Effect of Brownian Diffusion on Squeezing Elastico-Viscous Nanofluid Flow with Cattaneo-Christov Heat Flux Model in a Channel with Double Slip Effect — Oak Academic Publishing
Research ArticleOpen AccessGoogle Scholar indexed
Effect of Brownian Diffusion on Squeezing Elastico-Viscous Nanofluid Flow with Cattaneo-Christov Heat Flux Model in a Channel with Double Slip Effect
Department of Mathematics, Comilla University, Cumilla, Bangladesh
,
Department of Applied Mathematics, University of Dhaka, Dhaka, Bangladesh
1 Department of Mathematics, Comilla University, Cumilla, Bangladesh
2 Department of Applied Mathematics, University of Dhaka, Dhaka, Bangladesh
The present study deals with the analysis of heat transfer of the unsteady Maxwell nanofluid flow in a squeezed rotating channel of a porous extensile surface subject to the velocity and thermal slip effects incorporating the theory of heat flow intensity of Cattaneo-Christov model for the expression of the energy distribution in preference to the classical Fourier’s law. A set of transformations is occupied to renovate the current model in a system of nonlinear ordinary differential equations that are numerically decoded with the help of MATLAB integrated function bvp4c. The effects of various flow control parameters are investigated for the momentum, temperature and diffusion profiles, as well as for the wall shearing stress and the heat and mass transfer. The results are finally described from the material point of view. A comparison of heat flux models of Cattaneo-Christov and Fourier is also performed. An important result from the present work is that the squeezing parameter is strong enough in the middle of the channel to retard the fluid flow.
Fourier, J. (1822) Theorie analytique de la chaleur, par M. Fourier Chez Firmin Didot, père et fils.
Cattaneo, C. (1948) Sulla conduzione del calore. Attidel Seminario Matematico e Fisicodella Università di Modena, 3, 83-101.
Christov, C.I. (2009) On Frame Indifferent Formulation of the Maxwell—Cattaneo Model of Finite-Speed Heat Conduction. Mechanics Research Communications, 36, 481-486. https://doi.org/10.1016/j.mechrescom.2008.11.003
Alamri, S.Z., Khan, A.A., Azeez, M. and Ellahi, R. (2019) Effects of Mass Transfer on MHD Second Grade Fluid towards Stretching Cylinder: A Novel Perspective of Cattaneo-Christov Heat Flux Model. Physics Letters A, 383, 276-281. https://doi.org/10.1016/j.physleta.2018.10.035
Ciarletta, M. and Straughan, B. (2010) Uniqueness and Structural Stability for the Cattaneo-Christov Equations. Mechanics Research Communications, 37, 445-447. https://doi.org/10.1016/j.mechrescom.2010.06.002
Tibullo, V. and Zampoli, V. (2011) A Uniqueness Result for the Cattaneo-Christov Heat Conduction Model Applied to Incompressible Fluids. Mechanics Research Communications, 38, 77-79. https://doi.org/10.1016/j.mechrescom.2010.10.008
Han, S., Zheng, L., Li, C. and Zhang, X. (2014) Coupled Flow and Heat Transfer in Viscoelastic Fluid with Cattaneo-Christov Heat Flux Model. Applied Mathematics Letters, 38, 87-93. https://doi.org/10.1016/j.aml.2014.07.013
Layek, G.C. and Pati, N.C. (2017) Bifurcations and Chaos in Convection Taking Non-Fourier Heat-Flux. Physics Letters A, 381, 3568-3575. https://doi.org/10.1016/j.physleta.2017.09.020
Upadhya, S., Mamatha and Raju, C.S.K. (2018) Cattaneo-Christov Heat Flux Model for Magnetohydrodynamic Flow in a Suspension of Dust Particles towards a Stretching Sheet. Nonlinear Engineering, 7, 237-246. https://doi.org/10.1515/nleng-2017-0162
Al Sulti, F. (2019) Impact of Cattaneo-Christov Heat Flux Model on Stagnation-Point Flow toward a Stretching Sheet with Slip Effects. Journal of Heat Transfer, 141, Article ID: 022003. https://doi.org/10.1115/1.4041959
Pinkus, O. and Sternlicht, B. (1949) Theory of Hydrodynamic Lubrication. McGraw-Hill, New York.
Oldroyd, J.G. (1950) On the Formulation of Rheological Equations of State. Proceedings of the Royal Society of London. Series A. Mathematical and Physical Sciences, 200, 523-541. https://doi.org/10.1098/rspa.1950.0035
Cameron, A. and Mc Ettles, C.M. (1981) Basic Lubrication Theory. Ellis Horwood, New York.
Brust, M., Schaefer, C., Doerr, R., Pan, L., Garcia, M., Arratia, P.E. and Wagner, C. (2013) Rheology of Human Blood Plasma: Viscoelastic versus Newtonian Behavior. Physical Review Letters, 110, Article ID: 078305. https://doi.org/10.1103/PhysRevLett.110.078305
Li, X.K., Luo, Y., Qi, Y. and Zhang, R. (2011) On Non-Newtonian Lubrication with the Upper Convected Maxwell Model. Applied Mathematical Modelling, 35, 2309-2323. https://doi.org/10.1016/j.apm.2010.11.003
Sochi, T. (2010) Flow of Non-Newtonian Fluids in Porous Media. Journal of Polymer Science Part B: Polymer Physics, 48, 2437-2767. https://doi.org/10.1002/polb.22144
Fox, V.G., Erickson, L.E. and Fan, L.T. (1969) The Laminar Boundary Layer on a Moving Continuous Flat Sheet Immersed in a Non-Newtonian Fluid. AIChE Journal, 15, 327-333. https://doi.org/10.1002/aic.690150307
Rajagopal, K.R., Na, T.Y. and Gupta, A.S. (1984) Flow of a Viscoelastic Fluid over a Stretching Sheet. Rheologica Acta, 23, 213-215. https://doi.org/10.1007/BF01332078
Andersson, H.I., Bech, K.H. and Dandapat, B.S. (1992) Magnetohydrodynamic Flow of a Power-Law Fluid over a Stretching Sheet. International Journal of Non-Linear Mechanics, 27, 929-936. https://doi.org/10.1016/0020-7462(92)90045-9
Sadeghy, K. and Sharifi, M. (2004) Local Similarity Solution for the Flow of a Second-Grade Viscoelastic Fluid above a Moving Plate. International Journal of Non-Linear Mechanics, 39, 1265-1273. https://doi.org/10.1016/j.ijnonlinmec.2003.08.005
Bhattacharyya, K., Hayat, T. and Gorla, R.S.R. (2013) Heat Transfer in the Boundary Layer Flow of Maxwell Fluid over a Permeable Shrinking Sheet. Thermal Energy and Power Engineering, 2, 72-78.
Hayat, T., Abbas, Z. and Sajid, M. (2006) Series Solution for the Upper-Convected Maxwell Fluid over a Porous Stretching Plate. Physics Letters A, 358, 396-403. https://doi.org/10.1016/j.physleta.2006.04.117
Alarifi, I.M., Abokhalil, A.G., Osman, M., Lund, L.A., BenAyed, M., Belmabrouk, H. and Tlili, I. (2019) MHD Flow and Heat Transfer over Vertical Stretching Sheet with Heat Sink or Source Effect. Symmetry, 11, 297. https://doi.org/10.3390/sym11030297
Fetecau, C. and Fetecau, C. (2003) A New Exact Solution for the Flow of a Maxwell Fluid past an Infinite Plate. International Journal of Non-Linear Mechanics, 38, 423-427. https://doi.org/10.1016/S0020-7462(01)00062-2
Harris, J. (1966) Some Engineering Aspects of Non-Newtonian Flow. Nature, 211, 579-581. https://doi.org/10.1038/211579a0
Mustafa, M., Khan, J.A., Hayat, T. and Alsaedi, A. (2015) Simulations for Maxwell Fluid Flow past a Convectively Heated Exponentially Stretching Sheet with Nanoparticles. AIP Advances, 5, Article ID: 037133. https://doi.org/10.1063/1.4916364
Halim, N.A. and Noor, N.F.M. (2015) Analytical Solution for Maxwell Nanofluid Boundary Layer Flow over a Stretching Surface. AIP Conference Proceedings, 1682, Article ID: 020006. https://doi.org/10.1063/1.4932415
Choi, S. and Eastman, J.A. (1995) Enhancing Thermal Conductivity of Fluids with Nanoparticles. Argonne National Laboratory, Lemont.
Wong, K.V. and De Leon, O. (2010) Applications of Nanofluids: Current and Future. Advances in Mechanical Engineering, 2, Article ID: 519659. https://doi.org/10.1155/2010/519659
Uddin, M.J., Al Kalbani, K.S., Rahman, M.M., Alam, M.S., Al-Salti, N. and Eltayeb, I. (2016) Fundamentals of Nanofluids: Evolution, Applications and New Theory. International Journal of Biomathematics and Systems Biology, 2, 1-32.
Kuznetsov, A.V. and Nield, D.A. (2010) Natural Convective Boundary-Layer Flow of a Nanofluid past a Vertical Plate. The International Journal of Thermal Sciences, 49, 243-247. https://doi.org/10.1016/j.ijthermalsci.2009.07.015
Buongiorno, J. (2006) Convective Transport in Nanofluids. Journal of Heat Transfer, 128, 240-250. https://doi.org/10.1115/1.2150834
Stefan, M.J. (1874) Versuch über die scheinbare Adhäsion. Sitzungsber Abt II. Ö sterr Akad Wiss Math-Naturwiss Kl, 69, 713-721.
Phan-Thien, N. and Tanner, R.I. (1983) Viscoelastic Squeeze Film Flows-Maxwell Fluids. Journal of Fluid Mechanics, 129, 265-281. https://doi.org/10.1017/S0022112083000762
Mustafa, M., Hayat, T. and Obaidat, S. (2012) On Heat and Mass Transfer in the Unsteady Squeezing Flow between Parallel Plates. Meccanica, 47, 1581-1589. https://doi.org/10.1007/s11012-012-9536-3
Akmal, N., Sagheer, M. and Hussain, S. (2018) Numerical Study Focusing on the Entropy Analysis of MHD Squeezing Flow of a Nanofluid Model Using Cattaneo-Christov Theory. AIP Advances, 8, Article ID: 055201. https://doi.org/10.1063/1.5029959
Le Roux, C. (1999) Existence and Uniqueness of the Flow of Second-Grade Fluids with Slip Boundary Conditions. Archive for Rational Mechanics and Analysis, 148, 309-356. https://doi.org/10.1007/s002050050164
Jiang, Y., Qi, H., Xu, H. and Jiang, X. (2017) Transient Electroosmotic Slip Flow of Fractional Oldroyd-B Fluids. Microfluidics and Nanofluidics, 21, 7. https://doi.org/10.1007/s10404-016-1843-x
Navier, C.L.M.H. (1823) Memoirs de l’Academie. Royale des Sciences de l’Institut de France, 1, 414-416.
Reddy, J.V.R., Sugunamma, V. and Sandeep, N. (2018) Thermophoresis and Brownian Motion Effects on Unsteady MHD Nanofluid Flow over a Slendering Stretching Surface with Slip Effects. Alexandria Engineering Journal, 57, 2465-2473. https://doi.org/10.1016/j.aej.2017.02.014