Approximate Phase Change Solutions for Insulated Buried Cylinders

1983 ◽  
Vol 105 (1) ◽  
pp. 25-32 ◽  
Author(s):  
V. J. Lunardini
Keyword(s):  
Thermal Properties ◽  
Phase Change ◽  
Numerical Solutions ◽  
Single Point ◽  
Approximate Solutions ◽  
Burial Depth ◽  
Pipe Surface ◽  
Insulation Thickness ◽  
Theoretical Results ◽  
Good Agreement

The conduction problem for cylinders embedded in a medium with variable thermal properties cannot be solved exactly if phase change occurs. New, approximate solutions have been found using the quasi-steady method. These solutions consider heat flow from the entire pipe surface, rather than from a single point, as has been assumed in the past. The temperature field, phase change location, and pipe surface heat transfer can be evaluated using graphs presented for parametric ranges of temperature, thermal properties, burial depth, and insulation thickness. The theoretical results show good agreement with complete numerical solutions. The accuracy of the method increases as the Stefan number decreases and the results are of particular value for insulated hot pipes or refrigerated gas lines.

Phase Change Around Insulated Buried Pipes: Quasi-Steady Method

1981 ◽  
Vol 103 (3) ◽  
pp. 201-207 ◽  
Author(s):  
V. J. Lunardini
Keyword(s):  
Heat Transfer ◽  
Thermal Properties ◽  
Phase Change ◽  
Transfer Problem ◽  
Approximate Solutions ◽  
Burial Depth ◽  
Field Phase ◽  
Buried Pipes ◽  
Pipe Surface ◽  
Insulation Thickness

The heat transfer problem for cylinders embedded in a medium with variable thermal properties cannot be solved exactly if phase change occurs. Approximate solutions have been found using the quasi-steady method. The temperature field, phase change location, and pipe surface heat transfer can be estimated using graphs presented for parametric ranges of temperature, thermal properties, burial depth, and insulation thickness. The accuracy of the graphs increases as the Stefan number decreases and they should be of particular value for insulated hot pipes or refrigerated gas lines.

Free and Forced Vibrations of the Strongly Nonlinear Cubic-Quintic Duffing Oscillators

2017 ◽  
Vol 72 (1) ◽  
pp. 59-69 ◽  
Author(s):  
M.M. Fatih Karahan ◽  
Mehmet Pakdemirli
Keyword(s):  
Numerical Simulations ◽  
Numerical Solutions ◽  
Multiple Scales ◽  
Approximate Solutions ◽  
Response Curves ◽  
Strongly Nonlinear ◽  
Free And Forced Vibrations ◽  
Approximate Analytical Solutions ◽  
Strongly Nonlinear Oscillators ◽  
Good Agreement

AbstractStrongly nonlinear cubic-quintic Duffing oscillatoris considered. Approximate solutions are derived using the multiple scales Lindstedt Poincare method (MSLP), a relatively new method developed for strongly nonlinear oscillators. The free undamped oscillator is considered first. Approximate analytical solutions of the MSLP are contrasted with the classical multiple scales (MS) method and numerical simulations. It is found that contrary to the classical MS method, the MSLP can provide acceptable solutions for the case of strong nonlinearities. Next, the forced and damped case is treated. Frequency response curves of both the MS and MSLP methods are obtained and contrasted with the numerical solutions. The MSLP method and numerical simulations are in good agreement while there are discrepancies between the MS and numerical solutions.

The steady flow due to a rotating sphere at low and moderate Reynolds numbers

1980 ◽  
Vol 101 (2) ◽  
pp. 257-279 ◽  
Author(s):  
S. C. R. Dennis ◽  
S. N. Singh ◽  
D. B. Ingham
Keyword(s):  
Reynolds Number ◽  
Numerical Solutions ◽  
Equations Of Motion ◽  
Reynolds Numbers ◽  
Low Reynolds Numbers ◽  
Finite Set ◽  
Flow Variables ◽  
Theoretical Results ◽  
Radial Variable ◽  
Good Agreement

The problem of determining the steady axially symmetrical motion induced by a sphere rotating with constant angular velocity about a diameter in an incompressible viscous fluid which is at rest at large distances from it is considered. The basic independent variables are the polar co-ordinates (r, θ) in a plane through the axis of rotation and with origin at the centre of the sphere. The equations of motion are reduced to three sets of nonlinear second-order ordinary differential equations in the radial variable by expanding the flow variables as series of orthogonal Gegenbauer functions with argument μ = cosθ. Numerical solutions of the finite set of equations obtained by truncating the series after a given number of terms are obtained. The calculations are carried out for Reynolds numbers in the range R = 1 to R = 100, and the results are compared with various other theoretical results and with experimental observations.The torque exerted by the fluid on the sphere is found to be in good agreement with theory at low Reynolds numbers and appears to tend towards the results of steady boundary-layer theory for increasing Reynolds number. There is excellent agreement with experimental results over the range considered. A region of inflow to the sphere near the poles is balanced by a region of outflow near the equator and as the Reynolds number increases the inflow region increases and the region of outflow becomes narrower. The radial velocity increases with Reynolds number at the equator, indicating the formation of a radial jet over the narrowing region of outflow. There is no evidence of any separation of the flow from the surface of the sphere near the equator over the range of Reynolds numbers considered.

scholarly journals Analytic Approximate Solution for Falkner-Skan Equation

2014 ◽  
Vol 2014 ◽  
pp. 1-22 ◽  
Author(s):  
Vasile Marinca ◽  
Remus-Daniel Ene ◽  
Bogdan Marinca
Keyword(s):  
Differential Equation ◽  
Boundary Layer ◽  
Numerical Solutions ◽  
Approximate Solutions ◽  
Rapid Convergence ◽  
Boundary Layer Problem ◽  
Small Parameters ◽  
Optimal Homotopy Asymptotic Method ◽  
Good Agreement ◽  
Layer Problem

This paper deals with the Falkner-Skan nonlinear differential equation. An analytic approximate technique, namely, optimal homotopy asymptotic method (OHAM), is employed to propose a procedure to solve a boundary-layer problem. Our method does not depend upon small parameters and provides us with a convenient way to optimally control the convergence of the approximate solutions. The obtained results reveal that this procedure is very effective, simple, and accurate. A very good agreement was found between our approximate results and numerical solutions, which prove that OHAM is very efficient in practice, ensuring a very rapid convergence after only one iteration.

Calculated Pressure Distributions and Shock Shapes on Thick Conical Wings at High Supersonic Speeds

1967 ◽  
Vol 18 (2) ◽  
pp. 185-206 ◽  
Author(s):  
L. C. Squire
Keyword(s):  
Integral Equation ◽  
Cross Sections ◽  
Numerical Solutions ◽  
Approximate Solutions ◽  
Poor Agreement ◽  
Delta Wings ◽  
Newtonian Theory ◽  
Pressure Distributions ◽  
First Order Correction ◽  
Good Agreement

SummaryIn recent papers Messiter and Hida have proposed a first-order correction to simple Newtonian theory for the pressure distributions on the lower surfaces of lifting conical bodies with detached shocks. The method involves the solution of an integral equation which Messiter solved numerically for thin delta wings, while Hida gave an approximate solution for thick wings with diamond and bi-convex cross-sections. It is shown in the present paper that Hida’s approximate solutions give poor agreement with experiment, and a series of more precise numerical solutions of the equation are given for wings with diamond cross-sections. The pressures, and shock shapes, obtained from these solutions are in very good agreement with experiment at Mach numbers as low as 4·0.The method has also been extended to Nonweiler wings at off-design when the shock wave is detached from the leading edges. Again the agreement with experiment is good provided the integral equation is solved numerically.

Characteristics of Squeeze Air Film Between Nonparallel Plates

1983 ◽  
Vol 105 (1) ◽  
pp. 147-152 ◽  
Author(s):  
H. Takada ◽  
S. Kamigaichi ◽  
H. Miura
Keyword(s):  
Pressure Transducer ◽  
Dynamic Pressure ◽  
Air Flow ◽  
Approximate Solutions ◽  
Squeeze Film ◽  
Rectangular Plates ◽  
Flow Through ◽  
Air Film ◽  
Theoretical Results ◽  
Good Agreement

The dynamic pressure in a squeeze film and the air flow through the film were analyzed experimentally and theoretically. The dynamic pressure was measured in a squeeze film between two rectangular plates with a small pressure transducer. Approximate solutions for the rectangular squeeze film were obtained analytically. The results were valid for small excursion ratios. Next, a squeeze film between nonparallel plates (wedge film) was examined. In this case, steady air flow occurred due to the unsymmetry of the pressure distribution. To investigate this fact, the air flow was measured in a spherical squeeze film. The values showed good agreement with the theoretical results.

Amplitude Control of Limit Cycle in Chua System

2011 ◽  
Vol 328-330 ◽  
pp. 2079-2085
Author(s):  
Fu Lin Xu ◽  
Su Hua Liu
Keyword(s):  
Limit Cycle ◽  
Center Manifold ◽  
Numerical Solutions ◽  
Approximate Solutions ◽  
Analytical Control ◽  
Nonlinear Feedback ◽  
Amplitude Control ◽  
Convenient Approach ◽  
Manifold Theory ◽  
Good Agreement

The control of amplitude of limit cycle emerging from the Hopf bifurcation in Chua system under a nonlinear feedback controller is investigated in this paper, Explicit nonlinear control formulae and amplitude approximations in terms of control gains derived from the center manifold theory and normal form reduction present a convenient approach to obtain an effective analytical control and predict the amplitude of limit cycles in Chua system. The calculating simulations indicate that the approximate solutions are in good agreement with the numerical solutions.

scholarly journals An Optimal Iteration Method for Strongly Nonlinear Oscillators

2012 ◽  
Vol 2012 ◽  
pp. 1-11 ◽  
Author(s):  
Vasile Marinca ◽  
Nicolae Herişanu
Keyword(s):  
Numerical Solutions ◽  
Nonlinear Differential Equations ◽  
Nonlinear Oscillators ◽  
Approximate Solutions ◽  
High Accuracy ◽  
Restoring Force ◽  
Strongly Nonlinear ◽  
Convergence Of Approximate Solutions ◽  
Strongly Nonlinear Oscillators ◽  
Good Agreement

We introduce a new method, namely, the Optimal Iteration Perturbation Method (OIPM), to solve nonlinear differential equations of oscillators with cubic and harmonic restoring force. We illustrate that OIPM is very effective and convenient and does not require linearization or small perturbation. Contrary to conventional methods, in OIPM, only one iteration leads to high accuracy of the solutions. The main advantage of this approach consists in that it provides a convenient way to control the convergence of approximate solutions in a very rigorous way and allows adjustment of convergence regions where necessary. A very good agreement was found between approximate and numerical solutions, which prove that OIPM is very efficient and accurate.

scholarly journals Bound-state solutions and thermal properties of the modified Tietz–Hua potential

2021 ◽  
Vol 11 (1) ◽  
Author(s):  
C. A. Onate ◽  
M. C. Onyeaju ◽  
E. Omugbe ◽  
I. B. Okon ◽  
O. E. Osafile
Keyword(s):  
Thermal Properties ◽  
Vibrational Energy ◽  
Approximate Solutions ◽  
Bound State ◽  
Effect Of Temperature ◽  
Energy Eigenvalues ◽  
Radial Schrödinger Equation ◽  
Vibrational Energies ◽  
Good Agreement ◽  
Supersymmetric Approach

AbstractAn approximate solutions of the radial Schrödinger equation was obtained under a modified Tietz–Hua potential via supersymmetric approach. The effect of the modified parameter and optimization parameter respectively on energy eigenvalues were graphically and numerically examined. The comparison of the energy eigenvalues of modified Tietz–Hua potential and the actual Tietz–Hua potential were examined. The ro-vibrational energy of four molecules were also presented numerically. The thermal properties of the modified Tietz–Hua potential were calculated and the effect of temperature on each of the thermal property were examined under hydrogen fluoride, hydrogen molecule and carbon (ii) oxide. The study reveals that for a very small value of the modified parameter, the energy eigenvalues of the modified Tietz–Hua potential and that of the actual Tietz–Hua potential are equivalent. Finally, the vibrational energies for Cesium molecule was calculated and compared with the observed value. The calculated results were found to be in good agreement with the observed value.

On the stability of Kelvin waves

1989 ◽  
Vol 206 ◽  
pp. 1-23 ◽  
Author(s):  
W. K. Melville ◽  
G. G. Tomasson ◽  
D. P. Renouard
Keyword(s):  
Numerical Solutions ◽  
Nonlinear Resonance ◽  
Approximate Solutions ◽  
Kelvin Waves ◽  
Kelvin Wave ◽  
Governing Equations ◽  
Weakly Nonlinear ◽  
Approximate Analytical Solutions ◽  
The Stability ◽  
Good Agreement

We consider the evolution of weakly nonlinear dispersive long waves in a rotating channel. The governing equations are derived and approximate solutions obtained for the initial data corresponding to a Kelvin wave. In consequence of the small nonlinear speed correction it is shown that weakly nonlinear Kelvin waves are unstable to a direct nonlinear resonance with the linear Poincaré modes of the channel. Numerical solutions of the governing equations are computed and found to give good agreement with the approximate analytical solutions. It is shown that the curvature of the wavefront and the decay of the leading wave amplitude along the channel are attributable to the Poincaré waves generated by the resonance. These results appear to give a qualitative explanation of the experimental results of Maxworthy (1983), and Renouard, Chabert d'Hières & Zhang (1987).

Sign in / Sign up

Export Citation Format

Share Document