Exponential Periods Research Articles

Heat transfer and critical heat flux of subcooled water flow boiling in a HORIZONTAL circular tube

The steady-state turbulent heat transfer (THT) due to exponentially increasing heat inputs with various exponential periods (Q=Q0exp(t/τ), τ=6.55–21.81s) were systematically measured with the flow velocities, u, of 4.15, 7.05, 10.07 and 13.50m/s by an experimental water loop flow. Measurements were made on a 6mm inner diameter, a 59.2mm effective length and a 0.4mm thickness of HORIZONTAL Platinum (Pt) circular test tube. The relation between the steady-state turbulent heat transfer and the flow velocity was clarified. The steady state nucleate boiling heat transfer (NBHT) and the steady state critical heat fluxes (CHFs) of the subcooled water flow boiling for HORIZONTAL SUS304 circular test tube were systematically measured with the flow velocities (u=3.93–13.86m/s), the outlet and inlet subcoolings (ΔTsub,out=60.40–130.30K and ΔTsub,in=81.30–154.20K), the inlet pressures (Pin=786.29–960.93kPa) and the increasing heat input (Q0exp(t/τ), τ=8.36s). The HORIZONTAL SUS304 test tube of inner diameter (d=6mm), heated length (L=59.4mm), effective length (Leff=48.4mm), L/d (=9.9), Leff/d (=8.06) and wall thickness (δ=0.5mm) with surface roughness (Ra=3.89μm) was used in this work. The NBHT and the steady state CHFs of the subcooled water flow boiling for the HORIZONTAL SUS304 circular test tube were clarified at the flow velocities, u, ranging from 3.93–13.86m/s. The steady-state THT data, the NBHT ones and the steady state CHF ones were compared with the values calculated by authors’ THT correlation, their NBHT ones and their transient CHF ones against outlet and inlet subcoolings based on the experimental data for the VERTICAL circular test tubes with the flow velocities, u, ranging from 4.0 to 42.4m/s. The influences of test tube orientation on the THT, the NBHT and the subcooled flow boiling CHF are investigated into details and the widely and precisely predictable correlations of the THT, the NBHT and the transient CHFs against outlet and inlet subcoolings in a HORIZONTAL circular test tube are derived based on the experimental data. The THT correlation, the NBHT ones and the transient CHF ones for the HORIZONTAL test tube can describe the THT data, the NBHT ones and the subcooled flow boiling CHF ones for the wide ranges of ΔTsub,out, ΔTsub,in and u obtained in this work within ±15% difference.

Computational study of turbulent heat transfer for heating of water in a short vertical tube under velocities controlled

The steady-state turbulent heat transfer coefficients in a short vertical Platinum (Pt) test tube for the flow velocities (u = 4.11–41.07 m/s), the inlet liquid temperatures (Tin = 296.47–310.04 K), the inlet pressures (Pin = 810.40–1044.21 kPa) and the increasing heat inputs (Q0 exp(t/τ), exponential periods, τ, of 6.04–23.66 s) were systematically measured by an experimental water loop comprised of a multistage canned-type circulation pump with high pump head. Measurements were made on a 59.2 mm effective length and its three sections (upper, mid and lower positions), which were spot-welded four potential taps on the outer surface of the Pt test tube of a 6 mm inner diameter, a 69.6 mm heated length and a 0.4 mm thickness. Theoretical equations for turbulent heat transfer in a circular tube of a 6 mm in diameter and a 636 mm long were numerically solved for heating of water with heated section of a 6 mm in diameter and a 70 mm long by using PHOENICS code under the same condition as the experimental one considering the temperature dependence of thermo-physical properties concerned. The surface heat flux, q, and the average surface temperature, Ts,av, on the circular tube solved theoretically under the flow velocities, u, of 4.11–41.07 m/s were compared with the corresponding experimental values on heat flux, q, versus the temperature difference between average inner surface temperature and liquid bulk mean temperature, ΔTL [=Ts,av − TL, TL = (Tin + Tout)/2], graph. The numerical solutions of q and ΔTL are almost in good agreement with the corresponding experimental values of q and ΔTL with the deviations less than ±10% for the range of ΔTL tested here. The numerical solutions of local surface temperature, (Ts)z, local average liquid temperature, (Tf,av)z, and local liquid pressure drop, ΔPz, are within ±10% of the corresponding experimental data on (Ts)z, (Tf,av)z and ΔPz. The thickness of the thermal boundary layer, δTBL [=(Δr)out/2], and the non-dimensional thickness of thermal boundary layer, yTBL+[=(fF/2)0.5(ρluδVSL/μl)], for the turbulent heat transfer in a short vertical tube under velocities controlled are clarified based on the numerical solutions. It was confirmed in this study that authors’ steady-state turbulent heat transfer correlation based on the experimental data (Hata and Noda, 2008) can not only describe the experimental data of steady-state turbulent heat transfer but also the numerical solutions within ±10% difference for the wide ranges of temperature differences between heater inner surface temperature and liquid bulk mean temperature (ΔTL = 5–200 K) and flow velocities (u = 4.01–41.07 m/s).

Computational Study of Turbulent Heat Transfer for Heating of Water in a Vertical Circular Tube

The steady-state turbulent heat transfer coefficients in a vertical circular Platinum (Pt) test tube for the flow velocities (u=4.22 to 21.45 m/s), the inlet liquid temperatures (Tin=308.20 to 311.77 K), the inlet pressures (Pin=834.04 to 910.23 kPa) and the increasing heat inputs (Q0exp(t/τ), exponential periods, τ, of 6.04 to 32.13 s) were systematically measured by an experimental water loop comprised of a multistage canned-type circulation pump with high pump head. Measurements were made on Pt test tubes of 3, 6 and 9 mm inner diameters, 32.7, 69.6 and 49.6 mm heated lengths and 0.5, 0.4 and 0.3 mm thicknesses, respectively. Theoretical equations for turbulent heat transfer in circular tubes of 3, 6 and 9 mm in diameter and 492, 636 and 616 mm long were numerically solved for heating of water with heated sections of 3, 6 and 9 mm in diameter and 33, 70 and 50 mm long by using PHOENICS code under the same condition as the experimental one considering the temperature dependence of thermo-physical properties concerned. The surface heat flux, q, and the average surface temperature, Ts,av, on the circular tubes solved theoretically under the flow velocities, u, of 4.22 to 21.45 m/s were compared with the corresponding experimental values on heat flux, q, versus the temperature difference between average inner surface temperature and liquid bulk mean temperature, ΔTL [=Ts,av-TL, TL=(Tin+Tout)/2], graph. The numerical solutions of q and ΔTL are almost in good agreement with the corresponding experimental values of q and ΔTL with the deviations less than ±10 % for the range of ΔTL tested here. The numerical solutions of local surface temperature, (Ts)z, and local average liquid temperature, (Tf,av)z, are within ±10 % of the corresponding experimental data on (Ts)z and (Tf,av)z. The thickness of the conductive sub-layer, δCSL [=(Δr)out/2], and the non-dimensional thickness of conductive sub-layer, y+CSL [=(fF/2)0.5ρluδCSL/µl], for the turbulent heat transfer in various vertical tubes are clarified based on the numerical solutions. It was confirmed in this study that authors’ steady-state turbulent heat transfer correlation based on the experimental data [Hata and Noda, 2008] can not only describe the experimental data of steady-state turbulent heat transfer but also the numerical solutions within ±10 % difference for the wide ranges of tube inner diameters (3, 6 and 9 mm), temperature differences between average inner surface temperature and liquid bulk mean temperature (ΔTL=8 to 145 K) and flow velocities (u=4.22 to 21.45 m/s).

ICONE19-43190 TRANSIENT TURBULENT HEAT TRANSFER FOR HEATING OF WATER IN A SHORT VERTICAL TUBE

The transient turbulent heat transfer coefficients in a short vertical Platinum test tube were systematically measured for the flow velocities (u=4.0 to 13.6 m/s), the inlet liquid temperatures (T_<in>=296.93 to 304.81 K), the inlet pressures (Pin=794.39 to 858.27 kPa) and the increasing heat inputs (Q_0 exp(t/τ), exponential periods, τ, of 18.6 ms to 25.7 s) by an experimental water loop comprised of a multistage canned-type circulation pump with high pump head. The Platinum test tubes of test tube inner diameters (d=3 and 6 mm), heated lengths (L=66.5 and 69.6 mm), effective lengths (L_<eff>=56.7 and 59.2 mm), ratios of heated length to inner diameter (L/d=22.16 and 11.6), ratios of effective length to inner diameter (L_<eff>/d=18.9 and 9.87) and wall thickness (δ=0.5 and 0.4 mm) with average surface roughness (Ra=0.40 and 0.45 μm) were used in this work. The surface heat fluxes between the two potential taps were given the difference between the heat generation rate per unit surface area and the rate of change of energy storage in the test tube obtained from the faired average temperature versus time curve. The heater inner surface temperature between the two potential taps was also obtained by solving the unsteady heat conduction equation in the test tube under the conditions of measured average temperature and heat generation rate per unit surface area of the test tube. The transient turbulent heat transfer data for Platinum test tubes were compared with the values calculated by authors' correlation for the steady state turbulent heat transfer. The influence of inner diameter (d), ratio of effective length to inner diameter (L_<eff>/d), flow velocity (u) and exponential period (τ) on the transient turbulent heat transfer is investigated into details and the widely and precisely predictable correlation of the transient turbulent heat transfer for heating of water in a short vertical tube is given based on the experimental data and authors' studies for the transient critical heat fluxes (CHFs) of subcooled water flow boiling in a short vertical tube caused by exponentially, ramp-wise and stepwise increasing heat inputs. The correlation can describe the transient turbulent heat transfer coefficients obtained in this work for the wide range of the temperature difference between heater inner surface temperature and average bulk liquid temperature (ΔT_L=10 to 160 K) with the inner diameters (d=3 to 6 mm), L_<eff>/d (=9.87 to 18.9), the flow velocities (u=4.0 to 13.6 m/s) and the exponential periods (τ=18.6 ms to 25.7 s) within ±15 % difference.

Transient Turbulent Heat Transfer for Heating of Water in a Short Vertical Tube

The transient turbulent heat transfer coefficients in a short vertical Platinum test tube were systematically measured for the flow velocities (u=4.0 to 13.6 m/s), the inlet liquid temperatures (Tin=296.93 to 304.81 K), the inlet pressures (Pin=794.39 to 858.27 kPa) and the increasing heat inputs (Q0 exp(t/τ), exponential periods, τ, of 18.6 ms to 25.7 s) by an experimental water loop comprised of a multistage canned-type circulation pump with high pump head. The Platinum test tubes of test tube inner diameters (d=3 and 6 mm), heated lengths (L=66.5 and 69.6 mm), effective lengths (Leff=56.7 and 59.2 mm), ratios of heated length to inner diameter (L/d=22.16 and 11.6), ratios of effective length to inner diameter (Leff/d=18.9 and 9.87) and wall thickness (δ=0.5 and 0.4 mm) with average surface roughness (Ra=0.40 and 0.45 µm) were used in this work. The surface heat fluxes between the two potential taps were given the difference between the heat generation rate per unit surface area and the rate of change of energy storage in the test tube obtained from the faired average temperature versus time curve. The heater inner surface temperature between the two potential taps was also obtained by solving the unsteady heat conduction equation in the test tube under the conditions of measured average temperature and heat generation rate per unit surface area of the test tube. The transient turbulent heat transfer data for Platinum test tubes were compared with the values calculated by authors’ correlation for the steady state turbulent heat transfer. The influence of inner diameter (d), ratio of effective length to inner diameter (Leff/d), flow velocity (u) and exponential period (τ) on the transient turbulent heat transfer is investigated into details and the widely and precisely predictable correlation of the transient turbulent heat transfer for heating of water in a short vertical tube is given based on the experimental data and authors’ studies for the transient critical heat fluxes (CHFs) of subcooled water flow boiling in a short vertical tube caused by exponentially, ramp-wise and stepwise increasing heat inputs. The correlation can describe the transient turbulent heat transfer coefficients obtained in this work for the wide range of the temperature difference between heater inner surface temperature and average bulk liquid temperature, ΔTL, of 10 to 160 K with d=3 to 6 mm, Leff/d=9.87 to 18.9, u=4.0 to 13.6 m/s and τ=18.6 ms to 25.7 s within ±15 % difference.

ICONE19-43301 COMPUTATIONAL STUDY OF TURBULENT HEAT TRANSFER FOR HEATING OF WATER IN A SHORT VERTICAL TUBE

The steady-state turbulent heat transfer coefficients in a short vertical Platinum (Pt) test tube for the flow velocities (u=4.01 to 13.62 m/s), the inlet liquid temperatures (T_<in>=294.00 to 304.29 K), the inlet pressures (P_<in>=802.12 to 859.08 kPa) and the increasing heat inputs (Q_0exp(t/τ), exponential periods, τ, of 6.04 to 25.67 s) were systematically measured by an experimental water loop comprised of a multistage canned-type circulation pump with high pump head. Measurements were made on a 59.2 mm effective length and its three sections (upper, mid and lower positions), which was spot-welded four potential taps on the outer surface of a 6 mm inner diameter, a 69.6 mm heated length and a 0.4 mm thickness of the Pt test tube. The outer surface temperature distribution of the Pt test tube was also simultaneously observed by an infrared thermal imaging camera at intervals of 3 seconds. Theoretical equations for turbulent heat transfer in a circular tube of a 6 mm in diameter and a 636 mm long were numerically solved for heating of water with heated section of a 6 mm in diameter and a 70 mm long by using PHOENICS code under the same condition as the experimental one considering the temperature dependence of thermo-physical properties concerned. The surface heat flux, q, and the surface temperature, T_s, on the circular tube solved theoretically were compared with the corresponding experimental values on heat flux, q, versus the temperature difference between heater inner surface temperature and liquid bulk mean temperature, ΔT_L [=T_s-T_L, T_L=(T_<in> + T_<out>)/2], graph. The theoretical solutions of q and ΔT_L are almost in good agreement with the corresponding experimental values of q and ΔT_L with the deviations less than ±10 % for the range of ΔT_L tested here. The theoretical solutions of local surface temperature, (T_s)_z, local average liquid temperature, (T_<f,av>)_z, and local liquid pressure drop, ΔP_z, were also compared with the corresponding experimental data on (T_s)_z, (T_<f,av>)z and ΔP_z versus heated length, L, or distance from inlet of the test section, Z, graph, respectively. The theoretical solutions of local surface temperature, (T_s)z and local average liquid temperature, (T_<f,av>)_z are within ±10 % of the corresponding experimental data on (T_s)_z and (T_<f,av>)_z, although those of local liquid pressure drop, ΔP_z, become 37.6 % lower than the experimental ones. It was confirmed in this study that authors' steady-state turbulent heat transfer correlation, Eq. (1), based on the experimental data (Hata and Noda, 2008) Nu_d=0.02Re^<0.85>_dPr^<0.4>(L/d)^<-0.08>(μ_1/μ_w)^<0.14> (1) can not only describe the experimental data of steady-state turbulent heat transfer but also the theoretical solutions within ±10 % difference for the wide ranges of temperature differences between heater inner surface temperature and liquid bulk mean temperature (ΔT_L=5 to 200 K) and flow velocity (u=4.01 to 13.62 m/s).

Twisted-tape-induced swirl flow heat transfer and pressure drop in a short circular tube under velocities controlled

The twisted-tape-induced swirl flow heat transfer due to exponentially increasing heat inputs with various exponential periods ( Q = Q 0 exp( t/ τ), τ = 7, 14 and 23 s) and the twisted-tape-induced pressure drop were systematically measured with mass velocities, G, ranging from 4022 to 15,140 kg/m 2 s by an experimental water loop flow. Measurements were made on a 59.2 mm effective length which was spot-welded two potential taps on the outer surface of a 6 mm inner diameter, a 69.6 mm heated length and a 0.4 mm thickness of platinum circular test tube. The twisted tapes with twist ratios, y [= H/ d = (pitch of 180° rotation)/ d], of 2.39, 3.39 and 4.45 were used in this work. The relation between the swirl velocity and the pump input frequency and that between the fanning friction factor and Reynolds number ( Re d = 2.04 × 10 4 to 9.96 × 10 4) were clarified. The twisted-tape-induced swirl flow heat transfers with y = 2.39, 3.39 and 4.45 were compared with the values calculated by our correlation of the turbulent heat transfer for the empty tube and other worker's one for the circular tube with the twisted-tape insert. The influence of y and Reynolds numbers based on swirl velocity, Re sw , on the twisted-tape-induced swirl flow heat transfer was investigated into details and the widely and precisely predictable correlation of the twisted-tape-induced swirl flow heat transfer was derived based on the experimental data. The correlation can describe for the twisted-tape-induced swirl flow heat transfer for the wide ranges of twist ratios ( y = 2.39–4.45), mass velocities ( G = 4022–15140 kg/m 2 s) and Reynolds numbers based on swirl velocity ( Re sw = 2.88 × 10 4 to 1.22 × 10 5) within −10 to +30% difference.

On the expansion of some exponential periods in an integer base

We derive a lower bound for the subword complexity of the base-b expansion (b ≥ 2) of all real numbers whose irrationality exponent is equal to 2. This provides a generalization of a theorem due to Ferenczi and Mauduit. As a consequence, we obtain the first lower bound for the subword complexity of the number e and of some other transcendental exponential periods.

The SIS Great Circle Epidemic Model

We consider a stochastic SIS model for the spread of an epidemic amongst a population of n individuals that are equally spaced upon the circumference of a circle. Whilst infectious, an individual, i say, makes both local and global infectious contacts at the points of homogeneous Poisson point processes. Global contacts are made uniformly at random with members of the entire population, whilst local contacts are made according to a contact distribution centred upon the infective. Individuals at the end of their infectious period return to the susceptible state and can be reinfected. The emphasis of the paper is on asymptotic results as the population size n → ∞. Therefore, a contact process with global infection is introduced representing the limiting behaviour as n → ∞ of the circle epidemics. A branching process approximation for the early stages of the epidemic is derived and the endemic equilibrium of a major outbreak is obtained. Furthermore, assuming exponential infectious periods, the probability of a major epidemic outbreak and the proportion of the population infectious in the endemic equilibrium are shown to satisfy the same equation which characterises the epidemic process.

The SIS Great Circle Epidemic Model

We consider a stochastic SIS model for the spread of an epidemic amongst a population of n individuals that are equally spaced upon the circumference of a circle. Whilst infectious, an individual, i say, makes both local and global infectious contacts at the points of homogeneous Poisson point processes. Global contacts are made uniformly at random with members of the entire population, whilst local contacts are made according to a contact distribution centred upon the infective. Individuals at the end of their infectious period return to the susceptible state and can be reinfected. The emphasis of the paper is on asymptotic results as the population size n → ∞. Therefore, a contact process with global infection is introduced representing the limiting behaviour as n → ∞ of the circle epidemics. A branching process approximation for the early stages of the epidemic is derived and the endemic equilibrium of a major outbreak is obtained. Furthermore, assuming exponential infectious periods, the probability of a major epidemic outbreak and the proportion of the population infectious in the endemic equilibrium are shown to satisfy the same equation which characterises the epidemic process.

Controlled production of camembert-type cheeses: Part III role of the ripening microflora on free fatty acid concentrations

Phenomena generating FFAs, important flavour precursors, are significant in cheese ripening. In Camembert-like cheeses, it was intended to establish the relationships between the dynamics of FFA concentrations changes and the succession of ripening microflora during ripening. Experimental Camembert-type cheeses were prepared in duplicate from pasteurised milk inoculated with Kluyveromyces lactis, Geotrichum candidum, Penicillium camemberti, and Brevibacterium aurantiacum under aseptic conditions. For each cheese and each cheesy medium, concentrations of FFAs with odd-numbered carbons, except for 9:0 and 13:0, did not change over time. For long-chain FFAs, concentrations varied with the given cheese part (rind or core). K. lactis produced only short or medium-chain FFAs during its growth and had a minor influence on caproic, caprylic, capric, and lauric acids in comparison with G. candidum, the most lipolytic of the strains used here. It generated all short or medium-chain FFAs (4:0-12:0) during its exponential and slowdown growth periods and only long-chain ones (14:0-18:0) during its stationary phase. Pen. camemberti produced more long-chain FFAs (14:0-18:0) during its sporulation. Brev. aurantiacum did not generate any FFAs. The evidence of links between specific FFAs and the growth of a given microorganism is shown.

Metabolic flux analyses for serine alkaline protease production.

The intracellular metabolic fluxes through the central carbon pathways in Bacillus licheniformis in serine alkaline protease (SAP) production were calculated to predict the potential strategies for increasing the performance of the bacilli, by using two optimization approaches, i.e. the theoretical data-based (TDA) and the theoretical data-based capacity (TDC) analyses based on respectively minimum in-vivo SAP accumulation rate and maximum SAP synthesis rate assumptions, at low-, medium-, and high-oxygen transfer conditions. At all periods of low-oxygen transfer condition, in lag and early exponential periods of medium-oxygen transfer (MOT) condition, and SAP synthesis period of high-oxygen transfer (HOT) condition, the TDA and TDC analyses revealed that SAP overproduction capacity is almost equal to the observed SAP production due to the regulation effect of the oxygen transfer. In the growth and early SAP synthesis period and in SAP synthesis period at MOT condition the calculated results of the two analyses reveal that SAP synthesis rate of the microorganism can be increased 7.2 and 16.7 folds, respectively; whereas, in the growth and early SAP synthesis period at HOT condition it can be increased 12.6 folds. The diversions in the biochemical reaction network and the influence of the oxygen transfer on the performance of the bacilli were also presented. The results encourage the application of metabolic engineering for lifting the rate limitations and for improving the genetic regulations in order to increase the SAP production.

Design rules and equivalent capacity for bufferingof Pareto source

Formulae are developed that act as design rules when buffering an ON-OFF source with long range dependent (LRD) characteristics. These can be used to predict the buffer overflow probability, or the equivalent capacity required to ensure a specified buffer overflow probability. The traffic source has Pareto distributed ON and OFF periods, and therefore this analysis can be seen as an extension of earlier results for exponential ON and OFF periods.

INDIVIDUAL EQUILIBRIUM DYNAMIC ROUTING IN A MULTIPLE SERVER RETRIAL QUEUE

Customers arrive sequentially to a service system where the arrival times form a Poisson process of rate λ. The system offers a choice between a private channel and a public set of channels. The transmission rate at each of the public channels is faster than that of the private one; however, if all of the public channels are occupied, then a customer who commits itself to using one of them attempts to connect after exponential periods of time with mean μ−1. Once connection to a public channel has been made, service is completed after an exponential period of time, with mean ν−1. Each customer chooses one of the two service options, basing its decision on the number of busy channels and reapplying customers, with the aim of minimizing its own expected sojourn time. The best action for an individual customer depends on the actions taken by subsequent arriving customers. We establish the existence of a unique symmetric Nash equilibrium policy and show that its structure is characterized by a set of threshold-type strategies; we discuss the relevance of this concept in the context of a dynamic learning scenario.

Asymptotic results for multiplexing subexponential on-off processes

Consider an aggregate arrival process A N obtained by multiplexing N on-off processes with exponential off periods of rate λ and subexponential on periods τon. As N goes to infinity, with λN → Λ, A N approaches an M/G/∞ type process. Both for finite and infinite N, we obtain the asymptotic characterization of the arrival process activity period. Using these results we investigate a fluid queue with the limiting M/G/∞ arrival process A t ∞ and capacity c. When on periods are regularly varying (with non-integer exponent), we derive a precise asymptotic behavior of the queue length random variable Q t P observed at the beginning of the arrival process activity periods where ρ = 𝔼A t ∞ &amp;lt; c; r (c ≤ r) is the rate at which the fluid is arriving during an on period. The asymptotic (time average) queue distribution lower bound is obtained under more general assumptions regarding on periods than regular variation. In addition, we analyse a queueing system in which one on-off process, whose on period belongs to a subclass of subexponential distributions, is multiplexed with independent exponential processes with aggregate expected rate 𝔼e t . This system is shown to be asymptotically equivalent to the same queueing system with the exponential arrival processes being replaced by their total mean value 𝔼e t .

Asymptotic results for multiplexing subexponential on-off processes

Consider an aggregate arrival process AN obtained by multiplexing N on-off processes with exponential off periods of rate λ and subexponential on periods τon. As N goes to infinity, with λN → Λ, AN approaches an M/G/∞ type process. Both for finite and infinite N, we obtain the asymptotic characterization of the arrival process activity period.Using these results we investigate a fluid queue with the limiting M/G/∞ arrival process At∞ and capacity c. When on periods are regularly varying (with non-integer exponent), we derive a precise asymptotic behavior of the queue length random variable QtP observed at the beginning of the arrival process activity periods where ρ = 𝔼At∞ &lt; c; r (c ≤ r) is the rate at which the fluid is arriving during an on period. The asymptotic (time average) queue distribution lower bound is obtained under more general assumptions regarding on periods than regular variation.In addition, we analyse a queueing system in which one on-off process, whose on period belongs to a subclass of subexponential distributions, is multiplexed with independent exponential processes with aggregate expected rate 𝔼et. This system is shown to be asymptotically equivalent to the same queueing system with the exponential arrival processes being replaced by their total mean value 𝔼et.

Transient Pool Boiling Heat Transfer—Part 2: Boiling Heat Transfer and Burnout

Transient boiling heat transfer for exponential heat input to a platinum wire supported horizontally in a pool of water was investigated. Transient boiling heat transfer coefficient, transient DNB heat flux, and transient maximum heat flux were obtained for exponential periods ranging from 5 ms to 10 s and for system pressures ranging from 0.1 to 2.1 MPa. Transient boiling heat transfer coefficient after the commencement of boiling becomes lower than the steady boiling heat transfer coefficient at the same heat flux. This was explained to be as a result of the time lag of the activation of originally flooded cavities for the increasing rate of the heat input. Initial heat flux was varied from zero to near the steady maximum heat flux. Effect of initial boiling condition on transient DNB and maximum heat fluxes was negligible. Mechanism of transient boiling heat transfer beyond steady DNB heat flux was suggested.

Transient Pool Boiling Heat Transfer—Part 1: Incipient Boiling Superheat

Incipient boiling superheat for exponentially increasing heat inputs to a platinum wire supported horizontally in a pool of water was measured for exponential periods ranging from 5 ms to 10 s and for subcoolings ranging from 25 to 75K under atomospheric pressure. The heat transfer coefficient before the initiation of boiling was related to those by conduction and by natural convection. The heat flux at the incipient boiling point increased with the decrease in the period. The log-log plot of the heat flux against the superheat at the incipient boiling point had a single asymptotic line of slope 2 which was independent of subcoolings in the high heat flux region. On the other hand, as the heat flux decreased to zero, the superheat tended to approach to a constant value for each subcooling. This asymptotic superheat at zero heat flux was higher for higher subcooling. Transient incipient boiling superheat was reasonably explained by the combination of two kinds of incipient boiling models.

Chinese hamster cell monolayer cultures: II. X-ray sensitivity and sensitization by 5-bromodeoxycytidine in the exponential and plateau periods of growth

Survival following X-irradiation of HA2 Chinese hamster cells in monolayer culture during various periods of growth was described. Relatively small changes in D 0 and ñ occurred as culture age increased. 72-h exposure to 5 × 10 −5 M BCdR produced marked radiosensitization of cells from cultures in exponential growth. With cells from transition and plateau period cultures similarly treated, biphasic survival curves were obtained, demonstrating that only part of the cell population became sensitized. The size of this fraction of sensitized cells agreed with predictions based on measured cell renewal in plateau period cultures. Monolayer cell culture in the plateau period of growth is proposed as a useful in vitro model for in vivo tumor cell behavior.

EVALUATION OF AN ISOTOPE CORONARY PATENCY TEST BY ANGIOGRAPHY.

Following the rapid injection of a small volume of gamma-emitting isotope into a peripheral vein, a collimated radiation detector positioned over any portion of the body surface will respond to the primary passage of this radioactive material through the vascular channels in its field of detection. This response may be referred to as the “activity-time curve.” The small volume of isotope or radioactive “bolus” is diluted and elongated as it traverses the circulation. Consequently, the activity-time curves become gradually more prolonged as they are recorded by similar detectors at increasing distances from the point of injection. This prolongation is associated with decreased rates of disappearance of activity at any point of observation. In other words, the slope of the descending portion, “downslope,” of the activity-time curve decreases as the bolus is elongated. Thus, for instance, the downslope of the right heart curve will be steeper than the downslope of the left heart or aortic curve. Similarly, the aortic curve downslope is steeper than that of the brain curve (3). The downslope of the left heart curve, however, instead of being steeper is more prolonged than those recorded over the aorta or brain. This is exactly the opposite from what might be expected according to the bolus dilution principle that is mentioned above. This prolongation of the left heart downslope was reported by Mena et al. (5), who attributed it to the fraction of the radioactive bolus that accumulates in the coronary vascular bed during the washout of activity from the left ventricle. Hydrodynamic and mathematical models have not only suggested that such an effect might occur but have predicted its magnitude (4). The more rapid the coronary filling rate the greater the prolongation effect. Since constrictions in the coronary arteries would be expected to decrease the rate of filling, a relative lack of left heart curve prolongation in the coronary patient might be predicted. To estimate the magnitude of this prolongation effect, the left heart curve is compared with curves produced by the same bolus more distally in the circulation. The aorta, brachial artery, femoral artery, and brain have been investigated as possible sites for the measurement of activity or concentration curves for this comparison. The most promising results have derived from the use of the brain curve as a reference or base line. Since the slopes of these activity-time curves are very nearly exponential, they can be characterized by their exponential half periods (T1/2). Further, the difference between two downslopes may be expressed as the ratio of their T1/2 values. This ratio is an expression of the relative prolongation of the downslope of the left heart curve and, since this effect is thought to be related to coronary blood flow, the ratio will be referred to as the coronary flow index (C.F.I.), thus: