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

Previous Article
Optimal control of hybrid manufacturing systems by log-exponential smoothing aggregation
DCDS-S Home
This Issue
Next Article
Solving the time-fractional Schrodinger equation with the group preserving scheme

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 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 & Continuous Dynamical Systems - S, doi: 10.3934/dcdss.2020142

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. Google Scholar
[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. Google Scholar
[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. Google Scholar
[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. Google Scholar
[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. Google Scholar
[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. Google Scholar
[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. Google Scholar
[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. Google Scholar
[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. Google Scholar
[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. Google Scholar
[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. Google Scholar
[12]	M. Q. Brewster, Thermal Radiative Transfer and Properties, John Wiley and Sons, 1992. Google Scholar
[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. Google Scholar
[14]	S. U. S. Choi, Enhancing thermal conductivity of fluids with nanoparticles, ASME International Mechanical Engineering Congress and Exposition, 66 (1995), 99-105. Google Scholar
[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. Google Scholar
[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. Google Scholar
[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. Google Scholar
[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. Google Scholar
[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. Google Scholar
[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. Google Scholar
[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. Google Scholar
[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. Google Scholar
[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. Google Scholar
[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. Google Scholar
[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. Google Scholar
[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. Google Scholar
[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. Google Scholar
[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. Google Scholar
[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. Google Scholar
[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. Google Scholar
[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. Google Scholar
[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. Google Scholar
[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. Google Scholar
[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. Google Scholar
[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. Google Scholar
[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. Google Scholar
[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. Google Scholar
[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. Google Scholar
[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. Google Scholar
[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. Google Scholar
[41]	D. Nouri, M. P. Fard, M. J. Oboodi, O. Mahia and A. Z. Sahin, Entropy generation analysis of nanofluid flow over a spherical heat source inside a channel with sudden expansion and contraction, International Journal of Heat and Mass Transfer, 116 (2018), 1036-1043. doi: 10.1016/j.ijheatmasstransfer.2017.09.097. Google Scholar
[42]	M. Prakash and S. S. U. Devi, Hydromagnetic hybrid $Al_2O_3-Cu$ / water nanofluid flow over a slendering stretching sheet with prescribed surface temperature, Asian Journal of Humanities and Social Sciences, 6 (2016), 1921-1936. Google Scholar
[43]	S. Qayyum, T. Hayat and A. Alsaedi, Heat and mass transfer of Williamson nanofluid flow yield by an inclined Lorentz force over a nonlinear stretching sheet, Results in Physics, 8 (2018), 862-868. Google Scholar
[44]	S. Qayyum, T. Hayat and A. Alsaedi, Thermal Radiation and Heat Generation/Absorption Aspects in Third Grade Magnetonanofluid Over A Slendering Stretching Sheet with Newtonian Conditions, Physica B: Physics of Condensed Matter, 2018. Google Scholar
[45]	J. Qing, M. M. Bhatti, T. Abbas, M. M. Rashidi, M. E. Ali and Z. Yang, Entropy generation on MHD Casson nanofluid flow over a porous stretching/shrinking surface, Entropy, 18 (2016), Paper No. 123, 14 pp. doi: 10.3390/e18060224. Google Scholar
[46]	A. R. Rahmati, O. A. Akbari, A. Marzban, R. Karimi and F. Pourfattah, Simultaneous investigations the effects of non-Newtonian nanofluid flow in different volume fractions of solid nanoparticles with slip and no-slip boundary conditions, Thermal Science and Engineering Progress, 5 (2018), 263-277. doi: 10.1016/j.tsep.2017.12.006. Google Scholar
[47]	A. Rasheed and M. S. Anwar, Simulations of variable concentration aspects in a fractional nonlinear viscoelastic fluid flow, Commun. Nonlinear Sci. Numer. Simul., 65 (2018), 216-230. doi: 10.1016/j.cnsns.2018.05.012. Google Scholar
[48]	A. Rasheed and M. S. Anwar, Interplay of chemical reacting species in a fractional viscoelastic fluid flow, Journal of Molecular Liquids, 273 (2019), 576-588. doi: 10.1016/j.molliq.2018.10.028. Google Scholar
[49]	J. V. R. Reddy, V. Sugunamma and N. Sandeep, Impact of nonlinear radiation on 3D magnetohydrodynamic flow of methanol and kerosene based ferrofluids with temperature dependent viscosity, Journal of Molecular Liquids, 236 (2017), 93-100. Google Scholar
[50]	M. Sheikholeslami, A. M. Zeeshan and A. Majeed, Control volume based finite element simulation of magnetic nanofluid flow and heat transport in non-Darcy medium, Journal of Molecular Liquids, 268 (2018), 354-364. doi: 10.1016/j.molliq.2018.07.031. Google Scholar
[51]	M. Shen, S. Chen and F. Liu, Unsteady MHD flow and heat transfer of fractional Maxwell viscoelastic nanofluid with Cattaneo heat flux and different particle shapes, Chinese J. Phys., 56 (2018), 1199-1211. doi: 10.1016/j.cjph.2018.04.024. Google Scholar
[52]	H. Sithole, H. Mondal and P. Sibanda, Entropy generation in a second grade magnetohydrodynamics nanofluid flow over a convectively heated stretching sheet with nonlinear thermal radiation and viscous dissipation, Results in Physics, 9 (2018), 1077-1085. doi: 10.1016/j.rinp.2018.04.003. Google Scholar
[53]	S. Suresh, K. Venkitaraj, P. Selvakumar and M. Chandrasekar, Experimental investigation of mixed convection with synthesis of $Al_2O_3-water$ hybrid nanofluids using two step method and its thermo physical properties, Colloids Surface, 8 (2011), 41-48. Google Scholar
[54]	S. Suresh, K. Venkitaraj, P. Selvakumar and M. Chandrasekar, Effect of $Al_2O_3-water$ hybrid nanofluid in heat transfer, Experimental Thermal and Fluid Science, 8 (2012), 54-60. Google Scholar
[55]	M. D. Tausif, D. Das and P. K. kundu, Presence of Different Shapes of $Z_{r}O_{2}$ Nanoparticles in The Melting Heat Transfer of A Casson Flow, The European Physical Journal Plus, 2017. Google Scholar
[56]	A. R. D. Thorley and C. H. Tiley, Unsteady and transient flow of compressible fluids in pipelines - a review of theoretical and some experimental studies, International Journal of Heat and Fluid Flow, 8 (1987), 3-15. doi: 10.1016/0142-727X(87)90044-0. Google Scholar
[57]	I. Tlili, W. A. Khan and I. Khan, Multiple slips effects on MHD $SA-Al_{2}O_{(3)}$ and $SA-Cu$ non-Newtonian nanofluids flow over a stretching cylinder in porous medium with radiation and chemical reaction, Results in Physics, 8 (2018), 213-222. Google Scholar
[58]	X. Wang, X. Xu and S. Choi, Thermal conductivity of nanoparticles-fluid mixture, Journal of Thermophysics and Heat Transfer, 13 (1999). doi: 10.2514/2.6486. Google Scholar

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. Google Scholar
[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. Google Scholar
[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. Google Scholar
[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. Google Scholar
[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. Google Scholar
[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. Google Scholar
[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. Google Scholar
[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. Google Scholar
[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. Google Scholar
[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. Google Scholar
[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. Google Scholar
[12]	M. Q. Brewster, Thermal Radiative Transfer and Properties, John Wiley and Sons, 1992. Google Scholar
[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. Google Scholar
[14]	S. U. S. Choi, Enhancing thermal conductivity of fluids with nanoparticles, ASME International Mechanical Engineering Congress and Exposition, 66 (1995), 99-105. Google Scholar
[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. Google Scholar
[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. Google Scholar
[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. Google Scholar
[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. Google Scholar
[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. Google Scholar
[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. Google Scholar
[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. Google Scholar
[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. Google Scholar
[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. Google Scholar
[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. Google Scholar
[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. Google Scholar
[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. Google Scholar
[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. Google Scholar
[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. Google Scholar
[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. Google Scholar
[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. Google Scholar
[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. Google Scholar
[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. Google Scholar
[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. Google Scholar
[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. Google Scholar
[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. Google Scholar
[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. Google Scholar
[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. Google Scholar
[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. Google Scholar
[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. Google Scholar
[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. Google Scholar
[41]	D. Nouri, M. P. Fard, M. J. Oboodi, O. Mahia and A. Z. Sahin, Entropy generation analysis of nanofluid flow over a spherical heat source inside a channel with sudden expansion and contraction, International Journal of Heat and Mass Transfer, 116 (2018), 1036-1043. doi: 10.1016/j.ijheatmasstransfer.2017.09.097. Google Scholar
[42]	M. Prakash and S. S. U. Devi, Hydromagnetic hybrid $Al_2O_3-Cu$ / water nanofluid flow over a slendering stretching sheet with prescribed surface temperature, Asian Journal of Humanities and Social Sciences, 6 (2016), 1921-1936. Google Scholar
[43]	S. Qayyum, T. Hayat and A. Alsaedi, Heat and mass transfer of Williamson nanofluid flow yield by an inclined Lorentz force over a nonlinear stretching sheet, Results in Physics, 8 (2018), 862-868. Google Scholar
[44]	S. Qayyum, T. Hayat and A. Alsaedi, Thermal Radiation and Heat Generation/Absorption Aspects in Third Grade Magnetonanofluid Over A Slendering Stretching Sheet with Newtonian Conditions, Physica B: Physics of Condensed Matter, 2018. Google Scholar
[45]	J. Qing, M. M. Bhatti, T. Abbas, M. M. Rashidi, M. E. Ali and Z. Yang, Entropy generation on MHD Casson nanofluid flow over a porous stretching/shrinking surface, Entropy, 18 (2016), Paper No. 123, 14 pp. doi: 10.3390/e18060224. Google Scholar
[46]	A. R. Rahmati, O. A. Akbari, A. Marzban, R. Karimi and F. Pourfattah, Simultaneous investigations the effects of non-Newtonian nanofluid flow in different volume fractions of solid nanoparticles with slip and no-slip boundary conditions, Thermal Science and Engineering Progress, 5 (2018), 263-277. doi: 10.1016/j.tsep.2017.12.006. Google Scholar
[47]	A. Rasheed and M. S. Anwar, Simulations of variable concentration aspects in a fractional nonlinear viscoelastic fluid flow, Commun. Nonlinear Sci. Numer. Simul., 65 (2018), 216-230. doi: 10.1016/j.cnsns.2018.05.012. Google Scholar
[48]	A. Rasheed and M. S. Anwar, Interplay of chemical reacting species in a fractional viscoelastic fluid flow, Journal of Molecular Liquids, 273 (2019), 576-588. doi: 10.1016/j.molliq.2018.10.028. Google Scholar
[49]	J. V. R. Reddy, V. Sugunamma and N. Sandeep, Impact of nonlinear radiation on 3D magnetohydrodynamic flow of methanol and kerosene based ferrofluids with temperature dependent viscosity, Journal of Molecular Liquids, 236 (2017), 93-100. Google Scholar
[50]	M. Sheikholeslami, A. M. Zeeshan and A. Majeed, Control volume based finite element simulation of magnetic nanofluid flow and heat transport in non-Darcy medium, Journal of Molecular Liquids, 268 (2018), 354-364. doi: 10.1016/j.molliq.2018.07.031. Google Scholar
[51]	M. Shen, S. Chen and F. Liu, Unsteady MHD flow and heat transfer of fractional Maxwell viscoelastic nanofluid with Cattaneo heat flux and different particle shapes, Chinese J. Phys., 56 (2018), 1199-1211. doi: 10.1016/j.cjph.2018.04.024. Google Scholar
[52]	H. Sithole, H. Mondal and P. Sibanda, Entropy generation in a second grade magnetohydrodynamics nanofluid flow over a convectively heated stretching sheet with nonlinear thermal radiation and viscous dissipation, Results in Physics, 9 (2018), 1077-1085. doi: 10.1016/j.rinp.2018.04.003. Google Scholar
[53]	S. Suresh, K. Venkitaraj, P. Selvakumar and M. Chandrasekar, Experimental investigation of mixed convection with synthesis of $Al_2O_3-water$ hybrid nanofluids using two step method and its thermo physical properties, Colloids Surface, 8 (2011), 41-48. Google Scholar
[54]	S. Suresh, K. Venkitaraj, P. Selvakumar and M. Chandrasekar, Effect of $Al_2O_3-water$ hybrid nanofluid in heat transfer, Experimental Thermal and Fluid Science, 8 (2012), 54-60. Google Scholar
[55]	M. D. Tausif, D. Das and P. K. kundu, Presence of Different Shapes of $Z_{r}O_{2}$ Nanoparticles in The Melting Heat Transfer of A Casson Flow, The European Physical Journal Plus, 2017. Google Scholar
[56]	A. R. D. Thorley and C. H. Tiley, Unsteady and transient flow of compressible fluids in pipelines - a review of theoretical and some experimental studies, International Journal of Heat and Fluid Flow, 8 (1987), 3-15. doi: 10.1016/0142-727X(87)90044-0. Google Scholar
[57]	I. Tlili, W. A. Khan and I. Khan, Multiple slips effects on MHD $SA-Al_{2}O_{(3)}$ and $SA-Cu$ non-Newtonian nanofluids flow over a stretching cylinder in porous medium with radiation and chemical reaction, Results in Physics, 8 (2018), 213-222. Google Scholar
[58]	X. Wang, X. Xu and S. Choi, Thermal conductivity of nanoparticles-fluid mixture, Journal of Thermophysics and Heat Transfer, 13 (1999). doi: 10.2514/2.6486. Google Scholar

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

[1]	Liudmila A. Pozhar. Poiseuille flow of nanofluids confined in slit nanopores. Conference Publications, 2001, 2001 (Special) : 319-326. doi: 10.3934/proc.2001.2001.319
[2]	Ilyas Khan, Muhammad Saqib, Aisha M. Alqahtani. Channel flow of fractionalized H2O-based CNTs nanofluids with Newtonian heating. Discrete & Continuous Dynamical Systems - S, 2020, 13 (3) : 769-779. doi: 10.3934/dcdss.2020043
[3]	Xufeng Guo, Gang Liao, Wenxiang Sun, Dawei Yang. On the hybrid control of metric entropy for dominated splittings. Discrete & Continuous Dynamical Systems - A, 2018, 38 (10) : 5011-5019. doi: 10.3934/dcds.2018219
[4]	Vincent Giovangigli. Persistence of Boltzmann entropy in fluid models. Discrete & Continuous Dynamical Systems - A, 2009, 24 (1) : 95-114. doi: 10.3934/dcds.2009.24.95
[5]	Roman Chapko. On a Hybrid method for shape reconstruction of a buried object in an elastostatic half plane. Inverse Problems & Imaging, 2009, 3 (2) : 199-210. doi: 10.3934/ipi.2009.3.199
[6]	Caterina Calgaro, Meriem Ezzoug, Ezzeddine Zahrouni. Stability and convergence of an hybrid finite volume-finite element method for a multiphasic incompressible fluid model. Communications on Pure & Applied Analysis, 2018, 17 (2) : 429-448. doi: 10.3934/cpaa.2018024
[7]	Yue-Jun Peng, Shu Wang. Asymptotic expansions in two-fluid compressible Euler-Maxwell equations with small parameters. Discrete & Continuous Dynamical Systems - A, 2009, 23 (1&2) : 415-433. doi: 10.3934/dcds.2009.23.415
[8]	Nicola Zamponi. Some fluid-dynamic models for quantum electron transport in graphene via entropy minimization. Kinetic & Related Models, 2012, 5 (1) : 203-221. doi: 10.3934/krm.2012.5.203
[9]	Kamil Rajdl, Petr Lansky. Fano factor estimation. Mathematical Biosciences & Engineering, 2014, 11 (1) : 105-123. doi: 10.3934/mbe.2014.11.105
[10]	Amin Boumenir. Determining the shape of a solid of revolution. Mathematical Control & Related Fields, 2019, 9 (3) : 509-515. doi: 10.3934/mcrf.2019023
[11]	P. Alonso Ruiz, Y. Chen, H. Gu, R. S. Strichartz, Z. Zhou. Analysis on hybrid fractals. Communications on Pure & Applied Analysis, 2020, 19 (1) : 47-84. doi: 10.3934/cpaa.2020004
[12]	Kai-Uwe Schmidt, Jonathan Jedwab, Matthew G. Parker. Two binary sequence families with large merit factor. Advances in Mathematics of Communications, 2009, 3 (2) : 135-156. doi: 10.3934/amc.2009.3.135
[13]	Ryusuke Kon. Dynamics of competitive systems with a single common limiting factor. Mathematical Biosciences & Engineering, 2015, 12 (1) : 71-81. doi: 10.3934/mbe.2015.12.71
[14]	Ke Ruan, Masao Fukushima. Robust portfolio selection with a combined WCVaR and factor model. Journal of Industrial & Management Optimization, 2012, 8 (2) : 343-362. doi: 10.3934/jimo.2012.8.343
[15]	Yanming Ge. Analysis of airline seat control with region factor. Journal of Industrial & Management Optimization, 2012, 8 (2) : 363-378. doi: 10.3934/jimo.2012.8.363
[16]	Brandon Seward. Every action of a nonamenable group is the factor of a small action. Journal of Modern Dynamics, 2014, 8 (2) : 251-270. doi: 10.3934/jmd.2014.8.251
[17]	Shaoyong Lai, Yulan Zhou. A stochastic optimal growth model with a depreciation factor. Journal of Industrial & Management Optimization, 2010, 6 (2) : 283-297. doi: 10.3934/jimo.2010.6.283
[18]	Wu Chanti, Qiu Youzhen. A nonlinear empirical analysis on influence factor of circulation efficiency. Discrete & Continuous Dynamical Systems - S, 2019, 12 (4&5) : 929-940. doi: 10.3934/dcdss.2019062
[19]	Andrzej Nowakowski, Jan Sokolowski. On dual dynamic programming in shape control. Communications on Pure & Applied Analysis, 2012, 11 (6) : 2473-2485. doi: 10.3934/cpaa.2012.11.2473
[20]	Barbara Kaltenbacher, Gunther Peichl. The shape derivative for an optimization problem in lithotripsy. Evolution Equations & Control Theory, 2016, 5 (3) : 399-430. doi: 10.3934/eect.2016011

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

References:

References:

Tools

Metrics

Other articlesby authors

Tools

Tools

Tools

Metrics

Other articlesby authors

Other articles
by authors

Other articles
by authors