A Finite Element Simulation of the Active and Passive Controls of the MHD Effect on an Axisymmetric Nanofluid Flow with Thermo-Diffusion over a Radially Stretched Sheet

Processes - Tập 8 Số 2 - Trang 207
Bagh Ali1, Xiaojun Yu2, Muhammad Tariq Sadiq2, Ateeq Ur Rehman3, Liaqat Ali4
1Department of Applied Mathematics, School of Science, Northwestern Polytechnical University, Dongxiang Road, Chang’an District, Xi’an 710129, China
2School of Automation, Northwestern Polytechnical University, 127 West Youyi Road, Xi’an 710072, China
3College of Internet of Things Engineering, Hohai University, Changzhou Campus, Changzhou 213022, China
4School of Energy and Power, Xi'an Jiaotong University, No.28 Xianning west Road, Xi'an 7100049, China;

Tóm tắt

The present study investigated the steady magnetohydrodynamics of the axisymmetric flow of a incompressible, viscous, electricity-conducting nanofluid with convective boundary conditions and thermo-diffusion over a radially stretched surface. The nanoparticles’ volume fraction was passively controlled on the boundary, rather than actively controlled. The governing non-linear partial differential equations were transformed into a system of nonlinear, ordinary differential equations with the aid of similarity transformations which were solved numerically, using the very efficient variational finite element method. The coefficient of skin friction and rate of heat transfer, and an exact solution of fluid flow velocity, were contrasted with the numerical solution gotten by FEM. Excellent agreement between the numerical and exact solutions was observed. The influences of various physical parameters on the velocity, temperature, and solutal and nanoparticle concentration profiles are discussed by the aid of graphs and tables. Additionally, authentication of the convergence of the numerical consequences acquired by the finite element method and the computations was acquired by decreasing the mesh level. This exploration is significant for the higher temperature of nanomaterial privileging technology.

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Tài liệu tham khảo

Aziz, 2012, Free convection boundary layer flow past a horizontal flat plate embedded in porous medium filled by nanofluid containing gyrotactic microorganisms, Int. J. Therm. Sci., 56, 48, 10.1016/j.ijthermalsci.2012.01.011

Choi, S. (1995). Enhancing thermal conductivity of fluids with nanoparticle. Development and Applications of Non-Newtonian Flow, Argonne National Lab.

Ariel, 2001, Axisymmetric flow of a second grade fluid past a stretching sheet, Int. J. Eng. Sci., 39, 529, 10.1016/S0020-7225(00)00052-5

Akbari, 2016, A modified two-phase mixture model of nanofluid flow and heat transfer in a 3-D curved microtube, Adv. Powder Technol., 27, 2175, 10.1016/j.apt.2016.08.002

Abbassi, 2018, LBM simulation of free convection in a nanofluid filled incinerator containing a hot block, Int. J. Mech. Sci., 144, 172, 10.1016/j.ijmecsci.2018.05.031

Abdollahzadeh Jamalabadi, M.Y., Alamian, R., Yan, W.M., Li, L.K., Leveneur, S., and Safdari Shadloo, M. (2019). Effects of nanoparticle enhanced lubricant films in thermal design of plain journal bearings at high Reynolds numbers. Symmetry, 11.

Abdollahzadeh Jamalabadi, M.Y., Ghasemi, M., Alamian, R., Wongwises, S., Afrand, M., and Shadloo, M.S. (2019). Modeling of Subcooled Flow Boiling with Nanoparticles under the Influence of a Magnetic Field. Symmetry, 11.

Karimipour, 2016, Developing the laminar MHD forced convection flow of water/FMWNT carbon nanotubes in a microchannel imposed the uniform heat flux, J. Magn. Magn. Mater., 419, 420, 10.1016/j.jmmm.2016.06.063

Mustafa, 2012, Axisymmetric flow of a nanofluid over a radially stretching sheet with convective boundary conditions, Curr. Nanosci., 8, 328, 10.2174/157341312800620241

Akbari, 2017, The effect of velocity and dimension of solid nanoparticles on heat transfer in non-Newtonian nanofluid, Phys. E Low-Dimens. Syst. Nanostruct., 86, 68, 10.1016/j.physe.2016.10.013

Khan, 2018, A study of heat and mass transfer on magnetohydrodynamic (MHD) flow of nanoparticles, Propuls. Power Res., 7, 72, 10.1016/j.jppr.2018.02.001

Ashraf, 2012, Numerical simulation of MHD stagnation point flow and heat transfer of a micropolar fluid towards a heated shrinking sheet, Int. J. Numer. Methods Fluids, 69, 384, 10.1002/fld.2564

Afrand, 2015, Effect of induced electric field on magneto-natural convection in a vertical cylindrical annulus filled with liquid potassium, Int. J. Heat Mass Transf., 90, 418, 10.1016/j.ijheatmasstransfer.2015.06.059

Raza, J. (2019). Thermal radiation and slip effects on magnetohydrodynamic (MHD) stagnation point flow of Casson fluid over a convective stretching sheet. Propuls. Power Res.

Chen, 1998, Laminar mixed convection adjacent to vertical, continuously stretching sheets, Heat Mass Transf., 33, 471, 10.1007/s002310050217

Sankara, 1985, Micropolar flow past a stretching sheet, Zeitschrift für Angewandte Mathematik und Physik, 36, 845, 10.1007/BF00944898

Hamza, 1988, The magnetohydrodynamic squeeze film, J. Tribol., 110, 375, 10.1115/1.3261636

Rana, 2015, Mixed convection flow along an inclined permeable plate: Effect of magnetic field, nanolayer conductivity and nanoparticle diameter, Appl. Nanosci., 5, 569, 10.1007/s13204-014-0352-z

Thumma, 2017, Numerical study of heat source/sink effects on dissipative magnetic nanofluid flow from a non-linear inclined stretching/shrinking sheet, J. Mol. Liq., 232, 159, 10.1016/j.molliq.2017.02.032

Seth, 2015, MHD natural convection heat and mass transfer flow past a time dependent moving vertical plate with ramped temperature in a rotating medium with hall effects, radiation and chemical reaction, J. Mech., 31, 91, 10.1017/jmech.2014.71

Takhar, 1998, Mixed convection flow of a micropolar fluid over a stretching sheet, Heat Mass Transf., 34, 213, 10.1007/s002310050252

Khan, S.A., Nie, Y., and Ali, B. (2019). Multiple slip effects on magnetohydrodynamic axisymmetric buoyant nanofluid flow above a stretching sheet with radiation and chemical reaction. Symmetry, 11.

Faraz, F., Imran, S.M., Ali, B., and Haider, S. (2019). Thermo-diffusion and multi-slip effect on an axisymmetric Casson flow over a unsteady radially stretching sheet in the presence of chemical reaction. Processes, 7.

Faraz, 2020, Study of magneto-hydrodynamics (MHD) impacts on an axisymmetric Casson nanofluid flow and heat transfer over unsteady radially stretching sheet, SN Appl. Sci., 2, 14, 10.1007/s42452-019-1785-5

Mahmoodi, 2015, Magneto-natural convection in square cavities with a source-sink pair on different walls, Int. J. Appl. Electromagn. Mech., 47, 21, 10.3233/JAE-130097

Ali, L., Liu, X., Ali, B., Mujeed, S., and Abdal, S. (2019). Finite Element Analysis of Thermo-Diffusion and Multi-Slip Effects on MHD Unsteady Flow of Casson Nano-Fluid over a Shrinking/Stretching Sheet with Radiation and Heat Source. Appl. Sci., 9.

Kumar, L. (2014). Finite-element analysis of transient heat and mass transfer in microstructural boundary layer flow from a porous stretching sheet. Comput. Therm. Sci. Int. J.

Nayak, B., Mishra, S.R., and Krishna, G.G. (2019). Chemical reaction effect of an axisymmetric flow over radially stretched sheet. Propuls. Power Res., 1–6.

Shahzad, 2016, On heat transfer analysis of axisymmetric flow of viscous fluid over a nonlinear radially stretching sheet, Alex. Eng. J., 55, 2423, 10.1016/j.aej.2016.04.013

Sajid, 2008, Analytic solution for axisymmetric flow over a nonlinearly stretching sheet, Arch. Appl. Mech., 78, 127, 10.1007/s00419-007-0146-9

Khan, 2016, MHD flow and heat transfer of Sisko fluid over a radially stretching sheet with convective boundary conditions, J. Braz. Soc. Mech. Sci. Eng., 38, 1279, 10.1007/s40430-015-0437-y

Shahzad, 2017, Unsteady axisymmetric flow and heat transfer over time-dependent radially stretching sheet, Alex. Eng. J., 56, 35, 10.1016/j.aej.2016.08.030

Singh, 2018, Finite Element Analysis of MHD Flow of Micropolar Fluid over a Shrinking Sheet with a Convective Surface Boundary Condition, J. Eng. Thermophys., 27, 202, 10.1134/S1810232818020078

Reddy, J.N. (1993). Solutions Manual for an Introduction to the Finite Element Method, McGraw-Hill.

Rana, 2013, Finite element simulation of unsteady magneto-hydrodynamic transport phenomena on a stretching sheet in a rotating nanofluid, Proc. Inst. Mech. Eng. Part N J. Nanoeng. Nanosyst., 227, 77

Ali, L., Liu, X., Ali, B., Mujeed, S., and Abdal, S. (2019). Finite Element Simulation of Multi-Slip Effects on Unsteady MHD Bioconvective Micropolar nanofluid Flow Over a Sheet with Solutal and Thermal Convective Boundary Conditions. Coatings, 9.

Bhargava, 2011, Finite element solution to mixed convection in MHD flow of micropolar fluid along a moving vertical cylinder with variable conductivity, Int. J. Appl. Math Mech., 7, 29

Crane, 1970, Flow past a stretching plate, Zeitschrift für Angewandte Mathematik und Physik ZAMP, 21, 645, 10.1007/BF01587695

Ali, B., Nie, Y., Khan, S.A., Sadiq, M.T., and Tariq, M. (2019). Finite Element Simulation of Multiple Slip Effects on MHD Unsteady Maxwell Nanofluid Flow over a Permeable Stretching Sheet with Radiation and Thermo-Diffusion in the Presence of Chemical Reaction. Processes, 7.

Jalil, 2017, An Exact Solution of MHD Boundary Layer Flow of Dusty Fluid over a Stretching Surface, Math. Probl. Eng., 2017, 1, 10.1155/2017/2307469

Ishak, 2009, Boundary layer flow and heat transfer over an unsteady stretching vertical surface, Meccanica, 44, 369, 10.1007/s11012-008-9176-9

Mabood, 2019, Multiple slip effects on MHD unsteady flow heat and mass transfer impinging on permeable stretching sheet with radiation, Model. Simul. Eng., 2019, 3052790

Pal, 2011, Combined effects of non-uniform heat source/sink and thermal radiation on heat transfer over an unsteady stretching permeable surface, Commun. Nonlinear Sci. Numer. Simul., 16, 1890, 10.1016/j.cnsns.2010.08.023

Haile, 2014, Heat and Mass Transfer in the Boundary Layer of Unsteady Viscous Nanofluid along a Vertical Stretching Sheet, J. Comput. Eng., 2014, 1, 10.1155/2014/345153

Nandy, 2013, Effects of slip and heat generation/absorption on MHD stagnation flow of nanofluid past a stretching/shrinking surface with convective boundary conditions, Int. J. Heat Mass Transf., 64, 1091, 10.1016/j.ijheatmasstransfer.2013.05.040

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207

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