditions for the connectivity and proximal thresholds. Following the discussion of the initialization of parameters for the thresholds, corresponding qualitative arguments about the learning dynamics of the spatial pooler are discussed.

Keywords: hierarchical temporal memory, HTM, learning algorithms, machine learning, spatial pooler

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Authors: O. Eso, M. Mohammadi, J. Darkwa, J. Calautit

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Residential buildings are responsible for 22% of the global end-use energy demand and 17% of global CO₂ emissions. Tropical climates particularly present higher latent heat gains, leading to more cooling loads. However, the cooling processes are all based on conventional mechanical air conditioning systems which are energy and carbon intensive technologies. Passive cooling systems have in the past been considered as alternative technologies for minimizing energy consumption in buildings. Nevertheless, replacing mechanical cooling systems with passive ones will require a careful assessment of the passive cooling system heat transfer to determine if suitable to outperform their conventional counterparts. This is because internal heat gains, indoor-outdoor heat transfer, and heat transfer through envelope affects the performance of passive cooling systems. While many studies have investigated sensible heat transfer in passive cooling systems, not many studies have focused on their latent heat transfer capabilities. Furthermore, combining heat prevention, heat modulation and heat dissipation to passively cool indoor spaces in the tropical climates is critical to achieve thermal comfort. Since passive cooling systems use only one of these three approaches at a time, integrating more than one passive cooling system for effective indoor latent heat removal while still saving energy is studied. This study is a systematic review of recently published peer review journals on integrated passive cooling systems for tropical residential buildings. The missing links in the experimental and numerical studies with regards to latent heat reduction interventions are presented. Energy simulation studies of integrated passive cooling systems in tropical residential buildings are also discussed. The review has shown that comfortable indoor environment is attainable when two or more passive cooling systems are integrated in tropical residential buildings. Improvement occurs in the heat transfer rate and cooling performance of the passive cooling systems when thermal energy storage systems like phase change materials are included. Integrating passive cooling systems in tropical residential buildings can reduce energy consumption by 6-87% while achieving up to 17.55% reduction in indoor heat flux. The review has highlighted a lack of numerical studies regarding passive cooling system performance in tropical savannah climates. In addition, detailed studies are required to establish suitable latent heat transfer rate in passive cooling ventilation devices under this climate category. This should be considered in subsequent studies. The conclusions and outcomes of this study will help researchers understand the overall energy performance of integrated passive cooling systems in tropical climates and help them identify and design suitable climate specific options for residential buildings.

Keywords: energy savings, latent heat, passive cooling systems, residential buildings, tropical residential buildings

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Authors: Nalluri Lakshmi Ramu, C. Venkat Nihit, Narayana Kumar, Dillep

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Masonry bridges are the iconic heritage transportation infrastructure throughout the world. Continuous increase in traffic loads and speed have kept engineers in dilemma about their structural performance and capacity. Henceforth, research community has an urgent need to propose an effective methodology and validate on real-time bridges. The presented research aims to assess the structural health of an Eighty-year-old masonry railway bridge in India using wireless accelerometer sensors. The bridge consists of 44 spans with length of 24.2 m each and individual pier is 13 m tall laid on well foundation. To calculate the dynamic characteristic properties of the bridge, ambient vibrations were recorded from the moving traffic at various speeds and the same are compared with the developed three-dimensional numerical model using finite element-based software. The conclusions about the weaker or deteriorated piers are drawn from the comparison of frequencies obtained from the experimental tests conducted on alternative spans. Masonry is a heterogeneous anisotropic material made up of incoherent materials (such as bricks, stones, and blocks). It is most likely the earliest largely used construction material. Masonry bridges, which were typically constructed of brick and stone, are still a key feature of the world's highway and railway networks. There are 1,47,523 railway bridges across India and about 15% of these bridges are built by masonry, which are around 80 to 100 year old. The cultural significance of masonry bridges cannot be overstated. These bridges are considered to be complicated due to the presence of arches, spandrel walls, piers, foundations, and soils. Due to traffic loads and vibrations, wind, rain, frost attack, high/low temperature cycles, moisture, earthquakes, river overflows, floods, scour, and soil under their foundations may cause material deterioration, opening of joints and ring separation in arch barrels, cracks in piers, loss of brick-stones and mortar joints, distortion of the arch profile. Few NDT tests like Flat jack Tests are being employed to access the homogeneity, durability of masonry structure, however there are many drawbacks because of the test. A modern approach of structural health assessment of masonry structures by vibration analysis, frequencies and stiffness properties is being explored in this paper.

Keywords: masonry bridges, condition assessment, wireless sensors, numerical analysis modal frequencies

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Authors: Amar Khoukhi, Mohamed Shahab

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This paper presents the optimal control problem of mobile robot motion as a nonlinear programming problem (NLP) and solved using a direct method of numerical optimal control. The NLP is initialized with a B-Spline for which node locations are optimized using a genetic search. The system acceleration inputs and sampling periods are considered as optimization variables. Different scenarios with different objectives weights are implemented and investigated. Interesting results are found in terms of complying with the expected behavior of a mobile robot system and time-energy minimization.

Keywords: multi-objective control, non-holonomic systems, mobile robots, nonlinear programming, motion planning, B-spline, genetic algorithm

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Authors: Jihene Jlassi, Ahmed Frikha, Wazna Kortli

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The objectives of Nurse-Patient Assignment are the minimization of the overall hospital cost and the maximization of nurses ‘preferences. This paper aims to assess nurses' satisfaction related to the implementation of patient acuity tool-based assignments. So, we used an integer linear program that assigns patients to nurses while balancing nurse workloads. Then, the proposed model is applied to the Paediatrics Department at Kasserine Hospital Tunisia. Where patients need special acuities and high-level nursing skills and care. Hence, numerical results suggested that proposed nurse-patient assignment models can achieve a balanced assignment

Keywords: nurse-patient assignment, mathematical model, logistics, pediatrics department, balanced assignment

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Authors: Abdullahi Mohammed Auwal

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Formation and change or decamping from one political party to another have now become a common trend in Nigeria. Many of the parties’ members who could not secure positions and or win elections in their parties or are not very much satisfied with the trends occurring in the party’s internal democratic principles and mechanisms, change their respective parties. This paper developed/presented and analyzed the used of non linear mathematical model for defections between two political parties using epidemiological approach. The whole population was assumed to be a constant and homogeneously mixed. Equilibria have been analytically obtained and their local and global stability discussed. Conditions for the co-existence of both the political parties have been determined, in the study of defections between People Democratic Party (PDP) and All Progressive Congress (APC) in Nigeria using numerical simulations to support the analytical results.

Keywords: model, political parties, deffection, stability, equilibrium, epidemiology

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Authors: Yan-Ting Lin, Wei-Nian Su

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The purpose of this paper is to demonstrate the design of 5kW vertical axis wind turbine (VAWT) using DOE method. The NACA0015 airfoil was implemented for the design and 3D simulation. The critical design parameters are chord length, tip speed ratio (TSR), aspect ratio (AR) and pitch angle in this investigation. The RNG k-ε turbulent model and the sliding mesh method are adopted in the CFD simulation. The results show that the model with zero pitch, 0.3 m in chord length, TSR of 3, and AR of 10 demonstrated the optimum aerodynamic power under the uniform 10m/s inlet velocity. The aerodynamic power is 3.61kW and 3.89kW under TSR of 3 and 4 respectively. The aerodynamic power decreased dramatically while TSR increased to 5.

Keywords: vertical axis wind turbine, CFD, DOE, VAWT

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Authors: Wookyong Kwon, Sangmoon Lee

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In this paper, a sampled-data model predictive tracking control method is presented for mobile robots which is modeled as constrained continuous-time linear parameter varying (LPV) systems. The presented sampled-data predictive controller is designed by linear matrix inequality approach. Based on the input delay approach, a controller design condition is derived by constructing a new Lyapunov function. Finally, a numerical example is given to demonstrate the effectiveness of the presented method.

Keywords: model predictive control, sampled-data control, linear parameter varying systems, LPV

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Authors: Akram Khaleghei, Ghosheh Balagh, Viliam Makis

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In this paper, we investigate the residual life prediction problem for a partially observable system subject to two failure modes, namely a catastrophic failure and a failure due to the system degradation. The system is subject to condition monitoring and the degradation process is described by a hidden Markov model with unknown parameters. The parameter estimation procedure based on an EM algorithm is developed and the formulas for the conditional reliability function and the mean residual life are derived, illustrated by a numerical example.

Keywords: partially observable system, hidden Markov model, competing risks, residual life prediction

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Authors: Dodi Ikhsanshaleh

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When subjected to dynamic load, foundation oscillates in the way that depends on the soil behaviour, the geometry and inertia of the foundation and the dynamic exctation. The practical guideline to analysis block-type foundation excitated by dynamic load from vibrating machine is presented. The analysis use Lumped Mass Parameter Method to express dynamic properties such as stiffness and damping of soil. The numerical examples are performed on design block-type foundation supporting gas turbine compressor which is important equipment package in gas processing plant

Keywords: block foundation, dynamic load, lumped mass parameter

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Authors: Abhisek Sinha, Debobrata Rajak, Shilpa Rani, Ram Gopal, Vandana Sharma

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The interaction of femtosecond laser pulses with metallic tips has been studied extensively, and they have proved to be a very good source of ultrashort electron pulses. A study of the interaction of femtosecond Laguerre-Gaussian (LG) laser modes with Tungsten tips is presented here. Laser pulses of 35 fs pulse durations were incident on Tungsten tips, and their electron emission rates were studied for LG (l=1, p=0) and Gaussian modes. A change in the order of the interaction for LG beams is reported, and the difference in the order of interaction is attributed to ponderomotive shifts in the energy levels corresponding to the enhanced near-field intensity supported by numerical simulations.

Keywords: femtosecond, Laguerre-Gaussian, OAM, tip

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Authors: Irina Maria Artinescu, Costin Radu Boldea, Eduard-Ionut Matei

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The paper is a comparative study of two classical variants of parallel projection methods for solving the convex feasibility problem with their equivalents that involve variable weights in the construction of the solutions. We used a graphical representation of these methods for inpainting a convex area of an image in order to investigate their effectiveness in image reconstruction applications. We also presented a numerical analysis of the convergence of these four algorithms in terms of the average number of steps and execution time in classical CPU and, alternatively, in parallel GPU implementation.

Keywords: convex feasibility problem, convergence analysis, inpainting, parallel projection methods

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Authors: Nicolas Delcey, Philippe Baucour, Didier Chamagne, Geneviève Wimmer, Auditeau Gérard, Bausseron Thomas, Bouger Odile, Blanvillain Gérard

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This paper proposes a thermal study of the catenary/pantograph interface for a train in motion. A 2.5D complex model of the pantograph strip has been defined and created by a coupling between a 1D and a 2D model. Experimental and simulation results are presented and with a comparison allow validating the 2.5D model. Some physical phenomena are described and presented with the help of the model such as the stagger motion thermal effect, particular heats and the effect of the material characteristics. Finally it is possible to predict the critical thermal configuration during a train trip.

Keywords: electro-thermal studies, mathematical optimizations, multi-physical approach, numerical model, pantograph strip wear

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Authors: Lee Derk Huan, Nur Irmawati

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This paper aims to investigate the heat transfer and fluid flow characteristics of nanofluids used in spray cooling systems. The effect of spray height, type of nanofluids and concentration of nanofluids are numerically investigated. Five different nanofluids such as AgH2O, Al2O3, CuO, SiO2 and TiO2 with volume fraction range of 0.5% to 2.5% are used. The results revealed that the heat transfer performance decreases as spray height increases. It is found that TiO2 has the highest transfer coefficient among other nanofluids. In dilute spray conditions, low concentration of nanofluids is observed to be more effective in heat removal in a spray cooling system.

Keywords: numerical investigation, spray cooling, heat transfer, nanofluids

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Authors: Chiranjit Das, Sanjay Jharkharia

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This study is focused on transport mode selection under lead time variability and emissions constraint. In order to reduce the carbon emissions generation due to transportation, organization has often faced a dilemmatic choice of transport mode selection since logistic cost and emissions reduction are complementary with each other. Another important aspect of transportation decision is lead-time variability which is least considered in transport mode selection problem. Thus, in this study, we provide a comprehensive mathematical based analytical model to decide transport mode selection under emissions constraint. We also extend our work through analysing the effect of lead time variability in the transport mode selection by a sensitivity analysis. In order to account lead time variability into the model, two identically normally distributed random variables are incorporated in this study including unit lead time variability and lead time demand variability. Therefore, in this study, we are addressing following questions: How the decisions of transport mode selection will be affected by lead time variability? How lead time variability will impact on total supply chain cost under carbon emissions? To accomplish these objectives, a total transportation cost function is developed including unit purchasing cost, unit transportation cost, emissions cost, holding cost during lead time, and penalty cost for stock out due to lead time variability. A set of modes is available to transport each node, in this paper, we consider only four transport modes such as air, road, rail, and water. Transportation cost, distance, emissions level for each transport mode is considered as deterministic and static in this paper. Each mode is having different emissions level depending on the distance and product characteristics. Emissions cost is indirectly affected by the lead time variability if there is any switching of transport mode from lower emissions prone transport mode to higher emissions prone transport mode in order to reduce penalty cost. We provide a numerical analysis in order to study the effectiveness of the mathematical model. We found that chances of stock out during lead time will be higher due to the higher variability of lead time and lad time demand. Numerical results show that penalty cost of air transport mode is negative that means chances of stock out zero, but, having higher holding and emissions cost. Therefore, air transport mode is only selected when there is any emergency order to reduce penalty cost, otherwise, rail and road transport is the most preferred mode of transportation. Thus, this paper is contributing to the literature by a novel approach to decide transport mode under emissions cost and lead time variability. This model can be extended by studying the effect of lead time variability under some other strategic transportation issues such as modal split option, full truck load strategy, and demand consolidation strategy etc.

Keywords: carbon emissions, inventory theoretic model, lead time variability, transport mode selection

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Authors: Abdulrahman M. Homadi

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This study focuses on how to control the outlet temperature of a solar air heater in a way simpler than the existing methods. In this work, five cases have been studied by using ANSYS Fluent based on a CFD numerical method. All the cases have been simulated by utilizing the same criteria and conditions like the temperature, materials, areas except the geometry. The case studies are conducted in Little Rock (LR), AR, USA during the winter time supposedly on 15^th of December. A fresh air that is flowing with a velocity of 0.5 m/s and a flow rate of 0.009 m³/s. The results prove the possibility of achieving a controlled temperature just by changing the geometric shape of the heater. This geometry guarantees that the absorber plate always has a normal component of the solar radiation at any time during the day. The heater has a sectarian shape with a radius of 150 mm where the outlet temperature remains almost constant for six hours.

Keywords: solar energy, air heater, control of temperature, CFD

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Authors: Shubham Jaiswal

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In the present article, a drive is taken to compute the solution of spatial fractional order advection-dispersion equation having source/sink term with given initial and boundary conditions. The equation is converted to a system of ordinary differential equations using second-kind shifted Chebyshev polynomials, which have finally been solved using finite difference method. The striking feature of the article is the fast transportation of solute concentration as and when the system approaches fractional order from standard order for specified values of the parameters of the system.

Keywords: spatial fractional order advection-dispersion equation, second-kind shifted Chebyshev polynomial, collocation method, conservative system, non-conservative system

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Authors: Fanqiang Kong, Jindong Zhang, Daiyin Zhu

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Space-time adaptive processing (STAP) techniques have been motivated as a key enabling technology for advanced airborne radar applications. In this paper, the notion of cognitive radar is extended to STAP technique, and cognitive STAP is discussed. The principle for improving signal-to-clutter ratio (SCNR) based on slow-time coding is given, and the corresponding optimization algorithm based on cyclic and power-like algorithms is presented. Numerical examples show the effectiveness of the proposed method.

Keywords: space-time adaptive processing (STAP), airborne radar, signal-to-clutter ratio, slow-time coding

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Authors: Hamdy M. Youssef, Mowffaq Oreijah, Hunaydi S. Alsharif

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In this paper, a three-dimensional model of the generalized thermoelasticity with one relaxation time and variable thermal conductivity has been constructed. The resulting non-dimensional governing equations together with the Laplace and double Fourier transforms techniques have been applied to a three-dimensional half-space subjected to thermal loading with rectangular pulse and traction free in the directions of the principle co-ordinates. The inverses of double Fourier transforms, and Laplace transforms have been obtained numerically. Numerical results for the temperature increment, the invariant stress, the invariant strain, and the displacement are represented graphically. The variability of the thermal conductivity has significant effects on the thermal and the mechanical waves.

Keywords: thermoelasticity, thermal conductivity, Laplace transforms, Fourier transforms

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Authors: Tohru Kawabe

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In this paper, a new SMC (Sliding Mode Control) method with MP (Model Predictive Control) integral action for the slip suppression of EV (Electric Vehicle) under braking is proposed. The proposed method introduce the integral term with standard SMC gain , where the integral gain is optimized for each control period by the MPC algorithms. The aim of this method is to improve the safety and the stability of EVs under braking by controlling the wheel slip ratio. There also include numerical simulation results to demonstrate the effectiveness of the method.

Keywords: sliding mode control, model predictive control, integral action, electric vehicle, slip suppression

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Authors: Te Wen Tu, Sen Yung Lee

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An alternative approach is proposed to develop the analytic solution for one dimensional heat conduction with one mixed type boundary condition and general time-dependent heat transfer coefficient. In this study, the physic meaning of the solution procedure is revealed. It is shown that the shifting function takes the physic meaning of the reciprocal of Biot function in the initial time. Numerical results show the accuracy of this study. Comparing with those given in the existing literature, the difference is less than 0.3%.

Keywords: analytic solution, heat transfer coefficient, shifting function method, time-dependent boundary condition

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Authors: Carlos Alberto Riveros, Edwin Fabián García, Javier Enrique Rivero

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The measured data obtained from sensors in continuous monitoring of civil structures are mainly used for modal identification and damage detection. Therefore when modal identification analysis is carried out the quality in the identification of the modes will highly influence the damage detection results. It is also widely recognized that the usefulness of the measured data used for modal identification and damage detection is significantly influenced by the number and locations of sensors. The objective of this study is the numerical implementation of two widely known optimum sensor placement methods in beam-like structures

Keywords: optimum sensor placement, structural damage detection, modal identification, beam-like structures.

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Authors: Brian E. Usibe

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This paper addresses the problem of a linear crack located in the middle of a homogeneous elastic media under normal tension-compression harmonic loading. The problem of deformation of the fractured media is solved using the direct finite element numerical procedure, including the analysis of the dynamic field variables of the problem. A finite element algorithm that satisfies the unilateral Signorini contact constraint is also presented for the solution of the contact interaction of the crack faces and how this accounts for the qualitative and quantitative changes in the solution when determining the dynamic fracture parameter.

Keywords: harmonic loading, linear crack, fracture parameter, wave number, FEA, contact interaction

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Authors: Cleyton S. Stampa

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This paper addresses the perspectives of using low melting point metals (LMPMs) as phase change materials (PCMs) in latent thermal energy storage (LTES) units, through a numerical approach. This is a new class of PCMs that has been one of the most prospective alternatives to be considered in LTES, due to these materials present high thermal conductivity and elevated heat of fusion, per unit volume. The chosen type of LTES consists of several horizontal parallel slabs filled with PCM. The heat transfer fluid (HTF) circulates through the channel formed between each two consecutive slabs on a laminar regime through forced convection. The study deals with the LTES charging process (heat-storing) by using pure gallium as PCM, and it considers heat conduction in the solid phase during melting driven by natural convection in the melt. The transient heat transfer problem is analyzed in one arbitrary slab under the influence of the HTF. The mathematical model to simulate the isothermal phase change is based on a volume-averaged enthalpy method, which is successfully verified by comparing its predictions with experimental data from works available in the pertinent literature. Regarding the convective heat transfer problem in the HTF, it is assumed that the flow is thermally developing, whereas the velocity profile is already fully developed. The study aims to learn about the effect of the solid subcooling in the melting rate through comparisons with the melting process of the solid in which it starts to melt from its fusion temperature. In order to best understand this effect in a metallic compound, as it is the case of pure gallium, the study also evaluates under the same conditions established for the gallium, the melting process of commercial paraffin wax (organic compound) and of the calcium chloride hexahydrate (CaCl₂ 6H₂O-inorganic compound). In the present work, it is adopted the best options that have been established by several researchers in their parametric studies with respect to this type of LTES, which lead to high values of thermal efficiency. To do so, concerning with the geometric aspects, one considers a gap of the channel formed by two consecutive slabs, thickness and length of the slab. About the HTF, one considers the type of fluid, the mass flow rate, and inlet temperature.

Keywords: flat slab, heat storing, pure metal, solid subcooling

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