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Bejawada SG, Reddy YD, Jamshed W, Usman, Isa SSPM, El Din SM, Guedri K, Rehman MIU. Comprehensive examination of radiative electromagnetic flowing of nanofluids with viscous dissipation effect over a vertical accelerated plate. Sci Rep 2022; 12:20548. [DOI: 10.1038/s41598-022-25097-2] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 10/13/2022] [Accepted: 11/24/2022] [Indexed: 11/30/2022] Open
Abstract
AbstractThis research aims to establish the MHD radiating convective nanofluid flow properties with the viscous dissipation across an exponentially accelerating vertical plate. As the plate accelerates, its temperature progressively increases. There are two separate types of water-based nanofluids that include copper ($$Cu$$
Cu
) and titanium dioxide ($$Ti{O}_{2}$$
T
i
O
2
) nanoparticles, respectively. The most crucial aspect of this investigation is finding a closed-form solution to a nonlinear coupled partial differential equations scheme. Galerkin finite element method (G-FEM) is used to figure out the initial managing equations. Utilizing graphs, the effect of the flow phenomenon's contributing variables as well as the influence of other factors is determined and depicted. In the part dedicated to the findings and discussion, the properties of these emergent parameters are described in more depth. Nonetheless, the thermal radiation and heat sink factors increase the thermal profile. In addition, the greater density of the copper nanoparticles cause the nanoparticle volume fraction to lessen the velocity delineation.
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Zubair T, Usman M, Sooppy Nisar K, Khan I, Ghamkhar M, Ahmad M. Crank Nicholson scheme to examine the fractional-order unsteady nanofluid flow of free convection of viscous fluids. PLoS One 2022; 17:e0261860. [PMID: 35231029 PMCID: PMC8887771 DOI: 10.1371/journal.pone.0261860] [Citation(s) in RCA: 2] [Impact Index Per Article: 1.0] [Reference Citation Analysis] [Abstract] [MESH Headings] [Track Full Text] [Download PDF] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Received: 09/26/2021] [Accepted: 12/11/2021] [Indexed: 11/19/2022] Open
Abstract
Fractional fluid models are usually difficult to solve analytically due to complicated mathematical calculations. This difficulty in considering fractional model further increases when one considers nth order chemical reaction. Therefore, in this work an incompressible nanofluid flow as well as the benefits of free convection across an isothermal vertical sheet is examined numerically. An nth order chemical reaction is considered in the chemical species model. The specified velocity (wall’s) is time-based, and its motion is translational into mathematical form. The fractional differential equations are used to express the governing flow equations (FDEs). The non-dimensional controlling system is given appropriate transformations. A Crank Nicholson method is used to find solutions for temperature, solute concentration, and velocity. Variation in concentration, velocity, and temperature profiles is produced as a result of changes in discussed parameters for both Ag-based and Cu-based nanofluid values. Water is taken as base fluid. The fractional-order time evaluation has opened the new gateways to study the problem into a new direction and it also increased the choices due to the extended version. It records the hidden figures of the problem between the defined domain of the time evaluation. The suggested technique has good accuracy, dependability, effectiveness and it also cover the better physics of the problem specially with concepts of fractional calculus.
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Affiliation(s)
- Tamour Zubair
- School of Mathematical Sciences, Peking University, Beijing, China
- * E-mail:
| | - Muhammad Usman
- Department of Mathematics, National University of Modern Languages (NUML), Islamabad, Pakistan
| | - Kottakkaran Sooppy Nisar
- Department of Mathematics, College of Arts and Sciences, Wadi Aldawaser, Prince Sattam Bin Abdulaziz University, Al-Kharj, Saudi Arabia
| | - Ilyas Khan
- Department of Mathematics, College of Science Al-Zulfi, Majmaah University, Al-Majmaah, Saudi Arabia
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Thumma T, Bég OA, Sheri SR. Finite element computation of magnetohydrodynamic nanofluid convection from an oscillating inclined plate with radiative flux, heat source and variable temperature effects. PROCEEDINGS OF THE INSTITUTION OF MECHANICAL ENGINEERS, PART N: JOURNAL OF NANOMATERIALS, NANOENGINEERING AND NANOSYSTEMS 2017. [DOI: 10.1177/2397791417731452] [Citation(s) in RCA: 3] [Impact Index Per Article: 0.4] [Reference Citation Analysis] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 11/16/2022]
Affiliation(s)
- Thirupathi Thumma
- Department of Mathematics, B.V. Raju Institute of Technology, Medak, India
| | - O Anwar Bég
- Fluid Mechanics, Bio-Propulsion and Nanosystems, Aeronautical and Mechanical Engineering, University of Salford, Manchester, Manchester, UK
| | - Siva Reddy Sheri
- Department of Mathematics, Gandhi Institute of Technology and Management University, Medak, India
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Imran MA, Shah NA, Khan I, Aleem M. Applications of non-integer Caputo time fractional derivatives to natural convection flow subject to arbitrary velocity and Newtonian heating. Neural Comput Appl 2016. [DOI: 10.1007/s00521-016-2741-6] [Citation(s) in RCA: 22] [Impact Index Per Article: 2.8] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 10/20/2022]
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Hussanan A, Zuki Salleh M, Tahar RM, Khan I. Unsteady boundary layer flow and heat transfer of a Casson fluid past an oscillating vertical plate with Newtonian heating. PLoS One 2014; 9:e108763. [PMID: 25302782 PMCID: PMC4193750 DOI: 10.1371/journal.pone.0108763] [Citation(s) in RCA: 56] [Impact Index Per Article: 5.6] [Reference Citation Analysis] [Abstract] [MESH Headings] [Track Full Text] [Download PDF] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Received: 07/16/2014] [Accepted: 09/02/2014] [Indexed: 11/18/2022] Open
Abstract
In this paper, the heat transfer effect on the unsteady boundary layer flow of a Casson fluid past an infinite oscillating vertical plate with Newtonian heating is investigated. The governing equations are transformed to a systems of linear partial differential equations using appropriate non-dimensional variables. The resulting equations are solved analytically by using the Laplace transform method and the expressions for velocity and temperature are obtained. They satisfy all imposed initial and boundary conditions and reduce to some well-known solutions for Newtonian fluids. Numerical results for velocity, temperature, skin friction and Nusselt number are shown in various graphs and discussed for embedded flow parameters. It is found that velocity decreases as Casson parameters increases and thermal boundary layer thickness increases with increasing Newtonian heating parameter.
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Affiliation(s)
- Abid Hussanan
- Futures and Trends Research Group, Faculty of Industrial Science and Technology, Universiti Malaysia Pahang, Lebuhraya Tun Razak, Kuantan, Pahang, Malaysia
| | - Mohd Zuki Salleh
- Futures and Trends Research Group, Faculty of Industrial Science and Technology, Universiti Malaysia Pahang, Lebuhraya Tun Razak, Kuantan, Pahang, Malaysia
| | - Razman Mat Tahar
- Faculty of Industrial Management, Universiti Malaysia Pahang, Lebuhraya Tun Razak, Kuantan, Pahang, Malaysia
| | - Ilyas Khan
- College of Engineering, Majmaah University, Majmaah, Saudi Arabia
- * E-mail:
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Khan A, Khan I, Ali F, ulhaq S, Shafie S. Effects of wall shear stress on unsteady MHD conjugate flow in a porous medium with ramped wall temperature. PLoS One 2014; 9:e90280. [PMID: 24621775 PMCID: PMC3951237 DOI: 10.1371/journal.pone.0090280] [Citation(s) in RCA: 16] [Impact Index Per Article: 1.6] [Reference Citation Analysis] [Abstract] [MESH Headings] [Track Full Text] [Download PDF] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Received: 09/11/2013] [Accepted: 01/29/2014] [Indexed: 11/18/2022] Open
Abstract
This study investigates the effects of an arbitrary wall shear stress on unsteady magnetohydrodynamic (MHD) flow of a Newtonian fluid with conjugate effects of heat and mass transfer. The fluid is considered in a porous medium over a vertical plate with ramped temperature. The influence of thermal radiation in the energy equations is also considered. The coupled partial differential equations governing the flow are solved by using the Laplace transform technique. Exact solutions for velocity and temperature in case of both ramped and constant wall temperature as well as for concentration are obtained. It is found that velocity solutions are more general and can produce a huge number of exact solutions correlative to various fluid motions. Graphical results are provided for various embedded flow parameters and discussed in details.
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Affiliation(s)
- Arshad Khan
- Department of Mathematical Sciences, Faculty of Science, Universiti Teknologi Malaysia, Skudai, Malaysia
| | - Ilyas Khan
- College of Engineering, Majmaah University, Majmaah, Saudi Arabia
| | - Farhad Ali
- Department of Mathematical Sciences, Faculty of Science, Universiti Teknologi Malaysia, Skudai, Malaysia
| | - Sami ulhaq
- City University of Science and Information Technology, Peshawar, Pakistan
| | - Sharidan Shafie
- Department of Mathematical Sciences, Faculty of Science, Universiti Teknologi Malaysia, Skudai, Malaysia
- * E-mail:
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Rubbab Q, Vieru D, Fetecau C, Fetecau C. Natural convection flow near a vertical plate that applies a shear stress to a viscous fluid. PLoS One 2013; 8:e78352. [PMID: 24278110 PMCID: PMC3838369 DOI: 10.1371/journal.pone.0078352] [Citation(s) in RCA: 14] [Impact Index Per Article: 1.3] [Reference Citation Analysis] [Abstract] [MESH Headings] [Track Full Text] [Download PDF] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Received: 06/03/2013] [Accepted: 09/20/2013] [Indexed: 11/23/2022] Open
Abstract
The unsteady natural convection flow of an incompressible viscous fluid near a vertical plate that applies an arbitrary shear stress to the fluid is studied using the Laplace transform technique. The fluid flow is due to both the shear and the heating of the plate. Closed-form expressions for velocity and temperature are established under the usual Boussinesq approximation. For illustration purposes, two special cases are considered and the influence of pertinent parameters on the fluid motion is graphically underlined. The required time to reach the steady state in the case of oscillating shear stresses on the boundary is also determined.
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Affiliation(s)
- Qammar Rubbab
- Department of Mathematics, Air University, Multan Campus, Pakistan
| | - Dumitru Vieru
- Department of Theoretical Mechanics, Technical University of Iasi, Iasi, Romania
| | - Corina Fetecau
- Department of Theoretical Mechanics, Technical University of Iasi, Iasi, Romania
| | - Constantin Fetecau
- Department of Mathematics, Technical University of Iasi, Iasi, Romania
- Member of Academy of Romanian Scientists, Bucuresti, Romania
- * E-mail:
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Conjugate effects of heat and mass transfer on MHD free convection flow over an inclined plate embedded in a porous medium. PLoS One 2013; 8:e65223. [PMID: 23840321 PMCID: PMC3696000 DOI: 10.1371/journal.pone.0065223] [Citation(s) in RCA: 27] [Impact Index Per Article: 2.5] [Reference Citation Analysis] [Abstract] [Track Full Text] [Download PDF] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Received: 02/01/2013] [Accepted: 04/23/2013] [Indexed: 12/04/2022] Open
Abstract
The aim of this study is to present an exact analysis of combined effects of radiation and chemical reaction on the magnetohydrodynamic (MHD) free convection flow of an electrically conducting incompressible viscous fluid over an inclined plate embedded in a porous medium. The impulsively started plate with variable temperature and mass diffusion is considered. The dimensionless momentum equation coupled with the energy and mass diffusion equations are analytically solved using the Laplace transform method. Expressions for velocity, temperature and concentration fields are obtained. They satisfy all imposed initial and boundary conditions and can be reduced, as special cases, to some known solutions from the literature. Expressions for skin friction, Nusselt number and Sherwood number are also obtained. Finally, the effects of pertinent parameters on velocity, temperature and concentration profiles are graphically displayed whereas the variations in skin friction, Nusselt number and Sherwood number are shown through tables.
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Narahari M, Dutta BK. EFFECTS OF THERMAL RADIATION AND MASS DIFFUSION ON FREE CONVECTION FLOW NEAR A VERTICAL PLATE WITH NEWTONIAN HEATING. CHEM ENG COMMUN 2012. [DOI: 10.1080/00986445.2011.611058] [Citation(s) in RCA: 21] [Impact Index Per Article: 1.8] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 10/28/2022]
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Cortell R. Heat transfer in a fluid through a porous medium over a permeable stretching surface with thermal radiation and variable thermal conductivity. CAN J CHEM ENG 2011. [DOI: 10.1002/cjce.20639] [Citation(s) in RCA: 18] [Impact Index Per Article: 1.4] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/05/2022]
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