• Journal of the Korean Mathematical Society
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• v.60 no.3
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• pp.565-586
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• 2023

We study the Dirichlet problem for the degenerate nonlocal parabolic equation u_t - a(||∇u||²_L²(Ω))∆u = C_b ||u||^β_L²(Ω) |u|^q(x,t)-2 u log |u| + f in Q_T, where Q_T := Ω × (0, T), T > 0, Ω ⊂ ℝ^N, N ≥ 2, is a bounded domain with a sufficiently smooth boundary, q(x, t) is a measurable function in Q_T with values in an interval [q^-, q⁺] ⊂ (1, ∞) and the diffusion coefficient a(·) is a continuous function defined on ℝ₊. It is assumed that a(s) → 0 or a(s) → ∞ as s → 0⁺, therefore the equation degenerates or becomes singular as ||∇u(t)||2 → 0. For both cases, we show that under appropriate conditions on a, β, q, f the problem has a global in time strong solution which possesses the following global regularity property: ∆u ∈ L²(Q_T) and a(||∇u||²_L²(Ω))∆u ∈ L²(Q_T ).

• Korean Journal of Mathematics
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• v.19 no.2
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• pp.233-242
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• 2011

We get a theorem that there exist at least two solutions for the piecewise linear suspension bridge equation with variable coefficient jumping nonlinearity and Dirichlet boundary condition when the variable coefficient of the nonlinear term crosses first two successive negative eigenvalues. We obtain this multiplicity result by applying Leray-Schauder degree theory.

• Journal of the Chungcheong Mathematical Society
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• v.24 no.1
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• pp.121-130
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• 2011

We obtain multiplicity results for the biharmonic problem with a variable coefficient semilinear term. We show that there exist at least three solutions for the biharmonic problem with the variable coefficient semilinear term under some conditions. We obtain this multiplicity result by applying the Leray-Schauder degree theory.

• Journal of Korea Water Resources Association
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• v.49 no.12
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• pp.1015-1025
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• 2016

In general, manholes installed as urban drainage facilities are a variety forms such as straight path manholes, 90 degree bend manhole, three-way combining manhole, and four-way combining manhole. In particular, the surcharged flow at a four-way manholes installed in the downstream of urban sewer system is the main cause of the urban inundation caused by the energy loss. Therefore, it is necessary to analyze the flow characteristics and estimate the head loss coefficients at surcharged four-way combining manholes. The hydraulic experimental apparatus which can change the manhole shapes (square, circle) and flow ratios were installed to estimate the head loss coefficients. In the experiments, two inflows ($Q_m$, $Q_{lat}$) were varied from 0 to $4.8{\ell}/sec$ and 24 combinations were tested in total. The flow ratios $Q_{lat}/Q_{out}$ were varied from 0 to 1 for a total flow $Q_{out}$ ($Q_{out}=Q_m+2Q_{lat}$) of 2, 3, 4, and $4.8{\ell}/sec$, respectively. The variation of head losses were strongly influenced by the lateral inflow because the head loss coefficient increases as the flow ratios $Q_{lat}/Q_{out}$ increases. It was estimated head loss coefficients of the circular manhole is slightly lower than those of the square manhole. However, there was no significant difference of head loss as discharges change. The range of head loss coefficients at four-way combining manhole according to the change of the lateral inflow ratio was estimated to be 0.4 to 0.8. Also, the relation equations between the head loss coefficients (K) and the lateral inflow ratios ($Q_{lat}/Q_{out}$) were suggested in this paper.

• Clean Technology
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• v.23 no.2
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• pp.205-212
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• 2017

We investigated the performance of a jet loop reactor (JLR) with the two-fluid venturi-type swirl nozzle (TVSN) during experiment for ammonia removal by air stripping from a synthetic wastewater, and compared it with that of a JLR with the two-fluid venturi-type conventional nozzle (TVCN), with the variation of pH, liquid circulation rate ($Q_L$), and air flow rate ($Q_G$). Their performance levels were compared based on the ammonia removal efficiency and overall mass transfer coefficient ($K_La$). Investigated parameters in a JLR were pH (10-12), air flow rate ($Q_G=5-20L\;min^{-1}$), and liquid circulation rate ($Q_L=25-35L\;min^{-1}$). Throughout the experiment, the ammonia removal efficiency and $K_La$ in a JLR with TVSN was higher than in a JLR with TVCN. This may be due to the enhanced turbulent intensity by swirling flow formed in the JLR with TVSN compared to that with TVCN. Further, we obtained higher $K_La$ when pH, $Q_L$ and $Q_G$ were increased. In particular, $K_La$ was increased more efficiently by increasing $Q_G$ than by increasing pH and $Q_L$.

• Journal of Korea Water Resources Association
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• v.49 no.7
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• pp.615-623
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• 2016

This Study calculated the Submerged Flow Characteristics and Discharge coefficient by the rising angular change of the Improved-Pneumatic-Movable. According to the result, the smaller the ratio of weir height and weir length (L/W) or the weir standing angle, the bigger of the downstream head ($H_2$). The change of discharge reduction factor ($Q_s/Q_1$), by the hight from weir crest to downstream surface and the ratio form weir crest to upstream water height ($h_t/H$), was decreased when the $h_t/H$ closed to number 1. Although the weir water depth of the down-stream was shallower level than the up-stream, the velocity was faster then before. And the more the flow, the less the gab between the upper and lower reaches level. And when the same flow condition, the downstream head ($H_2$) was increased when the L/W was bigger. The Submerged Flow Discharge coefficient of Improved-Pneumatic-Movable weir was made by the upstream approach flow head and the upper lower stream flow condition, not by the physical data of Movable weir.

• Applied Chemistry for Engineering
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• v.25 no.2
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• pp.142-146
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• 2014

The separation of nitrogen heterocyclic compound (NHC) contained in a model coal tar fraction of nine components system was investigated by distribution equilibrium. The model coal tar fraction comprising NHC group (NHCs; indole (In), quinoline (Q), iso-quinoline (iQ), quinaldine(Qu)), bicyclic aromatic compound group (BACs; 1-methylnaphthalene (1MN), 2-methylnaphthalene (2MN), dimethylnaphthalene (DMN)), biphenyl (Bp) and phenyl ether (Pe) and the aqueous methanol were used as the raw materials and the solvent of this work, respectively. A batch-stirred tank was used as the liquid-liquid contact unit of this work. The distribution coefficient of NHCs increased by increasing the equilibrium operation temperature, whereas the selectivity of NHCs with respect to BACs decreased. Decreasing the initial volume ratio of water to the solvent resulted in deteriorating the selectivity of NHCs in reference to BACs, but improving the distribution coefficients of NHCs. At a fixed experimental condition, the sequence of the distribution coefficient and the selectivity with reference to BACs for each groups was increased in order of NHCs > Bp > BACs > Pe and NHCs > Bp> Pe, respectively. Also, the sequence of the distribution coefficient for entire compounds was in order of In > iQ = Q > Qu > Bp > 1MN = 2MN > Pe > DMN. The maximum yield of NHCs and the selectivity of NHCs based on BACs obtained by methanol extraction were 94 and 23%, respectively. Furthermore, the recovery process for NHCs from coal tar was studied by using the experimental results from this work.

• The Magazine of the Society of Air-Conditioning and Refrigerating Engineers of Korea
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• v.8 no.3
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• pp.131-150
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• 1979

Recently only a few correlations between various factors due to the different grades of surface roughness for the nucleate pool boiling have been proposed. The main purpose of this work is to test the validity of these types of correlations between related factors to nucleate pool boiling phenomena. The boiling experiments using distilled water were carried out at the heat flux ranging from $7.4\times10^4\;to\;2.4\times10^5kcal/m^2h$ on the sintered porous metal surface with the cavity diameter of 10, n, 40, 70, $100{\mu}$, respectively, at the atmospheric pressure, To determine the bubble sizes, number of nucleation sites, delay and growth time, frequency of bubble emission and rising velocities of bubbles, the high speed motion picture technique was employed. In the correlation $f{\propto}D_b^n$, where f denotes frequency of bubble emission and $D_b$ departure diameter, n, the power factor of $D_b$, have been found to be from -2 to -10/3. The correlation C in the correlation between heat flux q and density of nucleation sites $\frac{N}{A}$, $q=C(\frac{N}{A})^n$, was appeared to be more crucial than the power factor n. The correlation of the heat flux q to the temperature difference ${\Delta}T$ and the density of nucleation sites$\frac{N}{A}$, was proposed to be $$q-460{\Delta}T^{\frac{5}{4}}=K{\Delta}T{\frac{5}{3}}(\frac{N}{A})^{\frac{2}{3}}$$. The values of heat transfer coefficient obtained in this experiments for the porous sintered metal surface appeared to be very high in comparison with the formerly obtained results for the other surfaces.

• Journal of Korean Tunnelling and Underground Space Association
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• v.14 no.6
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• pp.617-635
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• 2012

In this study, correlations between the rock mass permeability before and after grouting & injection volume and the parameters of Q system were investigated on a grouted rock mass tunnel corresponding to rock class 4 and 5 in terms of Q classification system. As a result, it appears that the lower the Q value is, the higher the before-grouting permeability becomes and the smaller the injection volume of grouting becomes. Also RQD and Jn are the most influencing factors to the permeability of rock mass and the injection volume of grouting. In addition, it turned out that it was very difficult to lower the permeability of rock mass smaller than $1.0{\times}10^{-8}$ m/sec with the ordinary portland cement grout.

• Proceedings of the Korean Society of Agricultural Engineers Conference
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• 1999.10c
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• pp.753-758
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• 1999

Concentration and discharge have been intensively monitored at the drainage canal in a paddy field area during storm-periods. Among 4 storm runoffs, the No. 2 and No. 3 runoff was in the fertilizer application period. The specific load-specific discharge equation L=aQ\ulcorner have different characteristics for the pollutants. The coefficient of b generally shows values of more than 1 for T-N, about 1 for COD\ulcorner, and less than 1 for T-P. For same specific discharge, No. 2 runoff shows higher specific load than other runoffs. For the coefficient of determination of the L-Q equation, COD\ulcorner is higher than T-N and T-P. The mean concentration of direct runoff, significantly depending on the storm events, is 0.6 to 8.3mg/ιfor T-N, 0.05 to 0.51 mg/ι for T-P, and 10.0 to 18.3 mg/ι for COD\ulcorner.