171 research outputs found
Approximate analysis of two-massβspring systems and buckling of a column
AbstractMaxβMin Approach (MMA) is applied to obtain an approximate solution of three practical cases in terms of a nonlinear oscillation system. After finding maximal and minimal solution thresholds of a nonlinear problem, an approximate solution of the nonlinear equation can be easily achieved using He Chengtianβs interpolation. Numerical results indicate the effectiveness of the proposed method both in respect of the whole range of involved parameters as well as the excellent agreement with the approximate frequencies and periodic solutions with the exact ones. It is predicted that MMA can be found widely applicable in engineering
Ferrofluid convective heat transfer under the influence of external magnetic source
AbstractFerrofluid convective heat transfer in a cavity with sinusoidal cold wall is examined under the influence of external magnetic source. The working fluid is Fe3O4-water nanofluid. Single phase model is used to estimate the behavior of nanofluid. Vorticity stream function formulation is utilized to eliminate pressure gradient source terms. New numerical method is chosen namely Control volume base finite element method. Influences of Rayleigh, Hartmann numbers, amplitude of the sinusoidal wall and volume fraction of Fe3O4 on hydrothermal characteristics are presented. Results indicate that temperature gradient enhances as space between cold and hot walls reduces at low buoyancy force. Lorentz forces cause the nanofluid velocity to reduce and augment the thermal boundary layer thickness. Nusselt number augments with rise of buoyancy forces but it decreases with augment of Lorentz forces
Application of He's variational iteration method to nonlinear JaulentβMiodek equations and comparing it with ADM
AbstractInstead of finding a small parameter for solving nonlinear problems through perturbation method, a new analytical method called He's variational iteration method (VIM) is introduced to be applied to solve nonlinear JaulentβMiodek, coupled KdV and coupled MKdV equations in this article. In this method, general Lagrange multipliers are introduced to construct correction functionals for the problems. The multipliers can be identified optimally via the variational theory. The results are compared with exact solutions
Analytical investigation of the one dimensional heat transfer in logarithmic various surfaces
AbstractThe purpose of the present study was to investigate of the effect of temperature variation on the logarithmic surface. By using the appropriate similarity transformation for the generation components and temperature, the basic equations governing flow and heat transfer are reduced to a set of ordinary differential equations. These equations have been solved approximately subject to the relevant boundary conditions with numerical and analytical techniques. The reliability and performance of the present method have been compared with the numerical method (RungeβKutta fourth-rate) to solve this problem. Then, LSM is used to solve nonlinear equation in heat transfer. This method is useful and practical for solving the nonlinear equation in heat transfer. It is observed that the obtained results by present analytical method are very close to result of the numerical method. Furthermore, the results show that the temperature profiles decreased by increasing the Ξ± number, and, temperature profiles increased by increasing the Ξ² number
Application of VIM, HPM And CM To The System Of Strongly Nonlinear Fin Problem
The nonlinear fin problem with temperature-dependent thermal conductivity and heat transfer coefficient is analytically studied. Collocation method (CM), Variation iteration method (VIM) and Homotopy perturbation method (HPM) are used to solve the present problem. Also, fourth order RungeβKutta numerical method is applied as a numerical method for validation. Analytical results are presented through the graphs and the tables in various values of parameters. The results reveal that the CM is very effective, simple and more accurate than other techniques. Furthermore, we analyze the effects of some physical applicable parameters in this problem such as thermal conductivity parameter ( ), thermo-geometric fin parameter ( ) and heat transfer mode ( )
Preparation, Modeling, and Optimization of Mechanical Properties of Epoxy/H I PN/Silica Hybrid Nanocomposite Using Combination of Central Composite Design and Genetic Algorithm. Part 2. Studies on Flexural, Compression, and Impact Strength
In spite of good tensile strength of epoxy resins,
they have brittle nature and show poor resistance
to crack propagation. In view of enhancing
mechanical strength and fracture toughness
of epoxy-based nanocomposite simultaneously,
a new combination of thermoplastic and particulate
nanofiller is used as a modifier. Here, the obtained
ternary epoxy-based nanocomposite
includes high impact polystyrene (HIPS) as thermoplastic
and silica nanoparticles as its particulate
phases. Flexural, compression and impact
were the three different mechanical tests investigated,
in order to achieve higher strength without
attenuating other desired mechanical
properties. Central composite design (CCD) is
employed to present mathematical models to predict
mechanical behaviors of epoxy/HIPS/silica
nanocomposite as a function of physical factors.
The effective parameters investigated were
HIPS, SiOβ and hardener contents. Based on
mathematical functions obtained from CCD
model, the genetic algorithm β as one of the
most powerful optimization tools β is applied to
find the optimum values of mentioned mechanical
properties. We have found that a combination
of HIPS and silica nanoparticles
significantly increase compressive and impact
strengths of epoxy resin up to 57 and 421%, respectively.
Although flexural strength did not
change positively, the elongation at break for
flexural one increased up to 144%. Finally, the
morphology of fracture surface was studied by
energy-dispersive X-ray spectroscopy and scanning
electron microscopy.ΠΠ΅ΡΠΌΠΎΡΡΡ Π½Π° ΡΠΎ ΡΡΠΎ ΡΠΏΠΎΠΊΡΠΈΠ΄Π½ΡΠ΅ ΡΠΌΠΎΠ»Ρ ΠΎΠ±Π»Π°Π΄Π°ΡΡ Π²ΡΡΠΎΠΊΠΈΠΌ ΠΏΡΠ΅Π΄Π΅Π»ΠΎΠΌ ΠΏΡΠΎΡΠ½ΠΎΡΡΠΈ ΠΏΡΠΈ ΡΠ°ΡΡΡΠΆΠ΅Π½ΠΈΠΈ, ΠΎΠ½ΠΈ Ρ
ΡΡΠΏΠΊΠΈΠ΅ ΠΈ Ρ
Π°ΡΠ°ΠΊΡΠ΅ΡΠΈΠ·ΡΡΡΡΡ ΡΠ»Π°Π±ΡΠΌ ΡΠΎΠΏΡΠΎΡΠΈΠ²Π»Π΅Π½ΠΈΠ΅ΠΌ ΡΠ°Π·Π²ΠΈΡΠΈΡ ΡΡΠ΅ΡΠΈΠ½Ρ. Π‘ ΡΠ΅Π»ΡΡ
ΡΠ»ΡΡΡΠ΅Π½ΠΈΡ ΠΌΠ΅Ρ
Π°Π½ΠΈΡΠ΅ΡΠΊΠΎΠΉ ΠΏΡΠΎΡΠ½ΠΎΡΡΠΈ ΠΈ Π²ΡΠ·ΠΊΠΎΡΡΠΈ ΡΠ°Π·ΡΡΡΠ΅Π½ΠΈΡ ΡΠΏΠΎΠΊΡΠΈΠ΄Π½ΡΡ
Π½Π°Π½ΠΎΠΊΠΎΠΌΠΏΠΎΠ·ΠΈΡΠΎΠ² Π²
ΠΊΠ°ΡΠ΅ΡΡΠ²Π΅ ΠΌΠΎΠ΄ΠΈΡΠΈΠΊΠ°ΡΠΎΡΠ° ΠΈΡΠΏΠΎΠ»ΡΠ·ΠΎΠ²Π°Π»ΠΈ Π½ΠΎΠ²ΡΠΉ ΠΊΠΎΠΌΠ±ΠΈΠ½ΠΈΡΠΎΠ²Π°Π½Π½ΡΠΉ ΡΠ΅ΡΠΌΠΎΠΏΠ»Π°ΡΡΠΈΡΠ½ΡΠΉ Π΄ΠΈΡΠΏΠ΅ΡΡΠ½ΡΠΉ Π½Π°Π½ΠΎΠ½Π°ΠΏΠΎΠ»Π½ΠΈΡΠ΅Π»Ρ. ΠΠΎΠ»ΡΡΠ΅Π½Π½ΡΠΉ ΡΡΠ΅Ρ
ΠΊΠΎΠΌΠΏΠΎΠ½Π΅Π½ΡΠ½ΡΠΉ ΡΠΏΠΎΠΊΡΠΈΠ΄Π½ΡΠΉ Π½Π°Π½ΠΎΠΊΠΎΠΌΠΏΠΎΠ·ΠΈΡ ΡΠΎΠ΄Π΅ΡΠΆΠΈΡ
ΡΠ΄Π°ΡΠΎΠΏΡΠΎΡΠ½ΡΠΉ ΠΏΠΎΠ»ΠΈΡΡΠΈΡΠΎΠ» Π² Π²ΠΈΠ΄Π΅ ΡΠ΅ΡΠΌΠΎΠΏΠ»Π°ΡΡΠΈΡΠ½ΡΡ
ΠΈ ΠΊΡΠ΅ΠΌΠ½Π΅Π·Π΅ΠΌΠ½ΡΡ
Π½Π°Π½ΠΎΡΠ°ΡΡΠΈΡ, ΠΏΡΠ΅Π΄ΡΡΠ°Π²Π»ΡΡΡΠΈΡ
Π΅Π³ΠΎ Π΄ΠΈΡΠΏΠ΅ΡΡΠ½ΡΠ΅ ΡΠ°Π·Ρ. Π§ΡΠΎΠ±Ρ ΠΏΠΎΠ»ΡΡΠΈΡΡ Π±ΠΎΠ»Π΅Π΅ Π²ΡΡΠΎΠΊΠΈΠ΅ ΠΏΠΎΠΊΠ°Π·Π°ΡΠ΅Π»ΠΈ ΠΏΡΠΎΡΠ½ΠΎΡΡΠΈ Π±Π΅Π·
Π²ΠΎΠ·Π΄Π΅ΠΉΡΡΠ²ΠΈΡ Π½Π° Π΄ΡΡΠ³ΠΈΠ΅ Π·Π°Π΄Π°Π½Π½ΡΠ΅ ΠΌΠ΅Ρ
Π°Π½ΠΈΡΠ΅ΡΠΊΠΈΠ΅ ΠΏΠΎΠΊΠ°Π·Π°ΡΠ΅Π»ΠΈ, ΠΏΡΠΎΠ²ΠΎΠ΄ΠΈΠ»ΠΈ ΠΈΡΠΏΡΡΠ°Π½ΠΈΡ Π½Π° ΠΏΡΠΎΡΠ½ΠΎΡΡΡ ΠΏΡΠΈ ΠΈΠ·Π³ΠΈΠ±Π΅ ΠΈ ΡΠΆΠ°ΡΠΈΠΈ ΠΈ Π½Π° ΡΠ΄Π°ΡΠ½ΡΡ Π²ΡΠ·ΠΊΠΎΡΡΡ. ΠΠ»Ρ ΠΏΡΠ΅Π΄ΡΡΠ°Π²Π»Π΅Π½ΠΈΡ ΠΌΠ°ΡΠ΅ΠΌΠ°ΡΠΈΡΠ΅ΡΠΊΠΈΡ
ΠΌΠΎΠ΄Π΅Π»Π΅ΠΉ Ρ ΡΠ΅Π»ΡΡ ΠΏΡΠΎΠ³Π½ΠΎΠ·ΠΈΡΠΎΠ²Π°Π½ΠΈΡ ΠΌΠ΅Ρ
Π°Π½ΠΈΡΠ΅ΡΠΊΠΎΠ³ΠΎ ΠΏΠΎΠ²Π΅Π΄Π΅Π½ΠΈΡ Π³ΠΈΠ±ΡΠΈΠ΄Π½ΠΎΠ³ΠΎ Π½Π°Π½ΠΎΠΊΠΎΠΌΠΏΠΎΠ·ΠΈΡΠ° Π²
ΠΊΠ°ΡΠ΅ΡΡΠ²Π΅ ΡΡΠ½ΠΊΡΠΈΠΈ ΡΠΈΠ·ΠΈΡΠ΅ΡΠΊΠΈΡ
ΡΠ°ΠΊΡΠΎΡΠΎΠ² ΠΈΡΠΏΠΎΠ»ΡΠ·ΠΎΠ²Π°Π»ΠΈ ΡΠ΅Π½ΡΡΠ°Π»ΡΠ½ΡΠΉ ΠΊΠΎΠΌΠΏΠΎΠ·ΠΈΡΠΈΠΎΠ½Π½ΡΠΉ ΠΏΠ»Π°Π½.
ΠΡΡΠ»Π΅Π΄ΠΎΠ²Π°Π»ΠΈ ΡΠΎΠ΄Π΅ΡΠΆΠ°Π½ΠΈΠ΅ ΡΠ΄Π°ΡΠΎΠΏΡΠΎΡΠ½ΠΎΠ³ΠΎ ΠΏΠΎΠ»ΠΈΡΡΠΈΡΠΎΠ»Π°, ΠΊΡΠ΅ΠΌΠ½Π΅Π·Π΅ΠΌΠ° ΠΈ ΡΠΏΡΠΎΡΠ½ΡΡΡΠ΅Π³ΠΎ ΡΠ»Π΅ΠΌΠ΅Π½ΡΠ°
Π² Π½Π°Π½ΠΎΠΊΠΎΠΌΠΏΠΎΠ·ΠΈΡΠ΅. ΠΠ° ΠΎΡΠ½ΠΎΠ²Π΅ ΠΌΠ°ΡΠ΅ΠΌΠ°ΡΠΈΡΠ΅ΡΠΊΠΈΡ
ΡΡΠ½ΠΊΡΠΈΠΉ, ΠΏΠΎΠ»ΡΡΠ΅Π½Π½ΡΡ
ΠΏΠΎ ΠΌΠΎΠ΄Π΅Π»ΠΈ ΡΠ΅Π½ΡΡΠ°Π»ΡΠ½ΠΎΠ³ΠΎ
ΠΊΠΎΠΌΠΏΠΎΠ·ΠΈΡΠΈΠΎΠ½Π½ΠΎΠ³ΠΎ ΠΏΠ»Π°Π½Π°, Π΄Π»Ρ Π²ΡΠ²Π΅Π΄Π΅Π½ΠΈΡ ΠΎΠΏΡΠΈΠΌΠ°Π»ΡΠ½ΡΡ
Π·Π½Π°ΡΠ΅Π½ΠΈΠΉ ΠΌΠ΅Ρ
Π°Π½ΠΈΡΠ΅ΡΠΊΠΈΡ
ΡΠ²ΠΎΠΉΡΡΠ² ΠΈΡΠΏΠΎΠ»ΡΠ·ΠΎΠ²Π°Π»ΠΈ Π³Π΅Π½Π΅ΡΠΈΡΠ΅ΡΠΊΠΈΠΉ Π°Π»Π³ΠΎΡΠΈΡΠΌ, ΡΠ²Π»ΡΡΡΠΈΠΉΡΡ ΠΎΠ΄Π½ΠΈΠΌ ΠΈΠ· ΡΠ°ΠΌΡΡ
ΠΌΠΎΡΠ½ΡΡ
ΡΡΠ΅Π΄ΡΡΠ² ΠΎΠΏΡΠΈΠΌΠΈΠ·Π°ΡΠΈΠΈ.
Π£ΡΡΠ°Π½ΠΎΠ²Π»Π΅Π½ΠΎ, ΡΡΠΎ ΡΠΎΡΠ΅ΡΠ°Π½ΠΈΠ΅ Π½Π°Π½ΠΎΡΠ°ΡΡΠΈΡ Π½Π° ΠΎΡΠ½ΠΎΠ²Π΅ ΡΠ΄Π°ΡΠΎΠΏΡΠΎΡΠ½ΠΎΠ³ΠΎ ΠΏΠΎΠ»ΠΈΡΡΠΈΡΠΎΠ»Π° ΠΈ ΠΊΡΠ΅ΠΌΠ½Π΅Π·Π΅ΠΌΠ°
Π·Π½Π°ΡΠΈΡΠ΅Π»ΡΠ½ΠΎ ΡΠ²Π΅Π»ΠΈΡΠΈΠ²Π°Π΅Ρ ΡΠΎΠΏΡΠΎΡΠΈΠ²Π»Π΅Π½ΠΈΠ΅ ΡΠΏΠΎΠΊΡΠΈΠ΄Π½ΠΎΠΉ ΡΠΌΠΎΠ»Ρ ΡΠΆΠ°ΡΠΈΡ ΠΈ ΡΠ΄Π°ΡΡ Π½Π° 57 ΠΈ 421%
ΡΠΎΠΎΡΠ²Π΅ΡΡΡΠ²Π΅Π½Π½ΠΎ. ΠΡΠΈ ΡΠΎΠΏΡΠΎΡΠΈΠ²Π»Π΅Π½ΠΈΠΈ ΠΈΠ·Π³ΠΈΠ±Ρ ΠΏΠΎΠ»ΠΎΠΆΠΈΡΠ΅Π»ΡΠ½ΡΡ
ΠΈΠ·ΠΌΠ΅Π½Π΅Π½ΠΈΠΉ Π½Π΅ Π½Π°Π±Π»ΡΠ΄Π°Π΅ΡΡΡ,
ΡΠ΄Π»ΠΈΠ½Π΅Π½ΠΈΠ΅ ΠΏΡΠΈ ΠΈΠ·Π³ΠΈΠ±Π½ΠΎΠΌ ΡΠ°Π·ΡΡΠ²Π΅ ΡΠ²Π΅Π»ΠΈΡΠΈΠ²Π°Π΅ΡΡΡ Π΄ΠΎ 144%. Π‘ ΠΏΠΎΠΌΠΎΡΡΡ ΡΠ½Π΅ΡΠ³ΠΎΠ΄ΠΈΡΠΏΠ΅ΡΡΠΈΠΎΠ½Π½ΠΎΠ³ΠΎ
ΡΠ΅Π½ΡΠ³Π΅Π½ΠΎΠ²ΡΠΊΠΎΠ³ΠΎ ΠΈΠ·Π»ΡΡΠ΅Π½ΠΈΡ ΠΈ ΡΠΊΠ°Π½ΠΈΡΡΡΡΠ΅ΠΉ ΡΠ»Π΅ΠΊΡΡΠΎΠ½Π½ΠΎΠΉ ΠΌΠΈΠΊΡΠΎΡΠΊΠΎΠΏΠΈΠΈ ΠΏΡΠΎΠ²Π΅Π΄Π΅Π½ΠΎ ΠΈΡΡΠ»Π΅Π΄ΠΎΠ²Π°Π½ΠΈΠ΅
ΠΌΠΎΡΡΠΎΠ»ΠΎΠ³ΠΈΠΈ ΠΏΠΎΠ²Π΅ΡΡ
Π½ΠΎΡΡΠΈ ΡΠ°Π·ΡΡΡΠ΅Π½ΠΈΡ.ΠΠ΅Π·Π²Π°ΠΆΠ°ΡΡΠΈ Π½Π° ΡΠ΅ ΡΠΎ Π΅ΠΏΠΎΠΊΡΠΈΠ΄Π½Ρ ΡΠΌΠΎΠ»ΠΈ ΠΌΠ°ΡΡΡ Ρ
ΠΎΡΠΎΡΡ Π³ΡΠ°Π½ΠΈΡΡ ΠΌΡΡΠ½ΠΎΡΡΡ ΠΏΡΠΈ
ΡΠΎΠ·ΡΡΠ·Ρ, Π²ΠΎΠ½ΠΈ ΠΊΡΠΈΡ
ΠΊΡ Ρ Ρ
Π°ΡΠ°ΠΊΡΠ΅ΡΠΈΠ·ΡΡΡΡΡΡ ΡΠ»Π°Π±ΠΊΠΈΠΌ ΠΎΠΏΠΎΡΠΎΠΌ ΡΠΎΠ·Π²ΠΈΡΠΊΡ ΡΡΡΡΠΈΠ½ΠΈ. ΠΠ·
ΠΌΠ΅ΡΠΎΡ ΠΏΠΎΠΊΡΠ°ΡΠ°Π½Π½Ρ ΠΌΠ΅Ρ
Π°Π½ΡΡΠ½ΠΎΡ ΠΌΡΡΠ½ΠΎΡΡΡ Ρ Π²βΡΠ·ΠΊΠΎΡΡΡ ΡΡΠΉΠ½ΡΠ²Π°Π½Π½Ρ Π΅ΠΏΠΎΠΊΡΠΈΠ΄Π½ΠΈΡ
Π½Π°Π½ΠΎΠΊΠΎΠΌΠΏΠΎΠ·ΠΈΡΡΠ² ΡΠΊ ΠΌΠΎΠ΄ΠΈΡΡΠΊΠ°ΡΠΎΡ Π²ΠΈΠΊΠΎΡΠΈΡΡΠΎΠ²ΡΠ²Π°Π»ΠΈ Π½ΠΎΠ²ΠΈΠΉ ΠΊΠΎΠΌΠ±ΡΠ½ΠΎΠ²Π°Π½ΠΈΠΉ ΡΠ΅ΡΠΌΠΎΠΏΠ»Π°ΡΡΠΈΡΠ½ΠΈΠΉ Π΄ΠΈΡΠΏΠ΅ΡΡΠ½ΠΈΠΉ Π½Π°ΠΏΠΎΠ²Π½ΡΠ²Π°Ρ. ΠΠΎ ΡΠΊΠ»Π°Π΄Ρ ΠΎΡΡΠΈΠΌΠ°Π½ΠΎΠ³ΠΎ ΡΡΠΈΠΊΠΎΠΌΠΏΠΎΠ½Π΅Π½ΡΠ½ΠΎΠ³ΠΎ Π΅ΠΏΠΎΠΊΡΠΈΠ΄Π½ΠΎΠ³ΠΎ Π½Π°Π½ΠΎΠΊΠΎΠΌΠΏΠΎΠ·ΠΈΡΠ° Π²Ρ
ΠΎΠ΄ΠΈΡΡ ΡΠ΄Π°ΡΠΎΠΌΡΡΠ½ΠΈΠΉ ΠΏΠΎΠ»ΡΡΡΠΈΡΠΎΠ» Ρ Π²ΠΈΠ³Π»ΡΠ΄Ρ
ΡΠ΅ΡΠΌΠΎΠΏΠ»Π°ΡΡΠΈΡΠ½ΠΈΡ
Ρ ΠΊΡΠ΅ΠΌΠ½Π΅Π·Π΅ΠΌΠ½ΠΈΡ
Π½Π°Π½ΠΎΡΠ°ΡΡΠΈΠ½ΠΎΠΊ, ΡΠΎ ΡΠ²Π»ΡΡΡΡ ΡΠΎΠ±ΠΎΡ ΠΉΠΎΠ³ΠΎ
Π΄ΠΈΡΠΏΠ΅ΡΡΠ½Ρ ΡΠ°Π·ΠΈ. Π©ΠΎΠ± ΠΎΡΡΠΈΠΌΠ°ΡΠΈ Π±ΡΠ»ΡΡ Π²ΠΈΡΠΎΠΊΡ ΠΏΠΎΠΊΠ°Π·Π½ΠΈΠΊΠΈ ΠΌΡΡΠ½ΠΎΡΡΡ Π±Π΅Π· Π²ΠΏΠ»ΠΈΠ²Ρ
Π½Π° ΡΠ½ΡΡ Π·Π°Π΄Π°Π½Ρ ΠΌΠ΅Ρ
Π°Π½ΡΡΠ½Ρ ΠΏΠΎΠΊΠ°Π·Π½ΠΈΠΊΠΈ, ΠΏΡΠΎΠ²ΠΎΠ΄ΠΈΠ»ΠΈ Π²ΠΈΠΏΡΠΎΠ±ΡΠ²Π°Π½Π½Ρ Π½Π° ΠΌΡΡΠ½ΡΡΡΡ ΠΏΡΠΈ
Π·Π³ΠΈΠ½Ρ Ρ ΡΡΠΈΡΠΊΡ ΡΠ° Π½Π° ΡΠ΄Π°ΡΠ½Ρ Π²βΡΠ·ΠΊΡΡΡΡ. ΠΠ»Ρ ΠΏΡΠ΅Π΄ΡΡΠ°Π²Π»Π΅Π½Π½Ρ ΠΌΠ°ΡΠ΅ΠΌΠ°ΡΠΈΡΠ½ΠΈΡ
ΠΌΠΎΠ΄Π΅Π»Π΅ΠΉ Π· ΠΌΠ΅ΡΠΎΡ ΠΏΡΠΎΠ³Π½ΠΎΠ·ΡΠ²Π°Π½Π½Ρ ΠΌΠ΅Ρ
Π°Π½ΡΡΠ½ΠΎΡ ΠΏΠΎΠ²Π΅Π΄ΡΠ½ΠΊΠΈ Π³ΡΠ±ΡΠΈΠ΄Π½ΠΎΠ³ΠΎ Π½Π°Π½ΠΎΠΊΠΎΠΌΠΏΠΎΠ·ΠΈΡΠ° ΡΠΊ ΡΡΠ½ΠΊΡΡΡ ΡΡΠ·ΠΈΡΠ½ΠΈΡ
ΡΠΈΠ½Π½ΠΈΠΊΡΠ² Π²ΠΈΠΊΠΎΡΠΈΡΡΠ°Π»ΠΈ ΡΠ΅Π½ΡΡΠ°Π»ΡΠ½ΠΈΠΉ ΠΊΠΎΠΌΠΏΠΎΠ·ΠΈΡΡΠΉΠ½ΠΈΠΉ
ΠΏΠ»Π°Π½. ΠΠΎΡΠ»ΡΠ΄ΠΆΡΠ²Π°Π»ΠΈ Π²ΠΌΡΡΡ ΡΠ΄Π°ΡΠΎΠΌΡΡΠ½ΠΎΠ³ΠΎ ΠΏΠΎΠ»ΡΡΡΠΈΡΠΎΠ»Ρ, ΠΊΡΠ΅ΠΌΠ½Π΅Π·Π΅ΠΌΡ Ρ Π·ΠΌΡΡΠ½ΡΠ²Π°Π»ΡΠ½ΠΎΠ³ΠΎ Π΅Π»Π΅ΠΌΠ΅Π½ΡΠ° Π² Π½Π°Π½ΠΎΠΊΠΎΠΌΠΏΠΎΠ·ΠΈΡΡ. ΠΠ° ΠΎΡΠ½ΠΎΠ²Ρ ΠΌΠ°ΡΠ΅ΠΌΠ°ΡΠΈΡΠ½ΠΈΡ
ΡΡΠ½ΠΊΡΡΠΉ, ΠΎΡΡΠΈΠΌΠ°Π½ΠΈΡ
Π·Π° ΠΌΠΎΠ΄Π΅Π»Π»Ρ ΡΠ΅Π½ΡΡΠ°Π»ΡΠ½ΠΎΠ³ΠΎ ΠΊΠΎΠΌΠΏΠΎΠ·ΠΈΡΡΠΉΠ½ΠΎΠ³ΠΎ ΠΏΠ»Π°Π½Ρ, Π΄Π»Ρ Π²ΠΈΠ²Π΅Π΄Π΅Π½Π½Ρ ΠΎΠΏΡΠΈΠΌΠ°Π»ΡΠ½ΠΈΡ
Π·Π½Π°ΡΠ΅Π½Ρ ΠΌΠ΅Ρ
Π°Π½ΡΡΠ½ΠΈΡ
Π²Π»Π°ΡΡΠΈΠ²ΠΎΡΡΠ΅ΠΉ Π²ΠΈΠΊΠΎΡΠΈΡΡΠΎΠ²ΡΠ²Π°Π»ΠΈ Π³Π΅Π½Π΅ΡΠΈΡΠ½ΠΈΠΉ Π°Π»Π³ΠΎΡΠΈΡΠΌ, ΡΠΎ Ρ ΠΎΠ΄Π½ΠΈΠΌ ΡΠ· Π½Π°ΠΉΠΌΡΡΠ½ΡΡΠΈΡ
Π·Π°ΡΠΎΠ±ΡΠ² ΠΎΠΏΡΠΈΠΌΡΠ·Π°ΡΡΡ. Π£ΡΡΠ°Π½ΠΎΠ²Π»Π΅Π½ΠΎ, ΡΠΎ
ΠΏΠΎΡΠ΄Π½Π°Π½Π½Ρ Π½Π°Π½ΠΎΡΠ°ΡΡΠΈΠ½ΠΎΠΊ Π½Π° ΠΎΡΠ½ΠΎΠ²Ρ ΡΠ΄Π°ΡΠΎΠΌΡΡΠ½ΠΎΠ³ΠΎ ΠΏΠΎΠ»ΡΡΡΠΈΡΠΎΠ»Ρ Ρ ΠΊΡΠ΅ΠΌΠ½Π΅Π·Π΅ΠΌΡ
Π·Π±ΡΠ»ΡΡΡΡ ΠΎΠΏΡΡ Π΅ΠΏΠΎΠΊΡΠΈΠ΄Π½ΠΎΡ ΡΠΌΠΎΠ»ΠΈ ΡΡΠΈΡΠΊΡ Π½Π° 57%, ΡΠ΄Π°ΡΡ β Π½Π° 421%. Π£ ΡΠΎΠΉ ΠΆΠ΅
ΡΠ°Ρ ΠΏΠΎΠ·ΠΈΡΠΈΠ²Π½ΠΈΡ
Π·ΠΌΡΠ½ ΠΏΡΠΈ ΠΎΠΏΠΎΡΡ Π·Π³ΠΈΠ½Ρ Π½Π΅ Π²ΡΠ΄ΠΌΡΡΠ°ΡΡΡΡΡ, Π²ΠΈΠ΄ΠΎΠ²ΠΆΠ΅Π½Π½Ρ Π·Π° Π·Π³ΠΈΠ½Π°Π»ΡΠ½ΠΎΠ³ΠΎ ΡΠΎΠ·ΡΠΈΠ²Ρ Π·Π±ΡΠ»ΡΡΡΡΡΡΡΡ Π΄ΠΎ 144%. ΠΡΠΎΠ²Π΅Π΄Π΅Π½ΠΎ Π΄ΠΎΡΠ»ΡΠ΄ΠΆΠ΅Π½Π½Ρ ΠΌΠΎΡΡΠΎΠ»ΠΎΠ³ΡΡ
ΠΏΠΎΠ²Π΅ΡΡ
Π½Ρ ΡΡΠΉΠ½ΡΠ²Π°Π½Π½Ρ Π·Π° Π΄ΠΎΠΏΠΎΠΌΠΎΠ³ΠΎΡ Π΅Π½Π΅ΡΠ³ΠΎΠ΄ΠΈΡΠΏΠ΅ΡΡΡΠΉΠ½ΠΎΠ³ΠΎ Π²ΠΈΠΏΡΠΎΠΌΡΠ½ΡΠ²Π°Π½Π½Ρ Ρ
ΡΠΊΠ°Π½ΡΠ²Π°Π»ΡΠ½ΠΎΡ Π΅Π»Π΅ΠΊΡΡΠΎΠ½Π½ΠΎΡ ΠΌΡΠΊΡΠΎΡΠΊΠΎΠΏΡΡ
Numerical simulation of hydrothermal features of Cu-H2O nanofluid natural convection within a porous annulus considering diverse configurations of heater
The purpose of the current study is to numerically investigate the effects of shape factors of nanoparticles on natural convection in a fluid-saturated porous annulus developed between the elliptical cylinder and square enclosure. A numerical method called the control volume-based finite element method is implemented for solving the governing equations. The modified flow and thermal structures and corresponding heat transfer features are investigated. Numerical outcomes reveal very good grid independency and excellent agreement with the existing studies. The obtained results convey that at a certain aspect ratio, an increment in Rayleigh and Darcy numbers significantly augments the heat transfer and average Nusselt number. Further, enhancement of Rayleigh number increases the velocity of nanofluid, while that of aspect ratio of the elliptical cylinder shows the opposite trend
Analysis of Nonlinear Structural Dynamics and Resonance in Trees
Wind and gravity both impact trees in storms, but wind loads greatly exceed gravity loads in most situations. Complex behavior of trees in windstorms is gradually turning into a controversial concern among ecological engineers. To better understand the effects of nonlinear behavior of trees, the dynamic forces on tree structures during periods of high winds have been examined as a mass-spring system. In fact, the simulated dynamic forces created by strong winds are studied in order to determine the responses of the trees to such dynamic loads. Many of such nonlinear differential equations are complicated to solve. Therefore, this paper focuses on an accurate and simple solution, Differential Transformation Method (DTM), to solve the derived equation. In this regard, the concept of differential transformation is briefly introduced. The approximate solution to this equation is calculated in the form of a series with easily computable terms. Then, the method has been employed to achieve an acceptable solution to the presented nonlinear differential equation. To verify the accuracy of the proposed method, the obtained results from DTM are compared with those from the numerical solution. The results reveal that this method gives successive approximations of high accuracy solution
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