1
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Idris S, Jamaludin A, Nazar R, Pop I. Heat transfer characteristics of magnetized hybrid ferrofluid flow over a permeable moving surface with viscous dissipation effect. Heliyon 2023; 9:e15907. [PMID: 37223714 PMCID: PMC10200861 DOI: 10.1016/j.heliyon.2023.e15907] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Received: 01/06/2023] [Revised: 04/14/2023] [Accepted: 04/26/2023] [Indexed: 05/25/2023] Open
Abstract
Hybrid ferrofluid is a unique heat transfer fluid because it can be magnetically controlled and ideal in various applications. Further exploration to unleash its potential through studying heat transfer and boundary layer flow is crucial, especially in solving the thermal efficiency problem. Hence, this research focuses on the numerical examination of flow behaviour and heat transfer attributes of magnetized hybrid ferrofluid Fe3O4-CoFe2O4/water across a permeable moving surface considering the mutual effects of magnetohydrodynamic (MHD), viscous dissipation, and suction/injection. The problem was represented by the Tiwari and Das model with duo magnetic nanoparticle hybridization; magnetite Fe3O4 and cobalt ferrite CoFe2O4 immersed in water. The governing equations were transformed into ordinary differential equations using appropriate similarity variables and solved with bvp4c MATLAB. A dual solution is obtained, and via stability analysis, the first solution is stable and physically reliable. The significant influence of governing effects on the temperature and velocity profiles, the local skin friction coefficient and the local Nusselt number are analyzed and visually shown. The surge-up value of suction and CoFe2O4 ferroparticle volume concentration enhances the local skin friction coefficient and heat transfer rate. Additionally, the magnetic parameter and Eckert number reduced the heat transfer. Using a 1% volume fraction of Fe3O4 and CoFe2O4; the hybrid ferrofluid's convective heat transfer rate was shown to be superior to mono-ferrofluid and water by enhancing 2.75% and 6.91%, respectively. This present study also suggests implying a greater volume concentration of CoFe2O4 and lessening the magnetic intensity to maintain the laminar flow phase.
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Affiliation(s)
- Sakinah Idris
- Department of Mathematics, Universiti Pertahanan Nasional Malaysia, 57000, Kuala Lumpur, Malaysia
| | - Anuar Jamaludin
- Department of Mathematics, Universiti Pertahanan Nasional Malaysia, 57000, Kuala Lumpur, Malaysia
| | - Roslinda Nazar
- Department of Mathematical Sciences, Faculty of Science and Technology, Universiti Kebangsaan Malaysia, 43600, UKM, Bangi, Selangor, Malaysia
| | - Ioan Pop
- Department of Mathematics, Babeş-Bolyai University, R-400084, Cluj-Napoca, Romania
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2
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Suresh Kumar Y, Hussain S, Raghunath K, Ali F, Guedri K, Eldin SM, Khan MI. Numerical analysis of magnetohydrodynamics Casson nanofluid flow with activation energy, Hall current and thermal radiation. Sci Rep 2023; 13:4021. [PMID: 36899067 PMCID: PMC10006176 DOI: 10.1038/s41598-023-28379-5] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 11/03/2022] [Accepted: 01/17/2023] [Indexed: 03/12/2023] Open
Abstract
In this study we analyzed the flow, heat and mass transfer behavior of Casson nanofluid past an exponentially stretching surface under the impact of activation energy, Hall current, thermal radiation, heat source/sink, Brownian motion and thermophoresis. Transverse magnetic field with the assumption of small Reynolds number is implemented vertically. The governing partial nonlinear differential equations of the flow, heat and mass transfer are transformed into ordinary differential equations by using similarity transformation and solved numerically by using Matlab bvp4c package. The impact of each of the Hall current parameter, thermal radiation parameter, heat source/sink parameter, Brownian motion parameter, Prandtl number, thermophoresis parameter and magnetic parameter on velocity, concentration and temperature, is discussed through graphs. The skin friction coefficient along the x-and z-directions, the local Nusselt number and the Sherwood number are calculated numerically to look into the inside behavior of the emerging parameters. It is witnessed that the flow velocity is a diminishing function of the thermal radiation parameter and the behavior has observed in the case of Hall parameter. Moreover, mounting values of Brownian motion parameter reduce the nanoparticle concentration profile.
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Affiliation(s)
- Y Suresh Kumar
- Department of Mathematics, Koneru Lakshmaiah Education Foundation, R.V.S Nagar, Moinabad-Chilkur Rd, Near AP Police Academy, Aziznagar, Hyderabad, 500075, Telangana, India
| | - Shaik Hussain
- Department of Mechanical Engineering, Malla Reddy Engineering College, Hyderabad, Telangana, India
| | - K Raghunath
- Department of Humanities and Sciences, St. Johns College of Engineering and Technology, Yemmiganur, Kurnool, Andhra Pradesh, 518360, India
| | - Farhan Ali
- Department of Mathematical Sciences, Federal Urdu University of Arts, Sciences & Technology, Gulshan-e-Iqbal, Karachi, 75300, Pakistan
| | - Kamel Guedri
- Mechanical Engineering Department, College of Engineering and Islamic Architecture, Umm Al-Qura University, P.O. Box 5555, Makkah, 21955, Saudi Arabia
| | - Sayed M Eldin
- Center of Research, Faculty of Engineering, Future University in Egypt, New Cairo, 11835, Egypt
| | - M Ijaz Khan
- Department of Mechanical Engineering, Lebanese American University, Beirut, Lebanon. .,Department of Mathematics and Statistics, Riphah International University I-14, Islamabad, 44000, Pakistan.
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3
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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] [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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4
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A semi-analytical passive strategy to examine the water-ethylene glycol (50:50)-based hybrid nanofluid flow over a spinning disk with homogeneous-heterogeneous reactions. Sci Rep 2022; 12:17105. [PMID: 36224220 PMCID: PMC9556529 DOI: 10.1038/s41598-022-21080-z] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Download PDF] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Received: 07/20/2022] [Accepted: 09/22/2022] [Indexed: 01/04/2023] Open
Abstract
Scientists and researchers are much interested in studying graphene and silver nanoparticles for the enhancement of heat transport due to their extensive variety of applications in different areas of industrial and engineering such as drug delivery, medical devices, ultra-light, excellent electrical conductivity, strong medical strength, health care, consumer, food, etc. Therefore, in the existing investigation, the MHD flow of a mixed convective hybrid nanoliquid with graphene and silver nanoparticles past a rotating disk is considered. Water and ethylene glycol (50:50) is used as a base liquid in the existing model. The mechanism for heat transport is computed with the existence of thermal radiation and thermal convective condition. Homogeneous and heterogeneous chemical reactions are assumed in the flow behavior. The mathematical formulation of the proposed problem is based on the nonlinear PDEs which are then transformed to nonlinear ODEs by manipulating the appropriate similarity transformation. The simulation of the existing problem has been performed with the help of the homotopy analysis technique. The outcomes of the different flow parameters on the velocities, temperature, concentration, skin friction coefficient, and Nusselt number of the hybrid nanofluid are attained via graphs and tables. Some significant results from the existing problem demonstrate that the rate of heat transport is greater for the thermal Biot number and nanoparticles volume fraction. Further, it is noticed that the velocity of the liquid particles becomes lower for a higher magnetic field parameter.
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5
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Vishalakshi AB, Mahabaleshwar US, Hatami M. MHD Casson carbon nanotube flow with mass and heat transfer under thermosolutal Marangoni convection in a porous medium: analytical solution. Sci Rep 2022; 12:16071. [PMID: 36167793 PMCID: PMC9515169 DOI: 10.1038/s41598-022-20532-w] [Citation(s) in RCA: 1] [Impact Index Per Article: 0.5] [Reference Citation Analysis] [Abstract] [Track Full Text] [Download PDF] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Received: 07/06/2022] [Accepted: 09/14/2022] [Indexed: 11/29/2022] Open
Abstract
Current work portrays the flow of Marangoni convection Magneto hydrodynamics Casson fluid with carbon nanotubes under the effect of transpiration and radiation. The carbon nanotube particles namely water-single wall carbon nanotubes are inserted in the fluid to enhance better thermal efficiency. This type of flow problems is applicable for real life situations such as drying of silicon wafers, glues, crystal growth and heat exchangers and so on. The ordinary differential equations (ODEs) form of the result is yield to convert partial differential equations of the given equation by using similarity variables. Then this resulting ODEs are solved analytically, firstly using momentum equation to get solution domain and then by using this domain the energy equation solved to get the temperature profile in terms of Laguerre polynomial. Additionally, mass transpiration is also solved to get the concentration profile in terms of Laguerre polynomial. By using the different controlling parameters, the results can be discussed. And the effect of this parameters are discussed by using graphical arrangements. The newness of the present work is to explain the physically flow problem on the basis of chemically radiative thermosolutal Marangoni convective fluid.
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Affiliation(s)
- A B Vishalakshi
- Department of Mathematics, Davangere University, Shivagangotri, Davangere, 577007, India
| | - U S Mahabaleshwar
- Department of Mathematics, Davangere University, Shivagangotri, Davangere, 577007, India
| | - M Hatami
- Mechanical Engineering Department, Ferdowsi University of Mashhad, Mashhad, Iran.
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6
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Khan Z, Srivastava HM, Mohammed PO, Jawad M, Jan R, Nonlaopon K. Thermal boundary layer analysis of MHD nanofluids across a thin needle using non-linear thermal radiation. MATHEMATICAL BIOSCIENCES AND ENGINEERING : MBE 2022; 19:14116-14141. [PMID: 36654083 DOI: 10.3934/mbe.2022658] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Key Words] [MESH Headings] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 06/17/2023]
Abstract
An analysis of steady two-dimensional boundary layer MHD (magnetohydrodynamic) nanofluid flow with nonlinear thermal radiation across a horizontally moving thin needle was performed in this study. The flow along a thin needle is considered to be laminar and viscous. The Rosseland estimate is utilized to portray the radiation heat transition under the energy condition. Titanium dioxide (TiO$ _2 $) is applied as the nanofluid and water as the base fluid. The objective of this work was to study the effects of a magnetic field, thermal radiation, variable viscosity and thermal conductivity on MHD flow toward a porous thin needle. By using a suitable similarity transformation, the nonlinear governing PDEs are turned into a set of nonlinear ODEs which are then successfully solved by means of the homotopy analysis method using Mathematica software. The comparison result for some limited cases was achieved with earlier published data. The governing parameters were fixed values throughout the study, i.e., $ k_1 $ = 0.3, $ M $ = 0.6, $ F_r $ = 0.1, $ \delta_\mu $ = 0.3, $ \chi $ = 0.001, $ Pr $ = 0.7, $ Ec $ = 0.5, $ \theta_r $ = 0.1, $ \epsilon $ = 0.2, $ Rd $ = 0.4 and $ \delta_k $ = 0.1. After detailed analysis of the present work, it was discovered that the nanofluid flow diminishes with growth in the porosity parameter, variable viscosity parameter and magnetic parameter, while it upsurges when the rate of inertia increases. The thermal property enhances with the thermal conductivity parameter, radiation parameter, temperature ratio parameter and Eckert number, while it reduces with the Prandtl number and size of the needle. Moreover, skin friction of the nanofluid increases with corresponding growth in the magnetic parameter, porosity parameter and inertial parameter, while it reduces with growth in the velocity ratio parameter. The Nusselt number increases with increases in the values of the inertia parameter and Eckert number, while it decliens against a higher estimation of the Prandtl number and magnetic parameter. This study has a multiplicity of applications like petroleum products, nuclear waste disposal, magnetic cell separation, extrusion of a plastic sheet, cross-breed powered machines, grain storage, materials production, polymeric sheet, energy generation, drilling processes, continuous casting, submarines, wire coating, building design, geothermal power generations, lubrication, space equipment, biomedicine and cancer treatment.
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Affiliation(s)
- Ziad Khan
- Department of Mathematics, University of Swabi, Swabi 23561, Khyber Pakhtunkhwa, Pakistan
| | - Hari Mohan Srivastava
- Department of Mathematics and Statistics, University of Victoria, Victoria, British Columbia V8W3R4, Canada
- Department of Medical Research, China Medical University Hospital, China Medical University, Taichung 40402, Taiwan
- Department of Mathematics and Informatics, Azerbaijan University, 71 Jeyhun Hajibeyli Street, AZ1007 Baku, Azerbaijan
- Section of Mathematics, International Telematic University Uninettuno, I-00186 Rome, Italy
| | - Pshtiwan Othman Mohammed
- Department of Mathematics, College of Education, University of Sulaimani, Sulaimani 46001, Kurdistan Region, Iraq
| | - Muhammad Jawad
- Department of Mathematics, University of Swabi, Swabi 23561, Khyber Pakhtunkhwa, Pakistan
| | - Rashid Jan
- Department of Mathematics, University of Swabi, Swabi 23561, Khyber Pakhtunkhwa, Pakistan
| | - Kamsing Nonlaopon
- Department of Mathematics, Faculty of Science, Khon Kaen University, Khon Kaen 40002, Thailand
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7
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Guedri K, Khan A, Gul T, Mukhtar S, Alghamdi W, Yassen MF, Tag Eldin E. Thermally Dissipative Flow and Entropy Analysis for Electromagnetic Trihybrid Nanofluid Flow Past a Stretching Surface. ACS OMEGA 2022; 7:33432-33442. [PMID: 36157759 PMCID: PMC9494684 DOI: 10.1021/acsomega.2c04047] [Citation(s) in RCA: 1] [Impact Index Per Article: 0.5] [Reference Citation Analysis] [Abstract] [Grants] [Track Full Text] [Subscribe] [Scholar Register] [Received: 07/04/2022] [Accepted: 08/25/2022] [Indexed: 05/02/2023]
Abstract
The growth of hybrid nanofluids can be connected to their enhanced thermal performance as pertains to the dynamics of automobile coolant among others. In addition to that, the thermal characteristics of water-based nanofluids carrying three different types of nanoparticles are incredible. Keeping in view this new idea, the current investigation explores ternary hybrid nanofluid flow over a stretching sheet. Joule heating and viscous dissipation are addressed in the heat equation. Three distinct kinds of nanoparticles, namely, magnesium oxide, copper, and MWCNTs, are suspended in water to form a ternary hybrid nanofluid with the combination MgO-Cu-MWCNTs-H2O. To stabilize the flow of the ternary hybrid nanofluid, transverse magnetic and electric fields have been considered in the fluid model. The production of entropy has been analyzed for the modeled problem. A comparative study for ternary, hybrid, and traditional nanofluids has also been carried out by sketching statistical charts. The equations that govern the problem are shifted to dimension-free format by employing transformable variables, and then they are solved by the homotopy analysis method (HAM). It has been revealed in this work that the flow of fluid opposes by magnetic parameter and supports by electric field the volumetric fraction of ternary hybrid nanofluid, while thermal profiles are gained by the growing values of these parameters. Boosting values of the electric field, magnetic parameters, and Eckert number support the Bejan number and oppose the production of entropy. Statistically, it has been established in this work that a ternary hybrid nanofluid has a higher thermal conductivity than hybrid or traditional nanofluids.
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Affiliation(s)
- Kamel Guedri
- Mechanical
Engineering Department, College of Engineering and Islamic Architecture, Umm Al-Qura University, P.O. Box 5555, Makkah, 21955, Saudi Arabia
| | - Arshad Khan
- College
of Aeronautical Engineering, National University
of Sciences and Technology (NUST), Sector H-12, Islamabad, 44000, Pakistan
- E-mail:
| | - Taza Gul
- Department
of Mathematics, City University of Science
and IT, Peshawar, 25000, Pakistan
| | - Safyan Mukhtar
- Department
of Basic Sciences, Preparatory Year Deanship
King Faisal University, P.O. Box 400, Hofuf, Al-Ahsa, 31982, Saudi Arabia
| | - Wajdi Alghamdi
- Department
of Information Technology, Faculty of Computing and Information Technology, King Abdulaziz University, Jeddah, 80261, Saudi Arabia
| | - Mansour F. Yassen
- Department
of Mathematics, College of Science and Humanities in Al-Aflaj, Prince Sattam Bin Abdulaziz University, Al-Aflaj, 11912, Saudi Arabia
- Department
of Mathematics, Faculty of Science, Damietta
University, New Damietta34517Damietta, Egypt
| | - Elsayed Tag Eldin
- Faculty
of
Engineering and Technology, Future University
in EgyptNew Cairo, 11835, Egypt
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8
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Ramzan M, Shamshad U, Rehman S, Junaid MS, Saeed A, Kumam P. Analytical Simulation of Hall Current and Cattaneo–Christov Heat Flux in Cross-Hybrid Nanofluid with Autocatalytic Chemical Reaction: An Engineering Application of Engine Oil. ARABIAN JOURNAL FOR SCIENCE AND ENGINEERING 2022. [DOI: 10.1007/s13369-022-07218-1] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 11/02/2022]
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9
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Saeed A, Algehyne EA, Aldhabani MS, Dawar A, Kumam P, Kumam W. Mixed convective flow of a magnetohydrodynamic Casson fluid through a permeable stretching sheet with first-order chemical reaction. PLoS One 2022; 17:e0265238. [PMID: 35363789 PMCID: PMC8974958 DOI: 10.1371/journal.pone.0265238] [Citation(s) in RCA: 3] [Impact Index Per Article: 1.5] [Reference Citation Analysis] [Abstract] [MESH Headings] [Grants] [Track Full Text] [Download PDF] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Received: 12/14/2021] [Accepted: 02/26/2022] [Indexed: 11/19/2022] Open
Abstract
This research article presents the magnetohydrodynamic Casson fluid flow through an extending surface embedded in a porous medium. Furthermore, the Casson fluid flow is investigated under the effects of thermal radiation, Joule heating, viscous dissipation, and chemical reaction. The analytical solution of the modeled problem is utilized with the help of homotopy analysis method (HAM). The convergence region of the applied technique is portrayed graphically. The impacts of the embedded factors on the flow profiles are exhibited with the help of figures. Furthermore, numerical values of the surface drag force, heat, and mass transfer rates are highlighted via table. The results show that the augmented Darcy number, Casson and magnetic parameters have declined the velocity profile of the Casson fluid flow. Growth in Brownian motion augments the chaotic motion amongst the particles due to which the kinetic energy of the particles transforms to heat energy which consequently augmented the thermal profile, while reduced the concentration profile. The mass and energy profiles are positively effects with the increment of thermophoresis term. And the growing values of chemical reaction and Lewis number cause a reduction in the diffusivity of mass of fluid due to which less transfer of mass takes place that weakens the concentration layer thickness and declines the concentration profiles.
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Affiliation(s)
- Anwar Saeed
- Center of Excellence in Theoretical and Computational Science (TaCS-CoE), Faculty of Science, King Mongkut’s University of Technology Thonburi (KMUTT), Bang Mod, Thung Khru, Bangkok, Thailand
| | - Ebrahem A. Algehyne
- Department of Mathematics, Faculty of Science, University of Tabuk, Tabuk, Saudi Arabia
- Nanotechnology Research Unit (NRU), University of Tabuk, Tabuk, Saudi Arabia
| | - Musaad S. Aldhabani
- Department of Mathematics, Faculty of Science, University of Tabuk, Tabuk, Saudi Arabia
| | - Abdullah Dawar
- Department of Mathematics, Abdul Wali Khan University, Mardan, Khyber Pakhtunkhwa, Pakistan
| | - Poom Kumam
- Center of Excellence in Theoretical and Computational Science (TaCS-CoE), Faculty of Science, King Mongkut’s University of Technology Thonburi (KMUTT), Bang Mod, Thung Khru, Bangkok, Thailand
- Department of Medical Research, China Medical University Hospital, China Medical University, Taichung, Taiwan
- * E-mail:
| | - Wiyada Kumam
- Applied Mathematics for Science and Engineering Research Unit (AMSERU), Program in Applied Statistics, Department of Mathematics and Computer Science, Faculty of Science and Technology, Rajamangala University of Technology Thanyaburi, Thanyaburi, Pathumthani, Thailand
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10
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Hasanuzzaman M, Azad MAK, Hossain MM. Effects of Dufour and thermal diffusion on unsteady MHD free convection and mass transfer flow through an infinite vertical permeable sheet. SN APPLIED SCIENCES 2021. [DOI: 10.1007/s42452-021-04842-8] [Citation(s) in RCA: 2] [Impact Index Per Article: 0.7] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 10/19/2022] Open
Abstract
AbstractIn this paper, the effects of Dufour and thermal diffusion and on unsteady MHD (magnetohydrodynamic) free convection and mass transfer flow through an infinite vertical permeable sheet have been investigated numerically. The non-dimensional governing equations are solved numerically by using the superposition method with the help of “Tec plot” software. The numerical solution regarding the non-dimensional velocity, temperature, and concentration variables against the non-dimensional coordinate variable has been carried out for various values of pertinent numbers and parameters like the suction parameter $$\left( {v_{0} } \right)$$
v
0
, Prandtl number $$\left( {P_{r} } \right)$$
P
r
, magnetic parameter $$\left( M \right)$$
M
, Dufour number $$\left( {D_{f} } \right)$$
D
f
, Soret number $$\left( {S_{0} } \right)$$
S
0
, Schmidt number $$\left( {S_{c} } \right)$$
S
c
, and for constant values of modified local Grashof number $$\left( {G_{{\text{m}}} } \right)$$
G
m
and local Grashof number $$\left( {G_{r} } \right)$$
G
r
.The velocity field decreases for increasing the suction parameter which is focusing on the common fact that the usual suction parameter stabilizing the effect on the boundary layer growth. The thermal boundary layer thickness becomes thinner for rising values of the Dufour and Soret numbers. The skin friction enhances for uplifting values of Soret number and Dufour number but reduces for moving suction parameter, Magnetic force number, Prandtl number, and Schmidt number. The heat transfer rate increases for increasing the suction parameter, Dufour number, Prandtl number, and Soret number. The mass transfer rate increases for enhancing the values of suction parameter, Magnetic force number, Soret number, and Prandtl number but decreases for Dufour number and Schmidt number.
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11
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The MHD Newtonian hybrid nanofluid flow and mass transfer analysis due to super-linear stretching sheet embedded in porous medium. Sci Rep 2021; 11:22518. [PMID: 34795354 PMCID: PMC8602390 DOI: 10.1038/s41598-021-01902-2] [Citation(s) in RCA: 14] [Impact Index Per Article: 4.7] [Reference Citation Analysis] [Abstract] [Track Full Text] [Download PDF] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Received: 06/03/2021] [Accepted: 11/08/2021] [Indexed: 11/08/2022] Open
Abstract
The steady magnetohydrodynamics (MHD) incompressible hybrid nanofluid flow and mass transfer due to porous stretching surface with quadratic velocity is investigated in the presence of mass transpiration and chemical reaction. The basic laminar boundary layer equations for momentum and mass transfer, which are non-linear partial differential equations, are converted into non-linear ordinary differential equations by means of similarity transformation. The mass equation in the presence of chemical reaction is a differential equation with variable coefficients, which is transformed to a confluent hypergeometric differential equation. The mass transfer is analyzed for two different boundary conditions of concentration field that are prescribed surface concentration (PSC) and prescribed mass flux (PMF). The asymptotic solution of concentration filed for large Schmidt number is analyzed using Wentzel-Kramer-Brillouin (WKB) method. The parameters influence the flow are suction/injection, superlinear stretching parameter, porosity, magnetic parameter, hybrid nanofluid terms, Brinkman ratio and the effect of these are analysed using graphs.
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12
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Analytical Simulation for Magnetohydrodynamic Maxwell Fluid Flow Past an Exponentially Stretching Surface with First-Order Velocity Slip Condition. COATINGS 2021. [DOI: 10.3390/coatings11081009] [Citation(s) in RCA: 5] [Impact Index Per Article: 1.7] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 11/16/2022]
Abstract
The study of fluid flow upon an exponentially stretching surface has significant importance due to its applications in technological phenomena at the industrial level. These applications include condensing process of fluid film, heat exchanger processes, extrusion of plastic sheet in aerodynamics, cooling process of metal sheet, and growth of crystals, etc. Keeping in view all these applications, in this paper, we have discussed the magnetohydrodynamic flow of Maxwell fluid past an exponentially stretching sheet. The stretching surface is considered to be slippery by imposing the velocity slip condition. The magnetic field impact is taken into consideration. Furthermore, heat radiation, Joule heating, Brownian motion, and thermophoresis are also considered. The modeled system is reduced to ordinary differential equations with the help of similarity variables. For the analytical solution, we have used the homotopy analysis method. Furthermore, HAM is compared with the shooting method and found to be in great agreement. The squared residual error of the fluid flow problem at 15th order of approximations for Newtonian and non-Newtonian cases has been investigated. It is found that the fluid flow problem converges quickly for the case of non-Newtonian fluid as compared to Newtonian fluid. In addition, the velocity profile increases while the thermal and concentration profiles reduce with greater values of Darcy number. The thermal profile is the increasing function of the Brownian motion parameter and Eckert number whereas the concentration profile is the reducing function of the Brownian motion parameter and Eckert number. With the augmentation in Darcy number, the permeability strength of porous medium increases which concludes the increasing conduct of thermal and mass transportation.
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