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Li D, Dong J, Li H. Electromagnetohydrodynamic (EMHD) flow of Jeffrey fluid through a rough circular microchannel with surface charge-dependent slip. Electrophoresis 2024. [PMID: 38809093 DOI: 10.1002/elps.202300297] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Key Words] [Grants] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 12/13/2023] [Revised: 04/09/2024] [Accepted: 05/09/2024] [Indexed: 05/30/2024]
Abstract
This research examines the electromagnetohydrodynamic (EMHD) flow of Jeffrey fluid in a rough circular microchannel while considering the effect of surface charge on slip. The channel wall corrugations are described as periodic sinusoidal waves with small amplitudes. The perturbation method is employed to derive solutions for velocity and volumetric flow rate, and a combination of three-dimensional (3D) and two-dimensional (2D) graphical representations is utilized to effectively illustrate the impacts of relevant parameters on them. The significance of the Reynolds numberR e $Re$ in investigations of EMHD flow is particularly emphasized. Furthermore, the effect of wall roughness ε $\varepsilon $ and wave number k $k$ on velocity and the influence of wall roughness ε $\varepsilon $ and surface charge densityσ s ${\sigma }_s$ on volumetric flow rate are primarily focused on, respectively, at various Reynolds numbers. The results suggest that increasing the wall roughness leads to a reduction in velocity at low Reynolds numbers (R e = 1 $Re = 1$ ) and an increment at high Reynolds numbers (R e = 10 $Re = 10$ ). For any Reynolds number, a roughness with an odd multiple of wave number (k = 6 , 10 $k = 6,10$ ) will result in a more stable velocity profile compared to one with an even multiple of wave number (k = 4 , 8 $k = 4,8$ ). Decreasing the relaxation timeλ ¯ 1 ${\bar{\lambda }}_1$ while increasing the retardation timeλ ¯ 2 ${\bar{\lambda }}_2$ and Hartmann numberH a $Ha$ can diminish the impact of wall roughness ε $\varepsilon $ and surface charge densityσ s ${\sigma }_s$ on volumetric flow rate, independent of the Reynolds number. Interestingly, in the existence of wall roughness, further consideration of the effect of surface charge on slip leads to a 15% drop in volumetric flow rate atR e = 1 $Re = 1$ and a 32% slippage atR e = 10 $Re = 10$ . However, in the condition where the effect of surface charge on slip is considered, further examination of the presence of wall roughness only results in a 1.4% decline in volumetric flow rate atR e = 1 $Re = 1$ and a 1.6% rise atR e = 10 $Re = 10$ . These findings are crucial for optimizing the EMHD flow models in microchannels.
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Affiliation(s)
- Dongsheng Li
- College of Science, Inner Mongolia University of Technology, Hohhot, P. R. China
| | - Jiayin Dong
- College of Science, Inner Mongolia University of Technology, Hohhot, P. R. China
| | - Haibin Li
- College of Science, Inner Mongolia University of Technology, Hohhot, P. R. China
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Abbas S, Ahmad M, Nazar M, Ahmad Z, Amjad M, Garalleh HAL, Jan AZ. Soret Effect on MHD Casson Fluid over an Accelerated Plate with the Help of Constant Proportional Caputo Fractional Derivative. ACS OMEGA 2024; 9:10220-10232. [PMID: 38463321 PMCID: PMC10918829 DOI: 10.1021/acsomega.3c07311] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Grants] [Track Full Text] [Figures] [Subscribe] [Scholar Register] [Received: 09/22/2023] [Revised: 02/04/2024] [Accepted: 02/09/2024] [Indexed: 03/12/2024]
Abstract
Non-Newtonian fluid flow is significant in engineering and biomedical applications such as thermal exchangers, electrical cooling mechanisms, nuclear reactor cooling, drug delivery, blood flow analysis, and tissue engineering. The Caputo operator has emerged as a prevalent tool in fractional calculus, garnering widespread recognition. This research aims to introduce a novel derivative by merging the proportional and Caputo operators, resulting in the fractional operator known as the constant proportional Caputo. In order to demonstrate this newly defined operator's dynamic qualities, it was employed in the analysis of the unsteady Casson flow model. In addition, the current work shows an analytical analysis to determine the Soret effect on the fractionalized MHD Casson fluid over an oscillating vertical plate. Fractional partial differential equations (PDEs) are used to formulate the problem along with IBCs. The introduction of appropriate nondimensional variables converts the PDEs into dimensionless form. The precise solutions to the fractional governing PDEs are then determined by the Laplace transform method. Velocity, concentration, and temperature profiles; the impacts of the Prandtl number; fractional parameter β and γ; and Soret and Schmidt numbers are graphically depicted. The profiles of temperature, concentration, and velocity rise with rising time and fractional parameters. Interestingly, as the Casson flow parameter is higher, fluid velocity decreases closest to the plate but increases away from the plate. Tables showing the findings for the skin-friction coefficient, Sherwood, and Nusselt numbers for a range of flow-controlling parameter values are provided. Furthermore, an investigation is undertaken to compare fractionalized and ordinary velocity fields. The results suggest that the fractional model employing a constant proportional derivative exhibits a quicker decay than the model incorporating conventional Caputo and Caputo-Fabrizio operators.
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Affiliation(s)
- Shajar Abbas
- Centre
for Advanced Studies in Pure and Applied Mathematics, Bahauddin Zakariya University Multan 60000, Pakistan
| | - Mushtaq Ahmad
- Department
of Mathematics, Institute of Southern Punjab Multan 66000, Pakistan
| | - Mudassar Nazar
- Centre
for Advanced Studies in Pure and Applied Mathematics, Bahauddin Zakariya University Multan 60000, Pakistan
| | - Zubair Ahmad
- Applied
College, Mahala Campus, King Khalid University, P.O. Box 9004, Abha 61413, Saudi Arabia
- Center
of Bee Research and Its Products, King Khalid
University, P.O. Box 9004, Abha 61413, Saudi Arabia
| | - Muhammad Amjad
- Department
of Mathematics, Comsats University Islamabad, Vehari Campus, Vehari 61100, Pakistan
| | - Hakim AL Garalleh
- Department
of Mathematical Science, College of Engineering, University of Business and Technology-Dahban, Jeddah 21361, Saudi Arabia
| | - Ahmed Zubair Jan
- Faculty
of Mechanical Engineering, Wroclaw University
of Science and Technology, Wroclaw 50-370, Poland
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Chinnasamy P, Sivajothi R, Sathish S, Abbas M, Jeyakrishnan V, Goel R, Alqahtani MS, Loganathan K. Peristaltic transport of Sutterby nanofluid flow in an inclined tapered channel with an artificial neural network model and biomedical engineering application. Sci Rep 2024; 14:555. [PMID: 38177235 PMCID: PMC10767104 DOI: 10.1038/s41598-023-49480-9] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Key Words] [MESH Headings] [Grants] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 10/31/2023] [Accepted: 12/08/2023] [Indexed: 01/06/2024] Open
Abstract
Modern energy systems are finding new applications for magnetohydrodynamic rheological bio-inspired pumping systems. The incorporation of the electrically conductive qualities of flowing liquids into the biological geometries, rheological behavior, and propulsion processes of these systems was a significant effort. Additional enhancements to transport properties are possible with the use of nanofluids. Due to their several applications in physiology and industry, including urine dynamics, chyme migration in the gastrointestinal system, and the hemodynamics of tiny blood arteries. Peristaltic processes also move spermatozoa in the human reproductive system and embryos in the uterus. The present research examines heat transport in a two-dimensional deformable channel containing magnetic viscoelastic nanofluids by considering all of these factors concurrently, which is vulnerable to peristaltic waves and hall current under ion slip and other situations. Nanofluid rheology makes use of the Sutterby fluid model, while nanoscale effects are modeled using the Buongiorno model. The current study introduces an innovative numerical computing solver utilizing a Multilayer Perceptron feed-forward back-propagation artificial neural network (ANN) with the Levenberg-Marquardt algorithm. Data were collected for testing, certifying, and training the ANN model. In order to make the dimensional PDEs dimensionless, the non-similar variables are employed and calculated by the Homotopy perturbation technique. The effects of developing parameters such as Sutterby fluid parameter, Froude number, thermophoresis, ion-slip parameter, Brownian motion, radiation, Eckert number, and Hall parameter on velocity, temperature, and concentration are demonstrated. The machine learning model chooses data, builds and trains a network, and subsequently assesses its performance using the mean square error metric. Current results declare that the improving Reynolds number tends to increase the pressure rise. Improving the Hall parameter is shown to result in a decrease in velocity. When raising a fluid's parameter, the temperature profile rises.
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Affiliation(s)
- P Chinnasamy
- Department of Computer Science and Engineering, MLR Institute of Technology, Hyderabad, Telangana, India
| | - R Sivajothi
- Department of Management, R L Institute of Management Studies (A Unit of Subbalakshmi Lakshmipathy College of Science), Madurai, Tamil Nadu, India
| | - S Sathish
- Department of Mathematics, School of Science, National Institute of Technology, Tadepalligudem, Andhra Pradesh, India
| | - Mohamed Abbas
- Electrical Engineering Department, College of Engineering, King Khalid University, 61421, Abha, Saudi Arabia
| | - V Jeyakrishnan
- Department of Computer Science and Engineering, Manipal University Jaipur, Jaipur, Rajasthan, 303007, India
| | - Rajat Goel
- Department of Computer Science and Engineering, Manipal University Jaipur, Jaipur, Rajasthan, 303007, India
| | - Mohammed S Alqahtani
- Radiological Sciences Department, College of Applied Medical Sciences, King Khalid University, 61421, Abha, Saudi Arabia
- BioImaging Unit, Space Research Centre, Michael Atiyah Building, University of Leicester, Leicester, LE1 7RH, UK
| | - K Loganathan
- Department of Mathematics and Statistics, Manipal University Jaipur, Jaipur, Rajasthan, 303007, India.
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Sehra, Sadia H, Haq SU, Khan I. Time fractional Yang-Abdel-Cattani derivative in generalized MHD Casson fluid flow with heat source and chemical reaction. Sci Rep 2023; 13:16494. [PMID: 37779112 PMCID: PMC10543644 DOI: 10.1038/s41598-023-43630-9] [Citation(s) in RCA: 1] [Impact Index Per Article: 1.0] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 05/05/2023] [Accepted: 09/26/2023] [Indexed: 10/03/2023] Open
Abstract
This present research article investigates the exact analytical solution for the mathematical model of the generalized Casson fluid flow by using the new fractional operator with Rabotnov exponential kernel i.e. Yang-Abdel-Cattani operator. The impacts of heat source, magnetic hydrodynamics and chemical reactions on the flow of fractional Casson fluid through a vertical flat plate are studied in this article. For the sake of a better interpretation of the rheological behavior of Casson fluid we have used the new operator of fractional order with exponential kernel of Rabotnov known as Yang-Abdel-Cattani operator of fractional derivative. By making use of the technique of Laplace transform we have find the exact analytical solution of the problem in the Mittag-Leffler's form, for all the three governing equations i.e. Velocity, energy and concentration equation. It has been noticed from the literature that it is challenging to obtain analytical results from fractional fluid model derived by the various fractional operators. This article helps to address this issue by providing analytical solutions for fractionalized fluid models. To analyze the physical importance of different fluid parameters such as Schmidt number, Prandtl number, MHD and alpha on the heat, mass and momentum class are presented through graphs. The concentration of the fluid decreases with Schmidth number and temperature of the fluid decreases with the increasing Prandtl number. The velocity of the fluid decreases with increasing MHD effects and increases with increasing Alpha. The Yang-Abdel-Cattani operator of fractional order can describe the memory effects more suitably than the other fractional operators.
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Affiliation(s)
- Sehra
- Shaheed Benazir, Bhutto Women University Peshawar, Peshawar, Khyber Pakhtunkhwa, 25000, Pakistan
| | - Haleema Sadia
- Shaheed Benazir, Bhutto Women University Peshawar, Peshawar, Khyber Pakhtunkhwa, 25000, Pakistan.
| | - Sami Ul Haq
- Department of Mathematics, Islamia College Peshawar, Peshawar, Khyber Pakhtunkhwa, 25000, Pakistan.
| | - Ilyas Khan
- Department of Mathematics, College of Science Al-Zulfi, Majmaah University, Al-Majmaah, 11952, Saudi Arabia.
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Rehman AU, Riaz MB, Wojciechowski A. Thermo diffusion impacts on the flow of second grade fluid with application of (ABC), (CF) and (CPC) subject to exponential heating. Sci Rep 2022; 12:18437. [PMID: 36323744 PMCID: PMC9630548 DOI: 10.1038/s41598-022-21773-5] [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: 07/16/2022] [Accepted: 10/03/2022] [Indexed: 11/16/2022] Open
Abstract
The aim of this article is to investigate the exact solution by using a new approach for the thermal transport phenomena of second grade fluid flow under the impact of MHD along with exponential heating as well as Darcy's law. The phenomenon has been expressed in terms of partial differential equations, then transformed the governing equations in non-dimentional form. For the sake of better rheology of second grade fluid, developed a fractional model by applying the new definition of Constant Proportional-Caputo hybrid derivative (CPC), Atangana Baleanu in Caputo sense (ABC) and Caputo Fabrizio (CF) fractional derivative operators that describe the generalized memory effects. For seeking exact solutions in terms of Mittag-Leffler and G-functions for velocity, temperature and concentration equations, Laplace integral transformation technique is applied. For physical significance of various system parameters on fluid velocity, concentration and temperature distributions are demonstrated through various graphs by using graphical software. Furthermore, for being validated the acquired solutions, accomplished a comparative analysis with some published work. It is also analyzed that for exponential heating and non-uniform velocity conditions, the CPC fractional operator is the finest fractional model to describe the memory effect of velocity, energy and concentration profile. Moreover, the graphical representations of the analytical solutions illustrated the main results of the present work. Also, in the literature, it is observed that to derived analytical results from fractional fluid models developed by the various fractional operators, is difficult and this article contributing to answer the open problem of obtaining analytical solutions the fractionalized fluid models.
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Affiliation(s)
- Aziz Ur Rehman
- grid.444940.9Department of Mathematics, University of Management and Technology, 54770 Lahore, Pakistan
| | - Muhammad Bilal Riaz
- grid.444940.9Department of Mathematics, University of Management and Technology, 54770 Lahore, Pakistan ,grid.412284.90000 0004 0620 0652Faculty of Technical Physics, Information Technology and Applied Mathematics, Lodz University of Technology, 90-924 Lodz, Poland
| | - Adam Wojciechowski
- grid.412284.90000 0004 0620 0652Faculty of Technical Physics, Information Technology and Applied Mathematics, Lodz University of Technology, 90-924 Lodz, Poland
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Asifa, Kumam P, Tassaddiq A, Watthayu W, Shah Z, Anwar T. Modeling and simulation based investigation of unsteady MHD radiative flow of rate type fluid; a comparative fractional analysis. MATHEMATICS AND COMPUTERS IN SIMULATION 2022; 201:486-507. [DOI: 10.1016/j.matcom.2021.02.005] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 09/01/2023]
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7
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Ur Rehman A, Riaz MB, Atangana A. Time fractional analysis of Casson fluid with Rabotnov exponential memory based on the generalized Fourier and Fick...s law. SCIENTIFIC AFRICAN 2022. [DOI: 10.1016/j.sciaf.2022.e01385] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/11/2022] Open
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8
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Anwar T, Kumam P, Khan I, Thounthong P. Thermal analysis of MHD convective slip transport of fractional Oldroyd-B fluid over a plate. MECHANICS OF TIME-DEPENDENT MATERIALS 2022; 26:431-462. [DOI: 10.1007/s11043-021-09495-z] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Track Full Text] [Subscribe] [Scholar Register] [Received: 07/25/2020] [Accepted: 03/26/2021] [Indexed: 09/01/2023]
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Impact of Newtonian Heating via Fourier and Fick’s Laws on Thermal Transport of Oldroyd-B Fluid by Using Generalized Mittag-Leffler Kernel. Symmetry (Basel) 2022. [DOI: 10.3390/sym14040766] [Citation(s) in RCA: 3] [Impact Index Per Article: 1.5] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 01/25/2023] Open
Abstract
In this manuscript, a new approach to study the fractionalized Oldroyd-B fluid flow based on the fundamental symmetry is described by critically examining the Prabhakar fractional derivative near an infinitely vertical plate, wall slip condition on temperature along with Newtonian heating effects and constant concentration. The phenomenon has been described in forms of partial differential equations along with heat and mass transportation effect taken into account. The Prabhakar fractional operator which was recently introduced is used in this work together with generalized Fick’s and Fourier’s law. The fractional model is transfromed into a non-dimentional form by using some suitable quantities and the symmetry of fluid flow is analyzed. The non-dimensional developed fractional model for momentum, thermal and diffusion equations based on Prabhakar fractional operator has been solved analytically via Laplace transformation method and calculated solutions expressed in terms of Mittag-Leffler special functions. Graphical demonstrations are made to characterize the physical behavior of different parameters and significance of such system parameters over the momentum, concentration and energy profiles. Moreover, to validate our current results, some limiting models such as fractional and classical fluid models for Maxwell and Newtonian are recovered, in the presence of with/without slip boundary wall conditions. Further, it is observed from the graphs the velocity curves for classical fluid models are relatively higher than fractional fluid models. A comparative analysis between fractional and classical models depicts that the Prabhakar fractional model explains the memory effects more adequately.
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Anwar T, Kumam P, Asifa, Thounthong P, Muhammad S, Duraihem FZ. Generalized thermal investigation of unsteady MHD flow of Oldroyd-B fluid with slip effects and Newtonian heating; a Caputo-Fabrizio fractional model. ALEXANDRIA ENGINEERING JOURNAL 2022; 61:2188-2202. [DOI: 10.1016/j.aej.2021.06.090] [Citation(s) in RCA: 3] [Impact Index Per Article: 1.5] [Reference Citation Analysis] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 09/01/2023]
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Generalized Mittag-Leffler Kernel Form Solutions of Free Convection Heat and Mass Transfer Flow of Maxwell Fluid with Newtonian Heating: Prabhakar Fractional Derivative Approach. FRACTAL AND FRACTIONAL 2022. [DOI: 10.3390/fractalfract6020098] [Citation(s) in RCA: 4] [Impact Index Per Article: 2.0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 12/10/2022]
Abstract
In this article, the effects of Newtonian heating along with wall slip condition on temperature is critically examined on unsteady magnetohydrodynamic (MHD) flows of Prabhakar-like non integer Maxwell fluid near an infinitely vertical plate under constant concentration. For the sake of generalized memory effects, a new mathematical fractional model is formulated based on a newly introduced Prabhakar fractional operator with generalized Fourier’s law and Fick’s law. This fractional model has been solved analytically and exact solutions for dimensionless velocity, concentration, and energy equations are calculated in terms of Mittag-Leffler functions by employing the Laplace transformation method. Physical impacts of different parameters such as α, Pr, β, Sc, Gr, γ, and Gm are studied and demonstrated graphically by Mathcad software. Furthermore, to validate our current results, some limiting models such as classical Maxwell model, classical Newtonian model, and fractional Newtonian model are recovered from Prabhakar fractional Maxwell fluid. Moreover, we compare the results between Maxwell and Newtonian fluids for both fractional and classical cases with and without slip conditions, showing that the movement of the Maxwell fluid is faster than viscous fluid. Additionally, it is visualized that both classical Maxwell and viscous fluid have relatively higher velocity as compared to fractional Maxwell and viscous fluid.
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Wang F, Rehman S, Bouslimi J, Khaliq H, Qureshi MI, Kamran M, Alharbi AN, Ahmad H, Farooq A. Comparative study of heat and mass transfer of generalized MHD Oldroyd-B bio-nano fluid in a permeable medium with ramped conditions. Sci Rep 2021; 11:23454. [PMID: 34873194 PMCID: PMC8648785 DOI: 10.1038/s41598-021-02326-8] [Citation(s) in RCA: 11] [Impact Index Per Article: 3.7] [Reference Citation Analysis] [Abstract] [Key Words] [MESH Headings] [Grants] [Track Full Text] [Download PDF] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Received: 05/31/2021] [Accepted: 11/15/2021] [Indexed: 11/09/2022] Open
Abstract
This article aims to investigate the heat and mass transfer of MHD Oldroyd-B fluid with ramped conditions. The Oldroyd-B fluid is taken as a base fluid (Blood) with a suspension of gold nano-particles, to make the solution of non-Newtonian bio-magnetic nanofluid. The surface medium is taken porous. The well-known equation of Oldroyd-B nano-fluid of integer order derivative has been generalized to a non-integer order derivative. Three different types of definitions of fractional differential operators, like Caputo, Caputo-Fabrizio, Atangana-Baleanu (will be called later as [Formula: see text]) are used to develop the resulting fractional nano-fluid model. The solution for temperature, concentration, and velocity profiles is obtained via Laplace transform and for inverse two different numerical algorithms like Zakian's, Stehfest's are utilized. The solutions are also shown in tabular form. To see the physical meaning of various parameters like thermal Grashof number, Radiation factor, mass Grashof number, Schmidt number, Prandtl number etc. are explained graphically and theoretically. The velocity and temperature of nanofluid decrease with increasing the value of gold nanoparticles, while increase with increasing the value of both thermal Grashof number and mass Grashof number. The Prandtl number shows opposite behavior for both temperature and velocity field. It will decelerate both the profile. Also, a comparative analysis is also presented between ours and the existing findings.
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Affiliation(s)
- Fuzhang Wang
- Nanchang Institute of Technology, Nanchang, 30044, China
- School of Mathematics and Statistics, Xuzhou University of Technology, Xuzhou, 221018, China
| | - Sadique Rehman
- Department of Pure and Applied Mathematics, University of Haripur, Haripur, KPK, Pakistan
| | - Jamel Bouslimi
- Department of Physics, Faculty of Science, Taif University, P.O. Box 888, Taif, 21944, Saudi Arabia
| | - Hammad Khaliq
- Department of Pure and Applied Mathematics, University of Haripur, Haripur, KPK, Pakistan
| | - Muhammad Imran Qureshi
- Department of Mathematics, COMSATS University Islamabad, Vehari Campus, Vehari, 61100, Pakistan
| | - Muhammad Kamran
- Department of Mathematics, COMSATS University Islamabad, Wah Campus, Islamabad, 47040, Pakistan
| | - Abdulaziz N Alharbi
- Department of Physics, College of Science, Taif University, P. O. Pox 11099, Taif, 21944, Saudi Arabia
| | - Hijaz Ahmad
- Department of Basic Sciences, University of Engineering Technology, Peshawar, Pakistan
- Section of Mathematics, International Telematic University Uninettanu, Corso Vittorio Emanuele II, 39, 00186, Roma, Italy
| | - Aamir Farooq
- Department of Mathematics, Abbottabad University of Science and Technology, Abbottabad, Pakistan.
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Functional Effects of Permeability on Oldroyd-B Fluid under Magnetization: A Comparison of Slipping and Non-Slipping Solutions. APPLIED SCIENCES-BASEL 2021. [DOI: 10.3390/app112311477] [Citation(s) in RCA: 4] [Impact Index Per Article: 1.3] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 11/16/2022]
Abstract
In this article, the impact of Newtonian heating in addition to slip effects was critically examined on the unsteady magnetohydrodynamic (MHD) flow of an Oldroyd-B fluid near an infinitely vertical plate. The functional effects such as the retardation and relaxation of materials can be estimated for magnetized permeability based on the relative decrease or increase during magnetization. From this perspective, a new mathematical model was formulated based on non-slippage and slippage postulates for the Oldroyd-B fluid with magnetized permeability. The heat transfer induction was also examined through a non-fractional developed mathematical model for the Oldroyd-B fluid. The exact solution expressions for non-dimensional equations of velocity and temperature were explored by employing Laplace integral transformation under slipping boundary conditions under Newtonian heating. The heat transfer rate was estimated through physical interpretation by considering the limits on the solutions induced by the Nusselt number. To comprehensively discuss the dynamics of the considered problem, the physical impacts of different parameters were studied and reverberations were graphically highlighted and deliberated. Furthermore, in order to validate the results, two limiting models, namely the Maxwell model and the second grade model, were used to compare the relevant flow characteristics. Additionally, in order to perform the parametric analysis, the graphical representation was portrayed for non-slipping and slipping solutions for velocity and temperature.
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MHD Laminar Boundary Layer Flow of a Jeffrey Fluid Past a Vertical Plate Influenced by Viscous Dissipation and a Heat Source/Sink. MATHEMATICS 2021. [DOI: 10.3390/math9161896] [Citation(s) in RCA: 1] [Impact Index Per Article: 0.3] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 11/16/2022]
Abstract
This study investigates the effects of viscous dissipation and a heat source or sink on the magneto-hydrodynamic laminar boundary layer flow of a Jeffrey fluid past a vertical plate. The governing boundary layer non-linear partial differential equations are reduced to non-linear ordinary differential equations using suitable similarity transformations. The resulting system of dimensionless differential equations is then solved numerically using the bivariate spectral quasi-linearisation method. The effects of some physical parameters that include the Schmidt number, Eckert number, radiation parameter, magnetic field parameter, heat generation parameter, and the ratio of relaxation to retardation times on the velocity, temperature, and concentration profiles are presented graphically. Additionally, the influence of some physical parameters on the skin friction coefficient, local Nusselt number, and the local Sherwood number are displayed in tabular form.
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Anwar T, Kumam P, Asifa, Khan I, Thounthong P. Generalized Unsteady MHD Natural Convective Flow of Jeffery Model with ramped wall velocity and Newtonian heating; A Caputo-Fabrizio Approach. CHINESE JOURNAL OF PHYSICS 2020; 68:849-865. [DOI: 10.1016/j.cjph.2020.10.018] [Citation(s) in RCA: 4] [Impact Index Per Article: 1.0] [Reference Citation Analysis] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 09/01/2023]
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16
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Hydrodynamical Study of Creeping Maxwell Fluid Flow through a Porous Slit with Uniform Reabsorption and Wall Slip. MATHEMATICS 2020. [DOI: 10.3390/math8101852] [Citation(s) in RCA: 7] [Impact Index Per Article: 1.8] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 11/16/2022]
Abstract
The present theoretical study investigates the influence of velocity slip characteristics on the plane steady two-dimensional incompressible creeping Maxwell fluid flow passing through a porous slit with uniform reabsorption. This two-dimensional flow phenomenon is governed by the mathematical model having nonlinear partial differential equations together with non-homogeneous boundary conditions. An analytical technique, namely the recursive approach, is used successfully to find the solutions of the problem. The explicit expressions for stream function, velocity components, pressure distribution, wall shear stress and normal stress difference have been derived. The axial flow rate, leakage flux and fractional reabsorption are also found out. The points of maximum velocity are identified. Non-dimensionalization is carried out and graphs are portrayed at different positions of the channel to show the impact of pertinent parameters: slip parameter, Maxwell fluid parameter and absorption parameter, on flow variables and found that the fluid velocity is affected significantly due to these parameters. This study provides a mathematical basis to understand the physical phenomenon for fluid flows through permeable boundaries which exists in different problems like gaseous diffusion, filtration and biological mechanisms.
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Mathematical Analysis of Entropy Generation in the Flow of Viscoelastic Nanofluid through an Annular Region of Two Asymmetric Annuli Having Flexible Surfaces. COATINGS 2020. [DOI: 10.3390/coatings10030213] [Citation(s) in RCA: 29] [Impact Index Per Article: 7.3] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 11/17/2022]
Abstract
In this manuscript, the authors developed the mathematical model for entropy generation analysis during the peristaltic propulsion of Jeffrey nanofluids passing in a midst of two eccentric asymmetric annuli. The model was structured by implementation of lubrication perspective and dimensionless strategy. Entropy generation caused by the irreversible influence of heat and mass transfer of nanofluid and viscous dissipation of the considered liquid was taken into consideration. The governing equations were handled by a powerful analytical technique (HPM). The comparison of total entropy with the partial entropy was also invoked by discussing Bejan number results. The influence of various associated variables on the profiles of velocity, temperature, nanoparticle concentration, entropy generation and Bejan number was formulated by portraying the figures. Mainly from graphical observations, we analyzed that, in the matter of thermophoresis parameter and Brownian motion parameter, entropy generation is thoroughly enhanced while inverse readings were reported for the temperature difference parameter and the ratio of temperature to concentration parameters.
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