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Ali K, Jamshed W, Suriya Uma Devi S, Ibrahim RW, Ahmad S, Tag El Din ESM. A study of pressure-driven flow in a vertical duct near two current-carrying wires using finite volume technique. Sci Rep 2022; 12:21273. [PMID: 36481845 PMCID: PMC9732357 DOI: 10.1038/s41598-022-25756-4] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [What about the content of this article? (0)] [Affiliation(s)] [Abstract] [Key Words] [Track Full Text] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Received: 08/22/2022] [Accepted: 12/05/2022] [Indexed: 12/13/2022] Open
Abstract
For heating, ventilation or air conditioning purposes in massive multistory building constructions, ducts are a common choice for air supply, return, or exhaust. Rapid population expansion, particularly in industrially concentrated areas, has given rise to a tradition of erecting high-rise buildings in which contaminated air is removed by making use of vertical ducts. For satisfying the enormous energy requirements of such structures, high voltage wires are used which are typically positioned near the ventilation ducts. This leads to a consequent motivation of studying the interaction of magnetic field (MF) around such wires with the flow in a duct, caused by vacuum pump or exhaust fan etc. Therefore, the objective of this work is to better understand how the established (thermally and hydrodynamically) movement in a perpendicular square duct interacts with the MF formed by neighboring current-carrying wires. A constant pressure gradient drives the flow under the condition of uniform heat flux across the unit axial length, with a fixed temperature on the duct periphery. After incorporating the flow assumptions and dimensionless variables, the governing equations are numerically solved by incorporating a finite volume approach. As an exclusive finding of the study, we have noted that MF caused by the wires tends to balance the flow reversal due to high Raleigh number. The MF, in this sense, acts as a balancing agent for the buoyancy effects, in the laminar flow regime.
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Affiliation(s)
- Kashif Ali
- Department of Basic Sciences and Humanities, Muhammad Nawaz Sharif University of Engineering and Technology, Multan, 60000, Pakistan
| | - Wasim Jamshed
- Department of Mathematics, Capital University of Science and Technology (CUST), Islamabad, 44000, Pakistan.
| | - S Suriya Uma Devi
- Department of Mathematics, KPR Institute of Engineering and Technology, Coimbatore, 641407, India
| | - Rabha W Ibrahim
- Water Resources and Applied Mathematics Research Lab, Nagpur, 440027, India
| | - Sohail Ahmad
- Centre for Advanced Studies in Pure and Applied Mathematics, Bahauddin Zakariya University, Multan, Pakistan
| | - El Sayed M Tag El Din
- Electrical Engineering, Faculty of Engineering and Technology, Future University in Egypt, New Cairo, 11835, Egypt
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Al-Saadi A, Al-Farhany K, Idan Al-Chlaihawi KK, Jamshed W, Eid MR, Tag El Din ESM, Raizah Z. Improvement of the aerodynamic behavior of a sport utility vehicle numerically by using some modifications and aerodynamic devices. Sci Rep 2022; 12:20272. [PMID: 36434018 PMCID: PMC9700687 DOI: 10.1038/s41598-022-24328-w] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [What about the content of this article? (0)] [Affiliation(s)] [Abstract] [Key Words] [Track Full Text] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Received: 08/18/2022] [Accepted: 11/14/2022] [Indexed: 11/26/2022] Open
Abstract
The present study proposes aerodynamically optimized exterior designs of a sport utility vehicle using computational fluid dynamics analysis based on steady-state Reynolds-averaged Navier-Stokes turbulence models. To achieve an optimal design, modifications of the outer shape and adding some aerodynamic devices are investigated. This study focuses on modifying this vehicle model's upper and front parts. At the same time, the rear diffuser and spare tire on the back door as a fairing are used as aerodynamic devices for improving streamlines. All these modifications and add-on devices are simulated individually or in combination to achieve the best exterior design. A variety of Reynolds numbers are used for determining the optimization variables. Tetrahedral cells are used throughout the global domain because of the sharp edges in the geometry of the Discovery car model. At the same time, prism cells around car surfaces are adopted to improve the accuracy of the results. A good agreement between the numerical drag coefficient in the present study for the baseline models and the experimental data has been achieved. Changes in the drag and lift coefficients are calculated for all models. It is clear from the numerical results that the use of combined modifications and add-on devices has a significant effect in improving the overall aerodynamic behavior. As a result, the drag coefficient for the optimal design of the Discovery 4th generation is reduced from 0.4 to 0.352 by about 12% compared to the benchmark. Simultaneously, the lift coefficient is 0.037 for optimal design, and it is an acceptable value. It is found that combining all optimal modified configurations can improve both CD and CL simultaneously.
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Affiliation(s)
- Ahmed Al-Saadi
- Department of Mechanical Engineering, University of Al-Qadisiyah, Al Diwaniyah, Al-Qadisiyah, 58001, Iraq
| | - Khaled Al-Farhany
- Department of Mechanical Engineering, University of Al-Qadisiyah, Al Diwaniyah, Al-Qadisiyah, 58001, Iraq
| | - Kadhim K Idan Al-Chlaihawi
- Department of Mechanical Engineering, University of Al-Qadisiyah, Al Diwaniyah, Al-Qadisiyah, 58001, Iraq
| | - Wasim Jamshed
- Department of Mathematics, Capital University of Science and Technology (CUST), Islamabad, 44000, Pakistan.
| | - Mohamed R Eid
- Department of Mathematics, Faculty of Science, New Valley University, Al-Kharga, 72511, Al-Wadi Al-Gadid, Egypt
- Department of Mathematics, Faculty of Science, Northern Border University, Arar, 1321, Saudi Arabia
| | - El Sayed M Tag El Din
- Electrical Engineering, Faculty of Engineering and Technology, Future University in Egypt, New Cairo, 11835, Egypt
| | - Zehba Raizah
- Department of Mathematics, College of Science, King Khalid University, Abha, Saudi Arabia
- , Abha, Saudi Arabia
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Khan QU, Begum N, Rehman ZU, Khan AU, Tahir K, Tag El Din ESM, Alothman AA, Habila MA, Liu D, Bocchetta P, Javed MS. Development of Efficient and Recyclable ZnO-CuO/g-C 3N 4 Nanocomposite for Enhanced Adsorption of Arsenic from Wastewater. Nanomaterials (Basel) 2022; 12:3984. [PMID: 36432270 PMCID: PMC9698871 DOI: 10.3390/nano12223984] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [What about the content of this article? (0)] [Affiliation(s)] [Abstract] [Key Words] [Track Full Text] [Figures] [Subscribe] [Scholar Register] [Received: 08/20/2022] [Revised: 11/08/2022] [Accepted: 11/10/2022] [Indexed: 06/16/2023]
Abstract
Arsenic (III) is a toxic contaminant in water bodies, especially in drinking water reservoirs, and it is a great challenge to remove it from wastewater. For the successful extraction of arsenic (III), a nanocomposite material (ZnO-CuO/g-C3N4) has been synthesized by using the solution method. The large surface area and plenty of hydroxyl groups on the nanocomposite surface offer an ideal platform for the adsorption of arsenic (III) from water. Specifically, the reduction process involves a transformation from arsenic (III) to arsenic (V), which is favorable for the attachment to the -OH group. The modified surface and purity of the nanocomposite were characterized by SEM, EDX, XRD, FT-IR, HRTEM, and BET models. Furthermore, the impact of various aspects (temperatures, pH of the medium, the concentration of adsorbing materials) on adsorption capacity has been studied. The prepared sample displays the maximum adsorption capacity of arsenic (III) to be 98% at pH ~ 3 of the medium. Notably, the adsorption mechanism of arsenic species on the surface of ZnO-CuO/g-C3N4 nanocomposite at different pH values was explained by surface complexation and structural variations. Moreover, the recycling experiment and reusability of the adsorbent indicate that a synthesized nanocomposite has much better adsorption efficiency than other adsorbents. It is concluded that the ZnO-CuO/g-C3N4 nanocomposite can be a potential candidate for the enhanced removal of arsenic from water reservoirs.
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Affiliation(s)
- Qudrat Ullah Khan
- Greater Bay Area Institute of Precision Medicine (Guangzhou), Fudan University, Nansha District, Guangzhou 511458, China
- Zhongshan-Fudan Joint Innovation Center, Zhongshan 528437, China
| | - Nabila Begum
- School of Medicine, Foshan University, Foshan 528000, China
| | - Zia Ur Rehman
- Department of Chemistry, The University of Haripur, Haripur 22620, Pakistan
| | - Afaq Ullah Khan
- School of Chemistry and Chemical Engineering, Jiangsu University, 301 Xuefu Road, Zhenjiang 212013, China
| | - Kamran Tahir
- Institute of Chemical Sciences, Gomal University Dera Ismail Khan, Dera Ismail Khan 29220, Khyber Pakhtunkhwa, Pakistan
| | - El Sayed M. Tag El Din
- Electrical Engineering Department, Faculty of Engineering & Technology, Future University in Egypt, New Cairo 11835, Egypt
| | - Asma A. Alothman
- Department of Chemistry, College of Science, King Saud University, Riyadh 11451, Saudi Arabia
| | - Mohamed A. Habila
- Department of Chemistry, College of Science, King Saud University, Riyadh 11451, Saudi Arabia
| | - Dahai Liu
- School of Medicine, Foshan University, Foshan 528000, China
| | - Patrizia Bocchetta
- Dipartimento di Ingegneria dell’Innovazione, Università del Salento, via Monteroni, 73100 Lecce, Italy
| | - Muhammad Sufyan Javed
- School of Physical Science and Technology, Lanzhou University, Lanzhou 730000, China
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Zada L, Nawaz R, Jamshed W, Ibrahim RW, Tag El Din ESM, Raizah Z, Amjad A. New optimum solutions of nonlinear fractional acoustic wave equations via optimal homotopy asymptotic method-2 (OHAM-2). Sci Rep 2022; 12:18838. [DOI: 10.1038/s41598-022-23644-5] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [What about the content of this article? (0)] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 09/02/2022] [Accepted: 11/03/2022] [Indexed: 11/08/2022] Open
Abstract
AbstractThe second iteration of the optimal homotopy asymptotic technique (OHAM-2) has been protracted to fractional order partial differential equations in this work for the first time (FPDEs). Without any transformation, the suggested approach can be used to solve fractional-order nonlinear Zakharov–Kuznetsov equations. The Caputo notion of the fractional-order derivative, whose values fall within the closed interval [0, 1], has been taken into consideration. The method's appeal is that it provides an approximate solution after just one iteration. The suggested method's numerical findings have been contrasted with those of the variational iteration method, residual power series method, and perturbation iteration method. Through tables and graphs, the proposed method's effectiveness and dependability are demonstrated.
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Rehman MIU, Chen H, Hamid A, Qayyum S, Jamshed W, Raizah Z, Eid MR, Din ESMTE. Soret and Dufour influences on forced convection of Cross radiative nanofluid flowing via a thin movable needle. Sci Rep 2022; 12:18666. [PMID: 36333418 PMCID: PMC9636139 DOI: 10.1038/s41598-022-23563-5] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [What about the content of this article? (0)] [Abstract] [Track Full Text] [Download PDF] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Received: 08/21/2022] [Accepted: 11/02/2022] [Indexed: 11/06/2022] Open
Abstract
The main feature of the current investigation is to analyze the magnetohydrodynamic mixed convection flow of Cross fluid. Flow is due to a movable thin needle with Soret and Dufour effect. Heat generation/absorption and nonlinear heat radiation are used in the energy equation. Characteristics of the chemical reaction and thermal activation are given special attention. Appropriate variables are introduced for the transformation of partial differential equations to ordinary differential equations. With the assistance of Runge–Kutta Fehlberg's fourth- fifth-order method with the shooting technique, we determined the prominent result numerically. The prominent examined parameters range is velocity and temperature ratios, heat generation, Dufour, Hartmann, Schmidt numbers (\documentclass[12pt]{minimal}
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\begin{document}$$0.1\le{{\lambda}},{{{\theta}}}_{{{w}}},{{Q}},{{{D}}}_{{{u}}},\boldsymbol{ }{{M}},{{S}}{{c}}\le 0.7$$\end{document}0.1≤λ,θw,Q,Du,M,Sc≤0.7), needle thickness (\documentclass[12pt]{minimal}
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\begin{document}$$0\le {{a}}\le 15$$\end{document}0≤a≤15), radiative parameter (\documentclass[12pt]{minimal}
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\begin{document}$$5\le {{R}}{{d}}\le 8$$\end{document}5≤Rd≤8), and Weissenberg number (\documentclass[12pt]{minimal}
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\begin{document}$$0.01\le {{W}}{{e}}\le 0.09$$\end{document}0.01≤We≤0.09), respectively. Graphs for velocity, thermal, concentration, Skin friction coefficient, and heat and mass transport rates are displayed and analyzed for physical parameters. A similar observation of mixed convection and needle thickness parameter is seen on the velocity field. Temperature and heat transfer rate are reverse behavior in the frame of the Dufour effect. Moreover, an enhancement in chemical reaction shows decay to the concentration field.
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Al-Saadi A, Al-Farhany K, Faisal AE, Alomari MA, Jamshed W, Eid MR, Tag El Din ESM, Amjad A. Improvement of the aerodynamic behaviour of the passenger car by using a combine of ditch and base bleed. Sci Rep 2022; 12:18462. [PMID: 36323793 PMCID: PMC9630510 DOI: 10.1038/s41598-022-23183-z] [Citation(s) in RCA: 4] [Impact Index Per Article: 2.0] [Reference Citation Analysis] [What about the content of this article? (0)] [Affiliation(s)] [Abstract] [Key Words] [Track Full Text] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Received: 07/18/2022] [Accepted: 10/26/2022] [Indexed: 11/23/2022] Open
Abstract
The current study investigates different methods to minimize the drag coefficient (CD) without ignoring the safety factor related to the stability of a vehicle, i.e., the lift coefficient (CL). The study was carried out by employing an SUV car analyzed numerically using one of the CFD software, Ansys. Four different models such as realizable k-ε, standard k-ω, shear stress transport k-ω, and Reynolds stress model (RSM). The considered models have been validated with experimental data and found in good agreement. The considered inlet velocity varies from 28 to 40 m/s, the results showed that the drag coefficient and the stability are both improved by applying a modification on the roof of the considered car.
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Affiliation(s)
- Ahmed Al-Saadi
- grid.440842.e0000 0004 7474 9217Department of Mechanical Engineering, University of Al-Qadisiyah, Al-Qadisiyah, 58001 Iraq
| | - Khaled Al-Farhany
- grid.440842.e0000 0004 7474 9217Department of Mechanical Engineering, University of Al-Qadisiyah, Al-Qadisiyah, 58001 Iraq
| | - Ahmed Essa Faisal
- grid.440842.e0000 0004 7474 9217Department of Mechanical Engineering, University of Al-Qadisiyah, Al-Qadisiyah, 58001 Iraq
| | - Mohammed Azeez Alomari
- grid.440842.e0000 0004 7474 9217Department of Mechanical Engineering, University of Al-Qadisiyah, Al-Qadisiyah, 58001 Iraq
| | - Wasim Jamshed
- grid.509787.40000 0004 4910 5540Department of Mathematics, Capital University of Science and Technology (CUST), Islamabad, 44000 Pakistan
| | - Mohamed R. Eid
- grid.252487.e0000 0000 8632 679XDepartment of Mathematics, Faculty of Science, New Valley University, Al-Kharga, 72511 Al-Wadi Al-Gadid Egypt ,grid.449533.c0000 0004 1757 2152Department of Mathematics, Faculty of Science, Northern Border University, Arar, 1321 Saudi Arabia
| | - El Sayed M. Tag El Din
- grid.440865.b0000 0004 0377 3762Electrical Engineering, Faculty of Engineering and Technology, Future University in Egypt, New Cairo, 11835 Egypt
| | - Ayesha Amjad
- grid.6979.10000 0001 2335 3149Faculty of Organization and Management, Silesian University of Technology, 44-100 Gliwice, Poland
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Qayyum M, Ahmad E, Afzal S, Sajid T, Jamshed W, Musa A, Tag El Din ESM, Iqbal A. Fractional analysis of unsteady squeezing flow of Casson fluid via homotopy perturbation method. Sci Rep 2022; 12:18406. [PMID: 36319834 PMCID: PMC9626585 DOI: 10.1038/s41598-022-23239-0] [Citation(s) in RCA: 1] [Impact Index Per Article: 0.5] [Reference Citation Analysis] [What about the content of this article? (0)] [Affiliation(s)] [Abstract] [Key Words] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 08/05/2022] [Accepted: 10/27/2022] [Indexed: 01/24/2023] Open
Abstract
The objective of this article is to model and analyze unsteady squeezing flow of fractional MHD Casson fluid through a porous channel. Casson fluid model is significant in understanding the properties of non-Newtonian fluids such as blood flows, printing inks, sauces and toothpaste etc. This study provides important results as unsteady flow of Casson fluid in fractional sense with aforementioned effects has not been captured in existing literature. After applying similarity transformations along with fractional calculus a highly non-linear fractional-order differential equation is obtained. Modeled equation is then solved along with no-slip boundary conditions through a hybrid of Laplace transform with homotopy perturbation algorithm. For validity purposes, solution and errors at various values in fractional domain are compared with existing results. LHPM results are better in terms of accuracy than other available results in literature. Effects of fractional parameter on the velocity profile, skin friction and behaviors of involved fluid parameters is the focal point of this study. Comprehensive, quantitative and graphical analysis is performed for investigating the effects of pertinent fluid parameters on the velocity profile and skin friction. Analysis revealed that fractional parameter depicts similar effect in case of positive and negative squeeze number. Also, skin friction decreases with an increasing fractional parameter. Moreover, in fractional environment Casson parameter has shown similar effect on the velocity profile in case of positive and negative squeeze number.
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Affiliation(s)
- Mubashir Qayyum
- grid.444797.d0000 0004 0371 6725Department of Sciences and Humanities, National University of Computer and Emerging Sciences, Lahore, Pakistan
| | - Efaza Ahmad
- grid.444797.d0000 0004 0371 6725Department of Sciences and Humanities, National University of Computer and Emerging Sciences, Lahore, Pakistan
| | - Sidra Afzal
- grid.444797.d0000 0004 0371 6725Department of Sciences and Humanities, National University of Computer and Emerging Sciences, Lahore, Pakistan
| | - Tanveer Sajid
- grid.509787.40000 0004 4910 5540Department of Mathematics, Capital University of Science and Technology (CUST), Islamabad, 44000 Pakistan
| | - Wasim Jamshed
- grid.509787.40000 0004 4910 5540Department of Mathematics, Capital University of Science and Technology (CUST), Islamabad, 44000 Pakistan
| | - Awad Musa
- grid.449553.a0000 0004 0441 5588Department of Physics, College of Science and Humanities in Al-Aflaj, Prince Sattam Bin Abdulaziz University, Al-Aflaj, 11912 Saudi Arabia ,grid.440840.c0000 0000 8887 0449Department of Physics, College of Science, Sudan University of Science and Technology, Khartoum, Sudan
| | - El Sayed M. Tag El Din
- grid.440865.b0000 0004 0377 3762Electrical Engineering, Faculty of Engineering and Technology, Future University in Egypt, New Cairo, 11835 Egypt
| | - Amjad Iqbal
- grid.6979.10000 0001 2335 3149Department of Materials Technologies, Faculty of Materials Engineering, Silesian University of Technology, 44-100 Gliwice, Poland ,grid.8051.c0000 0000 9511 4342CEMMPRE—Centre for Mechanical Engineering Materials and Processes, Department of Mechanical Engineering, University of Coimbra, Rua Luı’s Reis Santos, 3030-788 Coimbra, Portugal
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Shahzad F, Jamshed W, Usman, Ibrahim RW, Aslam F, Tag El Din ESM, Khalifa HAEW, ElSeabee FAA. Galerkin finite element analysis for magnetized radiative-reactive Walters-B nanofluid with motile microorganisms on a Riga plate. Sci Rep 2022; 12:18096. [PMID: 36302798 PMCID: PMC9613994 DOI: 10.1038/s41598-022-21805-0] [Citation(s) in RCA: 4] [Impact Index Per Article: 2.0] [Reference Citation Analysis] [What about the content of this article? (0)] [Affiliation(s)] [Abstract] [Key Words] [Track Full Text] [Download PDF] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Received: 06/11/2022] [Accepted: 10/04/2022] [Indexed: 12/30/2022] Open
Abstract
In order to understand the characteristics of bio-convection and moving microorganisms in flows of magnetized Walters-B nano-liquid, we developed a model employing Riga plate with stretchy sheet. The Buongiorno phenomenon is likewise employed to describe nano-liquid motion in the Walters-B fluid. Expending correspondence transformations, the partial differential equation (PDE) control system has been transformed into an ordinary differential equation (ODE) control system. The COMSOL program is used to generate mathematical answers for non-linear equations by employing the Galerkin finite element strategy (G-FEM). Utilizing logical and graphical metrics, temperature, velocity, and microbe analysis are all studied. Various estimates of well-known physical features are taken into account while calculating nanoparticle concentrations. It is demonstrated that this model's computations directly relate the temperature field to the current Biot number and parameter of the Walters-B fluid. The temperature field is increased to increase the approximations of the current Biot number and parameter of the Walters-B fluid.
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Affiliation(s)
- Faisal Shahzad
- grid.509787.40000 0004 4910 5540Department of Mathematics, Capital University of Science and Technology (CUST), Islamabad, 44000 Pakistan
| | - Wasim Jamshed
- grid.509787.40000 0004 4910 5540Department of Mathematics, Capital University of Science and Technology (CUST), Islamabad, 44000 Pakistan
| | - Usman
- grid.412117.00000 0001 2234 2376Department of Computer Science, National University of Sciences and Technology, Balochistan Campus (NBC), Quetta, 87300 Pakistan
| | - Rabha W. Ibrahim
- Near East University, Mathematics Research Center, Department of Mathematics, Near East Boulevard, Nicosia/Mersin 10, PC: 99138 Turkey
| | - Farheen Aslam
- grid.444924.b0000 0004 0608 7936Department of Biotechnology, Lahore College for Women University, Lahore, 54000 Pakistan
| | - El Sayed M. Tag El Din
- grid.440865.b0000 0004 0377 3762Electrical Engineering, Faculty of Engineering and Technology, Future University in Egypt, New Cairo, 11835 Egypt
| | - Hamiden Abd El-Wahed Khalifa
- grid.7776.10000 0004 0639 9286Department of Operations Research, Faculty of Graduate Studies for Statistical Research, Cairo University, Giza, 12613 Egypt ,grid.412602.30000 0000 9421 8094Department of Mathematics, College of Science and Arts, Al-Badaya, Qassim University, Buraydah, 51951 Saudi Arabia
| | - Fayza Abdel Aziz ElSeabee
- grid.412093.d0000 0000 9853 2750Mathematics Department, Faculty of Science, Helwan University, Cairo, Egypt ,grid.412602.30000 0000 9421 8094Department of Mathematics, College of Science and Arts, Alasyah, Qassim University, Buraydah, Saudi Arabia
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Shahzad F, Jamshed W, Aslam F, Bashir R, Tag El Din ESM, Khalifa HAEW, Alanzi AM. MHD Pulsatile Flow of Blood-Based Silver and Gold Nanoparticles between Two Concentric Cylinders. Symmetry (Basel) 2022; 14:2254. [DOI: 10.3390/sym14112254] [Citation(s) in RCA: 2] [Impact Index Per Article: 1.0] [Reference Citation Analysis] [What about the content of this article? (0)] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 09/02/2023] Open
Abstract
Pulsatory movements appear in a variety of fascinating applications involving periodic flow propagation and control. Pulsing encourages mixing and, as a result, mass and heat exchange with the boundaries. Pulsing also helps to decrease surface fouling by allowing solid particles to migrate. An exact solution of the Navier–Stokes equations for the transport of an incompressible viscous fluid in a channel with arbitrary pressure distribution is described in this study. The flow is defined by two primary parameters: the pulsation parameter, which is determined by the periodic pressure gradient, and the kinetic Reynolds number, which is determined by the pulsation frequency. The purpose of employing hybrid nanofluid (HNF) is to increase the base fluid’s thermal conductivity. We regard Ag and Au as nanoparticles (NPs) and blood as a base fluid for this phenomenon. Broadening this reveals that the consideration of nanoparticles has impressively extended the warm movement at the parcels of both turbulent and laminar frameworks. Attention is paid to the slope of speed, temperature, and voltage. The geometric model is therefore described using a symmetry technique. We developed the governing equation for this problem’s analytical solutions. The velocity and temperature fields solution is given in the form of the Bessel and modified Bessel functions. Graph results show the mathematical benefits of the current limits: for instance, Hartmann number M, solid volume part of nanoparticles ϕ, Reynolds number Reβ, Prandtl number Pr, intermittent slob limit, etc. The strain angles introduced in the stress contrast, frictional force, velocity profile, and temperature profile were obtained, and the characteristics of the vortex were investigated. Resources at various boundaries of the perceptual flow are examined. As with the final essence, the smoothest results are analyzed and recorded. It has also been discovered that the velocity may be regulated by the external magnetic field, which affects the temperature profiles and hence the heat transfer, which can be enhanced or lowered by mastering the magnetic field.
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Ghani MU, Sultan F, Tag El Din ESM, Khan AR, Liu JB, Cancan M. A Paradigmatic Approach to Find the Valency-Based K-Banhatti and Redefined Zagreb Entropy for Niobium Oxide and a Metal-Organic Framework. Molecules 2022; 27:6975. [PMID: 36296567 PMCID: PMC9610924 DOI: 10.3390/molecules27206975] [Citation(s) in RCA: 10] [Impact Index Per Article: 5.0] [Reference Citation Analysis] [What about the content of this article? (0)] [Affiliation(s)] [Abstract] [Key Words] [MESH Headings] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 09/16/2022] [Revised: 10/12/2022] [Accepted: 10/13/2022] [Indexed: 07/27/2023] Open
Abstract
Entropy is a thermodynamic function in chemistry that reflects the randomness and disorder of molecules in a particular system or process based on the number of alternative configurations accessible to them. Distance-based entropy is used to solve a variety of difficulties in biology, chemical graph theory, organic and inorganic chemistry, and other fields. In this article, the characterization of the crystal structure of niobium oxide and a metal-organic framework is investigated. We also use the information function to compute entropies by building these structures with degree-based indices including the K-Banhatti indices, the first redefined Zagreb index, the second redefined Zagreb index, the third redefined Zagreb index, and the atom-bond sum connectivity index.
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Affiliation(s)
- Muhammad Usman Ghani
- Institute of Mathematics, Khawaja Fareed University of Engineering & Information Technology, Abu Dhabi Road, Rahim Yar Khan 64200, Pakistan
| | - Faisal Sultan
- Institute of Mathematics, Khawaja Fareed University of Engineering & Information Technology, Abu Dhabi Road, Rahim Yar Khan 64200, Pakistan
| | - El Sayed M. Tag El Din
- Center of Research, Faculty of Engineering, Future University in Egypt, New Caira 11835, Egypt
| | - Abdul Rauf Khan
- Department of Mathematics, Faculty of Science, Ghazi University, Dera Ghazi Khan 32200, Pakistan
| | - Jia-Bao Liu
- School of Mathematics and Physics, Anhui Jianzhu University, Hefei 230601, China
| | - Murat Cancan
- Faculty of Education, Yuzuncu Yil University, Van 65140, Turkey
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