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Khan NA, Alshammari FS, Tavera Romero CA, Sulaiman M, Mirjalili S. 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; 14:ma14247798. [PMID: 34947391 PMCID: PMC8707176 DOI: 10.3390/ma14247798] [Citation(s) in RCA: 8] [Impact Index Per Article: 2.7] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Download PDF] [Figures] [Subscribe] [Scholar Register] [Received: 10/11/2021] [Revised: 12/03/2021] [Accepted: 12/09/2021] [Indexed: 11/16/2022]
Abstract
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.
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Affiliation(s)
- Naveed Ahmad Khan
- Department of Mathematics, Abdul Wali Khan University, Mardan 23200, Pakistan; (N.A.K.); (M.S.)
| | - Fahad Sameer Alshammari
- Department of Mathematics, College of Science and Humanities in Alkharj, Prince Sattam bin Abdulaziz University, Al-Kharj 11942, Saudi Arabia
- Correspondence:
| | | | - Muhammad Sulaiman
- Department of Mathematics, Abdul Wali Khan University, Mardan 23200, Pakistan; (N.A.K.); (M.S.)
| | - Seyedali Mirjalili
- Centre for Artificial Intelligence Research and Optimisation, Torrens University Australia, Fortitude Valley, Brisbane, QLD 4006, Australia;
- Yonsei Frontier Lab, Yonsei University, Seoul 03722, Korea
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Farooq S, Khan MI, Riahi A, Chammam W, Khan WA. Modeling and interpretation of peristaltic transport in single wall carbon nanotube flow with entropy optimization and Newtonian heating. COMPUTER METHODS AND PROGRAMS IN BIOMEDICINE 2020; 192:105435. [PMID: 32203793 DOI: 10.1016/j.cmpb.2020.105435] [Citation(s) in RCA: 4] [Impact Index Per Article: 1.0] [Reference Citation Analysis] [Abstract] [Key Words] [MESH Headings] [Track Full Text] [Subscribe] [Scholar Register] [Received: 12/29/2019] [Revised: 03/02/2020] [Accepted: 03/03/2020] [Indexed: 06/10/2023]
Abstract
Due to some special characteristics like the effective thermal conductivities, appropriate mechanical features, and superior electrical properties, carbon nanostructures have been known as the proper materials to reach the desired characteristics of fluids. In the recent past fluid flows through peristaltic mechanism subject to carbon nanotubes are utilized to handle the overcome of industrial and physiological materials thermal properties. Due to rich thermal characteristics nanotubes are used into basic industrial materials to improve the required ability of thermal properties of these industrial materials. Thus various kinds of nanoparticles e.g. aluminum, copper, zinc oxides and carbon nanotubes are significantly utilized to increase the thermal abilities of base liquids. Because of the several significant special qualities such as improved thermal conductivities, applicable mechanical structures, and rich electrical properties, CNTs have been acknowledged as the accurate tools to reach the wanted features of fluids, due to such abilities CNTs are high demanding research topic in all domains. Keeping such efficiencies of CNTs in notice, this analysis is prepared for peristalsis of carbon nanotubes through non-uniform asymmetric channel. Flow mechanism is modeled in view of conservation principles under desired assumptions likely porous medium, non-linear mixed convection, heat generation absorption and Newtonian heating. Rate of total entropy is evaluated by using thermodynamics second law. Lubrication approach utilized here to attain the simplified form of the complex flow expressions. The pressure gradient, velocity along axial direction, temperature, effective heat transfer rate and entropy expressions subject to boundary conditions are evaluated numerically via built-in-Shooting procedure. Furthermore these numerical results are used to sketch the variations of all the above mentioned quantities against the pertinent parameters of interest. According to physical discussion temperature reduces for heat absorption case and enhances for heat generation case. Impact of Prandtl number on entropy indicates that entropy is minimum due to less fluid friction (i.e. Prandtl number less than 1).
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Affiliation(s)
- Shahid Farooq
- Deparment of Mathematics and Statistics, PMAS Arid Agriculture University Shamsabad, Rawalpindi, 46300, Pakistan
| | - M Ijaz Khan
- Department of Mathematics, Riphah International University, Faisalabad Campus, Faisalabad, 38000, Pakistan.
| | - Anis Riahi
- Department of Mathematics, College of Science Al-Zulfi, Majmaah University, P. O. Box 66, Al-Majmaah, 11952, Saudi Arabia
| | - Wathek Chammam
- Department of Mathematics, College of Science Al-Zulfi, Majmaah University, P. O. Box 66, Al-Majmaah, 11952, Saudi Arabia
| | - W A Khan
- School of Mathematics and Statistics, Beijing Institute of Technology, Beijing, 100081, China; Department of Mathematics, Mohi-ud-Din Islamic University, Nerian Sharif, Azad Kashmir, 12010, Pakistan
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Nadeem S, Abbas N, Elmasry Y, Malik MY. Numerical analysis of water based CNTs flow of micropolar fluid through rotating frame. COMPUTER METHODS AND PROGRAMS IN BIOMEDICINE 2020; 186:105194. [PMID: 31751872 DOI: 10.1016/j.cmpb.2019.105194] [Citation(s) in RCA: 10] [Impact Index Per Article: 2.5] [Reference Citation Analysis] [Abstract] [Key Words] [MESH Headings] [Track Full Text] [Subscribe] [Scholar Register] [Received: 10/26/2019] [Revised: 11/04/2019] [Accepted: 11/07/2019] [Indexed: 06/10/2023]
Abstract
BACKGROUND In this article, the nanomaterial flow of micropolar fluid in rotating frame is considered. The SWCNT and MWCNT with base fluid namely pure water is also taken into account to analyze the flow behavior over stretching surface. Mathematical model have been constructed under the nanomaterial of micropolar fluid. METHOD The governing equations have been developed in the form of system of partial differential equations. The partial differential equations are transformed into ordinary differential equations using similarity transformations. The transformed system has been solved through MAPLE software. RESULTS The physical parameters like as thermal slip effects, velocity slip effects and magnetic hydrodynamics on the micropolar nanofluid are presented by tables and graphs. Surprisingly in the rotating parameter, F''(0) and - θ'(0) increases for higher values of the rotating parameter while opposite to be noted for G''(0). The Nusselt number and skin friction increases for higher values of micropolar parameter but MWCNT achieves higher heat transfer as associated to SWCNT.
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Affiliation(s)
- S Nadeem
- Mathematics and its Applications in Life Sciences Research Group, Ton Duc Thang University, Ho Chi Minh City, Vietnam; Faculty of Mathematics and Statistics, Ton Duc Thang University, Ho Chi Minh City, Vietnam.
| | - Nadeem Abbas
- Department of Mathematics, Quaid-I-Azam University 45320, Islamabad 44000, Pakistan
| | - Yasser Elmasry
- Department of Mathematics, College of Sciences, King Khalid University, PO Box 9004, Abha 61413, Saudi Arabia
| | - M Y Malik
- Department of Mathematics, College of Sciences, King Khalid University, PO Box 9004, Abha 61413, Saudi Arabia
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Hayat T, Waqar Ahmad M, Ijaz Khan M, Alsaedi A. Entropy optimization in CNTs based nanomaterial flow induced by rotating disks: A study on the accuracy of statistical declaration and probable error. COMPUTER METHODS AND PROGRAMS IN BIOMEDICINE 2020; 184:105105. [PMID: 31627151 DOI: 10.1016/j.cmpb.2019.105105] [Citation(s) in RCA: 3] [Impact Index Per Article: 0.8] [Reference Citation Analysis] [Abstract] [Key Words] [MESH Headings] [Track Full Text] [Subscribe] [Scholar Register] [Received: 09/17/2019] [Revised: 09/29/2019] [Accepted: 09/30/2019] [Indexed: 06/10/2023]
Abstract
BACKGROUND CNTs (Carbon nanotubes) being allotropes of carbon, made of graphene and diameters of single and multi-walls carbon nanotubes are typically 0.8 to 2 nm and 5 to 20 mn, although diameter of MWCNTs can exceed 100 nm. Carbon nanotubes lengths range from less than 100 nm to 0.5 m. Their impressive structural, electronic and mechanical attributes subject to their small size and mass, their high electrical and thermal conductivities, and their strong mechanical potency. CNTs based materials are successfully applied in medicine and pharmacy subject to their huge surface area that is proficient of conjugating or adsorbing with a wide variety of genes, drugs, antibodies, vaccines and biosensors etc. Therefore, we have presented a theoretical study about mathematical modeling of CNTs based viscous material flow between two rotating disks. Both types of nanotubes i.e., SWCNTs and MWCNTs are considered. Xue model is used for the mathematical modeling. Fluid flow is due to rotating disks. Main focus here is given to probable error and statistical declaration. Entropy is calculated for both single and multi-walls nanotubes. METHOD Nonlinear PDEs are first converted into ODEs and then computed for homotopy convergent solutions. RESULTS AND CONCLUSION Statistical declaration and probable error for skin friction and Nusselt number are numerically computed and discussed through Tables. From obtained outcomes it is concluded that magnitude of skin friction increases at both disks surface for higher values of Reynolds number, lower stretching parameter and porosity parameter while it decays for both of disks versus larger rotation parameter. Nusselt number or heat transfer rate also enhances at both disks in the presence of radiation and Reynolds number while it decays against Eckert number.
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Affiliation(s)
- T Hayat
- Department of Mathematics, Quaid-I-Azam University 45320, Islamabad 44000, Pakistan; Nonlinear Analysis and Applied Mathematics (NAAM) Research Group, Faculty of Science, King Abdulaziz University, P. O. Box 80207, Jeddah 21589, Saudi Arabia.
| | - M Waqar Ahmad
- Department of Mathematics, Quaid-I-Azam University 45320, Islamabad 44000, Pakistan
| | - M Ijaz Khan
- Department of Mathematics, Quaid-I-Azam University 45320, Islamabad 44000, Pakistan.
| | - A Alsaedi
- Nonlinear Analysis and Applied Mathematics (NAAM) Research Group, Faculty of Science, King Abdulaziz University, P. O. Box 80207, Jeddah 21589, Saudi Arabia
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Farooq S, Ijaz Khan M, Waqas M, Hayat T, Alsaedi A. Transport of hybrid type nanomaterials in peristaltic activity of viscous fluid considering nonlinear radiation, entropy optimization and slip effects. COMPUTER METHODS AND PROGRAMS IN BIOMEDICINE 2020; 184:105086. [PMID: 31627153 DOI: 10.1016/j.cmpb.2019.105086] [Citation(s) in RCA: 5] [Impact Index Per Article: 1.3] [Reference Citation Analysis] [Abstract] [Key Words] [MESH Headings] [Track Full Text] [Subscribe] [Scholar Register] [Received: 07/19/2019] [Revised: 09/13/2019] [Accepted: 09/19/2019] [Indexed: 06/10/2023]
Abstract
BACKGROUND In last few decades, a new class of working materials which comprises from two solid materials dispersed in a continuous phase liquid was established and deeply scrutinized. These materials are called hybrid nanomaterials. This research article aims to investigate entropy optimization in hybrid nanomaterial flow through a rotating peristaltic channel walls. Flow behavior is analyzed between the channels which is caused by propagation of sinusoidal waves. Viscosity of fluid is considered variable instead of constant characteristics. Fluid saturates through porous attributes of channel walls. Nonliear radiative flux and convective condition are considered. Slip conditions are imposed at the boundary of walls. METHODS Built-in-Shooting technique is employed to obtain the numerical outcomes for the considered flow problem. RESULTS Impacts of sundry variables on the entropy, temperature and velocity are scrutinized through different graphs. Numerical result presents that the axial velocity escalates with the inclusion of hybrid nanomaterial. The temperature of fluid enhances through higher estimations of hybrid nanoparticles. CONCLUSIONS Here the flow behavior is discussed between the channels which are caused by propagation of sinusoidal waves with speed c. Entropy generation rate is minimum for variable viscosity and maximum for hybrid nanoparticles. Hybrid nanoparticles increase the temperature of fluid. Bejan number presents the similar impact for variable viscosity and thermal slip parameters. Temperature field decays through higher values of Brinkman number.
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Affiliation(s)
- S Farooq
- Department of Mathematics and Statistics, PMAS Arid Agriculture University Shamsabad, Rawalpindi 46300, Pakistan.
| | - M Ijaz Khan
- Department of Mathematics, Quaid-I-Azam University 45320, Islamabad 44000, Pakistan.
| | - M Waqas
- NUTECH School of Applied Sciences and Humanities, National University of Technology, Islamabad, Pakistan.
| | - T Hayat
- Department of Mathematics, Quaid-I-Azam University 45320, Islamabad 44000, Pakistan; Nonlinear Analysis and Applied Mathematics (NAAM) Research Group, Department of Mathematics, Faculty of Science, King Abdulaziz University, P.O. Box 80257, Jeddah 21589, Saudi Arabia
| | - A Alsaedi
- Nonlinear Analysis and Applied Mathematics (NAAM) Research Group, Department of Mathematics, Faculty of Science, King Abdulaziz University, P.O. Box 80257, Jeddah 21589, Saudi Arabia
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Alsaadi FE, Hayat T, Khan MI, Alsaadi FE. Heat transport and entropy optimization in flow of magneto-Williamson nanomaterial with Arrhenius activation energy. COMPUTER METHODS AND PROGRAMS IN BIOMEDICINE 2020; 183:105051. [PMID: 31526945 DOI: 10.1016/j.cmpb.2019.105051] [Citation(s) in RCA: 11] [Impact Index Per Article: 2.8] [Reference Citation Analysis] [Abstract] [Key Words] [MESH Headings] [Track Full Text] [Subscribe] [Scholar Register] [Received: 08/04/2019] [Revised: 08/21/2019] [Accepted: 08/24/2019] [Indexed: 06/10/2023]
Abstract
BACKGROUND A newly developed approach in the field of nanotechnology for solving problems and collection of information is the use of nanoparticles. This idea has been further utilized in a better way in pharmaceutical industries. By using nanotechnology, the field of pharmaceutical science has been modernized and redeveloped. The use of nanotechnology in such industries has convinced the scientist to obtain more economical and easier applications. Therefore, with such effectiveness in mind, a theoretical study has been conducted to examine the effects of nonlinear radiative heat flux and magnetohydrodynamics for nanomaterial flow of Williamson fluid over a convectively heated stretchable surface. Brownian diffusion is utilized in mathematical modeling. Furthermore, heat source/sink, viscous dissipation and nonlinear radiative heat flux are examined. Convective boundary condition is implemented. Salient effects of chemical reaction and Arrhenius activation energy in mass transfer are considered. Total entropy rate is obtained through implementation of thermodynamics second law. METHODS The nonlinear PDEs are reduced into ordinary ones by appropriate similarity transformations. A semi-analytical technique i.e., homotopy method is implemented to obtain the convergent series solutions. RESULTS The obtained results indicate that the velocity of fluid particles increases versus higher fluid parameter. Schmidt number and activation energy variable have opposite effect on concentration. Entropy rate grows up with fluid parameter and Brinkman and Biot numbers while opposite trend is seen for Bejan number. CONCLUSIONS Velocity of the material particles declines through larger estimations of magnetic variable while it upsurges for higher fluid parameter. Thermal distribution shows similar impact for radiative and magnetic variables. Mass concentration decreases against chemical reaction parameter while it increases via activation energy variable. Entropy and Bejan numbers show opposite impacts versus Brinkman number. Skin friction coefficient increases through larger Weissenberg number.
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Affiliation(s)
- Fawaz E Alsaadi
- Department of Information Technology, Faculty of Computing and Information Technology, King Abdulaziz University Jeddah, Saudi Arabia
| | - T Hayat
- Department of Information Technology, Faculty of Computing and Information Technology, King Abdulaziz University Jeddah, Saudi Arabia; Department of Mathematics, Quaid-I-Azam University 45320, Islamabad 44000, Pakistan
| | - M Ijaz Khan
- Department of Mathematics, Quaid-I-Azam University 45320, Islamabad 44000, Pakistan.
| | - Fuad E Alsaadi
- Department of Electrical and Computer Engineering, Faculty of Engineering, King Abdulaziz University Jeddah, Saudi Arabia
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Khan MI, Khan SA, Hayat T, Khan MI, Alsaedi A. Nanomaterial based flow of Prandtl-Eyring (non-Newtonian) fluid using Brownian and thermophoretic diffusion with entropy generation. COMPUTER METHODS AND PROGRAMS IN BIOMEDICINE 2019; 180:105017. [PMID: 31425940 DOI: 10.1016/j.cmpb.2019.105017] [Citation(s) in RCA: 8] [Impact Index Per Article: 1.6] [Reference Citation Analysis] [Abstract] [Key Words] [MESH Headings] [Track Full Text] [Subscribe] [Scholar Register] [Received: 07/25/2019] [Revised: 08/02/2019] [Accepted: 08/03/2019] [Indexed: 06/10/2023]
Abstract
BACKGROUND The augmentation of cooling or heating in a mechanical and industrial process may create a saving in energy, decrease process time, protract the working existence of hardware and raise thermal rating. A few procedures are even influenced subjectively by the action of increased heat transport. The advancement of high performance thermal frameworks for heat transport augmentation has turned out to be well known these days. Various works has been conducted to gain an understanding of heat transport execution for their viable application to heat transport enhancement. Consequently the appearance of high heat flow procedures has made huge interest for new innovations to increase the heat transport. Therefore, entropy generation in dissipative nanomaterial flow of Prandtl-Eyring nanofluid subject to heated stretchable surface. The impact of zero shear rate viscosity is discussed through Prandtl-Eyring fluid model. Through implementation of thermodynamics second law's total entropy rate is calculated. Heat and mass transfer features are discussed using Brownian diffusion and thermophoresis. Homogeneous and heterogeneous chemical reactions are also accounted. METHODS Nonlinear partial differential systems are leads to ordinary systems through adequate similarity transformations. The obtained nonlinear ordinary systems are solved by Newton built in shooting technique. RESULTS Behaviors of different flow parameters on velocity, temperature, entropy generation rate, Bejan number and concentration are graphically discussed. Skin friction coefficient and heat transfer rate are discussed through tables. Entropy generation rate enhances for larger estimation of material parameter and Brinkman number. Bejan number is equal to one when Brinkman number is equal to zero and then progressively decreases for higher values of Brinkman number. CONCLUSIONS A significant increment has been observed in the velocity field versus material parameter, while opposite trends is noticed forβ.Temperature field enhances against higher values of thermophoresis and Brownian parameters while it decays through larger Prandtl number. Mass concentration upsurges versus higher thermophoresis parameter and declined via larger Brownian parameter and homogeneous and heterogeneous parameters. Furthermore, entropy rate and Bejan number show contrast impact versus material parameter and Brinkman number.
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Affiliation(s)
- M Ijaz Khan
- Department of Mathematics, Quaid-I-Azam University 45320, Islamabad 44000, Pakistan.
| | - Sohail A Khan
- Department of Mathematics, Quaid-I-Azam University 45320, Islamabad 44000, Pakistan
| | - T Hayat
- Department of Mathematics, Quaid-I-Azam University 45320, Islamabad 44000, Pakistan; Nonlinear Analysis and Applied Mathematics (NAAM) Research Group, Faculty of Science, King Abdulaziz University P. O. Box 80207, Jeddah 21589, Saudi Arabia
| | - M Imran Khan
- Heriot Watt University, Edinburgh Campus, Edinburgh EH14 4AS, United Kingdom
| | - A Alsaedi
- Nonlinear Analysis and Applied Mathematics (NAAM) Research Group, Faculty of Science, King Abdulaziz University P. O. Box 80207, Jeddah 21589, Saudi Arabia
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