Heat transfer and entropy analysis of Maxwell hybrid nanofluid including effects of inclined magnetic field, Joule heating and thermal radiation

Asim Aziz; Wasim Jamshed; Yasir Ali; Moniba Shams

doi:10.3934/dcdss.2020142

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October 2020, 13(10): 2667-2690. doi: 10.3934/dcdss.2020142

Heat transfer and entropy analysis of Maxwell hybrid nanofluid including effects of inclined magnetic field, Joule heating and thermal radiation

Asim Aziz ^1,, , Wasim Jamshed ^1,2,3, , Yasir Ali ^1,2,3, and Moniba Shams ^1,2,3,

1.	College of Electrical and Mechanical Engineering, National University of Sciences and Technology, Rawalpindi, 46070, Pakistan
2.	Department of Mathematics, Capital University of Science and Technology, Islamabad 44000, Pakistan
3.	Department of Mathematics, School of Natural Sciences, National University of Sciences and Technology, Islamabad, 44000, Pakistan

^* Corresponding author: Asim Aziz

Received February 2019 Revised July 2019 Published October 2020 Early access November 2019

In this numerical study, researchers explore the flow, heat transfer and entropy of electrically conducting hybrid nanofluid over the horizontal penetrable stretching surface with velocity slip conditions at the interface. The non-Newtonian fluid models lead to better understanding of flow and heat transfer characteristics of nanofluids. Therefore, non-Newtonian Maxwell mathematical model is considered for the hybrid nanofluid and the uniform magnetic field is applied at an angle to the direction of the flow. The Joule heating and thermal radiation impact are also considered in the simplified model. The governing nonlinear partial differential equations for hybrid Maxwell nanofluid flow, heat transfer and entropy generation are simplified by taking boundary layer approximations and then reduced to ordinary differential equations using suitable similarity transformations. The Keller box scheme is then adopted to solve the system of ordinary differential equations. The Ethylene glycol based Copper Ethylene glycol ($ Cu $-$ EG $) nanofluid and Ferro-Copper Ethylene glycol ($ Fe_3O_4-Cu $-$ EG $) hybrid nanofluids are considered to produce the numerical results for velocity, temperature and entropy profiles as well as the skin friction factor and the local Nusselt number. The main findings indicate that hybrid Maxwell nanofluid is better thermal conductor when compared with the conventional nanofluid, the greater angle of inclination of magnetic field offers greater resistance to fluid motion within boundary layer and the heat transfer rate act as descending function of nanoparticles shape factor.

Keywords: Hybrid nanofluids, nanofluids, Maxwell fluid, shape factor, entropy.

Mathematics Subject Classification: Primary: 76A05, 76W05; Secondary: 82D80.

Citation: Asim Aziz, Wasim Jamshed, Yasir Ali, Moniba Shams. Heat transfer and entropy analysis of Maxwell hybrid nanofluid including effects of inclined magnetic field, Joule heating and thermal radiation. Discrete and Continuous Dynamical Systems - S, 2020, 13 (10) : 2667-2690. doi: 10.3934/dcdss.2020142

References:

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[2]	M. H. Abolbashari, N. Freidoonimehr, F. Nazari and M. M. Rashidi, Entropy analysis for an unsteady MHD flow past a stretching permeable surface in nano-fluid, Powder Technology, 267 (2014), 256-267. doi: 10.1016/j.powtec.2014.07.028.
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[30]	W. Jamshed and A. Aziz, A comparative entropy based analysis of $Cu$ and $Fe_{3}O_{4}$ /methanol Powell-Eyring nanofluid in solar thermal collectors subjected to thermal radiation, variable thermal conductivity and impact of different nanoparticles shape, Result in Physics, 9 (2018), 195-205.
[31]	P. Keblinski, S. R. Phillpot, S. Choi and J. A. Eastman, Mechanisms of heat flow in suspensions of nano-sized particles (nanofluids), International Journal of Heat and Mass Transfer, 45 (2002), 855-863. doi: 10.1016/S0017-9310(01)00175-2.
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show all references

References:

[1]	M. S. Abel, J. V. Tawade and M. M. Nandeppanavar, MHD flow and heat transfer for the upper-convected Maxwell fluid over a stretching sheet, Meccanica, 47 (2012), 385-393. doi: 10.1007/s11012-011-9448-7.
[2]	M. H. Abolbashari, N. Freidoonimehr, F. Nazari and M. M. Rashidi, Entropy analysis for an unsteady MHD flow past a stretching permeable surface in nano-fluid, Powder Technology, 267 (2014), 256-267. doi: 10.1016/j.powtec.2014.07.028.
[3]	M. Afrand, D. Toghraie and B. Ruhani, Effects of temperature and nanoparticles concentration on rheological behavior of $Fe_3O_4-Ag/EG$ hybrid nanofluid: An experimental study, Experimental Thermal and Fluid Science, 77 (2016), 38-44.
[4]	H. I. Andersson, J. B. Aarseth and B. S. Dandapat, Heat transfer in MHD viscoelastic fluid flow over a stretching sheet with variable thermal conductivity, non-uniform heat source and radiation, International Journal of Heat and Mass Transfer, 43 (2000), 69-74.
[5]	M. S. Anwar and A. Rasheed, Joule heating in magnetic resistive flow with fractional Cattaneo-Maxwell model, Journal of the Brazilian Society of Mechanical Sciences and Engineering, 40 (2018), 501. doi: 10.1007/s40430-018-1426-8.
[6]	T. Aziz, A. Aziz and C. M. Khalique, Exact solutions for stokes flow of a non-Newtonian nanofluid model: A lie similarity approach, Zeitschrift fur Naturforschung A, 71 (2016), 621. doi: 10.1515/zna-2016-0031.
[7]	A. Aziz, W. Jamshed and T. Aziz, Mathematical model for thermal and entropy analysis of thermal solar collectors by using Maxwell nanofluids with slip conditions, thermal radiation and variable thermal conductivity, Open Physics, 16 (2018), 123-136. doi: 10.1515/phys-2018-0020.
[8]	A. Aziz and W. Jamshed, Unsteady MHD slip flow of non-Newtonian Power-law nanofluid over a moving surface with temperature dependent thermal conductivity, Discrete and Continuous Dynamical Systems Series S, 11 (2018), 617-630. doi: 10.3934/dcdss.2018036.
[9]	M. Bahiraei and N. Mazaheri, Application of a novel hybrid nanofluid containing grapheme-platinum nanoparticles in a chaotic twisted geometry for utilization in miniature devices Thermal and energy efficiency considerations, International Journal of Mechanical Sciences, 138 (2018), 337-349.
[10]	P. Barnoon and D. Toghraie, Numerical investigation of laminar flow and heat transfer of non-Newtonian nanofluid within a porous medium, Powder Technology, 325 (2018), 78-91. doi: 10.1016/j.powtec.2017.10.040.
[11]	M. M. Bhatti, T. Abbas, M. M. Rashidi, M. E. Ali and Z. Yang, Entropy generation on MHD Eyring-Powell nanofluid through a permeable stretching surface, Entropy, 18 (2016), Paper No. 224, 14 pp. doi: 10.3390/e18060224.
[12]	M. Q. Brewster, Thermal Radiative Transfer and Properties, John Wiley and Sons, 1992.
[13]	P. Carragher and L. J. Crane, Heat transfer on a continuous stretching sheet, ZAMM - Journal of Applied Mathematics and Mechanics, 62 (1982), 564-565. doi: 10.1002/zamm.19820621009.
[14]	S. U. S. Choi, Enhancing thermal conductivity of fluids with nanoparticles, ASME International Mechanical Engineering Congress and Exposition, 66 (1995), 99-105.
[15]	R. Cortell, A note on flow and heat transfer of a viscoelastic fluid over a stretching sheet, International Journal of Non-Linear Mechanics, 41 (2006), 78-85. doi: 10.1016/j.ijnonlinmec.2005.04.008.
[16]	S. Das, S. Chakraborty, R. N. Jana and O. D. Makinde, Entropy analysis of unsteady magneto-nanofluid flow past accelerating stretching sheet with convective boundary condition, Appl. Math. Mech. (English Ed.), 36 (2015), 1593-1610. doi: 10.1007/s10483-015-2003-6.
[17]	S. S. U. Devi and S. P. A. Devi, Numerical investigation on three dimensional hybrid $Cu-Al_2O_3/water$ nanofluid flow over a stretching sheet with effecting Lorentz force subject to Newtonian heatings, Canadian Journal of Physics, 94 (2016), 490-496.
[18]	S. P. A. Devi and S. S. U. Devi, Numerical investigation of hydromagnetic hybrid $Cu-Al_2O_3$ water nanofluid flow over a permeable stretching sheet with suction, Journal of Nonlinear Science and Applications, 17 (2016), 249-257.
[19]	M. R. Eid, K. L. Mahny, T. Muhammad and M. Sheikholeslami, Numerical treatment for Carreau nanofluid flow over a porous nonlinear stretching surface, Results in Physics, 8 (2018), 1185-1139. doi: 10.1016/j.rinp.2018.01.070.
[20]	S. S. Ghadikolaei, M. Yassari, K. H. Hosseinzadeh and D. D. Ganji, Investigation on thermophysical properties of $TiO_2-Cu/H_2O$ hybrid nanofluid transport dependent on shape factor in MHD stagnation point flow, Powder Technology, 322 (2017), 428-438.
[21]	S. S. Ghadikolaei, K. H. Hosseinzadeh, M. Yassari, H. Sadeghi and D. D. Ganji, Analytical and numerical solution of non-Newtonian second-grade fluid flow on a stretching sheet, Thermal Science and Engineering Progress, 5 (2018), 309-316. doi: 10.1016/j.tsep.2017.12.010.
[22]	N. S. Gibanov, M. A. Sheremet, H. F. Oztop and N. A. Hamdeh, Mixed convection with entropy generation of nanofluid in a lid-driven cavity under the effects of a heat-conducting solid wall and vertical temperature gradient, Eur. J. Mech. B Fluids, 70 (2018), 148-159. doi: 10.1016/j.euromechflu.2018.03.002.
[23]	T. Hayat and S. Nadeem, Heat transfer enhancement with $Ag-CuO/water$ hybrid nanofluid, Results in Physics, 7 (2017), 2317-2324. doi: 10.1016/j.rinp.2017.06.034.
[24]	G. Huminic and A. Huminic, The heat transfer performances and entropy generation analysis of hybrid nanofluids in a flattened tube, International Journal of Heat and Mass Transfer, 119 (2018), 813-827. doi: 10.1016/j.ijheatmasstransfer.2017.11.155.
[25]	S. Hussain, S. E. Ahmed and T. Akbar, Investigation on thermophysical properties of $TiO_2-Cu/H_2O$ hybrid nanofluid transport dependent on shape factor in MHD stagnation point flow, International Journal of Heat and Mass Transfer, 114 (2017), 1054-1066.
[26]	Z. Iqbal, N. S. Akbar, E. Azhar and E. N. Maraj, Performance of hybrid nanofluid $(Cu-CuO/water)$ on MHD rotating transport in oscillating vertical channel inspired by Hall current and thermal radiation, Alexandria Engineering Journal, 57 (2018), 1943-1954. doi: 10.1016/j.aej.2017.03.047.
[27]	A. Ishak, R. Nazar and I. Pop, Mixed convection on the stagnation point flow towards a vertical, continuously stretching sheet., ASME, Journal of Heat Transfer, 129 (2007), 1087-1090.
[28]	A. Ishak, R. Nazar and I. Pop, Boundary layer flow and heat transfer over an unsteady stretching vertical surface, Meccanica, 44 (2009), 369-375. doi: 10.1007/s11012-008-9176-9.
[29]	W. Jamshed and A. Aziz, Cattaneo-Christov based study of $TiO_{2}-Cu/H_{2}O$ Casson hybrid nanofluid flow over a stretching surface with entropy generation, Applied Nanoscience, 8 (2008), 1-14.
[30]	W. Jamshed and A. Aziz, A comparative entropy based analysis of $Cu$ and $Fe_{3}O_{4}$ /methanol Powell-Eyring nanofluid in solar thermal collectors subjected to thermal radiation, variable thermal conductivity and impact of different nanoparticles shape, Result in Physics, 9 (2018), 195-205.
[31]	P. Keblinski, S. R. Phillpot, S. Choi and J. A. Eastman, Mechanisms of heat flow in suspensions of nano-sized particles (nanofluids), International Journal of Heat and Mass Transfer, 45 (2002), 855-863. doi: 10.1016/S0017-9310(01)00175-2.
[32]	H. B. Keller, A new difference scheme for parabolic problems, 1971 Numerical Solution of Partial Differential Equations, II (SYNSPADE 1970) (Proc. Sympos., Univ. of Maryland, College Park, Md., 1970), Academic Press, New York, 2 (1971), 327–350.
[33]	Y. B. Kho, A. Hussanan, N. M. Sarif, Z. Ismail and M. Z. Salleh, Thermal radiation effects on mhd with flow heat and mass transfer in casson nanofluid over a stretching sheet, MATEC Web of Conferences, 150 (2018), 06036. doi: 10.1051/matecconf/201815006036.
[34]	O. K. Koriko, I. L. Animasaun, M. G. Reddy and N. Sandeep, Scrutinization of thermal stratification, nonlinear thermal radiation and quartic autocatalytic chemical reaction effects on the flow of three-dimensional Eyring-Powell alumina-water nanofluid, Multidiscipline Modeling in Materials and Structures, 14 (2018), 261-283. doi: 10.1108/MMMS-08-2017-0077.
[35]	Y. Lin, L. Zheng, X. Zhang and G. Chen, MHD pseudo-plastic nanofluid unsteady flow and heat transfer in a finite thin film over stretching surface with internal heat generation, International Journal of Heat and Mass Transfer, 84 (2015), 903-911.
[36]	A. Mahmood, W. Jamshed and A. Aziz, Entropy and heat transfer analysis using Cattaneo-Christov heat flux model for a boundary layer flow of Casson nanofluid, Results in Physics, 10 (2018), 640-649. doi: 10.1016/j.rinp.2018.07.005.
[37]	M. Mehrali, E. Sadeghinezhad, A. R. Akhiani, S. T. Latibari, H. S. C. Metselaar, A. S. Kherbeet and M. Mehrali, Heat transfer and entropy generation analysis of hybrid graphene/$Fe_3O_4$ ferro-nanofluid flow under the influence of a magnetic field, Powder Technology, 308 (2017), 149-157.
[38]	G. G. Momin, Experimental Investigation of Mixed Convection with $Al_2O_3-water$ and Hybrid Nanofluid in Inclined Tube for Laminar Flow, International Journal of Scientific Research in Science, 2013.
[39]	S. Mukhopadhyay, Heat Transfer Analysis of The Unsteady Flow of A Maxwell Fluid Over A Stretching Surface in The Presence of A Heat Source/Sink, Chinese Physical Society, 2012. doi: 10.1088/0256-307X/29/5/054703.
[40]	W. N. Mutuku, Ethylene Glycol (EG).Based Nanofluids as A Coolant for Automotive Radiator, Asia Pacific Journal on Computational Engineering, 2016. doi: 10.1186/s40540-016-0017-3.
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Figure 1. Flow geometry

$ Pr $	$ Ishak $	$ Nazar $	$ Abolbashari $	$ Das $	$ Present $
	Results[27]	Results[28]	Results[2]	Results[16]	Results
0.72	0.8086	0.8086	0.80863135	0.80876122	0.80876181
1.0	1.0000	1.0000	1.00000000	1.00000000	1.00000000
3.0	1.9237	1.9236	1.92368259	1.92357431	1.92357420
7.0	3.0723	3.0722	3.07225021	3.07314679	3.07314651
10	3.7207	3.7006	3.72067390	3.72055436	3.72055429

Thermo-physical	$ \rho({kg}/{m^{3}}) $	$ c_p({J}/{kgK}) $	$ k({W}/{mK}) $	$ \sigma({S}/{m}) $
Ethylene glycol $ (EG) $	1114	2415	0.252	$ 5.5 \times 10^{-6} $
Pure water $ (H_2O) $	997.1	4179	0.613	$ 0.05 $
Copper $ (Cu) $	8933	385.0	401.00	$ 5.96 \times 10^{7} $
Ferro $ (Fe_3O_4) $	5180	670	9.7	$ 0.74 \times 10^{6} $
Copper oxide $ (Cu_O) $	6510	540	18	$ 5.96 \times 10^{7} $
Alumina $ (Al_{2}O_{3}) $	3970	765.0	40.000	$ 3.5 \times 10^{7} $
Titanium oxide $ (T_iO_{2}) $	4250	686.2	8.9538	$ 2.38 \times 10^{6} $

$ \beta $	$ A $	$ M $	$ \Gamma $	$ \phi $	$ \phi_{2} $	$ \Lambda $	$ Nr $	$ Ec $	$ Bi $	$ C_fRe_x^\frac{1}{2} $	$ C_fRe_x^\frac{1}{2} $	$ N_uRe_x^\frac{-1}{2} $	$ N_uRe_x^\frac{-1}{2} $
										$ Cu $-$ EG $	$ Fe_3O_4-Cu/EG $	$ Cu $-$ EG $	$ Fe_3O_4-Cu/EG $
0.01	0.6	0.6	$ \pi/4 $	0.18	0.09	0.1	0.2	0.2	0.1	1.1918	1.8311	0.0818	0.0824
0.1										2.0011	2.0673	0.0813	0.0819
0.3										2.1039	2.0894	0.0804	0.0808
	0.6									1.1918	1.8311	0.0818	0.0824
	1.6									2.2308	2.1736	0.0839	0.0879
	2.6									2.4621	2.3211	0.0896	0.0899
		0.6								1.1918	1.8311	0.0818	0.0824
		1.6								2.2661	2.1068	0.0809	0.0820
		2.6								2.4149	2.2922	0.0800	0.0815
			$ \pi/4 $							1.1918	1.8311	0.0818	0.0824
			$ \pi/3 $							1.2100	2.0138	0.0810	0.0821
			$ \pi/2 $							1.8610	2.0771	0.0802	0.0820
				0.09						2.1314	-	0.0801	-
				0.15						2.0229	-	0.0810	-
				0.18						1.1912	-	0.0818	-
					0.0					-	1.9597	-	0.0811
					0.06					-	1.9021	-	0.0818
					0.09					-	1.8311	-	0.0824
						0.0				2.0121	2.0065	0.0852	0.0858
						0.1				1.1918	1.8311	0.0818	0.0824
						0.2				1.1728	1.6216	0.0810	0.0820
							0.0			1.1918	1.8311	0.0818	0.0824
							0.2			1.1918	1.8311	0.0921	0.1269
							0.4			1.1918	1.8311	0.0996	0.2106
								0.2		1.1918	1.8311	0.0706	0.0580
								0.4		1.1918	1.8311	0.0818	0.0824
								0.6		1.1918	1.8311	0.0881	0.0829
									0.1	1.1918	1.8311	0.0828	0.0824
									0.2	1.1918	1.8311	0.013	0.0821
									0.6	1.1918	1.8311	0.0806	0.0815

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American Institute of Mathematical Sciences

Heat transfer and entropy analysis of Maxwell hybrid nanofluid including effects of inclined magnetic field, Joule heating and thermal radiation

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