scholarly journals An Optimistic Solver for the Mathematical Model of the Flow of Johnson Segalman Fluid on the Surface of an Infinitely Long Vertical Cylinder

Materials ◽  
2021 ◽  
Vol 14 (24) ◽  
pp. 7798
Author(s):  
Naveed Ahmad Khan ◽  
Fahad Sameer Alshammari ◽  
Carlos Andrés Tavera Romero ◽  
Muhammad Sulaiman ◽  
Seyedali Mirjalili

In this paper, a novel soft computing technique is designed to analyze the mathematical model of the steady thin film flow of Johnson–Segalman fluid on the surface of an infinitely long vertical cylinder used in the drainage system by using artificial neural networks (ANNs). The approximate series solutions are constructed by Legendre polynomials and a Legendre polynomial-based artificial neural networks architecture (LNN) to approximate solutions for drainage problems. The training of designed neurons in an LNN structure is carried out by a hybridizing generalized normal distribution optimization (GNDO) algorithm and sequential quadratic programming (SQP). To investigate the capabilities of the proposed LNN-GNDO-SQP algorithm, the effect of variations in various non-Newtonian parameters like Stokes number (St), Weissenberg number (We), slip parameters (a), and the ratio of viscosities (ϕ) on velocity profiles of the of steady thin film flow of non-Newtonian Johnson–Segalman fluid are investigated. The results establish that the velocity profile is directly affected by increasing Stokes and Weissenberg numbers while the ratio of viscosities and slip parameter inversely affects the fluid’s velocity profile. To validate the proposed technique’s efficiency, solutions and absolute errors are compared with reference solutions calculated by RK-4 (ode45) and the Genetic algorithm-Active set algorithm (GA-ASA). To study the stability, efficiency and accuracy of the LNN-GNDO-SQP algorithm, extensive graphical and statistical analyses are conducted based on absolute errors, mean, median, standard deviation, mean absolute deviation, Theil’s inequality coefficient (TIC), and error in Nash Sutcliffe efficiency (ENSE). Statistics of the performance indicators are approaching zero, which dictates the proposed algorithm’s worth and reliability.

2013 ◽  
Vol 19 (4) ◽  
pp. 513-527
Author(s):  
Kamran Alam ◽  
M.T. Rahim ◽  
S. Islam ◽  
A.M. Sidiqqui

In this study, the pseudo plastic model is used to obtain the solution for the steady thin film flow on the outer surface of long vertical cylinder for lifting and drainage problems. The non-linear governing equations subject to appropriate boundary conditions are solved analytically for velocity profiles by a modified homotopy perturbation method called the Optimal Homotopy Asymptotic method. Expressions for the velocity profile, volume flux, average velocity, shear stress on the cylinder, normal stress differences, force to hold the vertical cylindrical surface in position, have been derived for both the problems. For the non-Newtonian parameter ?=0, we retrieve Newtonian cases for both the problems. We also plotted and discussed the affect of the Stokes number St, the non-Newtonian parameter ? and the thickness ? of the fluid film on the fluid velocities.


2012 ◽  
Vol 7 (41) ◽  
pp. 3554-3565
Author(s):  
M Siddiqui A ◽  
Akram M ◽  
N Memon K ◽  
Islam S ◽  
khan Khalid

1984 ◽  
Vol 51 (3) ◽  
pp. 691-692 ◽  
Author(s):  
T. R. Roy

An accelerating laminar thin-film flow along a vertical wall is investigated in this paper. Using a cubic polynomial for the velocity profile inside the boundary layer the momentum integral equation is solved by a Runge-Kutta method to determine the boundary layer thickness. The corresponding film-thickness is then calculated for the entrance region. These results are compared with the existing results obtained by using a parabolic velocity profile.


2018 ◽  
Vol 44 ◽  
pp. 00069
Author(s):  
Nikolay Peganov ◽  
Aleksandr Tumanov ◽  
Vladimir Tumanov

In the work performed adaptation of artificial neural networks in modern security systems potentially dangerous technical objects — high-rise buildings as tools for assessing and forecasting in management decision. The study obtained the main scientific results: the mathematical model of risk assessment of man-made emergencies based on artificial neural networks; the mathematical model, adapted to the cumulative model of development technogene emergency-fire; provided risk assessment technique manmade emergencies based on artificial neural networks; represented private man-made fire risk assessment methodology using artificial neural networks.


2013 ◽  
Vol 54 ◽  
pp. 377 ◽  
Author(s):  
Lisa Cheree Mayo ◽  
Scott McCue ◽  
Timothy Moroney

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