TY - JOUR

T1 - An optimistic solver for the mathematical model of the flow of johnson segalman fluid on the surface of an infinitely long vertical cylinder

AU - Khan, Naveed Ahmad

AU - Alshammari, Fahad Sameer

AU - Romero, Carlos Andrés Tavera

AU - Sulaiman, Muhammad

AU - Mirjalili, Seyedali

N1 - Funding Information:
Funding: The APC was funded by Dirección General de Investigaciones of Universidad Santiago de Cali under call No. 01-2021.
Publisher Copyright:
© 2021 by the authors. Licensee MDPI, Basel, Switzerland.

PY - 2021/12/1

Y1 - 2021/12/1

N2 - 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.

AB - 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.

KW - Computational fluid dynamics

KW - Drainage problems

KW - Generalized normal distribution optimization

KW - Hybrid soft computing

KW - Johnson Segalman model

KW - Sequential quadratic programming

KW - Weighted legendre neural networks

UR - http://www.scopus.com/inward/record.url?scp=85121343297&partnerID=8YFLogxK

U2 - 10.3390/ma14247798

DO - 10.3390/ma14247798

M3 - Article

AN - SCOPUS:85121343297

VL - 14

JO - Materials

JF - Materials

SN - 1996-1944

IS - 24

M1 - 7798

ER -