Instantaneous Heat Transfer Research Articles

Study of heat transfer to supercritical pressure water across a wide range of parameters in pulse heating experiments

• Controlled pulse heating of supercritical pressure water was performed. • Unexpected response to the short-term release of high-power heat was revealed. • It is consistent with the character of the density change over supercritical isobars. • Reduced heat transfer coefficient exhibits a minimum at pseudocritical temperature. • We attribute this minimum to the suppression of fluctuations in short-term experiment. From experimental data on pulse heating of a thin wire probe in water pre-compressed to supercritical pressures at room temperature, the instantaneous heat transfer coefficient has been calculated over a wide temperature range from 250 °C to 700 °C. The pressure, being the parameter of the experiment, has been varied from the near-supercritical value (22.1 MPa) to 100 MPa. The heat flux density across the probe surface reached 10 MW/m 2 at a characteristic heating time of 20 ms. Under conditions of powerful heat release and small temporal and spatial scales, heat transfer is carried out mainly due to the heat conduction mode, which is the most physically determined mechanism of heat transfer. It has been revealed that the reduced heat transfer coefficient exhibits a minimum in the region of pseudocritical temperatures; this minimum becomes deeper, as the pressure value approaches the critical one. The obtained data can be useful in the design of heat exchange devices, the operation of which may include powerful local heat release, as well as in the simulation of emergencies associated with a sharp jump in reactivity in nuclear power units.

Effects of liquid subcooling on droplet-wall collision heat transfer in film boiling

The effects of subcooling on single droplet-wall collision heat transfer characteristics during film boiling were experimentally investigated. Water droplet subcooling was varied from 0 to 60 K under atmospheric conditions, while the collision velocity and substrate temperature remained constant at 0.7 m/s and 500 °C. The instantaneous and localized heat transfer properties associated with dynamic collision of a water droplet were measured by integrated high-speed shadowgraph and infrared thermometry. Liquid subcooling greatly affected heat transfer. The residence time, effective heat transfer area, and local heat flux were measured. Only the local heat flux correlated strongly with liquid subcooling. When heat flux partitioning at the liquid–vapor interface was considered, i.e., conduction heat transfer into the subcooled droplet and the heat required for evaporation, heat transfer effectiveness was accurately predicted under various subcooling conditions.

Multi-dimensional Simulation of Phase Change by a 0D-2D Model Coupling via Stefan Condition

Considering phase changes associated with a high-temperature molten material cooled down from the outside, this work presents an improvement of the modelling and the numerical simulation of such processes for an application pertaining to the safety of light water nuclear reactors. Postulating a core meltdown accident, the behaviour of the core melt (aka corium) into a steel vessel is of tremendous importance when evaluating the vessel integrity. Evaluating correctly the heat fluxes requires the numerical simulation of the interaction between the liquid material and its solid counterpart which forms during the solidification process, but also may melt back. To simulate this configuration, encountered in various industrial applications, one considers a bi-phase model constituted by a liquid phase in contact and interaction with its solid phase. The liquid phase may solidify in presence of low energetic source, while the solid phase may melt due to an intense heat flux from the high-temperature liquid. In the frame of the in-house legacy code, several simplifying assumptions (0D multi-layer discretization, instantaneous heat transfer via a quadratic temperature profile in solids) are made for the modelling of such phase changes. In the present work, these shortcomings are illustrated and further overcome by solving a 2D heat conduction model in the solid by a mixed Raviart-Thomas finite element method coupled to the liquid phase due to heat and mass exchanges through Stefan condition. The liquid phase is modeled with a 0D multi-layer approach. The 0D-liquid and 2D-solid models are coupled by a Stefan like phase change interface model. Several sanity checks are performed to assess the validity of the approach on 1D and 2D academical configurations for which exact or reference solutions are available. Then more advanced situations (genuine multi-dimensional phase changes and an “industrial-like scenario”) are simulated to verify the appropriate behavior of the obtained coupled simulation scheme.

Geometrically activated thermal mass: wood vs. concrete

Designing for climate resilience and carbon neutrality implies low-emission structures that double as thermal mass. In this study, the effect of using geometry to maximize natural surface convection on an internal thermal mass is investigated. Wood and concrete thermal masses are optimized for both instantaneous heat transfer and transient heat storage, and compared. It is found that the addition of optimally-sized fins can double or triple the convection coefficient at the interior surface, provided the thermal conductivity of the fins is sufficiently high. Doubling or tripling the surface heat transfer translates to an equivalent increase in dynamic energy storage, so long as the mass thickness, wall area, and vent openings are recalibrated to maintain thermal synchrony at the building-level.

Numerical study on instantaneous heat transfer characteristics of AC arc-fault

Studying the heat transfer characteristics of alternating current (AC) arc-fault to electrodes is a key issue in electrical fires. In this paper, an instantaneous heat transfer numerical model of AC arc-fault is developed based on the magneto-hydrodynamic principle. The temperature distribution of the AC arc at the microseconds level and the influence of heat transfer on electrodes at the seconds level when the arc heats are studied. The numerical simulation of the axial temperature of the electrodes is verified by experiments, and the temperature variation in the electrodes at different currents and times is discussed. The results show that the arc temperature varies periodically similar to the current at the microseconds level but it does not go out when the current passes zero. The high-temperature region of electrodes diffuses with the increase in current or time. However, the axial temperature gradient of the electrode decreases with time and increases with current. Furthermore, the range of temperature increase in the electrode position decreases with the increase in current and time, but the electrode position near the arc has a higher initial temperature increase.

Investigation of heat transfer between 22MnB5 and KDAHP1 hot work tool steel

The IHTC (Interfacial-Heat-Transfer-Coefficient) between 22MnB5 and KDAHP1 hot work tool steel during the hot stamping process is an important thermal parameter to reflect the heat transfer efficiency. The instantaneous heat transfer law for 22MnB5 blank is based on the cylindrical-die model, and the experiment is contained different contact pressure and gap conditions. The average IHTC value is calculated by the heat balance method (HBM) and finite element optimisation method (FEOM). There is a power function relationship between the average IHTC and both the contact pressure and the one-side gap. From the results of the one-side and bilateral gap condition, 0.2 mm can be considered as the ‘critical gap’ where the heat exchange between the blank and dies starts or ends.

Photo-assisted enhancement performance for rapid detoxification of chemical warfare agent simulants over versatile ZnIn2S4/UiO-66-NH2 nanocomposite catalysts

Constructing versatile materials with self-detoxification properties are highly desired for emergency destruction of chemical warfare agents (CWAs). Herein, we first reported in-situ fabrication of ZnIn2S4/UiO-66-NH2 nanocomposites (ZnInS/UiO) and their application in catalytic detoxification of two CWA simulants. For nerve agent simulant dimethyl 4-nitrophenyl phosphate (DMNP), the optimal ZnInS/UiO-23.9 displayed 5.9 times increase in hydrolysis rate having the turnover frequency (TOF) of 0.0586 s-1 under simulated solar light (SSL), which is superior to the reported UiO-based catalysts. Photo-assisted enhancement in DMNP detoxification was due to photothermal effect of ZnInS and close interfacial contact in ZnInS/UiO heterostructures, facilitating instantaneous heat transfer from ZnInS to UiO catalytic sites. As for mustard gas surrogate 2-chloroethyl ethyl sulfide (CEES), under SSL irradiation for 15 min, ZnInS/UiO-23.9 can eliminate 96.7% of CEES in droplet experiment, being 4.17 and 3.24 times of ZnInS and UiO accordingly. It was ascribed to spatial separation of photoinduced electron-hole pairs and photothermally-assisted charge transfer in ZnInS/UiO composites, improving catalytic activity for CEES detoxification. Besides, the detected products suggested that CEES conversion underwent reductive dechlorination, radical reactions and hydrolysis. This study can be extended to other multifunctional catalysts based on metal-organic frameworks and provides new opportunities for photoassisted enhanced detoxification of CWAs.

Residential Air Conditioning System Integrated with Packed Bed Cool Storage Unit for Promoting Rooftop Solar PV Power Generation

The increase in the share of renewable-based power in the gross power generation in most countries causes significant concerns over the addition of renewable power with the grid, results in stability issues in most developed nations. Energy storage is an emerging technology that is considered the ultimate solution in developing microgrids with distributed renewable power generation. The cool thermal storage plays a vital role in economically promoting renewable power among different storage units. The major objective of the research work is to demonstrate the integration of residential air-conditioning systems with packed bed cool storage units to promote rooftop solar power generation for residential space cooling applications. In order to achieve the said objective, an experimental investigation was made to study the charging/discharging characteristics of a packed bed cool-storage unit combined with a chiller and a cooling coil unit suitable for small capacity air-conditioning applications. The system consists of encapsulated spherical capsules filled with a phase change material blended with distilled water and pseudomonas (nucleating agent) and the heat transfer fluid as a combination of distilled water and Mono-ethylene glycol. A cooling coil unit was connected to the cool-storage tank to transfer cool energy from the storage tank to the space to be cooled when there is a demand. The important parameters, such as instantaneous and cumulative heat transfer during the charging/discharging processes, are presented. The average COP values of the chiller during the charging operation were estimated as 1, 0.93, and 0.89 when the HTF setpoint temperatures were -6°C, -9°C, and -12°C, which shows a decrease in performance as the setpoint temperature decreases. During the discharging process, a cooling load of 2.25 kW is obtained during the first cycle of operation and gradually reduces to 0.3 kW during the sixth cycle of operation. The increase in the HTF temperature during each cycle of operation indicates that the Phase Change Material (PCM) in the balls cannot release the heat as per the demand after a certain period of discharging. Hence, decreasing the internal thermal resistance by suitable measures is essential to achieve uniform heat flux and to operate the system successfully

Numerical investigation on the effects of spatial angle on oscillating flow and heat transfer characteristics of piston cooling galleries

• The SOCR and SHTC of gallery are affected by the inlet/outlet position. • The ICOR and IHTC in groups A and B are different at the same crank angle. • The spatial angle has a non-negligible influence on the piston cooling performance. • The results provide reference for piston improvement design of multi-cylinder diesel. The oscillating cooling method is currently one of the most efficient cooling solutions for highly reinforced pistons. Previous studies only focused on the piston galleries with the reciprocating motion along a specified direction relative to the direction of the gravity force, e.g., the vertical direction in inline multi-cylinder engines. There are strong needs to study the cooling performance of the pistons that are designed to have reciprocating motions with different directions relative to gravity. In this paper, a concept of spatial angle is introduced to describe the design angle between the direction of the piston reciprocating motion and the direction of the gravity force in a coordinate system. When the spatial angle is changed, the gravity components of the piston are changed along the direction of the piston axial motion and its perpendicular direction. Moreover, with a given spatial angle, different piston designs can be achieved to obtain different relative positions of the cooling oil inlet and outlet passages, being higher or lower relative to each other. Because both the spatial angle and the relative positions of the oil passages affect flow and cooling performance, several simulation models are established to cover five spatial angles including −90°, −45°, 0°, 45°, and 90° as well as two groups of relative positions, i.e., groups A and B. The CFD simulation is validated by experimental testing. The results show that the flow and heat transfer performance of group B is more stable than that of group A because the inlet and outlet of the cooling passages of group B are at the same height. It is found that the steady-state oil charge ratio and steady-state heat transfer coefficient of group A gradually decrease with the increase of the spatial angle. The fluctuation patterns of the instantaneous oil charge ratios and heat transfer coefficients of groups A and B are very similar, but their spatial distribution values are different at the same crank angle (CA). The maximum difference in the instantaneous heat transfer coefficients between A1 and A3 reaches 23.27% at 303° CA. Moreover, it is found that when the piston moves between 150° CA and 300° CA, a phenomenon of liquid plug attenuates with the increase of the spatial angle. These findings can support the cooling performance analysis and optimization design of the piston galleries of the V-type, W-type, and horizontal opposed-piston diesel engines.

Application of a MEMS heat flux sensor to heat transfer research on an impinging diesel jet

To clarify the mechanisms of heat transfer on an engine wall is an important challenge because the heat loss on the wall is one of the dominant factors that limit the thermal efficiency. A thin-film resistance type heat flux sensor fabricated with Micro-Electro-Mechanical Systems (MEMS) technologies was applied to research on the heat transfer of an impinging diesel jet. The MEMS sensor had a high sensitivity and multiple measurement points with a scale comparable to the turbulence of in-cylinder flow for the investigation of local instantaneous heat transfer characteristics in engines. Measurements of wall temperature and heat flux were conducted in a constant volume chamber under the reference conditions of Engine Combustion Network (ENC) Spray A with variations in injection pressure. As a result, the maximum heat flux and heat transfer coefficient reached about 5 MW/m2 and 3 MW/(m2 K), respectively. The results were compared to those obtained with a commercially available thermocouple, and both sensors produced similar trends. In addition, fluid motion near the wall was estimated from the heat flux fluctuations using a cross-correlation analysis. The relationship between heat transfer and flow was investigated in a dimensionless number fashion, and it was compared to a semi-theoretical prediction that was based on a steady state laminar flow heat transfer model.

Effect of jet inflow angle on heat transportation in an impinging jet interfering with a Couette flow

The effect of the incoming angle of a jet that interferes with a Couette flow is studied using numerical simulations. When the jet flows against the direction of the Couette flow, the instantaneous vortex structure and heat transfer on the jet-impinging surface become complex and irregular. In contrast, when the jet flows in the same direction as the Couette flow, the instantaneous vortex structure has a strong and distinct periodicity about the main flow direction as a vortex street with a sine wave velocity fluctuation. This periodicity also affects the heat transfer on the jet-impinging surface. The Strouhal number calculated from these time periodicity increases with increasing jet angle. In the time-averaged flows and temperature fields, the Nusselt number exhibits a few characteristic distributions. The heat transfer concentrates around the jet impingement region at a negative jet angle whereas the area associated with significant heat transfer coefficient separates symmetrically about the flow in spanwise direction at a positive jet angle and the value of heat transfer coefficient on the center axis is low. Furthermore, a large and strong counter-rotating vortex pair is formed when the jet flows in the same direction as the Couette flow. As reported in our previous study, this pair vortex involves a main flow fluid and results in a characteristic Nusselt number distribution. Comparing the overall heat transfers on the jet-impinging surface, the lowest time-averaged heat transfer is obtained when the jet is orthogonal to the Couette main flow. Generally, the heat transfer over the surface is higher when the jet flows against the Couette flow than when the jet flows in the same direction as the Couette flow. However, since the pressure loss also increases drastically at the same time, it is found that the ratio of heat transfer over pressure loss increases with increase in jet angle. Considering the temperature and velocity vector distributions, and plots of turbulent heat flux, when the jet flows against the Couette main flow, the effect of jet impingement is dominant on heat transfer. However, when the jet flows in the same direction as the Couette main flow, most of the heat transfer is carried by the pair vortex. Although the contributing vortex type is different from similar previous studies conducted, the mechanism of generating this pair vortex is based on time-averaging the legs of the periodic vortex street.

Experimental investigation on packed bed cool storage system for supply-demand management in building air-conditioning system suitable for micro thermal grid

In most of the developed nation, the increase in percentage share of renewable power in the total power generation causes major concerns over the integration of these renewable power with the grid resulting grid instability. Energy storage is a new frontier technology which is considered as the ultimate solution in developing micro-smart grid with distributed renewable power generation. Most of the hot countries like India spend nearly 24% of the electricity generated on air-conditioning and food preservation. Under such scenario, among the various types of storage systems, the cool thermal storage plays a vital role to promote renewable power in an economical way. Considering the importance in the present renewable energy scenario, in the present work, an experimental investigation was performed on a packed bed cool storage system integrated with a chiller system which has major advantages in central air-conditioning system for demand management strategies. The storage system consists of encapsulated spherical balls filled with a mixture of distilled water and pseudomonas (nucleating agent) as phase change material and a mixture of distilled water and mono-ethylene glycol as heat transfer fluid. The essential parameters such as reduction in subcooling, instantaneous, and cumulative heat transfer during the charging process are presented for the efficient operation.

Numerical Solution of Parabolic Partial Differential Equation by Using Finite Difference Method

In the real world, many physical problems like heat equation, wave equation, Laplace equation and Poisson equation are modeled by partial differential equations (PDEs). A PDE of the form ut = α uxx, (α > 0) where x and t are independent variables and u is a dependent variable; is a one-dimensional heat equation. This is an example of a prototypical parabolic equation. The heat equation has analytic solution in regular shape domain. If the domain has irregular shape, computing analytic solution of such equations is difficult. In this case, we can use numerical methods to compute the solution of such PDEs. Finite difference method is one of the numerical methods that is used to compute the solutions of PDEs by discretizing the given domain into finite number of regions. Here, we derived the Forward Time Central Space Scheme (FTCSS) for this heat equation. We also computed its numerical solution by using FTCSS. We compared the analytic solution and numerical solution for different homogeneous materials (for different values of diffusivity α). There is instantaneous heat transfer and heat loss for the materials with higher diffusivity (α) as compared to the materials of lower diffusivity. Finally, we compared simulation results of different non-homogeneous materials.

Aerothermal and aerodynamic performance of turbine blade squealer tip under the influence of guide vane passing wake

In this paper, the performance of the turbine blade squealer tip has been studied detailed aimed to highlight the impact of the upstream guide vane passing wake. The first stage of GE-E3 high-pressure turbine has been employed to perform the three-dimensional simulation and the computational domain has been scaled based on the domain scaling method. Boundary conditions are consistent with operating conditions of the annular cascade testing. Circumferential averaged and realistic non-uniform interface conditions have been used to obtain steady and unsteady characteristics respectively. The validation of the turbulent model and mesh independent test has been conducted detailed in previous work. Three squealer tips, including two widths and heights, have been designed and investigated to understand its influence. Results show that the aerothermal performance of the squealer tip is remarkably influenced by the upstream passing wake. Although steady and time-averaged results have a good agreement, the variation of instantaneous heat transfer coefficient (HTC) would be over 30%, especially on the Cavity Floor region. Changing the geometry of the squealer also has different impacts on both steady and unsteady performance. The unsteady aerodynamic has relatively small fluctuation within 10%, and the distribution of steady and time-averaged leakage flow as well as total pressure loss coefficient still have a satisfactory agreement.

Space–time characteristics of true and false sticker breakouts in mould during continuous casting

ABSTRACT In order to investigate the space–time characteristics of sticker breakout, the instantaneous heat transfer of mould copper plate was visualised. The spatial characteristics of hot and cold regions of true and false sticker breakouts, such as the area, temperature velocity, and location, were studied and analysed. The results show that the hot region area of sticker breakout is mainly concentrated in 1973 to 7795 pixels. The temperature velocity greater than 1.02°C s–1 is the necessary condition for sticker breakout. The temperature velocity of the cold region is in the range of −0.57 to −4.22°C s–1. The gathering location of hot and cold region of true sticker breakouts is concentrated in the range of 46th–64th and 5th–47th, respectively. These parameters were also used to distinguish true and false sticker breakouts. The results show that 98.7% of true and false sticker breakouts can be identified with these parameters.

Tomography-based investigation of flow and heat transfer inside reticulated porous ceramics

This study investigates the flow and heat transfer within reticulated porous ceramics, with the aim of enhancing the understanding of phenomena occurring at the pore scale in order to extract useful information for the optimisation of heat sinks or other reticulated porous devices in engineering applications. In this study, X-ray computed tomography is used to reconstruct the reticulated porous ceramic. From the voxel mesh, the real geometry of the foam sample can be obtained, and an unstructured mesh is generated using ICEM. Then, a fully coupled heat transfer model is established. Based on this model, the transient conjugate heat transfer between the airstream and the porous matrix is solved using FLUENT software. The numerical results show that the pressure drop vs. the superficial velocity follows the Darcy–Forchheimer equation, and the border-affected region is only 1–2 times the mean cell size. Moreover, a local thermal equilibrium lasting for 7–10 s is found in the transient coupled flow and heat transfer process in this study. Additionally, the local convective heat transfer coefficient, which mainly depends on the velocity, is constant along the flow direction, and the instantaneous volumetric heat transfer coefficient increases monotonically with time. The obtained results are important theoretical supplements for understanding the flow and heat transfer in porous materials, and are crucial for enhancing the heat transfer in applications of reticulated porous ceramic materials.

Heat and mass transport analysis of the drying of freshwater fishes by a forced convective air‐dryer

AbstractThe drying behavior of different freshwater fishes (with/without scales) is investigated using a simple convective heated air dryer. Drying processes are analyzed to study the kinetics of drying, shrinkage dependent variable effective diffusivity, convective heat and mass transport, and the energy aspect of drying. Among the drying kinetic models, Hasibuan–Daud and Haghi–Angiz‐I models produce the best fit for fishes with scales and Hii model produces the best fit for fish without scales. Diffusion analysis performed based on simplified solution of Fick's diffusion equation shows higher effective diffusivity for fish without scales, proving additional barrier from scales (for fish with scales) that need to be considered during dryer design. Calculated instantaneous heat and mass transfer coefficients (different for fish with or without scales) also agree with this observation, accentuating the difference based on scales. Drying process for all fishes obeys the heat‐mass transfer correlation. Estimated parameters such as effective diffusivity (0.2–1 × 10−9 m2/s) and convective heat and mass transfer coefficients (7–14 W/m2/K and 2.8–4.5 × 10−6 m/s, respectively) can be utilized in designing different fish drying systems. Average and instantaneous total energy consumption, specific moisture extraction ratio, and specific energy consumption are evaluated in order to provide a comprehensive picture of the drying process.Practical ApplicationsFresh‐ and salt‐water fishes account for major sources of protein‐rich food for substantial parts of the population in underdeveloped and developing nations. To circumvent the wastage associated with microbial contaminations during prolific seasons, fish drying has been widely employed as a way of preserving this perishable food. Convective drying of agricultural products as well as marine foods is a commonly employed drying method for food preservation. This study investigates the drying behavior of three different freshwater fishes using an in‐house constructed forced convective air dryer. The experimental drying characteristics and estimated parameters by model fitting during fish drying will be particularly applicable in the wide field of fish drying. The outcome of this study can also be utilized for more effectively designing and evaluating low‐cost convective fish dryers.

Thermal Calculation and Experimental Investigation of Electric Heating and Solid Thermal Storage System

Electric heating and solid thermal storage systems (EHSTSSs) are widely used in clean district heating and to flexibly adjust combined heat and power (CHP) units. They represent an effective way to utilize renewable energy. Aiming at the thermal design calculation and experimental verification of EHSTSS, the thermal calculation and the heat transfer characteristics of an EHSTSS are investigated in this paper. Firstly, a thermal calculation method for the EHSTSS is proposed. The calculation flow and calculation method for key parameters of the heating system, heat storage system, heat exchange system and fan-circulating system in the EHSTSS are studied. Then, the instantaneous heat transfer characteristics of the thermal storage system (TSS) in the EHSTSS are analyzed, and the heat transfer process of ESS is simulated by the FLUENT 15 software. The uniform temperature distribution in the heat storage and release process of the TSS verifies the good heat transfer characteristics of the EHSTSS. Finally, an EHSTSS test verification platform is built and the historical operation data of the EHSTSS is analyzed. During the heating and release thermal process, the maximum temperature standard deviation of each temperature measurement point is 28.3 °C and 59 °C, respectively. The correctness of the thermal calculation of the EHSTSS is thus verified.

Estimation of moving heat source for an instantaneous three-dimensional heat transfer system based on step-renewed Kalman filter

Inverse estimation of moving heat source is a common issue in many fields. A real-time method based on Kalman filter is proposed and further developed to identify the moving heat source in a three-dimensional heat transfer system. Firstly, a step-renewed state space model considering the source position is established according to principle of source contribution. Using this model, a technique coupling fuzzy adaptive Kalman filter with weight recursive least squares algorithm is implemented to realize the simultaneous estimation of moving heat source and temperature field. Different spatiotemporal changes of heat source and measurement noises are assumed to validate the feasibility and test its performances of this technique. Results illustrates that this method can be used to inversely estimate moving heat source with different changes rates and directions. When the moving velocity varies as 0.25, 0.50, 1.00 mm/s and the time period is employed as 100, 200, 400, 800 s, the estimated heat source can accurately agree with exact one while the reconstructed temperature field is of low deviation. The mean relative errors of estimated heat source are no more than 3.25% and mean relative errors of temperature are smaller than 1.37% while standard deviation of measurement noises increases from 0.01 to 5.00, which demonstrates that this method is of high robustness and can be used under a deteriorated condition.

Effect of rolling motion on heat transfer characteristics of narrow rectangular channel with high subcooled boiling

In this paper, the effects of vertical and rolling motion conditions on high subcooled boiling heat transfer in narrow rectangular channels of natural circulation system are investigated experimentally. To analyze the error of instantaneous heat transfer coefficient better, a calculation error method based on temperature difference is proposed. The results show that the error between the predicted heat transfer coefficient of Yan’s formula and the experimental value is less than 30% under vertical and rolling motion conditions.