
AIMS Mathematics, 2019, 4(5): 14161429. doi: 10.3934/math.2019.5.1416.
Research article
Export file:
Format
 RIS(for EndNote,Reference Manager,ProCite)
 BibTex
 Text
Content
 Citation Only
 Citation and Abstract
Numerical investigation of fractionalorder unsteady natural convective radiating flow of nanofluid in a vertical channel
1 School of Mathematical Sciences, Peking University, Beijing 100871, China;
2 BICESAT, College of Engineering, Peking University, Beijing 100871, China;
3 State Key Laboratory for Turbulence and Complex Systems, Department of Mechanics and Engineering Science, Peking University, Beijing 100871, China;
4 Institute of Ocean Research, Peking University, Beijing 100871, China;
5 Department of Electrical Engineering, Bahria University, Islamabad Campus, Islamabad 44000, Pakistan
Received: , Accepted: , Published:
Keywords: finite difference method; fractional calculus; nanofluid; magnetic effects; thermal radiation
Citation: M. Hamid, T. Zubair, M. Usman, R. U. Haq. Numerical investigation of fractionalorder unsteady natural convective radiating flow of nanofluid in a vertical channel. AIMS Mathematics, 2019, 4(5): 14161429. doi: 10.3934/math.2019.5.1416
References:
 1. T. Fujii, M. Takeuchi, M. Fujii, et al. Experiments on naturalconvection heat transfer from the outer surface of a vertical cylinder to liquids, Int. J Heat Mass Tran., 13 (1970), 753787.
 2. T. Fujii, H. Imura, Naturalconvection heat transfers from a plate with arbitrary inclination, Int. J Heat Mass Tran., 15 (1972), 755767.
 3. M. A. Ezzat, Thermoelectric MHD nonNewtonian fluid with fractional derivative heat transfer, Physica B, 405 (2010), 41884194.
 4. M. Arshad, M. H. Inayat, I. R. Chughtai, Experimental study of natural convection heat transfer from an enclosed assembly of thin vertical cylinders, Appl. Therm. Eng., 31 (2011), 2027.
 5. N. T. M. Eldabe, S. N. Sallam, M. Y. Abouzeid, Numerical study of viscous dissipation effect on free convection heat and mass transfer of MHD nonNewtonian fluid flow through a porous medium, Journal of the Egyptian mathematical society, 20 (2012), 139151.
 6. Q. Rubbab, D. Vieru, C. Fetecau, et al. Natural convection flow near a vertical plate that applies a shear stress to a viscous fluid, PloS one, 8 (2013), e78352.
 7. R. Ellahi, The effects of MHD and temperature dependent viscosity on the flow of nonNewtonian nanofluid in a pipe: analytical solutions, Appl. Math. Model., 37 (2013): 14511467.
 8. M. M. Molla, A. Biswas, A. AlMamun, et al. Natural convection flow along an isothermal vertical flat plate with temperature dependent viscosity and heat generation, Journal of computational engineering, 2014 (2014), 113.
 9. M. A. Ezzat, A. A. ElBary, A. S. Hatem, State space approach to unsteady magnetohydrodynamics natural convection heat and mass transfer through a porous medium saturated with a viscoelastic fluid, J. Appl. Mech. Tech. Phy., 55 (2014), 660671.
 10. S. R. Sheri, T. Thumma, Numerical study of heat transfer enhancement in MHD free convection flow over vertical plate utilizing nanofluids, Ain Shams Eng. J., 9 (2016), 11691180.
 11. S. Z. Alamri, A. A. Khan, M. Azeez, et al. Effects of mass transfer on MHD second grade fluid towards stretching cylinder: a novel perspective of CattaneoChristov heat flux model, Phys. Lett. A, 383 (2019), 276281.
 12. F. Ali, M. Saqib, I. Khan, et al. Application of CaputoFabrizio derivatives to MHD free convection flow of generalized Walters'B fluid model, Eur. Phys. J. Plus, 131 (2016), 377.
 13. M. Hamid, T. Zubair, M. Usman, et al. Natural convection effects on heat and mass transfer of slip flow of timedependent Prandtl fluid, Journal of Computational Design and Engineering, 2019.
 14. M. A. Yousif, H. F. Ismael, T. Abbas, et al. Numerical study of momentum and heat transfer of MHD Carreau nanofluid over an exponentially stretched plate with internal heat source/sink and radiation, Heat Transf. Res., 50 (2019), 649658.
 15. M. Hamid, M. Usman, R. U. Haq, Wavelets investigation of Soret and Dufour effects on stagnation point fluid flow in twodimension with variable thermal conductivity and diffusivity, Phys. Scripta, 2019.
 16. S. U. Choi, J. A. Eastman, Enhancing thermal conductivity of fluids with nanoparticles. ASME International Mechanical Engineering Congress & Exposition, 1995.
 17. S. U. S Choi, Z. G. Zhang, W. Yu, et al. Anomalous thermal conductivity enhancement in nanotube suspensions, Appl. Phys. Lett., 79 (2001), 22522254.
 18. S. Dinarvand, R. Hosseini, M. Abulhasansari, et al. Buongiorno's model for doublediffusive mixed convective stagnationpoint flow of a nanofluid considering diffusiophoresis effect of binary base fluid, Adv. Powder Technol., 26 (2015), 14231434.
 19. M. Sheikholeslami, R. Ellahi, Three dimensional mesoscopic simulation of magnetic field effect on natural convection of nanofluid, Int. J. Heat Mass Tran., 89 (2015), 799808.
 20. M. Sheikholeslami, D. D. Ganji, Nanofluid convective heat transfer using semi analytical and numerical approaches: a review, J. Taiwan Inst. Chem. E., 65 (2016), 4377.
 21. M. Usman, M. Hamid, U. Khan, et al. Differential transform method for unsteady nanofluid flow and heat transfer, Alex. Eng. J., 57 (2018), 18671875.
 22. M. Hassan, R. Ellahi, M. M. Bhatti, et al. A comparative study on magnetic and nonmagnetic particles in nanofluid propagating over a wedge. Can. J. Phys., 97 (2019), 277285.
 23. S. T. MohyudDin, M. Usman, K. Afaq, et al. Examination of carbonwater nanofluid flow with thermal radiation under the effect of Marangoni convection, Eng. Computations, 34 (2017), 23302343.
 24. M. Hamid, M. Usman, Z. H. Khan, et al. Numerical study of unsteady MHD flow of Williamson nanofluid in a permeable channel with heat source/sink and thermal radiation, Eur. Phys. J. Plus, 133 (2018), 527.
 25. N. A. Sheikh, F. Ali, M. Saqib, et al. Comparison and analysis of the AtanganaBaleanu and CaputoFabrizio fractional derivatives for generalized Casson fluid model with heat generation and chemical reaction, Results Phys., 7 (2017), 789800.
 26. M. A. Ezzat, A. A. ElBary, MHD free convection flow with fractional heat conduction law, Magnetohydrodynamics, 48 (2012).
 27. F. Ali, N. A. Sheikh, I. Khan, et al. Magnetic field effect on blood flow of Casson fluid in axisymmetric cylindrical tube: A fractional model, J. Magn. Magn. Mater., 423 (2017), 327336.
 28. M. A. Imran, I. Khan, M. Ahmad, et al. Heat and mass transport of differential type fluid with noninteger order timefractional Caputo derivatives, J. Mol. Liq., 229 (2017), 6775.
 29. M. Hamid, M. Usman, R. U. Haq, et al. Wavelets Analysis of Stagnation Point Flow of nonNewtonian Nanofluid, Appl. Math. Mech.Engl., 40 (2019), 12111226.
 30. I. Podlubny, Fractional diﬀerential equations, Academic press, San Diego, 1999.
 31. V. V. Kulish, J. L. Lage, Application of fractional calculus to fluid mechanics. J. Fluids Eng.T. Asme, 124 (2002), 803806.
 32. J. A. T. Machado, M. F. Silva, R. S. Barbosa, et al. Some applications of fractional calculus in engineering, Math. Probl. Eng., 2010 (2010), 134.
 33. T. Pfitzenreiter, A physical basis for fractional derivatives in constitutive equations, ZAMM‐Zeitschrift für angewandte mathematik und mechanic, 84 (2004), 284287.
 34. Y. Kawada, H. Nagahama, H. Hara, Irreversible thermodynamic and viscoelastic model for powerlaw relaxation and attenuation of rocks, Tectonophysics, 427 (2006), 255263.
 35. M. Usman, M. Hamid, T. Zubair, et al. Operationalmatrixbased algorithm for differential equations of fractional order with Dirichlet boundary conditions, Eur. Phys. J. Plus, 134 (2019), 279.
 36. M. Hamid, M. Usman, T. Zubair, et al. An efficient analysis for Nsoliton, Lump and lumpkink solutions of timefractional (2+1)KadomtsevPetviashvili equation, Physica A, 528 (2019), 121320.
 37. N. A. Shah, D. Vieru, C. Fetecau, Effects of the fractional order and magnetic field on the blood flow in cylindrical domains, J. Magn. Magn. Mater., 409 (2016), 1019.
 38. M. A. Ezzat, I. A. Abbas, A. A. ElBary, et al. Numerical study of the Stokes' first problem for thermoelectric micropolar fluid with fractional derivative heat transfer, Magnetohydrodynamics, 50 (2014).
 39. I. Khan, N. A. Shah, Y. Mahsud, et al. Heat transfer analysis in a Maxwell fluid over an oscillating vertical plate using fractional CaputoFabrizio derivatives, Eur. Phys. J. Plus, 132 (2017), 194.
 40. B. Ahmad, S. I. Shah, S. U. Haq, et al. Analysis of unsteady natural convective radiating gas flow in a vertical channel by employing the Caputo timefractional derivative, Eur. Phys. J. Plus, 132 (2017), 380.
 41. H. Sun, W. Chen, C. Li, et al. Finite difference schemes for variableorder time fractional diffusion equation, Int. J. Bifurcat. Chaos, 22 (2012), 1250085.
 42. C. Çelik, M. Duman, CrankNicolson method for the fractional diffusion equation with the Riesz fractional derivative, J. Comput. Phys., 231 (2012), 17431750.
 43. A. C. Cogley, W. G. Vincenti and S. E. Gilles, Differential Approximation for Radiative Transfer in a NonGrey Gas near Equilibrium, AIAA J., 6 (1968), 551553.
This article has been cited by:
 1. Khalil Ur Rehman, Qasem M. AlMdallal, Iskander Tlili, M.Y. Malik, Impact of heated triangular ribs on hydrodynamic forces in a rectangular domain with heated elliptic cylinder: Finite element analysis, International Communications in Heat and Mass Transfer, 2020, 112, 104501, 10.1016/j.icheatmasstransfer.2020.104501
 2. Ambreen Sarwar, Tao Gang, Muhammad Arshad, Iftikhar Ahmed, Construction of brightdark solitary waves and elliptic function solutions of spacetime fractional partial differential equations and their applications, Physica Scripta, 2020, 95, 4, 045227, 10.1088/14024896/ab6d46
 3. Zafar H. Khan, Waqar A. Khan, R.U. Haq, M. Usman, M. Hamid, Effects of volume fraction on waterbased carbon nanotubes flow in a rightangle trapezoidal cavity: FEM based analysis, International Communications in Heat and Mass Transfer, 2020, 116, 104640, 10.1016/j.icheatmasstransfer.2020.104640
 4. Manjappa Archana, Mundalamane Manjappa Praveena, Kondlahalli Ganesh Kumar, Sabir Ali Shehzad, Manzoor Ahmad, Unsteady squeezed Casson nanofluid flow by considering the slip condition and time‐dependent magnetic field, Heat Transfer, 2020, 10.1002/htj.21859
 5. Mostafa Abbaszadeh, Mehdi Dehghan, A PODbased reducedorder CrankNicolson/fourthorder alternating direction implicit (ADI) finite difference scheme for solving the twodimensional distributedorder Riesz spacefractional diffusion equation, Applied Numerical Mathematics, 2020, 10.1016/j.apnum.2020.07.020
 6. Kharabela Swain, Basavarajappa Mahanthesh, Fateh Mebarek‐Oudina, Heat transport and stagnation‐point flow of magnetized nanoliquid with variable thermal conductivity, Brownian moment, and thermophoresis aspects, Heat Transfer, 2020, 10.1002/htj.21902
 7. Sundar Sindhu, Bijjanal Jayanna Gireesha, Effect of nanoparticle shapes on irreversibility analysis of nanofluid in a microchannel with individual effects of radiative heat flux, velocity slip and convective heating, Heat Transfer, 2020, 10.1002/htj.21909
 8. Rahila Naz, Featuring the radiative transmission of energy in viscoelastic nanofluid with swimming microorganisms, International Communications in Heat and Mass Transfer, 2020, 117, 104788, 10.1016/j.icheatmasstransfer.2020.104788
 9. Sameh E Ahmed, Anas A M Arafa, Impacts of the fractional derivatives on unsteady magnetohydrodynamics radiative Casson nanofluid flow combined with Joule heating, Physica Scripta, 2020, 95, 9, 095206, 10.1088/14024896/abab37
 10. Iftikhar Ahmad, Samaira Aziz, Nasir Ali, Sami Ullah Khan, Radiative unsteady hydromagnetic 3D flow model for Jeffrey nanofluid configured by an accelerated surface with chemical reaction, Heat Transfer, 2020, 10.1002/htj.21912
 11. Umair Ali, Muhammad Sohail, Farah Aini Abdullah, An Efficient Numerical Scheme for VariableOrder Fractional SubDiffusion Equation, Symmetry, 2020, 12, 9, 1437, 10.3390/sym12091437
 12. Muhammad Imran Asjad, Muhammadish Danish Ikram, Ali Akgül, Analysis of MHD viscous fluid flow through porous medium with novel power law fractional differential operator, Physica Scripta, 2020, 95, 11, 115209, 10.1088/14024896/abbe4f
Reader Comments
© 2019 the Author(s), licensee AIMS Press. This is an open access article distributed under the terms of the Creative Commons Attribution Licese (http://creativecommons.org/licenses/by/4.0)
Associated material
Metrics
Other articles by authors
Related pages
Tools
your name: * your email: *