Journal of Applied and Computational Mechanics

Transient MHD Convective Flow of Fractional Nanofluid between Vertical Plates

Document Type : Research Paper

Authors

1 Abdus Salam School of Mathematical Sciences, GC University Lahore, Pakistan

2 Department of Mathematics, Lahore Leads University, Lahore Pakistan

3 Department of Mathematics, Islamia College University Peshawar Khyber Pakhtunkhwa 25000, Pakistan

4 Experimental Surgery Lab, Department of Surgery, Ghent University, De Pintelaan 185, 9000 Ghent, Belgium

5 Biofluid, Tissue and Solid Mechanics for Medical Applications Lab (IBiTech, bioMMeda), Ghent University, Gent, Belgium

Abstract

Effects of the uniform transverse magnetic field on the transient free convective flows of a nanofluid with generalized thermal transport between two vertical parallel plates have been analyzed. The fluid temperature is described by a time-fractional differential equation with Caputo derivatives. Closed form of the temperature field is obtained by using the Laplace transform and fractional derivatives of the Wright’s functions. A semi-analytical solution for the velocity field is obtained by using the Laplace transform coupled with the numerical algorithms for the inverse Laplace transform elaborated by Stehfest and Tzou. Effects of the derivative fractional order and physical parameters on the nanofluid flow and heat transfer are graphically investigated.

Keywords

Main Subjects

[1] Choi, S.U.S., Enhancing thermal conductivity of fluids with nanoparticles, in: The proceeding of the 1995 ASME International Mechanical Engineering Congress and Exposition, San Francisco, USA, ASME, FED 231/MD 66 (1995) p. 99-105.
[2] Xuan, Y. and Li, Q., Heat Transfer enhancement of nanofluids, International Journal of Heat and Fluid Flow, 21 (2000) 58-64.
[3] Khanafer, K. and Vafai, K., A critical synthesis of thermophysical characteristics of nanofluids, International Journal of Heat and Mass Transfer, 54 (2011) 4410-4428.
[4] Khanafer, K., Vafai, K. and Lightstone, M., Buoyancy-driven heat transfer enhancement in a two-dimensional enclosure utilizing nanofluids, International Journal of Heat and Mass Transfer, 46 (2003) 3639-3653.
[5] Santra, A.K., Sen, S. and Chakraborty, N., Study of heat transfer augmentation in a differently heated square cavity using copper-water nanofluid, International Journal of Thermal Sciences, 47 (2008) 1113-1122.
[6] Oztop, H.F. and Abu-Nada, E., Numerical study of natural convection in partially heated rectangular enclosures filled with nanofluids, International Journal of Heat and Fluid Flow, 29 (2008) 1326-1336.
[7] Basak, T. and Chamkha, A.J., Heatline analysis on nanural convection for nanofluids confined within square cavities with various thermal boundary conditions, International Journal of Heat and Mass Transfer, 55 (2012) 5526-5543.
[8] Oztop, H.F., Abu-Nada, E., Varol, Y. and Al-Salem, K., Computational analysis of non-isotherm temperature distribution on natural convection in nanofluid filled enclosures, Superlattices and Microstructures, 49(4) (2011) 453-467.
[9] Lin, K.C. and Violi, A., Natural convection heat transfer of nanofluid in a vertical cavity: Effects of nonuniform particle diameter and temperature on thermal conductivity, International Journal of Heat and Fluid Flow, 31 (2010) 236-245.
[10] Abu-Nada, E., Application of nanofluids for heat transfer enhancement of separated flows encountered in a back ground facing step, International Journal of Heat and Fluid Flow, 29 (2008) 242-249.
[11] Wang, X.Q. and Mujumder, A.S., Heat transfer characteristics of nanofluid: a review, International Journal of Thermal Sciences, 46 (2007) 1-19.
[12] Eastman, J.A., Choi, S.U.S., Li, S., Thompson, L.J. and Lee, S., Enhanced thermal conductivity through the development of nanofluids, in: 1996 Fall meeting of the Materials Research Society (MRS), Boston, USA (1997) p. 3-11.
[13] Oldham, K. B. and Spainier, J., The Fractional Calculus, Academic Press, New York, 1974.
[14] Benson, D. A., Wheatcraft, S. W. and Meerschaert, M. M., Application of a fractional advection-dispersion equation, Water Resources Research, 36(6) (2000) 1403-1412.
[15] Metzler, R. and Klafter, J., The random walk’s guide to anomalous diffusion: A fractional dynamic approach, Physics Reports, 339 (2000) 1-77.
[16] Zaslavsky, G. M., Choas Fractional kinetics and anomalous transport, Physics Reports, 371(6) (2002) 461-580.
[17] Podlubny, Igor J., Fractional differential equation, Academic Press, New York, 1999.
[18] Azhar, W. A., Vieru, D., Fetecau, C., Free convection flow of some fractional nanofluids over a moving vertical plate with uniform heat flux and heat source, Physics of Fluids, 29 (2017) 082001.
[19] Imran, M.A., Shah, N.A., Khan, I., Aleem, M., Applications of non-integer Caputo time fractional derivatives to natural convection flow subject to arbitrary velocity and Newtonian heating, Neural Computing and Applications, 30(5) (2018) 1589-1599.
[20] Shah, N.A., Khan, I., Heat transfer analysis in a second grade fluid over and oscillating vertical plate using fractional Caputo–Fabrizio derivatives, European Physical Journal C, 76 (2016) p. 362.
[21] Imran, M.A., Khan, I., Ahmad, M., Shah, N.A., Nazar, M., Heat and mass transport of differential type fluid with non-integer order time-fractional Caputo derivatives, Journal of Molecular Liquids, 229 (2016) 67-75.
[22] Prakash, D., Suriyakumar, P., Transient hydromagnetic convection flow of nanofluid between asymmetric vertical plates with heat generation, International Journal of Pure and Applied Mathematics, 113(12) (2017) 1-10.
[23] Ahmed, N., Shah, N. A., Vieru, D., Natural convection with damped thermal flux in a vertical circular cylinder, Chinese Journal of Physics, 56 (2018) 630-644.
[24] Hristov, J., Derivatives with non-singular kernels. From Caputo-Fabrizio definition and beyond. Frontiers in Fractional Calculus, 1st Edition, Betham Science Publishers, Editor Sachin Bhalekar, p. 269-340, 2017.
[25] Stehfest, H., Algorithm 368: Numerical inversion of Laplace transforms, Communications of the ACM, 13 (1970) 47-49.
[26] Tzou, D.Y., Macro to micro scale heat transfer: The lagging behavior, Taylor and Francis, Washington, 1997.
Journal of Applied and Computational Mechanics
Volume 5, Issue 4
June 2019
Pages 592-602