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The objective of this study is to design a hull-mounted sonar dome of a ship using OpenFOAM with a bulbous bow effect at cruise speed in calm water. Verification and validation for the original sonar dome simulation are conducted. Next, the 1.44 million grid size is selected to study different dome lengths. By protruding the dome forward 7.5% of the ship’s length, the optimal 17% resistance reduction is achieved and is mainly caused by the pressure resistance decrease. The optimal sonar dome not only functions in the same way as a bulbous bow, but the viscous flow behaviors are also improved. The protrusion corresponding to 90 deg phase lag reduces the bow wave amplitude. The flow acceleration outside the boundary layer and ship wake velocity are higher coinciding with the much lower total resistance. A smaller flow separation and thinner boundary layer are also observed behind the sonar dome because its back slope is less steep. The high pressure covers a smaller area around the bow, and the smaller bow wave crest does not hit the ship’s flare to form high pressure. Consequently, the lower high pressure on the dome front and higher low pressure on the dome back result in the decreases in pressure resistance. The vortical structures are also improved.

In fiber drawing, axial tension is applied to long, thin viscous threads to increase their length and consequently reduce their cross-sectional area. This process is used to manufacture rods and threads of glass and polymer such as optical fibers and filaments for textiles. Drawing is described mathematically using the Trouton model for extensional flow in a long, narrow cylinder. This leading-order description gives simple expressions for fiber radius and one-dimensional axial velocity in the long, slender limit. In this paper we determine the next-order corrections, showing that they can be an order of magnitude larger than previously assumed.

Numerical simulations of steady and unsteady viscous flows are presented by adopting two different numerical methodologies: the Smoothed Particle Hydrodynamics formulation implemented in the open-source code DualSPHysics and an in-house lattice Boltzmann code based on a concise central-moments scheme. Both methods employ a weakly compressible assumption to simulate incompressible flow, which means the fluid is assumed barotropic and the density and pressure are related through an equation of state. The accuracy of the two approaches is evaluated against well-defined and consolidated benchmark tests. Advantages and disadvantages of the two methodologies are discussed and substantiated by quantitative comparisons that focus on accuracy and efficacy of the two methodologies against other well-established computational methods. Overall, both formulations proposed herein are able to capture the relevant flow physics with a good level of accuracy when compared to other more affirmed techniques. Remarkably, this is observed in spite of the proposed two methods lacking key strategies commonly used in grid-based methods, such as adaptive mesh refinement.

This article considers the hydrodynamic problem of an oblique flow of a viscous incompressible fluid around the tip of a dendritic crystal. Approximate analytical solutions of Oseen's hydrodynamic equations are obtained in 2D and 3D cases using special curvilinear coordinates. It is shown that the projections of the fluid velocity change significantly with a change in the flow slope and Reynolds number. The theory developed in this work has a limiting transition to the previously known solutions for the rectilinear (without tilt) fluid flow around a dendrite. © 2021 John Wiley & Sons, Ltd. Russian Foundation for Basic Research, РФФИ: 20-08-00199; Ministry of Education and Science of the Russian Federation, Minobrnauka: FEUZ-2020-0057 This work contains two parts, theoretical and numerical. The first of them was supported by the Russian Foundation for Basic Research (project no. 20-08-00199). The second part was supported by the Ministry of Science and Higher Education of the Russian Federation (project no. FEUZ-2020-0057).

An exhaustive numerical investigation is carried out to analyze the role of an isothermal heated thin fin on fluid flow and temperature distribution visualization in an enclosure. Natural convection within square enclosures finds remarkable pragmatic applications. In the present study, a finite difference approach is performed on two-dimensional laminar flow inside an enclosure with cold side walls and adiabatic horizontal walls. The fluid flow equations are reconstructed into vorticity - stream function formulation and these equations are employed utilizing the finite-difference strategy with incremental time steps. The parametric study includes a wide scope of Rayleigh number, Ra, and inclination angle ϴ of the thin fin. The effect of different Rayleigh numbers ranging Ra = 104-106 with Pr=0.71 for all the inclination angles from 0°-360° with uniform rotational length of angle 450 of an inclined heated fin on fluid flow and heat transfer have been investigated. The heat transfer rate within the enclosure is measured by means of local and average Nusselt numbers. Regardless of inclination angles of the thin fin, a slight enhancement in the average Nusselt number is observed when Rayleigh number increased for both the cases of the horizontal and vertical position of the thin fin. When the fin has inclined no change in average Nusselt number is noticed for distinct Rayleigh numbers.

Several new devices that demonstrate a variety of known phenomena in fluid dynamics are presented. These add on to a recent collection of demonstrations and follow the same design features as documented earlier (self-contained, easy to use, low cost). Descriptions are provided to enable replication by others, using readily available materials. The significance of each demonstration is outlined and background information on the relevant physics can be found in the cited references. The devices can be generally used in classroom lecture demonstrations, outreach activities, or other student-based projects. However, pedagogical details are left to readers’ discretion, depending on the scope of local interests and constraints. Video samples of demonstrations are available online.

This paper presents the results of an investigation of the influence of the aluminum-powder concentration on the thermomechanical characteristics of the composites based on the high-density polyethylene. We show that use of a compatibilizer—maleic anhydride–polyethylene graft copolymer—in a mixture with high-density polyethylene has an influence on the regularity of variation of the thermomechanical curves. We study the influence of various cross-linking agents (dicumyl peroxide and sulfur) on the thermomechanical properties of composites. At a particular dicumyl peroxide and sulfur concentration, the composites might reside in three physical states: solid, highly elastic, and viscous flow.

Silica ceramic cores have played an important part in the manufacture of hollow blades due to their excellent chemical stability and moderate high-temperature mechanical properties. In this study, silica-based ceramics were prepared with Al2O3 addition by stereolithography, and the influence of Al2O3 content on mechanical properties of the silica-based ceramics was investigated. The Al2O3 in silica-based ceramics can improve the mechanical properties by playing a role as a seed for the crystallization of fused silica into cristobalite. As a result, with the increase of Al2O3 content, the linear shrinkage of the silica-based ceramics first decreased and then increased, while the room-temperature flexural strength and the high-temperature flexural strength first increased and then decreased. As the Al2O3 content increased to 1.0 vol%, the linear shrinkage was reduced to 1.64% because of the blocked viscous flow caused by Al2O3. Meanwhile, the room-temperature flexural strength and the high-temperature flexural strength were improved to 20.38 and 21.43 MPa with 1.0 vol% Al2O3, respectively, due to the increased α-cristobalite and β-cristobalite content. Therefore, using the optimal content of Al2O3 in silica-based ceramics can provide excellent mechanical properties, which are suitable for the application of ceramic cores in the manufacturing of hollow blades.

The growing demand for fluxes, dictated by the shift toward porcelain stoneware, is urging the ceramic tile industry to find a viable alternative to feldspathic materials. Sericite, a microcrystalline form of muscovite, is present in many ceramic raw materials. It melts during firing and can be a suitable substitute for potassic feldspar. The aim of this study is to understand in depth the effects of replacing feldspar with sericite in porcelain stoneware batches with nearly the same chemical composition. Characterization includes phase composition (X-ray powder diffraction, XRPD Rietveld), melt chemical composition (calculated), sintering behavior (optical thermo-dilatometry), and microstructure (scanning electron microscope (SEM). The results indicate a different vitrification path, mostly in the early stage of sintering, related to the different mineralogical composition and particle size distribution of sericite for K-feldspar. Nevertheless, at temperatures higher than 1150 degrees C, the bodies have similar phase composition, microstructure, melt chemical composition, and physical properties. Densification kinetics is faster in the batch with sericite, while the body with feldspar is able to reach a higher bulk density.

The viscosity of different concentrations of sunflower oil + DMF and corn oil + DMF solvents in the presence of potassium iodide was measured at temperatures of 303.15–323.15 K in steps of 5.0 K. The viscosity increased with the increase in the concentration of potassium iodide and oil, while an increase in temperature decreased the viscosity. The change in the viscosity was used to evaluate the structural changes and electrostatic interactions produced by the addition of potassium iodide to the oil + DMF solvent. The structure-breaking or structure-promoting behavior of potassium iodide was evaluated by applying the Jones–Dole, Vand, and Breslau–Miller equations. The increase in viscosity B-coefficients with the temperature confirmed the structure-breaking behavior of potassium iodide in the oil + DMF solvent. The ionic B-coefficients were evaluated by subjecting the experimental data to the mathematical approximations available in the literature. The Moulik and Einstein relations were also found applicable to the viscosity of the oil + DMF solvent while deviations were observed from the Thomas relation. The thermodynamic parameters of the viscous flow also supported the obtained results about the ionic interactions.

Earthquake simulation and hazard prediction are strongly hampered by insufficient physical knowledge of the constitutive behavior of faults. Laboratory studies of carbonate fault friction suggest that seismogenic rupture on faults in carbonate terrains can be explained by a transition from high friction at low initial sliding velocities (V) to low friction at seismic slip velocities, that is, by rapid dynamic weakening. One proposed explanation for this weakening, invokes frictional heating resulting in deformation by grain boundary sliding accommodated by solid-state diffusion (sometimes referred to as “viscous” or “superplastic” flow). We recently added this dynamic weakening mechanism to a microphysically based model addressing the (rate-and-state) frictional behavior of granular gouges undergoing low V shear characteristic of rupture nucleation and arrest. In the present study, we applied the full model to simulate seismic slip in laboratory carbonate faults. Assuming that slip localizes in a principal shear band within the fault (gouge) zone, and accounting for grain size evolution with velocity and temperature, the model reproduces the frictional, thermal and (micro-)structural evolution observed during seismic slip experiments. In particular, it predicts spatial and temporal evolutions of grain size, porosity, and dominant deformation mechanisms, within and outside the assumed shear band, consistent with trends identified in the laboratory and natural fault zones.

Unsteady two-dimensional Reynolds Averaged Navier-Stokes (RANS) equations coupled with the k−ε turbulence model was developed to simulate the viscous flow field near seawalls. The complex free-surface configuration was captured using the particle level set method (PLSM). An innovative solid-fluid coupling method was employed to mimic the solid-fluid interaction on fixed Cartesian grids. The proposed numerical model was applied to investigate the viscous flow fields induced by periodic waves propagating on three different seawalls, including vertical and steep seawalls, which are commonly designed in Taiwan with slopes of 1:2 and 1:5. The results reveal that the wave run-up height is closely related to Iribarren number and breaking wave. Partial standing wave or asymmetric recirculating cells in front of a steep seawall lose symmetry with increasing slope. The wave pressure on the seawall face increases as the Ursell number or seawall slope increases. The undertow caused by breaking waves has a significant effect on the bottom shear stress in front of the seawall.

The present work is to modify the stern duct of Japan bulk carrier (JBC) to reduce the ship total resistance for Froude number 0.142. The research method is to use the CFD (computational fluid dynamics) tool OpenFOAM to predict the total resistance and viscous flow field around the ship hull considering the free surface. First, the V&V (verification and validation) analysis was conducted to ensure our CFD method is reliable, and to estimate its error and uncertainty range for the original JBC with and without the original stern duct. Second, the angle of attack (AoA) of the foil section of the stern duct was adjusted, thus forming a series of different ducts axisymmetric along the propeller shaft axis. The CFD simulations were performed for each duct appended behind the ship hull. By comparing the total resistance with and without the duct, the ship hull resistance reduction effect caused by the duct would be obtained. Finally, the duct with 7° AoA achieved the best resistance reduction of 2.49%. The original duct (with 20° AoA) could only provide a 0.6~0.7% reduction. The nominal wake was also analyzed with the ducts, in order to understand the detailed flow phenomena which had an essential influence on propeller inflow.

Non-isothermal differential scanning calorimetry (DSC) was used to study the influences of particle size (daver) and heating rate (q+) on the structural relaxation, crystal growth and decomposition kinetics of amorphous indomethacin. The structural relaxation and decomposition processes exhibited daver-independent kinetics, with the q+ dependences based on the apparent activation energies of 342 and 106 kJ·mol−1, respectively. The DSC-measured crystal growth kinetics played a dominant role in the nucleation throughout the total macroscopic amorphous-to-crystalline transformation: the change from the zero-order to the autocatalytic mechanism with increasing q+, the significant alteration of kinetics, with the storage below the glass transition temperature, and the accelerated crystallization due to mechanically induced defects. Whereas slow q+ led to the formation of the thermodynamically stable γ polymorph, fast q+ produced a significant amount of the metastable α polymorph. Mutual correlations between the macroscopic and microscopic crystal growth processes, and between the viscous flow and structural relaxation motions, were discussed based on the values of the corresponding activation energies. Notably, this approach helped us to distinguish between particular crystal growth modes in the case of the powdered indomethacin materials. Ediger’s decoupling parameter was used to quantify the relationship between the viscosity and crystal growth. The link between the cooperativity of structural domains, parameters of the Tool-Narayanaswamy-Moynihan relaxation model and microscopic crystal growth was proposed.

We encounter stickiness in many areas of our daily life and as humans, we are able to discriminate different levels of stickiness. Yet attempts to measure stickiness with instruments have been challenging. One of the commonest approaches has been the "tack test" in which a probe is brought into contact with the sticky food and then pulled away while measuring the resisting force-various indices, such as the maximum force or the area below the force curve have been used to describe stickiness. This work rationalizes results from tack tests for liquid foods and helps us explain the influence of probe geometry. Photographic evidence of the way that the liquid adheres/detaches from the probe suggests that the terms "cohesive" and "adhesive" failure depend on the speed of the test. Application of a fixed deformation with time shows rapid loss of adhesive force suggesting that liquid samples flow from the probe. We propose that stickiness of liquid foods is entirely due to the liquid's viscosity and surface tension, and that measurements of tack for liquid foods-while highly reproducible-are entirely artifacts of the test method employed and are in effect snapshots in time of non-equilibrium processes.

We study the asymptotic spatial behavior of the vorticity field, $$\omega (x,t)$$ , associated to a time-periodic Navier–Stokes flow past a body, $${\mathscr {B}}$$ , in the class of weak solutions satisfying a Serrin-like condition. We show that, outside the wake region, $${\mathcal {R}}$$ , $$\omega $$ decays pointwise at an exponential rate, uniformly in time. Moreover, denoting by $${\bar{\omega }}$$ its time-average over a period and by $$\omega _P:=\omega -{\bar{\omega }}$$ its purely periodic component, we prove that inside $${\mathcal {R}}$$ , $${\bar{\omega }}$$ has the same algebraic decay as that known for the associated steady-state problem, whereas $$\omega _P$$ decays even faster, uniformly in time. This implies, in particular, that “sufficiently far” from $${\mathscr {B}}$$ , $$\omega (x,t)$$ behaves like the vorticity field of the corresponding steady-state problem.

Two-dimensional dynamics of the wake in transitional flow around a circular cylinder is studied using weakly compressible smoothed particle hydrodynamics scheme up to 10 cylinder diameters downstre...

Bioglass 45S5 is widely known for its ability to regenerate bone. However, this glass cannot be fully densified by viscous flow due to its very high tendency for crystallization. In this work, we evaluate the sintering and bioactivity of Bioglass 45S5-based compositions in which Na2O is incrementally replaced by K2O. Our sintering tests demonstrated that the densification of Bioglass 45S5 powders can be significantly enhanced due to a decreased crystallization tendency. The composition in which half of the original Na2O content was substituted by K2O exhibits the highest densification rate, evidencing the mixed alkali effect (MAE) in the viscous-flow-driven sintering process. The replacement of Na2O by K2O significantly improved both the densification rate and the in vitro performance. These results are very relevant for this particular glass and also for the design of new bioactive glasses with improved sinterability.

During the spark plasma sintering (SPS) consolidation process, the pressure affects the densification and microstructure evolution of the sintered body. In this paper, the W-Cr-Y-Zr alloy powder was heated to 1000 °C under different applied pressure conditions using spark plasma sintering process, and the effect of pressure on the densification process and microstructure was analyzed. Due to the low sintering temperature, the crystalline size of all the produced W-Cr-Y-Zr alloy is less than 10 nm, which is close to that of the original powders. Cr-rich phase can be detected in the sintered samples due to spinodal decomposition. It is found in this work that the external pressure will increase the contact area between the powder particles, resulting in a higher local pressure at the particle contact, which promotes densification by sliding between the particles under the condition of softening of the particle surface. Additionally, according to the viscous flow theory, the viscous flow activation energy decreases with the increase of pressure. This is because the pressure provides additional driving force to the powder viscous flow process and accelerates the powder shrinkage.

The objective of this study is to design the hull-mounted sonar dome of a ship. The goal is to reduce the ship total resistance and improve the flow field around the sonar dome for the ship design speed. OpenFOAM 6 was applied to analyze the viscous flow around the ship bow and then optimize the sonar dome geometry. The length, width and depth of the original geometry were maintained. Only the local geometry was fine-tuned considering the back slope and front tip by using Rhinoceros 6. The verification and validation was performed for the original hull form against towing tank resistance data. The grid independence was checked for the optimal design in different design stages. To ensure less influence on the interior equipment installation and to be able to re-use the non-steel dome part, the best resistance reduction is almost 2%. With a larger allowance of shape deformation, the maximal reduction could reach slightly higher than 3%. The flow field is improved for smaller flow separation and vortex, and less fluid nose in sonar detection is expected. The main reason of the resistance reduction is the decrease of the pressure component. In conclusion, a sonar dome design procedure is proposed, and an optimal geometry is suggested.

One of efficient directions for pasta press designs modernization is installation of special conical-and-cylindrical inserts in the matrix wells in front of the dies having, like Venturi tubes, narrowing zones (convergent), expansion (divergent) and a cylindrical path located between them. However, rheological aspects of such method of forming tool modernizing in relation to pasta presses have not been studied, recommendations for structural elements calculation and design have not been developed. All this is a significant obstacle for using the method in engineering and industrial practice. The research purpose is to develop rheological models the pasta dough flow in the conical-cylindrical channels of convergent-divergent inserts and to evaluate with their help the impact of structural dimensions and rheological properties on resistance to pasta dough flow. Pasta dough was considered as a rheological complex nonlinearly viscous plastic material. In technical calculations contribution of shear strength was neglected and a rheological analysis was performed using the Oswald-de-Vila power law equation. Analytical dependences obtained make it possible to calculate the pressure drops in the convergent-divergent insert and its elements. Numerical modeling was performed and calculated data were obtained regarding the impact of dimensions of structural elements of the insert and rheological parameters of pasta dough on its resistance to viscous flow. The results obtained can form the basis of engineering and technological calculations in design of convergent-divergent inserts for laboratory and industrial matrices of pasta presses.

A pore network model is proposed to simulate the complex process of in situ foam generation, destruction, and propagation as a drainage process. Motivated by the need to account for viscous flow ef...

Purpose The purpose of this study to analyze the unsteady magneto hydrodynamic incompressible viscous fluid flow along the porous parallel plates in which constant periodic suction/injection takes place at lower and upper plate, respectively. By the proper choice of stream function, they obtained exact solution analytically. Velocity components are obtained from exact solution. Design/methodology/approach Emissions of the pollutants from the aviation sectors are doubled compared to 2000. There are many recent developments that are actively developed to combat the emission by increasing the performance of the Jet engines. The role of the computational fluid dynamics and the numerical approaches are crucial in terms of research and development. Findings Velocity profiles like axial and radial have been drawn for various values of M, D, α and θ. The exact solutions have been solved by differential transformation method. The closed form analytical solutions are obtained for the stream function, axial and radial velocities and flow velocity. Originality/value The effects of Darcy parameter, magnetic parameter, Suction Reynolds number and frequency parameter on lower and upper plates are discussed through graphs.

The kinematic viscosity of Fe–Mn–C melts is measured with Mn contents of 5.0, 7.5, 10.0, 12.0, 15.0, 17.5, 20.0, and 25.0 wt % and C contents of 0.4 to 2.2 wt %. The kinematic viscosity is measured using damped torsional vibrations of a crucible with a melt upon the heating and subsequent cooling of the samples. The temperatures at which the characteristics of the viscous flow change and the liquid–liquid structural transition occurs in Fe–Mn–C melts are determined using the results from measuring the kinematic viscosity.

The temperature dependences of the dynamic viscosity of the InBi100 – xPbx (where x = 19, 40, 60, 80, and 100 at %) melts are studied in the range from the liquidus temperature to 1200 K by the oscillating crucible method. The temperature dependences of the viscosities of melts of these compositions are well described by the Arrhenius equation. The viscosity of the InBi–Pb melts at a constant temperature has small negative deviations from the ideal mixture viscosity. The activation energy of a viscous flow has negative deviations from additive values with a minimum near 20 at % Pb. The concentration dependences of the viscosities of the melts are calculated using the well-known equations based on the thermodynamic properties. The obtained results are compared with the experimental data.

It is found in the present attempt that the variations in parameters of G, & Ec the velocity on Z=0 & Z=1/2 indicates movement of the flow towards the upward direction as we move in the normal direction from y=0 to 1. In all the cases however the maximum is attained at y=0.4 while at Z=1/2 level the maximum across at y=1. The enhancement in G leads to a depreciation in θ at y=0&1/2. The fluctuations of θ with is shown in 17&18. It is found that the actual temperature enhances with increase

Heat and mass transfer in a viscous flow over a non-uniform porous plate of variable thickness is investigated in this paper. The variably heated plate is stretched/shrunk in a stagnant fluid with variable velocity and has the non-uniform species concentration. The governing partial differential equations are simplified and solved numerically. The transport of heat and mass in the flow regime is governed by a set of PDE’s satisfying certain necessary boundary conditions. The governing PDE’s are simplified by using boundary layer approximations and transformed into a set of ODE’s by invoking a set of new transformations. The system of ODE’s contains several dimensionless numbers (parameters) which demonstrates the behavior of all field quantities. All the unknown variables, rates of heat and mass transfer are evaluated and effects of the existing parameters are seen on them, whereas, they are significantly changed with the variation of these dimensionless quantities. New solutions and results are presented in graphs and tables, whereas, they are thoroughly examined and discussed. In addition to that the modeled problem and its solutions are exactly matched with the classical problems and their corresponding solutions for specific numerical values of the governing parameters involved in the current modeled problem. The engineering applications of heat and mass transfer problems are very famous in many industrial processes. Therefore, these two phenomena are widely discussed and analyzed, whereas, they are frequently utilized for the formation of metallic devices/objects while using additive manufacturing processes, cryogenics, formation of reasonable and suitable heat exchangers, falling film evaporation and the steam boilers. However, most of the engineering systems with or without magnetized and electrically conducting surfaces cannot be expressed in usual coordinates i.e. cartesian coordinate system, moreover, most of the engineering processes involve fluids of different nature and kinds, whereas, sometime they also require different physical and environmental conditions. Therefore, in such situations we need, to upgrade and modify the present modeled problem according to prevailing situations.

The transport dynamics of a rigid filament in a slow viscous flow modeled by the Stokes equations in a three-dimensional domain are considered. The relation between the transport velocities, extern...

The paper considers the issue of improving the quality of the numerical experiment in the calculation of viscous gas in the flowing part of a low-flow centrifugal compressor stage. The choice of turbulence model in creating a calculation model for calculations by methods of computational fluid dynamics is substantiated. As object of research is chosen low-flow stage with conditional flow coefficient Ф=0,008 and relative width at impeller outlet b2 /D2 =0,0133. The issue of qualitative modeling of friction losses in low-flow stages is of fundamental importance and is directly related to the choice of turbulence model. It is shown that the choice of low-Reynolds turbulence models in the case of unloaded and discontinuous low-flow stages can be made from the main common models (SpalartAllmaras, SST, k-ω) based on the economy of calculations, speed of convergence, solution stability and adequacy of the obtained results. For models with wall functions, the quality of the mesh model and the observance of the dimensionless distance to the wall y+ throughout the calculation domain are particularly important. For highReynolds turbulence models, at values of y+=25...50 on all friction surfaces of the computational domain in the optimal mode of operation, the grid independence of the solution for the entire gas-dynamic characteristic is ensured. It is unacceptable for y+ to fall into the transition region of 4...15 between the viscous sublayer and the region of the logarithmic velocity profile

Viscosity is an important property of fuels used for diesel engine affecting engine’s efficiency and harmful gases emission. Viscosity of liquid fuels depends especially on fuels composition and temperature. The dynamic viscosity of diesel fuel, biodiesel and blends of diesel with biodiesel, i-propanol and n-butanol was measured for temperature ranging from 293.15 K to 323.15 K and atmospheric pressure. It has been verified that well-known Arrhenius derived equations can be used to estimate with good accuracy, viscosity at different temperatures for diesel, biodiesel, diesel+biodiesel blends, but also for diesel blends with propanol and butanol. Values of activation parameters: activation energy, activation enthalpy and activation entropy for the viscous flow were derived based on linearized Eyring’s type equation. The values of the activation energy for viscous flow of fuels and fuels blends calculated based on measured values of dynamic viscosity in the temperature range of 273.15 K and 323.15 K were similar to those presented in the literature for some hydrocarbons, esters, and alcohols, respectively.

The thermodynamic characteristics of the process of viscous flow of mineral base lubricating oils (SGK grade AU, naphthenic T-110) and synthetic (Synfluid PAO 6 cSt) were found. It was found that the activation energy and the change in the activation entropy of the viscous flow of mineral oils, considered trade marks, are higher than that of synthetic oil. The obtained thermodynamic data made it possible to establish the mechanism of the flow of lubricating oils.

A pressure-driven viscous flow through groovy curved channels of small width compared to the groove wavelength is studied. The Reynolds number is assumed to be very small, such that the flow is dominated by the viscous and the pressure-gradient forces. The effects of the channel geometry on the inertial free flow are analyzed. Two distinct flow directions are considered: (i) flow transverse to the grooves and (ii) flow longitudinal to the grooves. The velocities for both flow directions are obtained, and their distributions are found to be significantly affected by the grooves and channel curvature. The axial pressure gradient for the transverse flow is examined as a function of the amplitude and the phase difference. The results further indicate that the flow rate can be increased by the grooves for longitudinal flow, irrespective of the phase difference, unlike transverse flow This is because the latter is more affected by grooves for the same radius of curvature and phase difference.

In this paper, we present a linear hydrodynamic stability analysis of the fluid, flowing in a porous curved channel. The motion is due to Pressure gradient acting round the curved channel and an imposed radial flow. The analytical solution of the eigen value problem is obtained by using the Galerkin’s method, for the wide gap case. Results for critical wave number and Dean Number are obtained and are compared with earlier result. The agreement is very good. Also, the stability curve, amplitude of the radial velocity and the cell-pattern are shown on graphs. The results show that the flow is strongly stabilized by an outward radial flow and weakly stabilized by a strong inward radial flow, while it is destabilized by a weak inward radial flow. In presence of outward flow, wide gap systems show stronger stability than the small gap system.

A two-dimensional viscous flow in a rough curved channel is investigated. The roughness are considered to be sinusoidal corrugations. The asymptotic solution is obtained using boundary perturbation technique for small amplitude of the corrugations. It is found that, for any radius of curvature, the flow rate is invariably decreased by the corrugations. The effect of corrugations on the flow rate increases with the corrugation wavenumber, as well as the phase difference between the corrugated curved walls. For sufficiently large corrugation wavenumbers, the phase difference between the corrugated walls becomes insignificant. The findings of this study indicate that a smooth curved channel with no corrugations, will give more flow rate than a corrugated curved channel, comparatively, for the same radius of curvature, as the flow resistance is relatively higher for the latter, due to the effects of the wall-surface roughness.

The resistance model has been employed to derive an expression for the permeability of a composite membrane taking into account the viscous flow of a gas and the porous structure of a membrane support. Mathematical simulation has been used to show that, when the material of a selective layer does not penetrate into the pores of the skin layer of the support, the viscous flow of a gas in the support may noticeably affect the permeability and selectivity of the composite membrane, and the effect is enhanced with a decrease in the effective porosity and an increase in the permeability of the selective layer. It has been found that the influence of the porous structure of the support on the permeability of the composite membrane diminishes with a rise in the effective porosity of the support skin layer and the average pore size. The case in which selective layer material fills the pores of the support to the entire depth of the skin layer has been analyzed in detail. It has been shown that, in this case, the effect of the support on the membrane permeability is governed only by the porosity of the skin layer and the ratio between the thicknesses of the support skin layer and the selective layer.

The relevance of the topic is determined by the search for the transcendental frequency equations that are reduced to algebraic and the influence of both boundary conditions at the edges of a rectangular plate and geometric and mechanical characters on the inherent oscillatory frequencies of rectangular flat elements is considered and the previous results for a rectangular plate whose material satisfies a viscoelastic model of Maxwell is generalized. When studying oscillatory processes in a solid deformable body, it is advisable to take the kernel of viscoelastic operators regularly, since only such operators describe the instantaneous elasticity and then the viscous flow, which is characteristic of deformable solids. Integro-differential equations with regular kernels are known to be equivalent to partial differential equations.

An attempted is made on the free convection flow of an incompressible viscous fluid in the profile in terms of heat characteristics were analyzed. The flow is assumed to be along the axis of the channel. The uniform temperature is considered in the study. The momentum conservation equations for the fully developed flow are based on the Brinkman model. The viscous and Darcy dissipation are taken into account in the energy equation as the modification of the heat flow. By using the finite element method, the fluid and the porous matrix are in local thermal equilibrium and the flow is unidirectional along the direction of the buoyancy. The non-linear equations governing the flow, heat and mass transfer have been analyzed. Various parameters such as the velocity, temperature, concentration, Nusselt number, and Sherwood number are analyzed and their behavior is interpreted in the paper.

The use of Computational Fluid Dynamics as a tool for design and analysis of aerospace systems is well established. Since the results generated by a CFD solver are numerical approximations, the solution is inherently produced with errors and uncertainties. In this paper, a simple fluid flow problem of laminar, incompressible flow past a circular cylinder at Reynolds number of 20 is allowed to be solved by the well-known finite-volume solver ANSYS Fluent. The effect of variations in mesh resolution, domain boundary location and residual criteria settings is investigated. For all the cases, finite, structured meshes of acceptable quality are used. The influence of variables on the cylinder’s drag results is analyzed and discussed. An interesting pattern in results has been observed. The study on the variation in mesh resolution showed no presence of mesh independent solution. The study on the variation of the domain distance showed that it is necessary to increase the diameter of the circle several thousand times to obtain a domain independent solution.

This article presents a two-dimensional steady viscous flow simulation past circular and square cylinders at low Reynolds numbers (based on the diameter) by the finite volume method with a non-orthogonal body-fitted grid. Diffusive fluxes are discretized using central differencing scheme, and for convective fluxes upwind and central differencing schemes are blended using a ‘deferred correction’ approach. A simplified pressure correction equation is derived, and proper under-relaxation factors are used so that computational cost is reduced without adversely affecting the convergence rate. The governing equations are expressed in Cartesian velocity components and solution is carried out using the SIMPLE algorithm for collocated arrangement of variables. The mesh yielding grid-independent solution is then utilized to study, for the very first time, the effect of the Reynolds number on the separation bubble length, separation angle, and drag coefficients for both circular and square cylinders. Finally, functional relationships between the computed quantities and Reynolds number (Re) are proposed up to Re = 40. It is found that circular cylinder separation commences between Re= 6.5-6.6, and the bubble length, separation angle, total drag vary as Re, Re −0.5 , Re −0.5 respectively. Extrapolated results obtained from the empirical relations for the circular cylinder show an excellent agreement with established data from the literature. For a square cylinder, the bubble length and total drag are found to vary as Re and Re −0.666 , and are greater than these for a circular cylinder at a given Reynolds number. The numerical results substantiate that a square shaped cylinder is more bluff than a circular one.

The problem of the coating of steel has been considered in several Mathematics in Industry study groups. In this process, after passing through a bath of molten alloy, steel sheeting is drawn upward to allow draining under gravity and stripping using an air knife, leaving a coating of desirable thickness. Here we discuss some aspects of the problem and in particular the gravity draining component. The problem is a very nice introduction to industrial modelling for students, but is also relevant for manufacturing. References Elsaadawy, E. A., Hanumanth, G. S., Balthazaar, A. K. S., McDermid, J. R., Hrymak, A. N. and Forbes, J.F. ``Coating weight model for the continuous hot-dip galvanizing process'', Metal. Mat. Trans. B, 38:413–424, 2007. doi:10.1007/s11663-007-9037-2 Hocking, G. C., Sweatman, W. L., Fitt, A. D., and Roberts M. ``Coating Deformation in the jet stripping process'' in Proceedings of the 2009 Mathematics and Statistics in Industry Study Group, Eds. T. Marchant, M. Edwards, G. Mercer. Wollongong, Austealia, 2010. https://documents.uow.edu.au/content/groups/public/@web/@inf/@math/documents/doc/uow073330.pdf Hocking, G. C., Sweatman, W. L., Fitt, A. D., and Breward, C. ``Deformations arising during air-knife stripping in the galvanization of steel'', in Progress in Industrial Mathematics at ECMI 2010, Eds. M. Gunther, A. Bartel, M. Brunk, S. Schops, M. Striebel. Mathematics in Industry 17, pp. 311-317. Springer, Berlin Heidelberg, 2011. doi:10.1007/978-3-642-25100-9_36 Hocking, G. C., Lavalle, G., Novakovic, R., O'Kiely, D., Thomson, S., Mitchell, S. J., Herterich, R. ``Bananas–-defects in the jet stripping process''. Proceedings of the European Study Group with Industry in Mathematics and Statistics Research Collection. Rome Italy, 2016. https://researchrepository.ucd.ie/handle/10197/10215 Howison, S. D. and King, J. R. ``Explicit solutions to six free-boundary problems to fluid flow and diffusion''. IMA J. Appl. Math. 42:155–175, 1989. doi:10.1093/imamat/42.2.155 Hocking, G. C., Sweatman, W., Fitt, A. D. and Breward, C. ``Deformations during jet-stripping in the galvanizing process''. J. Eng. Math. Tuck Special Issue, 70:297–306, 2011. doi:10.1007/s10665-010-9394-8 Thornton, J. A. and Graff, H. F. ``An analytical description of the jet-finishing process for hot-dip metallic coatings on strip''. Metal. Mat. Trans. B, 7:607–618, 1976. doi:10.1007/BF02698594 Tuck, E. O. ``Continuous coating with gravity and jet stripping''. Phys. Fluids, 26(9):2352–2358, 1983. doi:10.1063/1.864438 Tuck, E. O., Bentwich, M., and van der Hoek, J. ``The free boundary problem for gravity-driven unidirectional viscous flows''. IMA J. Appl. Math. 30:191–208, 1983. doi:10.1093/imamat/30.2.191

In this article it is proposed to solve numerically the Blasius viscous flow problem of fluid mechanics using wavelet Galerkin method. The spline wavelet system is used for this purpose. It is assu...

In this article, the vibration analysis of a double-walled carbon nanotube (DWCNT) conveying viscous flow with the aid of modified strain gradient theory has been investigated. The visco-Pasternak ...