Abstract
In the present paper, we examined the buoyancy effects on MHD two-dimensional boundary layer flow in the presence of heat transfer of Hematite–water nanofluid over a stretching sheet. We consider Hematite as nanoparticle and water as its base liquid. The nonlinear coupled partial differential equations are transformed into the set of nonlinear ordinary differential equations utilizing suitable similarity transformations and are then solved analytically by optimal homotopy analysis method. The graphs are presented and discussed for different parameters of the velocity and temperature profiles. The values of skin friction and local Nusselt number for various parameters are presented graphically and also through tabulated form. It is anticipated from the graph that magnitude of rate of heat transfer enhances as we augmented the nanoparticle volume fraction. Moreover, it is observed that magnitude of rate of heat transfer declines with the augmentation of Eckert number.
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References
Ostrach S (1988) Natural convection in enclosures. J Heat Transf 110:1175–1190
Crane LJ (1970) Flow past a stretching plate. Z Angew Math Phys 21:645–647
Wang CW (1984) The three-dimensional flow due to a stretching flat surface. Phys Fluids 27:1915–1917
Ibrahim W, Shankar B (2013) MHD boundary layer flow and heat transfer of a nanofluid past a permeable stretching sheet with velocity, thermal and solute slip boundary conditions. Comp Fluids 75:1–10
Rosca AV, Pop I (2013) Flow and heat transfer over a vertical permeable stretching/shrinking sheet with a second order slip. Int J Heat Mass Transf 60:355–364
Nazar R, Jaradat M, Arifin NM, Pop I (2011) Stagnation point flow past a shrinking sheet in a nanofluid. Cent Eur J Phys 9(5):1195–1202
Nandy SK, Mahapatra TR (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 64:1091–1100
Kumaran V, Banerjee AK, Vanav Kumar A, Pop I (2011) Unsteady MHD flow and heat transfer with viscous dissipation past a stretching sheet. Int Comm Heat Mass Transf 38:335–339
Turkyilmazoglu M (2011) Multiple solutions of heat and mass transfer of MHD slip flow for the viscoelastic fluid over a stretching sheet. Int J Therm Sci 50:2264–2276
Ishak A, Nazar R, Pop I (2006) Unsteady mixed convection boundary layer flow due to a stretching vertical surface. Arab J Sci Eng 31:165–182
Ishak A, Nazar R, Pop I (2008) MHD boundary-layer flow due to a moving extensible surface. J Eng Math 62:23–33
Ishak A, Nazar R, Pop I (2008) Magnetohydrodynamic (MHD) flow and heat transfer due to a stretching cylinder. Energy Convers Manag 49:3265–3269
Hsiao KL (2016) Numerical solution for Ohmic Soret–Dufour heat and mass mixed convection of viscoelastic fluid over a stretching sheet with multimedia physical features. J. Aerosp Eng. doi:10.1061/(ASCE)AS(2016)1943-5525.0000681
Yacob NA, Ishak A, Pop I, Vajravelu K (2011) Boundary layer flow past a stretching/shrinking surface beneath an external uniform shear flow with a convective surface boundary condition in a nanofluid. Nanoscale Res Lett 6:314
Hussain M, Ashraf M, Nadeem S, Khan M (2013) Radiation effects on the thermal boundary layer flow of a micropolar fluid towards a permeable stretching sheet. J Franklin Inst 350:194–210
Choi SUS (1995) Enhancing thermal conductivity of fluids with nanoparticles, J Non-Newtonian Fluid Mech FED-vol.231/MDvol 66: 99–105
Mahian O, Kianifar A, Kalogirou SA, Pop I, Wongwises S (2013) A review of the applications of nanofluids in solar energy. Int J Heat Mass Transf 57:582–594
Khan WA, Pop I (2010) Boundary-layer flow of a nanofluid past a stretching sheet. Int J Heat Mass Transf 53:2477
Makinde OD, Aziz A (2011) Boundary layer flow of a nanofluid past a stretching sheet with a convective boundary conditions. Int J Therm Sci 50:1326–1332
Fan J, Wang L (2010) Nanofluids research: key issues. Nanoscale Res Lett 5:1241–1252
Khanafer K, Vafai K, Lightstone M (2003) Buoyancy-driven heat transfer enhancement in a two-dimensional enclosure utilizing nanofluids. Int J Heat Mass Transf 46(19):3639–3653
Hwang KS, Lee J-H, Jang SP (2007) Buoyancy-driven heat transfer of water based Al2O3 nanofluids in a rectangular cavity. Int J Heat Mass Transf 50:4003–4010
Tiwari RK, Das MK (2007) Heat transfer augmentation in a two-sided liddriven differentially heated square cavity utilizing nanofluids. Int J Heat Mass Transf 50:2002–2018
Oztop HF, Abu-Nada E (2008) Numerical study of natural convection in partially heated rectangular enclosures filled with nanofluids. Int J Heat Fluid Flow 29:1326–1336
Akbar NS, Raza M, Ellahi R (2016) Copper oxide nanoparticles analysis with water as base fluid for peristaltic flow in permeable tube with heat transfer. Comput Methods Programs Biomed 130:22–30
Sandeep N, Sulochana C (2016) Stagnation point flow and heat transfer behavior of Cu–water nanofluid towards horizontal and exponentially stretching/shrinking cylinders. Appl Nanosci 6(3):451–459
Hayat T, Nadeem S (2016) Induced magnetic field stagnation point flow of nanofluid past convectively heated stretching sheet with Buoyancy effects. Chin Phys B 25(11):114701
Khan M, Khan WA, Alshomrani AS (2016) Non-linear radiative flow of three-dimensional Burgers nanofluid with new mass flux effect. Int J Heat Mass Transf 101:570–576
Khan WA, Irfan M, Khan M, Alshomrani AS, Alzahrani AK, Alghamdi MS (2017) Impact of chemical processes on magneto nanoparticle for the generalized Burgers fluid. J Mol Liq 234:201–208
Ellahi R, Hassan M, Zeeshan A (2015) Shape effects of nanosize particles in Cu–H2O nanofluid on entropy generation. Int J Heat Mass Transf 81:449–456
Ul Haq R, Nadeem S, Khan ZH, Noor NFM (2015) Convective heat transfer in MHD slip flow over a stretching surface in the presence of carbon nanotubes. Phys B 457:40–47
Ul Haq R, Rajotia D, Noor NFM (2016) Thermophysical effects of water driven copper nanoparticles on MHD axisymmetric permeable shrinking sheet: dual-nature study. Eur Phys J E 39:33
Ul Haq R, Noor NFM, Khan ZH (2016) Numerical simulation of water based magnetite nanoparticles between two parallel disks. Adv Powder Technol 27:1568–1575
Abdelsalam SI, Vafai K (2017) Combined effects of magnetic field and rheological properties on the peristaltic flow of a compressible fluid in a microfluidic channel. Eur J Mech B/Fluids. doi:10.1016/j.euromechflu.2017.02.002
Soliman R, Koumy El, Barakat ESI, Abdelsalam SI (2012) Hall and porous boundaries effects on peristaltic transport through porous medium of a Maxwell model. Transp Porous Medium 94:643–658
Mekheimer KS, Komy SR, Abdelsalam SI (2013) Simultaneous effects of magnetic field and space porosity on compressible Maxwell fluid transport induced by a surface acoustic wave in a microchannel. Chin Phys B 22:124702
Turkyilmazoglu M (2016) An effective approach for evaluation of the optimal convergence control parameter in the homotopy analysis method. FILOMAT 30:1633–1650
Ullah H, Nawaz R, Islam S, Idrees M, Fiza M (2015) The optimal homotopy asymptotic method with application to modified Kawahara equation. J Assoc Arab Univ Basic Appl Sci 18:82–88
Makinde OD, Khan WA, Khan ZH (2013) Buoyancy effects on MHD stagnation point flow and heat transfer of a nanofluid past a convectively heated stretching/shrinking sheet. Int J Heat Mass Transf 62:526–533
Liao SJ (2012) Homotopy analysis method in non-linear differential equations. Springer and Higher Education Press, Heidelberg
Shampine LF, Gladwell I, Thompson S (2003) Solving ODEs with Matlab. Cambridge University Press, Cambridge
Shampine LF, Reichelt MW, Kierzenka J Solving boundary value problems for ordinary differential equations in MATLAB with bvp4c. http://www.mathworks.com/bvptutorial
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Hayat, T., Nadeem, S. The effects of MHD and buoyancy on Hematite water-based fluid past a convectively heated stretching sheet. Neural Comput & Applic 31, 1083–1090 (2019). https://doi.org/10.1007/s00521-017-3139-9
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DOI: https://doi.org/10.1007/s00521-017-3139-9