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DOE OSTI2020

Impact of uranium oxide (UO 2 ) fuel with molybdenum (Mo) inserts on pressurized water reactor performance and safety

This work investigates nuclear reactor performance and safety characteristics of UO 2 with high thermal conductivity Mo insert structures by using multiphysics modeling techniques. Additionally, the purpose of this study is to use scoping analyses to quantify the impact of using Mo inserts from neutronic and heat transfer standpoints. Attention is given to reactor performance parameters, such as cycle length, maximum fuel temperature, temperature gradients in the fuel, and stored energy in the fuel. The finite-element code BISON and the Monte Carlo particle transport code Serpent were used to perform sensitivity analyses on the Mo insert geometry to optimize the insert design and inform larger scale modeling that required the homogenization of the UO 2 and Mo. Although BISON is often used as a fuel performance analysis tool, it is used in this context for heat transfer analysis only. Fuel performance optimization is outside the scope of the current study, but would be important for future work focused on this concept. The results showed that the insert had little impact on neutronic performance and that homogenizing the UO 2 and Mo was acceptable for reactor physics calculations. Reactivity temperature coefficients calculated using homogeneous UO 2 -Mo were shown to be relatively similar to UO 2 , but higher Mo content and 235 U enrichment can reduce the worth of soluble boron and control rods. The effect of insert geometry on heat transfer was much greater, and an approximately 15–20% difference in maximum fuel temperature was predicted between the best and worst performing heat transfer geometries. Furthermore, thermal conductivity calibration based on the finite element analysis results was performed to improve the accuracy of temperature predictions in reactor analysis models that homogenized the UO 2 -Mo fuel. Compared with UO 2 in a pressurized water reactor (PWR), the optimized UO 2 -Mo design increased the margin to fuel melt by 13–32% across the fuel cycle, but it requires the 235U enrichment to exceed 5% to match the cycle length of conventional UO 2 .

11 NUCLEAR FUEL CYCLE AND FUEL MATERIALS↗

NASA NTRS1987

Effect of flow oscillations on axial energy transport in a porous material

The effects of flow oscillations on axial energy diffusion in a porous medium, in which the flow is continuously disrupted by the irregularities of the porous structure, are analyzed. The formulation employs an internal heat transfer coefficient that couples the fluid and solid temperatures. The final relationship shows that the axial energy transport per unit cross-sectional area and time is directly proportional to the axial temperature gradient and the square of the maximum fluid displacement.

Siegel, R.↗

DOE OSTI2021

Radiative Heat Transport and Optical Characterization of High Temperature Molten Salts

The goal of this project was to advance the field of molten fluoride radiative heat transfer (RHT), through optical property measurements, heat transfer loop construction and operation, and computational fluid dynamics simulations. The following outcomes have been accomplished. A comprehensive review has been conducted to compile all available RHT-relevant optical absorption data for molten fluorides. The various measurement methods have also been compiled and critiqued. Thermal emission measurement methods have been refined and documented. A unique thermal emissivity measurement facility has been constructed and used to measure the emissivity of flowing FLiBe-exposed SS316 samples. A slight increase has been observed in the emissivity compared to unexposed SS316. A dual reflectance-emission setup was partially demonstrated for the purpose of molten fluoride absorption measurement. Preliminary infrared edge data for FLiNaK was obtained. A visible near-infrared (NIR) measurement setup has been constructed and will be used to measure absorption of corrosion products in FLiBe. A new multi-band thermal radiation method using blackbody-weighted spectral bands for the absorption-coefficient was deployed to investigate the thermal performance of the UW Natural Circulation FLiBe Loop under various power levels and operating conditions. The results showed an increasing and decreasing trend in the overall heat transfer with optical thickness with a maximum at optical thickness τ D ≈Ο(1). A forced convection FLiBe loop was constructed for the purpose of studying corrosion and thermal hydraulic phenomena. A vertical cantilever pump is used to achieve up to 5 gpm and 5 m/s flow velocity in hot and cold test sections. A methodology has been established for modeling radiative heat transfer (RHT) in molten salt coolants for the purpose of quantifying the contribution of thermal radiation in conditions relevant to FHR or MSR systems. The comparison between the results obtained for forced and mixed convection showed that in the studied ranges of optical thickness, the maximum effect of RHT on overall heat transfer was 60% improvement observed at z/D = 250 for forced convection; whereas for mixed convection, that value was higher at 170% observed at z/D = 30. The highest effect of RHT on the overall energy distribution was observed at τ D ≈3.4. Negligible effect (<20%) was observed above τ D =18 and below τ D ≈0.002. A CFD code-to-code comparison was conducted using COMSOL Multiphysics at UW-Madison and STAR-CCM at MIT, for a forced and mixed convection laminar flow for a grey medium in a vertical heated using both COMSOL Multiphysics at UW-Madison and STAR-CCM at MIT. The relative error was the largest at τ D =40 for the radiative heat flux, bulk temperature, and Nusselt number. On the other hand, the relative error was the least at τ D =0.002 for the conductive heat flux, bulk temperature, and Nusselt number.

Anderson, Mark↗

DOE OSTI2021

A molecular dynamics study of collisional heat transfer to nanoclusters in the gas phase

Nanoclusters in the gas phase grow by condensation and coagulation, which heat up nanoclusters, creating thermal non-equilibrium with the surrounding gas. The extent of non-equilibrium for nanoclusters is dependent upon the rate of heating relative to the rate of cooling brought about by nanocluster-gas molecule collisions, hence the latter process plays an important role in nanocluster energy evolution during growth. We apply molecular dynamics simulations to investigate heat transfer between metal nanoclusters and gas molecules relevant to high temperature aerosol systems. In analysis, we first define a thermal reemission coefficient (TRC), which is a correction factor for the portion of energy possessed by reemitted gas molecules after collision. Here, the TRC differs from the thermal accommodation coefficient (TAC), which is a correction factor for the maximum possible energy transfer rate from nanoclusters to gas molecules based on the diffusive collision model. We find the TRC is insensitive to nanocluster size but is affected by the nanocluster to gas temperature ratio and the nanocluster to gas atomic mass ratio. Comparison to the traditionally-defined TAC shows that the TAC is insensitive to temperature, a phenomenon that has been widely indicated in literature but not quantitatively explained. We show how the temperature insensitivity of the TAC arises because of the manner in which TRCs vary with both nanocluster and gas temperature, i.e. the manner in which the reemitted gas molecule energy from a surface varies with the temperature of that surface relative to that of the gas. In addition, while calculations ultimately reveal temperature insensitive TACs and justify their continued use in modeling gas-phase heat transfer, we argue that the TRC is more appropriate to calculate a priori in analyzing simulations; it is physically more realistic to first introduce a correction factor solely for the energy of reemitted gas molecules after a collision (as TRCs) instead of a correction factor applying to both the reemission energy and the initial energy (as TACs), as the latter is exactly calculable and independent of nanocluster properties. In line with prior work, for monoatomic gases we find the TAC decreases as the nanocluster to gas atomic mass increases, approaching 0.08 for gold nanoclusters in helium.

77 NANOSCIENCE AND NANOTECHNOLOGY↗

DOE OSTI2021

Experimental and Numerical Evaluation of the Thermal-Fluid Characteristics of the Helium-Cooled Modular Divertor with Multiple Jets Using a Reversed Heat Flux Approach

A single-finger unit of the Helium-Cooled Modular Divertor with Multiple Jets (HEMJ) with a plasma-facing surface (PFS) area of about 2 cm 2 has been studied in a helium (He) loop at He mass flow rates m˙ H ≤ 8 g/s and nearly prototypical conditions. Based on previous studies of the single finger of the HEMJ, our Georgia Institute of Technology group is planning to experimentally study larger divertors. Given that the HEMJ test section was heated with an induction heater and that it is impractical to scale this up to divertors with larger PFS areas, a reversed heat flux approach is being considered to measure heat transfer coefficients (HTCs). In this approach, the direction of the heat flux is reversed with water cooling and high-temperature He heating of the outer shell attached to the PFS. This work presents an initial experimental and numerical evaluation of this approach for a single HEMJ finger. Experiments with brass and copper-chromium-zirconium outer shells were conducted at dimensionless He mass flow rates or Reynolds numbers Re = 1 × 10 4 to 4.7 × 10 4 , an inlet pressure of 10 MPa, temperatures as great as 673 K, and maximum heat flux of 8.4 MW/m 2 . The experiments verify that the He-side HTCs are independent of the direction of the heat flux. Here, the results agree well with previous Nusselt number correlation and pressure loss coefficients for the HEMJ obtained using the normal heating approach.

42 ENGINEERING↗

NASA NTRS1993

Analysis and design of an ultrahigh temperature hydrogen-fueled MHD generator

A coupled gas dynamics/radiative heat transfer analysis of partially ionized hydrogen, in local thermodynamic equilibrium, flowing through an ultrahigh temperature (10,000-20,000 K) magnetohydrodynamic (MHD) generator is performed. Gas dynamics are modeled by a set of quasi-one-dimensional, nonlinear differential equations which account for friction, convective and radiative heat transfer, and the interaction between the ionized gas and applied magnetic field. Radiative heat transfer is modeled using nongray, absorbing-emitting 2D and 3D P-1 approximations which permit an arbitrary variation of the spectral absorption coefficient with frequency. Gas dynamics and radiative heat transfer are coupled through the energy equation and through the temperature- and density-dependent absorption coefficient. The resulting nonlinear elliptic problem is solved by iterative methods. Design of such MHD generators as onboard, open-cycle, electric power supplies for a particular advanced airbreathing propulsion concept produced an efficient and compact 128-MWe generator characterized by an extraction ratio of 35.5 percent, a power density of 10,500 MWe/cu m, and a specific (extracted) energy of 324 MJe/kg of hydrogen. The maximum wall heat flux and total wall heat load were 453 MW/sq m and 62 MW, respectively.

Moder, Jeffrey P.↗

DOE OSTI2026

Heat Transfer Experiments of a 1st Stage Blade Cascade for Supercritical CO2 Oxy-Combustion Turbine Application

The results of internally cooled 1st stage blade (S1B) cascade testing in a supercritical CO2 environment is presented. The turbine blade design has been previously established for the end application of an oxy-combustion turbine operating in the Allam-Fetvedt cycle with turbine inlet conditions of 305 bar and 1150°C. The internally cooled blade features leading edge (LE) region impingement cooling, mid-section ribbed serpentine passages, and a pin-finned trailing edge (TE) region before cooling ejection holes. The geometry for the tested blade cascade has a cooled central blade with un-cooled blades on either side to match flowpath areas of the actual turbine. The flowpath reuses internal components previously employed for mid-section region ribbed serpentine passage experiments that established Nusselt number enhancement ratios over a range of Reynolds numbers from 100,000-400,000. New components include flow conditioning plates upstream and downstream of the blade cascade to adequately represent the flow field and blade external heat transfer coefficient profiles for the actual turbine. The cooled central blade utilizes uniform crystal temperature sensors (UCTS) with six sensors each on the blade pressure and suction surfaces distributed radially and from LE to TE. The post-processed UCTS quantified the maximum wall temperature seen at each installed sensor location. The test procedure consisted of establishing supercritical CO2 cooling flow temperature and flow rate and maintaining it throughout the test. The flow rate aims to match that for the actual in-service turbine blade design and is maintained through an orifice restriction to keep the pressure differential between internal cooling flow and external hot flow nearly constant. For the sCO2 flow path external to the blade, temperatures were ramped throughout the test via control of the test loop’s natural gas burner heater. The maximum temperature seen was 468°C and held constant for a duration of 10 minutes at which the blade metal temperature was predicted to be at its maximum before ramping down. For the turbine blade design for service inlet conditions, external flow path computational fluid dynamics (CFD) results and an internal cooling 1-D thermal and hydraulic flow network model using experimentally validated correlations served as thermal finite element (FE) boundary conditions to predict blade metal temperatures. These predicted temperatures were subsequently utilized in a structural FE model to predict blade life ratings dictated by Haynes 282 creep strength data, having a strong dependence on temperature. The boundary conditions experienced during testing are used in the same workflow and compared to the experimental results, with the goal of validating the analysis methodology and providing insight on the uncertainty in local metal temperature predictions.

20 FOSSIL-FUELED POWER PLANTS↗

DOE OSTI2023

Narrow-Channel, Fluidized Beds for Effective Particle Thermal Energy Transport and Storage

Colorado School of Mines (Mines) led this program in collaboration with Sandia National Laboratories (Sandia) to characterize narrow-channel fluidized beds of aluminosilicate particles – supplied by Carbo Ceramics – as a means for releasing high-temperature thermal energy in particle heat exchangers and for capturing concentrated solar energy in indirect particle receivers. Single-channel, heat transfer experiments at Mines and reduced-order 1-D models and 3-D two-fluid, CFD models explored many aspects of counterflow, bubbling fluidized beds (net downward particle flow and upward gas flow) for enhancing particle-wall heat transfer at elevated temperatures. Results at Mines on single-channel test sections consistently showed that mild bubbling fluidization increases particle-wall heat transfer coefficients (h T,w ) regularly by more than 4.0x over h T,w values without fluidization at similar conditions (mean particle diameter d p , bed depth Δz b , and bed particle temperatures T p ). Insights from lab-scale tests and modeling studies provided Nusselt number correlations for h T,w and informed the design and fabrication (by Vacuum Process Engineering) of a nominal 40-kWth, particle-sCO 2 plate heat exchanger (HX) with 12 parallel narrow-channel, fluidized beds bounded by stainless-steel walls with embedded microchannels for high-pressure sCO 2 flows. Tests of the 40-kW th HX at the particle-sCO 2 HX test stand at Sandia's National Solar Thermal Test Facility (NSTTF) were limited, due to HX design, to particle inlet temperatures T p,in ≤ 520°C with maximum sCO 2 outlet temperatures T sCO2,out ≈ 440°C, which are well below design conditions for a primary HX in a sCO 2 power cycle for a Gen-3 concentrating solar power (CSP) plant. Total heat transfer $\dot{Q}_{HX}$ remains relatively constant with increased fluidization for fixed particle and sCO 2 inlet conditions because higher h T,w due to fluidization is offset by increased axial dispersion, which suppresses temperature differences between the particles and sCO 2 in the counterflow configuration. The axial dispersion reduces the effective overall heat transfer coefficient U based on T p,in to values around 200 W m -2 K -1 .

14 SOLAR ENERGY↗

NASA NTRS1994

A Method for Thermal Analysis of Spiral Bevel Gears

A modeling method for analyzing the three-dimensional thermal behavior of spiral bevel gears has been developed. The model surfaces are generated through application of differential geometry to the manufacturing process for face-milled spiral bevel gears. Contact on the gear surface is found by combining tooth contact analysis with three-dimensional Hertzian theory. The tooth contact analysis provides the principle curvatures and orientations of the two surfaces. This information is then used directly in the Hertzian analysis to find the contact size and maximum pressure. Heat generation during meshing is determined as a function of the applied load, sliding velocity, and coefficient of friction. Each of these factors change as the point of contact changes during meshing. A nonlinear finite element program was used to conduct the heat transfer analysis. This program permitted the time- and position-varying boundary conditions, found in operation, to be applied to a one-tooth model. An example model and analytical results are presented.

Handschuh, Robert F.↗

NASA NTRSDate not supplied

Influence of Airfoil Angle of Attack on Ice Accretion Roughness

The influence of airfoil angle attack on roughness evolution and spatial variation was investigated in the Icing Research Tunnel (IRT) at the NASA Glenn Research Center. Two airfoil models were used for the study: a 53.34-cm (21-in.) NACA 0012 model and a 152.4-cm (60-in.) HAARP-II model. For the NACA 0012, the angle of attack was varied from 0° to 3°, and the ice accretion roughness was characterized while keeping the other icing parameters such as freestream velocity, freestream stagnation temperature, accumulation parameter, and median volumetric diameter (MVD) constant. For the HAARP-II, the angle of attack was varied from -1.9°, which is the non-lifting angle of attack for the airfoil, to 3°. A series of accumulation time progression cases for the HAARP-II at 2.3° angle of attack was also performed in Appendix C and Appendix O conditions and compared to the measurements presented by McClain et al. (2018) for the non-lifting angle of attack condition. The results demonstrate the strong influence of the changing local static pressure along the surface influencing the roughness characteristics. A correlation approach for the maximum equivalent sand-grain roughness along the surface of an airfoil is presented and considers the scaled accumulation time, the stagnation point freezing fraction, and the surface pressure relative to the static and stagnation pressures of the flow. Finally, an attempt to relate the maximum roughness quantities to local pressure coefficients and local icing quantities is presented and discussed.

Icing↗

DOE OSTI2022

Machine learning-based optimization of air-cooled heat sinks

Machine learning-based models using Artificial Neural Network (ANN) and greedy search algorithm are used to optimize air-cooled parallel plate-finned heat sinks (PPFHSs) subjected to laminar flow over an extensive range of design parameters. Here, the thermal and hydraulic performances of PPFHSs are represented by heat transfer coefficient (h) and pressure drop (ΔP), respectively. Optimization objectives for PPFHS designs can vary from industry to industry depending on their design priorities. The present study proposes a novel and generalized optimization method that defines practical optimization objectives and provides an accurate optimization process to design effective PPFHSs for a wide range of industrial applications with different design requirements. Three optimization objectives are presented in this study: (i) the largest h PΔ, (ii) the largest h within a specified maximum allowed flow rate, and (iii) the lowest weight that maximizes h for operation within the maximum allowed flow rate. While the shortcoming of the first objective is demonstrated, the other two objectives are found to be suitable for designing effective heat sinks (HSs) across different applications. Results suggest a promising trend from the third objective to develop HSs with ~ 37-68% lower weight, 80-85% reduced ΔP, and negligible penalty in h compared with optimized HSs obtained from the second objective. However, since the third objective leads to HSs with thinner fins, structural analysis should be performed to ensure reliable operation of the HSs.

42 ENGINEERING↗

DOE OSTI2025

Reduced order modeling of a fluidized bed particle receiver for concentrating solar power with thermal energy storage

Oxide particles can serve as both the heat transfer and thermal energy storage (TES) media for next-generation concentrating solar power (CSP) plants where high-temperature TES enables dispatchable electricity from efficient power cycles with firing temperatures above 600 °C. Transferring heat to flowing particles at such high temperatures in a MW-scale central tower receiver remains a challenge for the CSP community. For indirect receivers with external walls to contain the particles, maintaining wall temperatures below the limits of structural metal alloys requires high heat transfer coefficients between the wall and the moving particle stream. Bubbling fluidization of downward-flowing particles can sustain high bed-wall heat transfer coefficients (> 1000 W m -2 K -1 ). Using experimentally calibrated correlations for bed-wall heat transfer and vertical particle dispersion, this study implements an axially discretized zonal model of a counterflow fluidized bed receiver to explore how bubbling fluidization may enable indirect cavity particle receivers. High bed-wall heat transfer coefficients support solar fluxes on angled cavity walls > 200 kW m -2 at peak aperture fluxes of 980 kW m -2 while maintaining external wall temperatures < 950 °C. Lateral particle dispersion enables hotter particles near the receiver leading edge to mix with cooler particles further from the leading edge to lower maximum external wall temperatures. Parametric studies identify how mass fluxes, particle dispersion, and solar concentrations impact indirect receiver thermal efficiency and uniformity for a CSP plant. These studies provide a basis for the design of indirect fluidized-bed cavity receivers that can maintain particle outlet temperatures for TES above 750 °C.

14 SOLAR ENERGY↗

NASA NTRS1951

Analysis of turbulent free-convection boundary layer on flat plate

With the use of Karman's integrated momentum equation for the boundary layer and data on the wall-shearing stress and heat transfer in forced-convection flow, a calculation was carried out for the flow and heat transfer in the turbulent free-convection boundary layer on a vertical flat plate. The calculation is for a fluid with a Prandtl number that is close to 1. A formula was derived for the heat-transfer coefficient that was in good agreement with experimental data in the range of Grashof numbers from 10sup10 to 10sup12. Because of the good agreement between the theoretical formula and the experimental data, the formula may be used to obtain data for high Grashof numbers. The calculation also yielded formulas for the maximum velocity in the boundary layer and for boundary-layer thickness.

Eckert, E R G↗

NASA NTRS1956

Investigation of Heat Transfer From

The convective heat transfer from the surface of an ellipsoidal forebody of fineness ratio 3 and 20-inch maximum diameter was investigated in clear air for both stationary and rotating operation over a range of conditions including air speeds up to 240 knots, rotational speeds up to 1200 rpm, and angles of attack of 0 deg, 3 deg, and 6 deg. The results are presented in the form of heat-transfer coefficients and the correlation of Nusselt and Reynolds numbers. Both a uniform surface temperature and a uniform input heater density distribution were used. The experimental results agree well with theoretical predictions for uniform surface temperature distribution. Complete agreement was not obtained with uniform input heat density in the laminar-flow region because of conduction effects. No significant effects of rotation were obtained over the range of airstream and rotational speeds investigated. Operation at angle of attack had only minor effects on the local heat transfer. Transition from laminar to turbulent heat transfer occurred over a wide range of Reynolds numbers. The location of transition depended primarily on surface roughness and pressure and temperature gradients. Limited transient heating data indicate that the variation of surface temperature with time followed closely an exponential relation.

Lewis, James P.↗

NASA NTRS1984

Multiple-pass trajectories for an aeroassisted orbital transfer vehicle

This paper investigates the use of multiple-pass trajectories for aeroassisted orbital transfer vehicles (AOTV) as a means of reducing the severe aeroheating environment and the extreme sensitivity to off-nominal trajectory and atmospheric conditions. One-, two-, and three-pass trajectories were calculated for AOTV's with ballistic coefficients ranging from 5 to 150 psf. Compared to the single-pass case, the maximum heat rate was reduced by 30 percent for two passes and 45 percent for three passes, while the maximum acceleration was reduced by 40 percent and 55 percent, respectively. The sensitivity of the trajectories to variations in atmospheric and orbital parameters was not significantly reduced.

Rehder, J. J.↗

NASA NTRS1941

The design of fins for air-cooled cylinders

An analysis was made to determine the proportions of fins made of aluminum, copper, magnesium, and steel necessary to dissipate maximum quantities of heat for different fin widths, fin weights, and air-flow conditions. The analysis also concerns the determination of the optimum fin proportions when specified limits are placed on the fin dimensions. The calculation of the heat flow in the fins is based on experimentally verified, theoretical equations. The surface heat-transfer coefficients used with this equation were taken from previously reported experiments. In addition to the presentation of fin-design information, this investigation shows that optimum fin dimensions are inappreciably affected by the differences in air flow that are obtained with different air-flow arrangements or by small changes in the length of the air-flow path.

Biermann, Arnold E↗

NASA NTRS1985

Effects of cooling system parameters on heat transfer in PAFC stack

Analytical and experimental study for the effects of cooling system parameters on the heat transfer and temperature distribution in the electrode plates of a phosphoric acid fuel-cell has been conducted. An experimental set-up that simulates the operating conditions prevailing in a phosphoric-acid fuel-cell stack was designed and constructed. The set-up was then used to measure the overall heat transfer coefficient, the thermal contact resistance, and the electrode temperature distribution for two different cooling plate configurations. Two types of cooling plate configurations, serpentine and straight, were tested. Air, water, and oil were used as coolants. Measurements for the heat transfer coefficient and the thermal contact resistance were made for various flow rates ranging from 16 to 88 Kg/hr, and stack clamping pressure ranging from O to 3448 Kpa. The experimental results for the overall heat transfer coefficient were utilized to derive mathematical relations for the overall heat transfer coefficient as a function of stack clamping pressure and Reynolds number for the three coolants. The empirically derived formulas were incorporated in a previously developed computer program to predict electrodes temperature distribution and the performance of the stack cooling system. The results obtained were then compared with those available in the literature. The comparison showed maximum deviation of +/- 11%.

Abdul-Aziz, Ali A.↗

NASA NTRS1978

A numerical simulation of seasonal stratospheric climate. I - Zonal temperatures and winds

Two numerical experiments were designed to isolate the effects of seasonal and latitudinal variations in longwave radiative transfer processes. The first experiment aimed at computing the rate of temperature change in the stratosphere due to longwave radiative transfer by CO2, H2O and O3 from Ramanathan's (1976) radiative-convective model applied to the troposphere-stratosphere circulation. The second experiment employs the Newtonian cooling approximation in which the rate of temperature change in the stratosphere by longwave radiative transfer is set equal to the product of the Newtonian cooling coefficient 'h' and the departure of the local temperature from a reference temperature. It is shown that the latitudinal temperature distribution of the lower stratosphere is maintained by the combined effects of dynamics, O3 solar heating and the longwave radiative coupling between troposphere and stratosphere. The latitudinal gradient in the troposphere-stratosphere longwave radiative coupling is maximum during winter and spring. The radiative response time (1/h) of the middle and upper stratosphere undergoes significant latitudinal and seasonal variations, largely due to the temperature dependence of h.

Ramanathan, V.↗