The problem of stagnation point flow over a stretching/shrinking sheet immersed in a micropolar fluid is analyzed
numerically. The governing partial differential equations are transformed into a system of ordinary (similarity) differential
equation and are then solved numerically using the boundary value problem solver (bvp4c) in Matlab software. The
effects of various parameters on the velocity and the angular velocity as well as the skin friction coefficient and the couple
stress are shown in tables and graphs. The noticeable results are found that the micropolar and the slip parameters
decrease the skin friction coefficient and the couple stress in the existence of magnetic field. Dual solutions appear for
certain range of the shrinking strength. A stability analysis is performed to determine which one of the solutions is stable.
Practical applications include polymer extrusion, where one deals with stretching of plastic sheets and in metallurgy
that involves the cooling of continuous strips.
In this paper, the steady Falkner-Skan solution for gravity-driven film flow of a micropolar fluid is theoretically investigated. The resulting nonlinear ordinary differential equations are solved numerically using an implicit finite-difference scheme. The results obtained for the skin friction coefficient as well as the velocity and microrotation or angular velocity profiles are shown in table and figures for different values of the material or micropolar parameter K.
This paper presents a numerical analysis of a stagnation-point flow towards a nonlinearly stretching/shrinking sheet immersed in a viscous fluid. The stretching/shrinking velocity and the external flow velocity impinges normal to the stretching/shrinking sheet are assumed to be in the form U ~ xm, where m is a constant and x is the distance from the stagnation point. The governing partial differential equations are converted into ordinary ones by a similarity transformation, before being solved numerically. The variations of the skin friction coefficient and the heat transfer rate at the surface with the governing parameters are graphed and tabulated. Different from a stretching sheet, it is found that the solutions for a shrinking sheet are non-unique for m > 1/3.
As of today, ultra-high molecular weight polyethylene (UHMWPE) is a thermoplastic material normally used as bearing
components for human joint replacements. However, formation of wear debris from UHMWPE after certain service
periods may cause adverse effects which remain as unresolved issues. In this study, mechanical and dry sliding wear
properties of UHMWPE reinforced with different loading of talc particles were investigated. The wear test was carried
out using Ducom TR-20 pin-on-disc tester at different pressure velocity (pv) factors under dry sliding conditions. The
worn surfaces and transfer films of pure UHMWPE and talc/UHMWPE composites were observed under scanning electron
microscope (SEM). The experimental results showed that the microhardness increased with the increase of talc loadings
in UHMWPE. The 20 wt. % talc/UHMWPE composites showed a 17% increment in microhardness as compared with pure
UHMWPE. The dry sliding wear behaviour of UHMWPE was also improved upon the reinforcement of talc. The wear rate
of UHMWPE decreased after incorporation of talc particles. The coefficient of friction (COF) increased slightly under low
pv conditions. At high pv conditions, the COF decreased in values with increasing talc loadings. The improvement in
wear behaviour may be attributed to the increase in load-carrying capacity and surface hardness of the talc/UHMWPE
composites. SEM micrographs on worn surfaces showed that plastic deformation and grooving wear were dominant for
UHMWPE. The plastic deformation and grooving wear were reduced upon the reinforcement of talc particles. The talc/
UHMWPE composites produced smoother and uniform transfer films as compared to pure UHMWPE.
Invention of milling combined laser sintering system (MLSS) is able to reduce the mould manufacturing time and improve the mould accuracy. Thus, more study is needed to increase the understanding for the laser sintered material machining characteristic to gain benefit from the invention of MLSS. This paper clarified the analysis of laser sintered material machinability with the application of Finite Element Method (FEM). Mild steel AISI1055 was applied in developing the Finite Element model in this study due to its popularity in machinability test and adequate level of data availability. 2D orthogonal cutting was employed on edge design tools with updated Lagrangian coupled thermo mechanical plane strain model. Adaptive meshing, tool edge radius and various types of friction models were assigned to obtain efficient simulations and precise cutting results. Cutting force and cutting-edge temperature estimated by Finite Element Method are validated against corresponding experimental values by previous researchers. In the study, cutting force increases when radial depth increases and lowest error acquired when the shear friction factor of 0.8 was applied. Machining simulation for laser sintered materials estimated lower cutting force compared with mild steel AISI1055 due to lower Young modulus. Higher cutting temperature estimated for machining simulation laser sintered material compared with machining simulation mild steel AISI1055 due to its low thermal conductivity.
A steady laminar mixed convection boundary layer flow about an isothermal solid sphere embedded in a porous medium filled with a nanofluid has been studied for both cases of assisting and opposing flows. The transformed boundary layer equations were solved numerically using an implicit finite-difference scheme. Three different types of nanoparticles, namely Cu, Al2O3 and TiO2 in water-based fluid were considered. Numerical solutions were obtained for the skin friction coefficient, the velocity and temperature profiles. The features of the flow and heat transfer characteristics for various values of the nanoparticle volume fraction and the mixed convection parameters were analyzed and discussed.
Dry sliding wear of polyester hybrid composites containing carboxylic functionalized multi-walled carbon nanotubes (cNT) and microparticles, silica (Si02) was studied at different sliding distances. An attempt has been made to produce uniform dispersion of nano- and micro- particles in the test samples by ultrasonication. The tribological properties of the hybrid composites were performed by using pin-on-disc (POD) tester against grey cast iron countersurface. The dry sliding wear tests were carried out under pressure-velocity (pv) condition of 0.4 MPa and 4 m/s for total sliding distance of 28800 m and at an interval of every sliding distance of 3600 m, wear properties and behavior were studied. The samples containing 10 wt.% silica (microparticles) with and without CNT always show increase in coefficient of friction at the expense of wear rate. However, samples containing only ci'rr have the lowest wear rate with the increase in coefficient of friction. Sliding distance studies also provide the information on wear rates which were ever changing at different sliding distances whereas average coefficient of friction did not vary throughout the tests. SEM observations of wear surfaces showed different wear morphologies when reinforcement (cNT or Si02) incorporated into the composites either alone or in combination.
Oleic acid (OA) capped wolfram (VI) oxide, WO3 nanoparticles were chemically synthesized and characterized by means of Fourier Transform-Infrared spectroscopy (FT-IR) and transmission electron microscopy (TEM). The tribological properties of the capped WO3 nanoparticles as an additive in base oils were investigated using a four-ball machine. Results show that OA-capped WO3 nanoparticles are able to prevent water adsorption and capable of being dispersed stable in organic solvents which is base oils. The as-prepared capped WO3 nanoparticles have an average size of 15 nm. In addition, OA-capped WO3 nanoparticles as an additive in base oils perform good anti-wear (AW) and anti-friction (AF) properties owing to the formation of a boundary film.
The magnetohydrodynamic (MHD) boundary-layer flow and heat transfer due to a shrinking sheet in a porous medium is considered for the first time. The Navier-Stokes equations and the heat equation are reduced to two nonlinear ordinary differential equations via similarity transformations. The transformed equations are solved by a semi-analytic method. The effects of the suction and porosity parameters, the Prandtl and Hartmann numbers on the skin friction, heat transfer rate, velocity and temperature profiles are discussed and presented, respectively.
We study and discuss the effect of thermal slip on steady free convection flow of a viscous, incompressible micropolar fluid past a vertical moving plate in a saturated porous medium. The effect of viscous dissipation is incorporated in the energy equation. The associated partial differential equations are transformed into a system of ordinary differential equations using similarity transformations generated by a group method and this system is then solved numerically. The effect of controlling parameters on the dimensionless velocity, angular velocity and temperature as well as friction factor, couple stress factor and heat transfer rate are shown graphically and discussed in detail. It is found that the dimensional velocity and angular velocity decrease whilst the temperature increases with velocity slip parameter. It is further found that thermal slip decreases the dimensional velocity and temperature but increases the dimensional angular velocity. Data from published work and our results are found to be in good agreement.
A combined similarity-numerical solution of the magnetohydrodynamic boundary layer slip flow of an electrically conducting non-Newtonian power-law nanofluid along a heated radiating moving vertical plate is explored. Our nanofluid model incorporates the influences of the thermophoresis and the Brownian motion. The basic transport equations are made dimensionless first and then suitable similarity transformations are applied to reduce them into a set of nonlinear ordinary differential equations with the associated boundary conditions. The reduced equations are then solved numerically. Graphical results for the non-dimensional flow velocity, the temperature and the nanoparticles volume fraction profiles as well as for the friction factor, the local Nusselt and the Sherwood numbers are exhibited and examined for various values of the controlling parameters to display the interesting aspects of the solutions. It was found that the friction factor increases with the increase of the magnetic field (M), whilst it is decreased with the linear momentum slip parameter (a). The linear momentum slip parameter (a) reduces the heat transfer rates and the nanoparticles volume fraction rates. Our results are compatible with the existing results for a special case.
Induced magnetic field stagnation point flow for unsteady two-dimensional laminar forced convection of water based nanofluid containing microorganisms along a vertical plate has been investigated. We have incorporated zero mass flux boundary condition to get physically realistic results. The boundary layer equations with three independent variables are transformed into a system of ordinary differential equations by using appropriate similarity transformations. The derived equations are then solved numerically by using Maple which use the fourth-fifth order Runge-Kutta-Fehlberg algorithm to solve the system of similarity differential equations. The effects of the governing parameters on the dimensionless velocity, induced magnetic field, temperature, nanoparticle volume fraction, density of motile microorganisms, skin friction coefficient, local Nusselt number and motile density of microorganisms transfer rate are illustrated graphically and tabular form. It is found that the controlling parameters strongly affect the fluid flow and heat transfer characteristics. We compare our numerical results with published results for some limiting cases and found excellent agreement.
The purpose of this study was to examine the effect of viscous dissipation on mixed convection flow of viscoelastic
nanofluid past a horizontal circular cylinder. Carboxymethyl cellulose solution (CMC) is chosen as the base fluid and
copper as a nanoparticle with the Prandtl number Pr = 6.2. The transformed boundary layer equations for momentum
and temperature subject to the appropriate boundary conditions are solved numerically by using Keller-box method. The
influenced of the dimensionless parameters such as Eckert number, mixed convection parameter, nanoparticles volume
fraction and viscoelastic parameter on the flow and heat transfer characteristics is analyzed in detail and presented
graphically. The results come out with the velocity profiles are increased while the temperature profiles are decreased
by increasing the values of nanoparticles volume fraction and viscoelastic parameter, respectively. The graph shows
that, increasing Eckert number the skin friction is also increases. The values of skin friction are increased by increasing
mixed convection parameter, but the values of Nusselt number produce an opposite behavior. The present study has many
applications especially in heat exchangers technology and oceanography. Therefore, in future, it is hoping to study the
viscoelastic nanofluid flow past a different geometric such as sphere and cylindrical cone.
This paper delves into the problem of mixed convection boundary layer flow from a horizontal circular cylinder filled in
a Jeffrey fluid with viscous dissipation effect. Both cases of cooled and heated cylinders are discussed. The governing
equations which have been converted into a dimensionless form using the appropriate non-dimensional variables are solved
numerically through the Keller-box method. A comparative study is performed and authentication of the present results
with documented outcomes from formerly published works is excellently achieved. Tabular and graphical representations
of the numerical results are executed for the specified distributions, considering the mixed convection parameter, Jeffrey
fluid parameters and the Prandtl and Eckert numbers. Interestingly, boundary layer separation for mixed convection
parameter happens for some positive (assisting flow) and negative (opposing flow) values. Strong assisting flow means
the cylinder is heated, which causes the delay in boundary layer separation, whereas strong opposing flow means the
cylinder is cooled, which conveys the separation point close to the lower stagnation point. Contradictory behaviours
of both Jeffrey fluid parameters are observed over the velocity and temperature profiles together with the skin friction
coefficient and Nusselt number. The increase of the Prandtl number leads to the decrement of the temperature profile,
while the increase of the Eckert number results in the slight increment of the skin friction coefficient and decrement of
the Nusselt number. Both velocity and temperature profiles of Eckert number show no effects at the lower stagnation
point of the cylinder.
Shear strength is currently a significant parameter in the design of cemented sand gravel and rock (CSGR) dams. Shear strength tests were carried out to compare material without layers noumenon and layer condition. The experimental results showed good linearity in the curves of shear strength and pure grinding tests with correlation coefficients of nearly 97%. The friction coefficient was similar to that of C10 roller-compacted concrete (RCC), but the cohesion value was weaker than that of RCC. The shear strength of the CSGR layers decreased by 40% when retarding mixtures were not added and the layer was paved immediately after 4 h of waiting interval.
Lattice Boltzmann Model for Shallow Water Equation with Turbulence Modeling (LABSWETM) is used to study the flow patterns of sidewall friction effects. The lattice Boltzmann method (LBM) approach in recovery the macroscopic governing equation which is shallow water equation from the microscopic flow behavior of particle movement as described by kinetic theory is explored. With the solution of force term to be used in lattice Boltzmann equation, the boundary condition of LBM is explored. With the use of bed and wall friction coefficients, the importance of Manning’s coefficient in determining the outcome of flow patterns simulation is explained. For model verification, the model represents a straight channel with a circular cavity attached to it. The result of this simulation includes the water circulation patterns, cross-section of average velocity distribution, and water depth. For validation, the cross-sections of the model in term of velocity vectors are compared against alternative numerical and experimental data.
The steady two-dimensional stagnation-point flow and heat transfer past a permeable stretching/shrinking sheet with effects of viscous dissipation, Joule heating and partial velocity slip in the presence of a magnetic field is investigated. The partial differential equations are reduced to nonlinear ordinary differential equations by using a similarity transformation, before being solved numerically by shooting technique. Results indicate that the skin friction coefficient and the local Nusselt number increase as magnetic parameter increases. It is found that for the stretching sheet the solution is unique while for the shrinking sheet there exist nonunique solutions (dual solutions) in certain range of parameters. The stability analysis shows that the upper branch solution is stable while the lower branch solution is unstable.
This paper is about the stagnation point flow and mass transfer with chemical reaction past a stretching/shrinking cylinder. The governing partial differential equations in cylindrical form are transformed into ordinary differential equations by a similarity transformation. The transformed equations are solved numerically using a shooting method. Results for the skin friction coefficient, Schmidt number, velocity profiles as well as concentration profiles are presented for different values of the governing parameters. Effects of the curvature parameter, stretching/shrinking parameter and Schmidt number on the flow and mass transfer characteristics are examined. The study indicates that dual solutions exist for the shrinking cylinder but for the stretching cylinder, the solution is unique. It is observed that the surface shear stress and the mass transfer rate at the surface increase as the curvature parameter increases.
In this paper, the unsteady stagnation-point boundary layer flow and heat transfer of a special third grade fluid past a permeable stretching/shrinking sheet has been studied. Similarity transformation is used to transform the system of boundary layer equations which is in the form of partial differential equations into a system of ordinary differential equations. The system of similarity equations is then reduced to a system of first order differential equations and has been solved numerically by using the bvp4c function in Matlab. The numerical solutions for the skin friction coefficient and heat transfer coefficient as well as the velocity and temperature profiles are presented in the forms of tables and graphs. Dual solutions exist for both cases of stretching and shrinking sheet. Stability analysis is performed to determine which solution is stable and valid physically. Results from the stability analysis depict that the first solution (upper branch) is stable and physically realizable, while the second solution (lower branch) is unstable.
It is a theoretical exportation for mass transpiration and thermal transportation of Casson nanofluid over an extending cylindrical surface. The Stagnation point flow through porous matrix is influenced by magnetic field of uniform strength. Appropriate similarity functions are availed to yield the transmuted system of leading differential equations. Existence for the solution of momentum equation is proved for various values of Casson parameter [Formula: see text], magnetic parameter M, porosity parameter [Formula: see text] and Reynolds number Re in two situations of mass transpiration (suction/injuction). The core interest for this study aroused to address some analytical aspects. Therefore, existence of solution is proved and uniqueness of this results is discussed with evaluation of bounds for existence of solution. Results for skin friction factor are established to attain accuracy for large injection values. Thermal and concentration profiles are delineated numerically by applying Runge-Kutta method and shooting technique. The flow speed retards against M, [Formula: see text] and [Formula: see text] for both situations of mass injection and suction. The thermal boundary layer improves with Brownian and thermopherotic diffusions.