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Anjum N, Azeem Khan W, Ali M, Muhammad T, Hussain Z. Melting heat transfer analysis in magnetized bioconvection flow of sutterby nanoliquid conveying gyrotactic microorganisms. Heliyon 2023; 9:e21910. [PMID: 38045202 PMCID: PMC10689871 DOI: 10.1016/j.heliyon.2023.e21910] [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: 04/24/2023] [Revised: 10/28/2023] [Accepted: 10/31/2023] [Indexed: 12/05/2023] Open
Abstract
In biotechnology and biosensors bioconvection along with microorganisms play a important role. This article communicates a theoretic numerical analysis concerning the bioconvective Sutterby nanofluid flow over a stretchable wedge surface. Bioconvection is a remarkable occurrence of undercurrents fluid that is produced owing to the turning of microbes. It is considered for hydrodynamics unsteadiness and forms classified in interruption of inclined swimming microbes. Bioconvection is perceived practically in many uses for example pharmaceutical products, bio sensing applications, biomedical, bio-micro systems, biotechnology advancements and refining of mathematical models. Additionally, unsteady parameter influences are taken into account. Furthermore, no mass flux as well as heat sink/source consequences are measured in existing analysis. The similarity transformation are established for the non-linear PDEs of microorganism's field, nanofluid concentration, energy, momentum and mass for bioconvection flow of Sutterby nanofluid. Then, altered non-linear ODEs are resolved by utilizing the bvp4c technique. Moreover, nanofluids are declining in thermal and concentration fields and the greater number of Peclet number declines the field of microorganisms. Acquired numerical data displays that temperature field of nanofluid increases for more thermophoretic and unsteady parameters.
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Affiliation(s)
- Nazash Anjum
- Department of Mathematics, Mohi-ud-Din Islamic University, Nerian Sharif, Azad Jammu & Kashmir, 12010, Pakistan
| | - Waqar Azeem Khan
- Department of Mathematics, Mohi-ud-Din Islamic University, Nerian Sharif, Azad Jammu & Kashmir, 12010, Pakistan
| | - Mehboob Ali
- School of Mathematics and Physics, Center for Applied Mathematics of Guangxi, Guangxi Minzu University, Nanning, 530006, China
| | - Taseer Muhammad
- Department of Mathematics, College of Science, King Khalid University, Abha, Saudi Arabia
| | - Zakir Hussain
- Department of Mathematics, COMSATS University Islamabad, Abbottabad Campus, Pakistan
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Darvesh A, Altamirano GC, Salas S AH, Sánchez Chero M, Carrión Barco G, Bringas Salvador JL, Ayub A. Infinite Shear Rate Viscosity Model of Cross Fluid Flow Containing Nanoparticles and Motile Gyrotactic Microorganisms Over 3-D Cylinder. JOURNAL OF NANOFLUIDS 2023. [DOI: 10.1166/jon.2023.1968] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 01/22/2023]
Abstract
Cross nanofluidic model yields extraordinary results and describes the behaviour of nanofluid at very high and very low shear rate. In this paper infinite shear rate viscosity model of cross nanofluid flow containing nanoparticles and motile gyrotactic microorganisms over three dimensional
horizontal cylinder is taken. In this attempt simultaneous utilization of nanoparticles along with motile microorganisms attached mathematical model of cross fluid and three-dimensional geometry of cylinder has been carried out as an innovation. For the inspection of velocity profile of cross
nanofluid inclined magnetic field is scrutinized. Temperature of Cross nanofluid and its concentration is also carried out with several facts. Mass flux and heat flux values for motile microorganisms and nanoparticles are calculated through statistical graphs. This attempt reveals that small
variation of Brownian motion parameter gives lower concentration of nanoparticle about 80.21% and 78.44% reduction is found in concentration of motile microorganisms.
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Affiliation(s)
- Adil Darvesh
- Department of Mathematics, Hazara University, Mansehra, 21300, Pakistan
| | | | | | | | | | | | - Assad Ayub
- Department of Mathematics, Hazara University, Mansehra, 21300, Pakistan
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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] [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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Ali L, Manan A, Ali B. Maxwell Nanofluids: FEM Simulation of the Effects of Suction/Injection on the Dynamics of Rotatory Fluid Subjected to Bioconvection, Lorentz, and Coriolis Forces. NANOMATERIALS (BASEL, SWITZERLAND) 2022; 12:3453. [PMID: 36234581 PMCID: PMC9565906 DOI: 10.3390/nano12193453] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Figures] [Subscribe] [Scholar Register] [Received: 08/27/2022] [Revised: 09/13/2022] [Accepted: 09/20/2022] [Indexed: 06/16/2023]
Abstract
In this study, the relevance of Lorentz and Coriolis forces on the kinetics of gyratory Maxwell nanofluids flowing against a continually stretched surface is discussed. Gyrotactic microbes are incorporated to prevent the bioconvection of small particles and to improve consistency. The nanoparticles are considered due to their valuable properties and ability to enhance thermal dissipation, which is important in heating systems, advanced technology, microelectronics, and other areas. The main objective of the analysis is to enhance the rate of heat transfer. An adequate similarity transformation is used to convert the primary partial differential equations into non-linear dimensionless ordinary differential equations. The resulting system of equations is solved using the finite element method (FEM). The increasing effects of the Lorentz and Coriolis forces induce the velocities to moderate, whereas the concentration and temperature profiles exhibit the contrary tendency. It is observed that the size and thickness of the fluid layers in the axial position increase as the time factor increases, while the viscidity of the momentum fluid layers in the transverse path decreases as the time factor decreases. The intensity, temperature, and velocity variances for the suction scenario are more prominent than those for the injection scenario, but there is an opposite pattern for the physical quantities. The research findings are of value in areas such as elastomers, mineral productivity, paper-making, biosensors, and biofuels.
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Affiliation(s)
- Liaqat Ali
- School of Sciences, Xi’an Technological University, Xi’an 710021, China
| | - Abdul Manan
- Department of Physics and Mathematics, Faculty of Sciences, Superior University, Lahore 54000, Pakistan
| | - Bagh Ali
- Department of Computer Science and Information Technology, Faculty of Sciences, Superior University, Lahore 54000, Pakistan
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Significance of nanoparticles aggregation on the dynamics of rotating nanofluid subject to gyrotactic microorganisms, and Lorentz force. Sci Rep 2022; 12:16258. [PMID: 36171248 PMCID: PMC9519940 DOI: 10.1038/s41598-022-20485-0] [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: 06/21/2022] [Accepted: 09/14/2022] [Indexed: 11/29/2022] Open
Abstract
The significance of nanoparticle aggregation, Lorentz and Coriolis forces on the dynamics of spinning silver nanofluid flow past a continuously stretched surface is prime significance in modern technology, material sciences, electronics, and heat exchangers. To improve nanoparticles stability, the gyrotactic microorganisms is consider to maintain the stability and avoid possible sedimentation. The goal of this report is to propose a model of nanoparticles aggregation characteristics, which is responsible to effectively state the nanofluid viscosity and thermal conductivity. The implementation of the similarity transforQ1m to a mathematical model relying on normal conservation principles yields a related set of partial differential equations. A well-known computational scheme the FEM is employed to resolve the partial equations implemented in MATLAB. It is seen that when the effect of nanoparticles aggregation is considered, the temperature distribution is enhanced because of aggregation, but the magnitude of velocities is lower. Thus, showing the significance impact of aggregates as well as demonstrating themselves as helpful theoretical tool in future bioengineering and industrial applications.
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Siddique I, Abdal S, Din ISU, Awrejcewicz J, Pawłowski W, Hussain S. Significance of concentration-dependent viscosity on the dynamics of tangent hyperbolic nanofluid subject to motile microorganisms over a non-linear stretching surface. Sci Rep 2022; 12:12765. [PMID: 35896639 PMCID: PMC9329284 DOI: 10.1038/s41598-022-16601-9] [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: 12/05/2021] [Accepted: 07/12/2022] [Indexed: 11/27/2022] Open
Abstract
The communication describes a theoretical framework for tangent hyperbolic fluid of nano-biofilm due to an extending or shrinking sheet that comprises a stagnation point flow, chemical reaction with activation energy, and bioconvection of gyrotactic microorganisms. The varying transport features due to dynamic viscosity, thermal conductivity, nano-particle mass permeability and microbe organisms diffusivity are taken into account for the novelty of this work. The inspiration is developed to enhance heat transfer. A set of leading partial differential equations is formed along with appropriate boundary constraints. Using similarity transformations, the basic formulation is transitioned into non-linear differential equations. To produce observational data, the shooting technique and Runge-Kutta fourth order method are employed. The coding of numerical scheme is developed in Matlab script. The visual representation of the effects of diverse fluid transport properties and distinctive parameters on speed, temperature, concentration and motile density are evaluated. The velocity become faster when the parameters \documentclass[12pt]{minimal}
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\begin{document}$$V_0$$\end{document}V0 are enhanced. Brownian motion, thermal conductivity, heat generation as well as thermophoresis factors all strengthen the temperature distribution, however the nano-particle concentration profile is enhanced as the nano-particle mass conductivity variable, activation energy as well as the thermophoresis variable are boosted. The microorganism density improves significantly when the microorganism diffusivity factor increases. The skin friction, Sherwood number, Nusselt number and motile density number decline against the incremented transport parameters.
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Affiliation(s)
- Imran Siddique
- Department of Mathematics, University of Management and Technology, Lahore, 54770, Pakistan.
| | - Sohaib Abdal
- Department of Mathematics, Khwaja Fareed University of Engineering and Information Technology, Rahim Yar Khan, Pakistan.,School of Mathematics, Northwest University, No. 229 North Taibai Avenue, Xi'an, 7100069, China
| | - Irfan Saif Ud Din
- Department of Mathematics, University of Management and Technology, Lahore, 54770, Pakistan
| | - Jan Awrejcewicz
- Department of Automation, Biomechanics and Mechatronics, Lodz University of Technology, 1/15 Stefanowskiego St., 90-924, Lodz, Poland
| | - Witold Pawłowski
- Institute of Machine Tools and Production Engineering, Lodz University of Technology, Lodz, Poland
| | - Sajjad Hussain
- School of Aerospace and Mechanical Engineering, Nanyang Technological University, Singapore, Singapore
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Magodora M, Mondal H, Motsa S, Sibanda P. Effect on Entropy Generation Analysis for Heat Transfer Nanofluid Near a Rotating Disk Using Quasilinearization Method. JOURNAL OF NANOFLUIDS 2022. [DOI: 10.1166/jon.2022.1848] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 11/23/2022]
Abstract
The study considers gold-water nanofluid flow past a porous rotating disk while accounting for prescribed heat flux and suction at the boundary layer of the disk. The physical parameters of the nanoparticle volume fraction, magnetic parameter and entropy generation are investigated
and presented in this paper. The numerically solved nonlinear equations by the spectral quasilinearization technique. The main findings are presented in graphical form and discussed for variations of the flow parameters. The findings indicate that increased nanoparticle volume concentration
fall in velocity but a overshoot in temperature, while enhancing the magnetic parameter is associated with reduced velocity distribution and increased skin friction. Among other findings, the results also show that increasing the Brinkman number leads to increased entropy generation but reduced
Bejan number, while the Reynolds number increasing in the generation of elevated levels of entropy production. The reliability, error analysis and accuracy are checked through convergence of the method. The accuracy is further tested through a comparison of results for limiting cases with
those in the literature. The findings of this study have significant applications in engineering, science and technology.
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Affiliation(s)
- Mangwiro Magodora
- School of Mathematics, Statistics and Computer Science, University of KwaZulu-Natal, Private Bag X01, Scottsvile, 3209, Pietermaritzburg, South Africa
| | - Hiranmoy Mondal
- Department of Applied Mathematics, Maulana Abul Kalam Azad University of Technology, Kolkata 741249, West Bengal, India
| | - Sandile Motsa
- School of Mathematics, Statistics and Computer Science, University of KwaZulu-Natal, Private Bag X01, Scottsvile, 3209, Pietermaritzburg, South Africa
| | - Precious Sibanda
- School of Mathematics, Statistics and Computer Science, University of KwaZulu-Natal, Private Bag X01, Scottsvile, 3209, Pietermaritzburg, South Africa
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Almakki M, Mondal H, Mburu Z, Sibanda P. Entropy Generation in Double Diffusive Convective Magnetic Nanofluid Flow in Rotating Sphere with Viscous Dissipation. JOURNAL OF NANOFLUIDS 2022. [DOI: 10.1166/jon.2022.1847] [Citation(s) in RCA: 1] [Impact Index Per Article: 0.5] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 11/23/2022]
Abstract
We scrutinize the numerically investigates entropy generation for unsteady magnetic nanofluid with stagnation region of an impulsively rotating sphere with viscous dissipation and chemical reaction effects. Employing the similarity technique, the equations modeling are switched into
highly nonlinear differential equations with boundary layer flow. These equations are numerically executed with bivariate spectral quasilinearization method. The entropy generation effect of varying various pertinent different parameters are taken into account and the results analyzed graphically.
The rate of entropy generation and energy related temperature profiles increased with increased of thermal radiation parameter, chemical reaction and rotation parameters while increased values of the magnetic number had a negative impact impact on rate of entropy generation. Variables of engineering
interest which includes the skin friction coefficient, the Nusselt number and the Sherwood number were also analyzed in a table. These numerical results will be of great value to chemists, biologists, physicists, and engineers interested in the theory and applications of entropy generation.
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Affiliation(s)
- Mohammed Almakki
- School of Mathematical and Nature Sciences, American University of Ras Al Khaimah, Ras Al Khaimah, P.O. Box 10021, United Arab Emirates
| | - Hiranmoy Mondal
- Department of Applied Mathematics, Maulana Abul Kalam Azad University of Technology, Kolkata 700064, West Bengal, India
| | - Zack Mburu
- School of Mathematics, Statistics and Computer Science, University of KwaZulu-Natal, Scottsville, 3209, Pietermaritzburg, South Africa
| | - Precious Sibanda
- School of Mathematics, Statistics and Computer Science, University of KwaZulu-Natal, Scottsville, 3209, Pietermaritzburg, South Africa
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Natural Convection Flow over a Vertical Permeable Circular Cone with Uniform Surface Heat Flux in Temperature-Dependent Viscosity with Three-Fold Solutions within the Boundary Layer. COMPUTATION 2022. [DOI: 10.3390/computation10040060] [Citation(s) in RCA: 3] [Impact Index Per Article: 1.5] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 01/25/2023]
Abstract
The aim of this study is to investigate the effects of temperature-dependent viscosity on the natural convection flow from a vertical permeable circular cone with uniform heat flux. As part of numerical computation, the governing boundary layer equations are transformed into a non-dimensional form. The resulting nonlinear system of partial differential equations is then reduced to local non-similarity equations which are solved computationally by three different solution methodologies, namely, (i) perturbation solution for small transpiration parameter (ξ), (ii) asymptotic solution for large ξ, and (iii) the implicit finite difference method together with a Keller box scheme for all ξ. The numerical results of the velocity and viscosity profiles of the fluid are displayed graphically with heat transfer characteristics. The shearing stress in terms of the local skin-friction coefficient and the rate of heat transfer in terms of the local Nusselt number (Nu) are given in tabular form for the viscosity parameter (ε) and the Prandtl number (Pr). The viscosity is a linear function of temperature which is valid for small Prandtl numbers (Pr). The three-fold solutions were compared as part of the validations with various ranges of Pr numbers. Overall, good agreements were established. The major finding of the research provides a better demonstration of how temperature-dependent viscosity affects the natural convective flow. It was found that increasing Pr, ξ, and ε decrease the local skin-friction coefficient, but ξ has more influence on increasing the rate of heat transfer, as the effect of ε was erratic at small and large ξ. Furthermore, at the variable Pr, a large ξ increased the local maxima of viscosity at large extents, particularly at low Pr, but the effect on temperature distribution was found to be less significant under the same condition. However, at variable ε and fixed Pr, the temperature distribution was observed to be more influenced by ε at small ξ, whereas large ξ dominated this scheme significantly regardless of the variation in ε. The validations through three-fold solutions act as evidence of the accuracy and versatility of the current approach.
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Boger nanofluid: significance of Coriolis and Lorentz forces on dynamics of rotating fluid subject to suction/injection via finite element simulation. Sci Rep 2022; 12:1612. [PMID: 35102186 PMCID: PMC8804036 DOI: 10.1038/s41598-022-05487-2] [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: 05/12/2021] [Accepted: 11/25/2021] [Indexed: 11/08/2022] Open
Abstract
This study briefings the roles of Coriolis, and Lorentz forces on the dynamics of rotating nanofluids flow toward a continuously stretching sheet. The nanoparticles are incorporated because of their unusual qualities like upgrade the thermal transportation, which are very important in heat exchangers, modern nanotechnology, electronics, and material sciences. The primary goal of this study is to improve heat transportation. Appropriate similarity transformations are applied for the principal PDEs to transform into nonlinear dimensionless PDEs. A widely recognized Numerical scheme known as the Finite Element Method is employed to solve the resultant convective boundary layer balances. Higher input in the solvent fraction parameter has a rising effect on the primary velocity and secondary velocity magnitude, and decreasing impact on the distributions of temperature. It is seen that growing contributions of the Coriolis, and Lorentz forces cause to moderate the primary and secondary velocities, but the temperature and concentration functions show opposite trend. The concentration, temperature, and velocities distributions for suction case is prominently than that of injection case, but inverse trend is observed for local Nusselt and Sherwood numbers. These examinations are relevant to the field of plastic films, crystal growing, paper production, heat exchanger, and bio-medicine.
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