Tion Point Research Articles

The development of forced convection heat transfer near a forward stagnation point with Newtonian heating

A mathematical model for the unsteady forced convection boundary-layer flow near a forward stagna- tion point is considered when there is Newtonian heating on the surface whereby the heat transfer is proportional to the local surface temperature. In a previous paper (Salleh et al. J Eng Math 69:101-110, 2011), a critical value γc, dependent on the Prandtl number σ , of the heat transfer coefficient γ was identified, with solutions for the corresponding steady problem possible only for γ γ c, the solution still continues to large time, now growing exponentially with time. This rate of growth is determined by an eigenvalue problem which we solve numerically for general values of γ and σ and asymptotically for large γ and both large and small σ .

Twinkling fractal theory of the glass transition: Rate dependence and time–temperature superposition

AbstractThe twinkling fractal theory (TFT) of the glass transition temperature Tg provides a new method of analyzing rate effects and time–temperature superposition in amorphous materials. The rate dependence of Tg was examined in the light of new experimental and theoretical evidence for the nature of the dynamic heterogeneity near Tg. As Tg is approached from above, dynamic solid fractal clusters begin to form and eventually percolate rigidity at Tg. The percolation cluster is a solid fractal and to the observer, appears to “twinkle” as solid and liquid clusters interchange in dynamic equilibrium with a vibrational density of states g(ω) ∼ ω. The solid‐to‐liquid twinkling frequencies ωTF are controlled by the Boltzmann population of intermolecular oscillators in excited energy levels of their anharmonic potential energy functions U(x) such that ωTF = ω exp −B(T*2 − T2)/kT in which T* ≈ 1.2Tg. An oscillator changes from a solid to a liquid when a thermal fluctuation causes it to expand beyond its inflection point in the anharmonic potential. This leads to a continuous solid fraction Ps near Tg given by PS ≈ 1−[(1 − pc) T/Tg] where pc ≈ 1/2 is the rigidity percolation threshold. Since g(ω) is continuous from very low to very high frequencies, the complex twinkling dynamics existing near Tg produces a continuous relaxation spectrum with many different length scales and times associated with the fractal clusters. The twinkling frequencies control the kinetics of Tg such that for a given observation time t when the rate γ > 1/t, only those parts of the twinkling spectrum with ω > γ can contribute to relaxation or percolation upto time t. The most important results in this article are as follows: The TFT describes the rate dependence of Tg, both for DSC thermal heating/cooling rates and DMA frequencies as the classic Tg − lnγ law as Tg(γ) = Tgo + (k/2B) ln γ/γo in which the constant B = 0.3 cal/mol K2. The constant B appears quite universal for the 17 thermoset polymers investigated in this study and 18 linear polymers investigated by others. Many other amorphous metal and ceramic glass materials exhibited the same rate law but required a new B value approximately half that for polymers. The same B = 0.3 value was also used to successfully describe the TTS shift factors using the twinkling fractal frequencies ωTF = ωexp −B(T*2 − T2)/kT, as ln aT(TFT) = exp B(TR2 − T2)/kT, which gave comparable results with the classical WLF equation, log aT = [−C1(T − TR)]/[C2 + (T − TR)]. The advantage of the TFT over the WLF is that C1 and C2 are not universal constants and must be determined for every material, whereas the TFT uses one known constant B which appears to be the same for all polymers. The TFT has also been found to describe the strong and fragile nature of the viscosity behavior of liquids and the rate and temperature dependence of the yield stress in polymers. © 2009 Wiley Periodicals, Inc. J Polym Sci Part B: Polym Phys 47: 2578–2590, 2009

Production of carbon dioxide by Lactococcus lactis strains with attenuated lactate dehydrogenase activity, in pure cultures and in mixed cultures with an acidifying strain

Lactic acid bacteria that produce CO2 are used in the dairy industry to favor the formation of openings in some types of cheeses. This work was undertaken to characterize the gas producing ac- tivity of Lactococcus lactis strains that over-produce CO2 as a result of their attenuated lactate dehydrogenase activity. The method used involved following the concentration of dissolved CO2 and the quantity of CO2 released into the gas phase in standard conditions. Five mutants with attenuated lactate dehydrogenase activity were tested in pure culture in milk. Total CO2 production after 24 h of culture varied between 47 and 88 mmol.L -1 , while that of the parental strain was only 17 mmol.L -1 . CO2 was released into the gas phase only after the concentration of dissolved CO2 reached the satura- tion point in the culture medium, i.e. about 29 mmol.L -1 . Its release was then linear vs. pH. Co-cultur- ing these mutants with an acidifying strain of L. lactis increased the rate of acidification of cultures and reduced CO2 production and the pH below which CO2 was released into the gas phase. This effect increased with the size of the inoculum of the acidifying strain. These results show that very different changes in pH and CO2 production can be obtained by using strains L. lactis strains with attenuated lactate dehydrogenase activity and by the conditions of combining these strains with an acidifying Lactococcus. For a given cheese technology, this could lead to a more precise determination of the optimal characteristics of acidification and CO2 production for the formation of openings. Lactococcus lactis / CO2 / lactate dehydrogenase / cheese

渦流崩壊を伴う管内旋回流の速度分布測定

The oil tracer injection method was applied to measure the velocity profiles of a swirling water flow in the presence of a vortex breakdown. Droplets of kerosene mixed with white paint were used as the tracer particles, and photographs of their loci were taken with the help of a stroboscope in order to determine the velocity. Axial and swirl velocity profiles were measured for three types of vortex breakdown, viz. triangular sheet, axisymmetric and spiral types, from the inlet section of the test pipe to the position of breakdown. It was found that in the cases of the axisymmetric and spiral types the break- down was preceded by an abrupt deceleration near the axis, and was characterized by a stagna- tion point on the axis, while in the triangular sheet case the axial velocity profile was nearly uniform at the position of breakdown.In addition, the type and position of breakdown were observed by color tracer injection method. When the swirl ratio was kept constant at the inlet section of the test pipe, the position of breakdown was found to shift downstream with an increase of the REYNOLDS number.

Spring Run off Forecasts from Snow Assessments in the Malmagen Area at 62° N in Sweden

The spring run-off was forecast by evaluating the snow pack, the precipitation, the evaporation and the change in water and soil moisture during the melt season. The snow pack is the most important run-off factor. A snow map has been made up from a number of measuring points to serve as ground truth (key) in order to simplify the methods of as- sessing the snow pack, i.e. measuring the snow depth and de- termining the snow density along some suitable profiles. The height above sea level has to be determined for every observa- tion point. The results obtained deviated at the most 10% from results gained by the snow map. The run-off forecasts proved between 2% too low and 20% too high for three investigation areas during two subsequent years. Aerial photographs of the investigation area have suggested a connection between the percentage of snow covered and the remaining run-off during two years.

A survey of research on the simulation startup problem

To reduce the effects of initial conditions on the results of a simulation experiment, several authors have proposed startup policies that specify how to minimize the warmup period and identify the trunca tion point beyond which observations are to be re corded and analyzed. Other approaches to this prob- Zem have used results from time-series analysis and queueing theory. This paper surveys research on the simulation startup problem; a companion paper which follows presents a procedure for evaluating startup policies when the mean of the truncated sample is to be used to estimate the steady-state mean of the underlying process.

Generalized Theory of Condensing Systems. V

Discussions are given of the validity of the G-condition, which was used as the start­ ing point of the theory of condensing systems in the author's previous papers, and which was considered to represent the essential features of the volume-dependent cluster integrals of the physical real systems. In particular, for classical systems with two-body forces of finite range, the concept of maximum length of a cluster is introduced, and, with the use of this, some theorems are established which are useful for testing the validity of (G· 3) [which is the third item of the G-condition and assumes the independence, upon u (volume per molecule), of the contribution per molecule to the (infinitely large) cluster integral in some range of values of u]. The validity of the assumptions in the theorems is discussed from the physical point of view. In this connection, some arguments are made about the analytical properties of the condensa­ tion point, strongly supporting the identity of the condensation point of the classical real system and that of the (0) -system (i. e. the system consisting of volume-independent cluster integrals). Some remarks are given on the G-condition in the case of the general system (quantal or classical). Finally, analytical examples of functions satisfying the G-condition are shown.

Blunt-Body Heat Transfer at Hypersonic Speed and Low Reynolds Numbers

with the computed value given by the analysis of Fay and Riddell using the actual measured pressure gradient which, in turn, agrees with the modified Newtonian formula; therefore, the analytical results are made nondimensional with respect to the value given by the analysis of Fay and Riddell. In order to make a correct comparison between these results and others, one must insure that the Reynolds number is calculated in the same way, and the qzeTO vorticity used is equal to the value given by the Fay and Riddell method, with the actual pressure gradient at the stagnation point. If these points are kept in consideration , then the results given by the methods of Refs. 2-4 are apparently in good agree­ ment with the experimental results and with the analysis of Ref. 1. Fig. 1 presents a comparison between experimental results, the results of Cheng's method, and the method of Ref. 1. The figure has been obtained in the following way. The ana­ lytical data of CH published in Ref. 2 have been used. These values have been divided by the CH value given by the Fay and Riddell method, using the actual pressure gradient at the stagna­ tion point of a sphere. In the figure other experimental results published by Witliff and Wilson are also included.4 In Fig. 11 of Ref. 4, the results of Ref. 4 and those of Ref. 1 are compared. Again, the differences are small. Similar considerations appear to be valid for the numerical comparison made in Ref. 3. In this case the ratio between the heat transfer with and without vorticity is given in the form 1 + Ke, where e is a function of the Reynolds number and Mach number. First, it is not .clear from the report if the value of heat transfer with zero vorticity obtained for this analysis is in agreement with the value given by Fay and Riddell or with experiments. We are discussing differences of 10 percent; therefore, any small difference in the value for zero vorticity is surely important. The second point is that some of the numbers presented in the report do not seem consistent with the definitions used. Specifically, on p. 43 of Ref. 3 a numerical analysis for Ma> = °°, for 7 = 7/5, is presented. The results are compared with results of Ref. 1 at Mm = 8. In this process the following transformation is presented [Eq. (3-28)]: Re«_A>_R:/hi~

Population Growth in the Puget Sound Region

Acting upon the suggestion of ter highway. News of the discov an English geographer that ninetyery of gold in California came by nine percent of geography can be boat in 1848 and almost depopulat expressed in maps, a series of seved the struggling settlements. A en dot and circle maps has been territorial census taken in 1849 prepared to show the growth of showed 304 people in all Oregon Puget Sound cities by census denorth of the Columbia River, only cades from 1870 to 1930. The re189 of whom were American citi marks that follow represent an atzens. By 1851 many of the origin tempt to evaluate some of the geoal settlers had returned from the graphic conditions that help to exgold fields bringing with them not plain the facts thus illustrated. only increased capital and new re Old Fort Ni squally, the first cruits> but what was more valu white settlement on Puget Sound, able> knowledge that San Fran was established by the Hudson's Cisco offered a ready market for Bay Fur Co. as an agricultural stajbe mb€T aac* agricultural pro tion and transfer point in 1833. ducts of the Sound Region. The The permanent occupation of the federal census of 1850 had already region began a few years later, reflected this return, a total of however, through the expansion of i ft P®r®ons bein£ counted north American settlement northward °* tbe Columbia, from the Willamette Valley. TurnThe decade from 1850 to 1860 water, at the head of Budd's Inlet was the pioneer period of settle where the eighty-five foot fall of ment in the Puget Sound Region, the Deschutes River within three The economic possibilities of the hundred feet provided power for Sound littoral were thoroughly in a mill site, was settled in 1845. vestigated and their development From this location contact with begun. By 1855 there Were six the -Columbia River settlements teen saw-mills in operation at wide was relatively easy by way of the ly scattered locations ; crews of numerous prairies and the Cowlitz men at work getting out logs, piles River. Fertile prairies nearby enand ship's spars along the water's couraged subsistence agriculture, edge; coal had been discovered at difficult elsewhere along the heavseveral easily accessible locations ily wooded shores of the Sound. and was soon being shipped in The equivalent of a cash crop exsmall quantities to California ; in isted in hand-split shingles from iad, the economic life of the region straight grained Western Red Cewas well established. By 1860 there dar which could be exchanged for were 11,000 people in Washington supplies at the Hudson's Bay Co. Territory, about half of whom were store at Fort Nisqually. located in the Sound region. Once the westward moving wave The development of towns pro of American settlement had reachceeded slowly during the next two ed Puget Sound, it spread rapidly decades. The census of 1870 shows along the shores of this great waonly two cities with a population