scholarly journals Series Solution for Steady Three-Dimensional Flow due to Spraying on Inclined Spinning Disk by Homotopy Perturbation Method

2012 ◽  
Vol 2012 ◽  
pp. 1-15 ◽  
Author(s):  
Saeed Dinarvand
Keyword(s):  
Perturbation Method ◽  
Series Solution ◽  
Homotopy Perturbation Method ◽  
Three Dimensional ◽  
Free Surface Flows ◽  
Three Dimensional Flow ◽  
Dimensional Flow ◽  
Homotopy Perturbation ◽  
Spinning Disk ◽  
Through Flow

The steady three-dimensional flow of condensation or spraying on inclined spinning disk is studied analytically. The governing nonlinear equations and their associated boundary conditions are transformed into the system of nonlinear ordinary differential equations. The series solution of the problem is obtained by utilizing the homotopy perturbation method (HPM). The velocity and temperature profiles are shown and the influence of Prandtl number on the heat transfer and Nusselt number is discussed in detail. The validity of our solutions is verified by the numerical results. Unlike free surface flows on an incline, this through flow is highly affected by the spray rate and the rotation of the disk.

Three-Dimensional Flow Field Measurements in a Radial Inflow Turbine Scroll Using LDV

1987 ◽  
Vol 109 (2) ◽  
pp. 163-169 ◽  
Author(s):  
M. F. Malak ◽  
A. Hamed ◽  
W. Tabakoff
Keyword(s):  
Experimental Study ◽  
Flow Field ◽  
Flow Velocity ◽  
Three Dimensional ◽  
Field Measurements ◽  
Three Dimensional Flow ◽  
Cold Flow ◽  
Dimensional Flow ◽  
Through Flow ◽  
Radial Inflow Turbine

The results of an experimental study of the three-dimensional flow field in a radial inflow turbine scroll are presented. A two-color LDV system was used in the measurement of three orthogonal velocity components at 758 points located throughout the scroll and the unvaned portion of the nozzle. The cold flow experimental results are presented for through-flow velocity contours and the cross velocity vectors.

The Homotopy Perturbation Method for Accurate Orbits of the Planets in the Solar System: The Elliptical Kepler Equation

2017 ◽  
Vol 72 (10) ◽  
pp. 933-940
Author(s):  
Aisha Alshaery
Keyword(s):  
Solar System ◽  
Perturbation Method ◽  
Series Solution ◽  
Homotopy Perturbation Method ◽  
Approximate Solutions ◽  
Accurate Solution ◽  
Homotopy Perturbation ◽  
Halley's Comet ◽  
The Mean ◽  
Kepler Equation

AbstractAccurate trajectories for the orbits of the planets in our solar system depends on obtaining an accurate solution for the elliptical Kepler equation. This equation is solved in this article using the homotopy perturbation method. Several properties of the periodicity of the obtained approximate solutions are introduced through some lemmas. Numerically, our calculations demonstrated the applicability of the obtained approximate solutions for all the planets in the solar system and also in the whole domain of eccentricity and mean anomaly. In the whole domain of the mean anomaly, 0≤M≤2π, and by using the different approximate solutions, the residuals were less than 4×10−17 for e∈[0, 0.06], 4×10−9 for e∈[0.06, 0.25], 3×10−8 for e∈[0.25, 0.40], 3×10−7 for e∈[0.40, 0.50], and 10−6 for e∈[0.50, 1.0]. Also, the approximate solutions were compared with the Bessel–Fourier series solution in the literature. In addition, the approximate homotopy solutions for the eccentric anomaly are used to show the convergence and periodicity of the approximate radial distances of Mercury and Pluto for three and five periods, respectively, as confirmation for some given lemmas. It has also been shown that the present analysis can be successfully applied to the orbit of Halley’s comet with a significant eccentricity.

Three-dimensional Flow between Two Parallel Porous Plates with Heat Transfer

2001 ◽  
Vol 56 (8) ◽  
pp. 596-600
Author(s):  
K. D. Singh ◽  
Rakesh Sharma
Keyword(s):  
Heat Transfer ◽  
Constant Velocity ◽  
Series Solution ◽  
Viscous Incompressible Fluid ◽  
Three Dimensional ◽  
Three Dimensional Flow ◽  
Suction Velocity ◽  
Dimensional Flow ◽  
Linear Partial Differential Equations ◽  
Stationary Plate

Abstract A theoretical analysis of the steady three-dimensional flow of a viscous, incompressible fluid between two parallel infinite porous horizontal plates is presented. The fluid is injected with constant velocity through the lower stationary plate and removed with a transverse sinusoidal suction velocity through the upper one in uniform horizontal motion. A series solution of the non-linear partial differential equations is obtained and discussed.

scholarly journals Three-Dimensional Flow Measurements in a Turbine Scroll

1984 ◽  
Vol 106 (2) ◽  
pp. 516-522 ◽  
Author(s):  
W. Tabakoff ◽  
B. V. R. Vittal ◽  
B. Wood
Keyword(s):  
Flow Velocity ◽  
Secondary Flow ◽  
Flow Behavior ◽  
Three Dimensional ◽  
Three Dimensional Flow ◽  
Flow Measurements ◽  
Dimensional Flow ◽  
Through Flow ◽  
Hot Film ◽  
Hot Film Anemometry

A study was conducted to determine experimentally the flow behavior in combined scroll nozzle assembly of a radial inflow turbine. Hot film anemometry technique was used to measure the three-dimensional flow velocity in the scroll. The through-flow and secondary flow velocity components are measured at various points in three scroll sections.

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