The results of this article can be useful in science and technology advancement, such as nanofluidics, micro mixing and energy conversion. The purpose of this article is to examine the impacts of nanoparticle shape on Al2O3-water nanofluid and heat transfer over a non-linear radically stretching sheet in the existence of magnetic field and thermal radiation. The different shapes of Al2O3 nanoparticles that have under contemplation are column, sphere, hexahedron, tetrahedron, and lamina. The governing partial differential equations (PDEs) of the problem are regenerated into set of non-linear ordinary differential equations (ODEs) by using appropriate similarity transformation. The bvp4c program has used to solve the obtained non-linear ordinary differential equation (ODEs). The Nusselt number for all shapes of Al2O3 nanoparticle shapes in pure water with is presented in graphical form. It has reported that the heat transfer augmentation in lamina shapes nanoparticles is more than other shapes of nanoparticle. The relation of thermal boundary layer with shapes of nanoparticles, solid volume fraction, magnetic field and thermal radiation has also presented with the help of graphical representation. It is also demonstrated that lamina shape nanoparticles have showed large temperature distribution than other shapes of nanoparticles.
References
[1]
Ellahi, R. and Riaz, A. (2010) Analytical Solutions for MHD Flow in a Third-Grade Fluid with Variable Viscosity. Mathematical and Computer Modelling, 52, 1783-1793. https://doi.org/10.1016/j.mcm.2010.07.005
[2]
Aziz, A. (2010) Hydrodynamic and Thermal Slip Flow Boundary Layers over a Flat Plate with Constant Heat Flux Boundary Condition. Communications in Nonlinear Science and Numerical Simulation, 15, 573-580. https://doi.org/10.1016/j.cnsns.2009.04.026
[3]
Nadeem, S., Hussain, A. and Khan, M. (2010) HAM Solutions for Boundary Layer Flow in the Region of the Stagnation Point towards a Stretching Sheet. Communications in Nonlinear Science and Numerical Simulation, 15, 475-481. https://doi.org/10.1016/j.cnsns.2009.04.037
[4]
Noor, N.F.M., Awang Kechil, S. and Hashim, I. (2010) Simple Non-Perturbative Solution for MHD Viscous Flow due to a Shrinking Sheet. Communications in Nonlinear Science and Numerical Simulation, 15, 144-148. https://doi.org/10.1016/j.cnsns.2009.03.034
[5]
Khan, W.A. and Pop, I. (2010) Boundary-Layer Flow of a Nanofluid past a Stretching Sheet. International Journal of Heat and Mass Transfer, 53, 2477-2483. https://doi.org/10.1016/j.ijheatmasstransfer.2010.01.032
[6]
Rashidi, M.M. and Erfani, E. (2011) The Modified Differential Transform Method for Investigating Nano Boundary-Layers over Stretching Surfaces. International Journal of Numerical Methods for Heat and Fluid Flow, 21, 864-883. https://doi.org/10.1108/09615531111162837
[7]
Sheikholeslami, M. and Ganji, D.D. (2014) Numerical Investigation for Two Phase Modeling of Nanofluid in a Rotating System with Permeable Sheet. Journal of Molecular Liquids, 194, 13-19. https://doi.org/10.1016/j.molliq.2014.01.003
[8]
Makinde, O.D., Khan, W.A. and Khan, Z.H. (2017) Stagnation Point Flow of MHD Chemically Reacting Nanofluid over a Stretching Convective Surface with Slip and Radiative Heat. Proceedings of the Institution of Mechanical Engineers, Part E: Journal of Process Mechanical Engineering, 231, 695-703. https://doi.org/10.1177/0954408916629506
[9]
Choi, S.U.S. and Eastman, A. (1995) Enhancing Thermal Conductivity of Fluids with Nanoparticles. Proceedings of the 1995 ASME International Mechanical Engineering Congress and Exposition, Vol. 66, San Francisco, 12-17 November 1995, 99-105.
[10]
Nadeem, S. and Lee, C. (2012) Boundary Layer Flow of Nanofluid over an Exponentially Stretching Surface. Nanoscale Research Letters, 7, Article No. 94. http://www.nanoscalereslett.com/content/7/1/94 https://doi.org/10.1186/1556-276X-7-94
[11]
Rana, P. and Bhargava, R. (2012) Flow and Heat Transfer of a Nanofluid over a Nonlinearly Stretching Sheet: A Numerical Study. Communications in Nonlinear Science and Numerical Simulation, 17, 212-226. https://doi.org/10.1016/j.cnsns.2011.05.009
[12]
Sheikholeslami, M. and Chamkha, A.J. (2017) Influence of Lorentz Forces on Nanofluid Forced Convection Considering Marangoni Convection. Journal of Molecular Liquids, 225, 750-757. https://doi.org/10.1016/j.molliq.2016.11.001
[13]
Ul Haq, R., Nadeem, S., Hayat Khan, Z. and Sher Akbar, N. (2015) Thermal Radiation and Slip Effects on MHD Stagnation Point Flow of Nanofluid over a Stretching Sheet. Physica E: Low-Dimensional Systems and Nanostructures, 65, 17-23. https://doi.org/10.1016/j.physe.2014.07.013
[14]
Som, N.M., Arifin, N., Ali, F., Bachok, N. and Nazar, R. (2014) Slip Effects on MHD Non-Darcy Boundary Layer Flow over a Stretching Sheet in a Porous Medium with Radiation and Ohmic Dissipation. Mathematical and Computational Methods in Science and Engineering, 1, 174-178.
[15]
Ashorynejad, H.R., Mohamad, A.A. and Sheikholeslami, M. (2013) Magnetic Field Effects on Natural Convection Flow of a Nanofluid in a Horizontal Cylindrical Annulus Using Lattice Boltzmann Method. International Journal of Thermal Sciences, 64, 240-250. https://doi.org/10.1016/j.ijthermalsci.2012.08.006
[16]
Sheikholeslami, M., Gorji-Bandpay, M. and Ganji, D.D. (2012) Magnetic Field Effects on Natural Convection around a Horizontal Circular Cylinder inside a Square Enclosure Filled with Nanofluid. International Communications in Heat and Mass Transfer, 39, 978-986. https://doi.org/10.1016/j.icheatmasstransfer.2012.05.020
[17]
Yadav, D., Kim, C., Lee, J. and Cho, H.H. (2015) Influence of Magnetic Field on the Onset of Nanofluid Convection Induced by Purely Internal Heating. Computers and Fluids, 121, 26-36. https://doi.org/10.1016/j.compfluid.2015.07.024
[18]
Xuan, Y., Li, Q. and Ye, M. (2007) Investigations of Convective Heat Transfer in Ferrofluid Microflows Using Lattice-Boltzmann Approach. International Journal of Thermal Sciences, 46, 105-111. https://doi.org/10.1016/j.ijthermalsci.2006.04.002
[19]
Rashad, A.M. (2008) Influence of Radiation on MHD Free Convection from a Vertical Flat Plate Embedded in Porous Media with Thermophoretic Deposition of Particles. Communications in Nonlinear Science and Numerical Simulation, 13, 2213-2222. https://doi.org/10.1016/j.cnsns.2007.07.002
[20]
Ghasemi, B. and Aminossadati, S.M. (2009) Natural Convection Heat Transfer in an Inclined Enclosure Filled with a Water-Cuo Nanofluid. Numerical Heat Transfer: Part A: Applications, 55, 807-823. https://doi.org/10.1080/10407780902864623
[21]
Mahmoudi, A.H., Pop, I. and Shahi, M. (2012) Effect of Magnetic Field on Natural Convection in a Triangular Enclosure Filled with Nanofluid. International Journal of Thermal Sciences, 59, 126-140. https://doi.org/10.1016/j.ijthermalsci.2012.04.006
[22]
Hamad, M.A.A. (2011) Analytical Solution of Natural Convection Flow of a Nanofluid over a Linearly Stretching Sheet in the Presence of Magnetic Field. International Communications in Heat and Mass Transfer, 38, 487-492. https://doi.org/10.1016/j.icheatmasstransfer.2010.12.042
[23]
Sheikholeslami, M. and Rashidi, M.M. (2015) Ferrofluid Heat Transfer Treatment in the Presence of Variable Magnetic Field. European Physical Journal Plus, 130, Article No. 115. https://doi.org/10.1140/epjp/i2015-15115-4
[24]
Sheikholeslami, M. and Ellahi, R. (2015) Three Dimensional Mesoscopic Simulation of Magnetic Field Effect on Natural Convection of Nanofluid. International Journal of Heat and Mass Transfer, 89, 799-808. https://doi.org/10.1016/j.ijheatmasstransfer.2015.05.110
[25]
Shen, X., Nie, X., Hu, H. and Tjong, J. (2012) Effects of Coating Thickness on Thermal Conductivities of Alumina Coatings and Alumina/Aluminum Hybrid Materials Prepared Using Plasma Electrolytic Oxidation. Surface and Coatings Technology, 207, 96-101. https://doi.org/10.1016/j.surfcoat.2012.06.009
[26]
Musil, J., Blazek, J., Zeman, P., Prokšová, Š., Šašek, M. and Cerstvy, R. (2010) Thermal Stability of Alumina Thin Films Containing γ-Al2O3 Phase Prepared by Reactive Magnetron Sputtering. Applied Surface Science, 257, 1058-1062. https://doi.org/10.1016/j.apsusc.2010.07.107
[27]
Vanbesien, K., De Visschere, P., Smet, P.F. and Poelman, D. (2006) Electrical Properties of Al2O3 Films for TFEL-Devices Made with Sol-Gel Technology. Thin Solid Films, 514, 323-328. https://doi.org/10.1016/j.tsf.2006.02.034
[28]
Balasubramanyam, A., Sailaja, N., Mahboob, M., Rahman, M.F., Misra, S., Hussain, S.M., et al. (2009) Evaluation of Genotoxic Effects of Oral Exposure to Aluminum Oxide Nanomaterials in Rat Bone Marrow. Mutation Research—Genetic Toxicology and Environmental Mutagenesis, 676, 41-47. https://doi.org/10.1016/j.mrgentox.2009.03.004
[29]
M’rad, I., Jeljeli, M., Rihane, N., Hilber, P., Sakly, M. and Amara, S. (2018) Aluminium Oxide Nanoparticles Compromise Spatial Learning and Memory Performance in Rats. EXCLI Journal, 17, 200-210.
[30]
Miziolek, A.W. (2012) Nanoenergetics: An Emerging Technology Area of National Importance. The AMPTIAC Newsletter, 6, 43-48.
[31]
Ghanta, S.R. and Muralidharan, K. (2013) Chemical Synthesis of Aluminum Nanoparticles. Journal of Nanoparticle Research, 15, 1715. https://doi.org/10.1007/s11051-013-1715-1
[32]
Wagner, A.J., Bleckmann, C.A., Murdock, R.C., Schrand, A.M., Schlager, J.J. and Hussain, S.M. (2007) Cellular Interaction of Different Forms of Aluminum Nanoparticles in Rat Alveolar Macrophages. Journal of Physical Chemistry B, 111, 7353-7359. https://doi.org/10.1021/jp068938n
[33]
Klapötke, T. and Piercey, D. (2010) Nanoscale Aluminum—Metal Oxide (Thermite) Reactions for Application in Energetic Materials. Central European Journal of Energetic Materials, 7, 115-129.
[34]
Tyner, K.M., Schiffman, S.R. and Giannelis, E.P. (2004) Nanobiohybrids as Delivery Vehicles for Camptothecin. Journal of Controlled Release, 95, 501-514. https://doi.org/10.1016/j.jconrel.2003.12.027
[35]
Esfe, M.H., Arani, A.A.A., Azizi, T., Mousavi, S.H. and Wongwises, S. (2017) Numerical Study of Laminar-Forced Convection of Al2O3-Water Nanofluids between Two Parallel Plates. Journal of Mechanical Science and Technology, 31, 785-796. https://doi.org/10.1007/s12206-017-0130-4
[36]
Lin, Y., Li, B., Zheng, L. and Chen, G. (2016) Particle Shape and Radiation Effects on Marangoni Boundary Layer Flow and Heat Transfer of Copper-Water Nanofluid Driven by an Exponential Temperature. Powder Technology, 301, 379-386. https://doi.org/10.1016/j.powtec.2016.06.029
[37]
Ali, R., Shahzad, A., Khan, M. and Ayub, M. (2016) Analytic and Numerical Solutions for Axisymmetric Flow with Partial Slip. Engineering with Computers, 32, 149-154. https://doi.org/10.1007/s00366-015-0405-2
[38]
Hamilton, R.L. (1962) Thermal Conductivity of Heterogeneous Two-Component Systems. Industrial and Engineering Chemistry Fundamentals, 1, 187-191. https://doi.org/10.1021/i160003a005
