Influences of blowing and internal heating processes on steady MHD mixed convective boundary layer flows of radiating titanium dioxide-ethylene glycol nanofluids. (English) Zbl 07859462
Summary: The present analysis intends predominantly to explore the multiple behaviors of radiating ethylene glycol-based titanium dioxide nanofluids during their steady boundary layer flows near a vertical permeable surface under the prominent impacts of uniform blowing and nonuniform internal heating processes. By incorporating the dynamical contribution of Lorentz and buoyancy forces in the momentum equation and adopting the single-phase nanofluid approach along with the constitutive equations of the second-grade rheological model and Corcione’s correlations, the governing partial differential equations and their appropriate boundary conditions are derived mathematically based on the boundary layer theory and other admissible physical approximations. After several simplifications, the aforesaid differential formulation is converted into a set of ordinary differential equations and realistic boundary conditions, which are solved thereafter numerically using GDQ’s-NT method. Moreover, it is demonstrated that the strengthening in the blowing and internal heating processes has a boosting effect on the velocity and temperature profiles. However, the other influencing parameters show dissimilar dynamical and thermal trends. Furthermore, it is witnessed that the mixed convective heat transfer, the viscoelasticity trend of the nanofluidic medium, and the nanoparticles’ loading exhibit an enhancing impression on the surface heat transfer rate.
© 2024 Wiley-VCH GmbH.
© 2024 Wiley-VCH GmbH.
MSC:
| 80Axx | Thermodynamics and heat transfer |
| 76Rxx | Diffusion and convection |
| 76Wxx | Magnetohydrodynamics and electrohydrodynamics |
References:
| [1] | Buongiorno, J., Venerus, D.C., Prabhat, N., McKrell, T., et al. A benchmark study on the thermal conductivity of nanofluids. J. Appl. Phys.106, 94312 (2009) https://doi.org/10.1063/1.3245330 · doi:10.1063/1.3245330 |
| [2] | Angayarkanni, S.A., Philip, J.: Review on thermal properties of nanofluids: Recent developments. Adv. Colloid Interface Sci.225, 146-176 (2015) https://doi.org/10.1016/j.cis.2015.08.014 · doi:10.1016/j.cis.2015.08.014 |
| [3] | Abbas, N., Awan, M.B., Amer, M., Ammar, S.M., Sajjad, U., Ali, H.M., Zahra, N., Hussain, M., Badshah, M.A., Jafry, A.T.: Applications of nanofluids in photovoltaic thermal systems: A review of recent advances. Phys. A Stat. Mech. Appl.536, 122513 (2019) https://doi.org/10.1016/j.physa.2019.122513 · doi:10.1016/j.physa.2019.122513 |
| [4] | Babar, H., Ali, H.M.: Towards hybrid nanofluids: Preparation, thermophysical properties, applications, and challenges. J. Mol. Liq.281, 598-633 (2019) https://doi.org/10.1016/j.molliq.2019.02.102 · doi:10.1016/j.molliq.2019.02.102 |
| [5] | Shah, T.R., Ali, H.M.: Applications of hybrid nanofluids in solar energy, practical limitations and challenges: A critical review. Sol. Energy183, 173-203 (2019) https://doi.org/10.1016/j.solener.2019.03.012 · doi:10.1016/j.solener.2019.03.012 |
| [6] | Li, C., Ali, H.M.: Enhanced heat transfer mechanism of nanofluid MQL cooling grinding. IGI Global, Hershey, PA (2020). https://doi.org/10.4018/978‐1‐7998‐1546‐4 · doi:10.4018/978‐1‐7998‐1546‐4 |
| [7] | Choi, S.U.S.: Enhancing thermal conductivity of fluids with nanoparticles. ASME, Fed.231, 99-105 (1995) |
| [8] | Tembhare, S.P., Barai, D.P., Bhanvase, B.A.: Performance evaluation of nanofluids in solar thermal and solar photovoltaic systems: A comprehensive review. Renew. Sustain. Energy Rev.153, 111738 (2022) https://doi.org/10.1016/j.rser.2021.111738 · doi:10.1016/j.rser.2021.111738 |
| [9] | Abdullatif Alshuhail, L., Shaik, F., Syam Sundar, L.: Thermal efficiency enhancement of mono and hybrid nanofluids in solar thermal applications: A review. Alexandria Eng. J.68, 365-404 (2023) https://doi.org/10.1016/j.aej.2023.01.043 · doi:10.1016/j.aej.2023.01.043 |
| [10] | Jadeja, K.M., Bumataria, R., Chavda, N.: Nanofluid as a coolant in internal combustion engine: A review. Int. J. Ambient Energy44, 363-380 (2023) https://doi.org/10.1080/01430750.2022.2127891 · doi:10.1080/01430750.2022.2127891 |
| [11] | Baldin, V., daSilva, L.R.R., Machado, A.R., Houck, C.F.: State of the art of biodegradable nanofluids application in machining processes. Int. J. Precis. Eng. Manuf. Technol.10, 1299-1336 (2023) https://doi.org/10.1007/s40684‐022‐00486‐0 · doi:10.1007/s40684‐022‐00486‐0 |
| [12] | Koo, J., Kleinstreuer, C.: Laminar nanofluid flow in microheat‐sinks. Int. J. Heat Mass Transf.48, 2652-2661 (2005) https://doi.org/10.1016/j.ijheatmasstransfer.2005.01.029 · Zbl 1189.76122 · doi:10.1016/j.ijheatmasstransfer.2005.01.029 |
| [13] | Li, J.: Computational analysis of nanofluid flow in micro‐channels with applications to micro‐heat sinks and bio‐MEMS. (2008) |
| [14] | Timofeeva, E.V, Routbort, J.L., Singh, D.: Particle shape effects on thermophysical properties of alumina nanofluids. J. Appl. Phys.106, 14304 (2009) https://doi.org/10.1063/1.3155999 · doi:10.1063/1.3155999 |
| [15] | Corcione, M.: Empirical correlating equations for predicting the effective thermal conductivity and dynamic viscosity of nanofluids. Energy Convers. Manag.52, 789-793 (2011) https://doi.org/10.1016/j.enconman.2010.06.072 · doi:10.1016/j.enconman.2010.06.072 |
| [16] | Vajjha, R.S., Das, D.K.: Experimental determination of thermal conductivity of three nanofluids and development of new correlations. Int. J. Heat Mass Transf.52, 4675-4682 (2009) https://doi.org/10.1016/j.ijheatmasstransfer.2009.06.027 · Zbl 1176.80044 · doi:10.1016/j.ijheatmasstransfer.2009.06.027 |
| [17] | Vajjha, R.S., Das, D.K.: Specific heat measurement of three nanofluids and development of new correlations. J. Heat Transfer131, 1-7 (2009) https://doi.org/10.1115/1.3090813 · doi:10.1115/1.3090813 |
| [18] | Vajjha, R.S., Das, D.K., Kulkarni, D.P.: Development of new correlations for convective heat transfer and friction factor in turbulent regime for nanofluids. Int. J. Heat Mass Transf.53, 4607-4618 (2010) https://doi.org/10.1016/j.ijheatmasstransfer.2010.06.032 · doi:10.1016/j.ijheatmasstransfer.2010.06.032 |
| [19] | Esfe, M.H., Abbasian Arani, A.A., Shafiei Badi, R., Rejvani, M.: ANN modeling, cost performance and sensitivity analyzing of thermal conductivity of DWCNT‐SiO2/EG hybrid nanofluid for higher heat transfer. J. Therm. Anal. Calorim.131, 2381-2393 (2018) https://doi.org/10.1007/s10973‐017‐6744‐z · doi:10.1007/s10973‐017‐6744‐z |
| [20] | Esfe, M.H., Esfandeh, S., Amiri, M.K., Afrand, M.: A novel applicable experimental study on the thermal behavior of SWCNTs(60 · doi:10.1016/j.powtec.2018.10.008 |
| [21] | Esfe, M.H., Sadati Tilebon, S.M.: Statistical and artificial based optimization on thermo‐physical properties of an oil based hybrid nanofluid using NSGA‐II and RSM. Phys. A Stat. Mech. Its Appl.537, 122126 (2020) https://doi.org/10.1016/j.physa.2019.122126 · doi:10.1016/j.physa.2019.122126 |
| [22] | Esfe, M.H., Esfandeh, S., Hassan Kamyab, M., Toghraie, D.: Analysis of rheological behavior of MWCNT‐Al2O3 (10:90)/5W50 hybrid non‐Newtonian nanofluid with considering viscosity as a three‐variable function. J. Mol. Liq.341, 117375 (2021) https://doi.org/10.1016/j.molliq.2021.117375 · doi:10.1016/j.molliq.2021.117375 |
| [23] | Esfe, M.H., Alidoust, S., Mohammadnejad Ardeshiri, E., Kamyab, M.H., Toghraie, D.: Experimental study of rheological behavior of MWCNT‐Al2O3/SAE50 hybrid nanofluid to provide the best nano‐lubrication conditions. Nanoscale Res. Lett.17(4), 1-13 (2022) https://doi.org/10.1186/s11671‐021‐03639‐3 · doi:10.1186/s11671‐021‐03639‐3 |
| [24] | Esfe, M.H., Toghraie, D., Mohammadnejad Ardeshiri, E., Experimental study of rheological behavior of MWCNT (50 · doi:10.1016/j.anucene.2022.109575 |
| [25] | Chamkha, A.J.: Non‐Darcy hydromagnetic free convection from a cone and a wedge in porous media. Int. Commun. Heat Mass Transf.23, 875-887 (1996) https://doi.org/10.1016/0735‐1933(96)00070‐X · doi:10.1016/0735‐1933(96)00070‐X |
| [26] | Chamkha, A.J.: Non‐Darcy fully developed mixed convection in a porous medium channel with heat generation/absorption and hydromagnetic effects. Numer. Heat Transf. Part A Appl.32, 653-675 (1997) https://doi.org/10.1080/10407789708913911 · doi:10.1080/10407789708913911 |
| [27] | Krishna, M.V., Ahammad, N.A., Chamkha, A.J.: Radiative MHD flow of Casson hybrid nanofluid over an infinite exponentially accelerated vertical porous surface. Case Stud. Therm. Eng.27, 101229 (2021) https://doi.org/10.1016/j.csite.2021.101229 · doi:10.1016/j.csite.2021.101229 |
| [28] | Magyari, E., Chamkha, A.J.: Combined effect of heat generation or absorption and first‐order chemical reaction on micropolar fluid flows over a uniformly stretched permeable surface: The full analytical solution. Int. J. Therm. Sci.49, 1821-1828 (2010) https://doi.org/10.1016/j.ijthermalsci.2010.04.007 · doi:10.1016/j.ijthermalsci.2010.04.007 |
| [29] | Chamkha, A.J., Issa, C., Khanafer, K.: Natural convection from an inclined plate embedded in a variable porosity porous medium due to solar radiation. Int. J. Therm. Sci.41, 73-81 (2002) https://doi.org/10.1016/S1290‐0729(01)01305‐9 · doi:10.1016/S1290‐0729(01)01305‐9 |
| [30] | Alghamdi, M., Wakif, A., Muhammad, T.: Efficient passive GDQLL scrutinization of an advanced steady EMHD mixed convective nanofluid flow problem via Wakif‐Buongiorno approach and generalized transport laws. Int. J. Mod. Phys. B2450418 (2024) https://doi.org/10.1142/S0217979224504186 · doi:10.1142/S0217979224504186 |
| [31] | Chamkha, A.J.: MHD‐free convection from a vertical plate embedded in a thermally stratified porous medium with Hall effects. Appl. Math21, 603-609 (1997) https://doi.org/10.1016/S0307‐904X(97)00084‐X · Zbl 0901.76077 · doi:10.1016/S0307‐904X(97)00084‐X |
| [32] | Takhar, H.S., Chamkha, A.J., Nath, G.: MHD flow over a moving plate in a rotating fluid with magnetic field, Hall currents and free stream velocity. Int. J. Eng. Sci.40, 1511-1527 (2002) https://doi.org/10.1016/S0020‐7225(02)00016‐2 · Zbl 1211.76157 · doi:10.1016/S0020‐7225(02)00016‐2 |
| [33] | Madhu, M., Kishan, N., Chamkha, A.J.: Unsteady flow of a Maxwell nanofluid over a stretching surface in the presence of magnetohydrodynamic and thermal radiation effects. Propuls. Power Res.6, 31-40 (2017) https://doi.org/10.1016/j.jppr.2017.01.002 · doi:10.1016/j.jppr.2017.01.002 |
| [34] | Chamkha, A.J., Khaled, A.‐R.A.: Similarity solutions for hydromagnetic simultaneous heat and mass transfer by natural convection from an inclined plate with internal heat generation or absorption. Heat Mass Transf.37, 117-123 (2001) https://doi.org/10.1007/s002310000131 · doi:10.1007/s002310000131 |
| [35] | Pandey, A.K., Kumar, M.: Chemical reaction and thermal radiation effects on boundary layer flow of nanofluid over a wedge with viscous and Ohmic dissipation. St. Petersbg. Polytech. Univ. J. Phys. Math.3, 322-332 (2017) https://doi.org/10.1016/j.spjpm.2017.10.008 · doi:10.1016/j.spjpm.2017.10.008 |
| [36] | Hassan, M., Ellahi, R., Bhatti, M.M., Zeeshan, A.: A comparative study on magnetic and non‐magnetic particles in nanofluid propagating over a wedge. Can. J. Phys.97, 277-285 (2018) https://doi.org/10.1139/cjp‐2018‐0159 · doi:10.1139/cjp‐2018‐0159 |
| [37] | Thameem Basha, H., Sivaraj, R., Subramanyam Reddy, A., Chamkha, A.J.: SWCNH/diamond‐ethylene glycol nanofluid flow over a wedge, plate and stagnation point with induced magnetic field and nonlinear radiation‐ solar energy application. Eur. Phys. J. Spec. Top228, 2531-2551 (2019) https://doi.org/10.1140/epjst/e2019‐900048‐x · doi:10.1140/epjst/e2019‐900048‐x |
| [38] | Ahmed, S.E., Arafa, A.A.M., Hussein, S.A., Raizah, Z.A.S.: Novel treatments for the bioconvective radiative Ellis nanofluids wedge flow with viscous dissipation and an activation energy. Case Stud. Therm. Eng.40, 102510 (2022) https://doi.org/10.1016/j.csite.2022.102510 · doi:10.1016/j.csite.2022.102510 |
| [39] | Vasu, B., Gorla, R.S.R., Bég, O.A., Murthy, P.V.S.N., Prasad, V.R., Kadir, A.: Unsteady flow of a nanofluid over a sphere with nonlinear Boussinesq approximation. J. Thermophys. Heat Transf.33, 343-355 (2018) https://doi.org/10.2514/1.T5516 · doi:10.2514/1.T5516 |
| [40] | Swalmeh, M.Z., Alkasasbeh, H.T., Hussanan, A., Mamat, M.: Heat transfer flow of Cu‐water and Al_2O_3‐water micropolar nanofluids about a solid sphere in the presence of natural convection using Keller‐box method. Results Phys.9, 717-724 (2018) https://doi.org/10.1016/j.rinp.2018.03.033 · doi:10.1016/j.rinp.2018.03.033 |
| [41] | Vedavathi, N., Dharmaiah, G., Noeiaghdam, S., Fernandez‐Gamiz, U.: A chemical engineering application on hyperbolic tangent flow examination about a sphere with Brownian motion and thermophoresis effects using BVP5C. Case Stud. Therm. Eng.40, 102491 (2022) https://doi.org/10.1016/j.csite.2022.102491 · doi:10.1016/j.csite.2022.102491 |
| [42] | Ramesh, G.K., Madhukesh, J.K., Shah, N.A, Yook, S.‐J.: Flow of hybrid CNTs past a rotating sphere subjected to thermal radiation and thermophoretic particle deposition. Alexandria Eng. J.64, 969-979 (2023) https://doi.org/10.1016/j.aej.2022.09.026 · doi:10.1016/j.aej.2022.09.026 |
| [43] | Koteswara Reddy, G., Yarrakula, K., Raju, C.S.K., Rahbari, A.: Mixed convection analysis of variable heat source/sink on MHD Maxwell, Jeffrey, and Oldroyd‐B nanofluids over a cone with convective conditions using Buongiorno’s model. J. Therm. Anal. Calorim.132, 1995-2002 (2018) https://doi.org/10.1007/s10973‐018‐7115‐0 · doi:10.1007/s10973‐018‐7115‐0 |
| [44] | Vedavathi, N., Dharmaiah, G., Abdul Gaffar, S., Venkatadri, K.: Entropy analysis of magnetohydrodynamic nanofluid transport past an inverted cone: Buongiorno’s model. Heat Transf.50, 3119-3153 (2021) https://doi.org/10.1002/htj.22021 · doi:10.1002/htj.22021 |
| [45] | Rana, P., Gupta, G.: FEM solution to quadratic convective and radiative flow of Ag‐MgO/H2O hybrid nanofluid over a rotating cone with Hall current: Optimization using response surface methodology. Math. Comput. Simul.201, 121-140 (2022) https://doi.org/10.1016/j.matcom.2022.05.012 · Zbl 1540.76191 · doi:10.1016/j.matcom.2022.05.012 |
| [46] | Dharmaiah, G., Dinarvand, S., Durgaprasad, P., Noeiaghdam, S.: Arrhenius activation energy of tangent hyperbolic nanofluid over a cone with radiation absorption. Results Eng. 16, 100745 (2022) https://doi.org/10.1016/j.rineng.2022.100745 · doi:10.1016/j.rineng.2022.100745 |
| [47] | Mehryan, S.A.M., Izadpanahi, E., Ghalambaz, M., Chamkha, A.J.: Mixed convection flow caused by an oscillating cylinder in a square cavity filled with Cu‐Al_2O_3/water hybrid nanofluid. J. Therm. Anal. Calorim.137, 965-982 (2019) https://doi.org/10.1007/s10973‐019‐08012‐2 · doi:10.1007/s10973‐019‐08012‐2 |
| [48] | Rooman, M., Jan, M.A., Shah, Z., Vrinceanu, N., Ferrándiz Bou, S., Iqbal, S., Deebani, W.: Entropy optimization on axisymmetric Darcy‐Forchheimer Powell‐Eyring nanofluid over a horizontally stretching cylinder with viscous dissipation effect. Coatings12, 1-15 (2022) https://doi.org/10.3390/coatings12060749 · doi:10.3390/coatings12060749 |
| [49] | Basha, H.T., Sivaraj, R., Prasad, V.R., Beg, O.A.: Entropy generation of tangent hyperbolic nanofluid flow over a circular cylinder in the presence of nonlinear Boussinesq approximation: A non‐similar solution. J. Therm. Anal. Calorim.143, 2273-2289 (2021) https://doi.org/10.1007/s10973‐020‐09981‐5 · doi:10.1007/s10973‐020‐09981‐5 |
| [50] | Ramzan, M., Shaheen, N., Chung, J.D., Kadry, S., Chu, Y.M., Howari, F.: Impact of Newtonian heating and Fourier and Fick’s laws on a magnetohydrodynamic dusty Casson nanofluid flow with variable heat source/sink over a stretching cylinder. Sci. Rep.11, 1-19 (2021) https://doi.org/10.1038/s41598‐021‐81747‐x · doi:10.1038/s41598‐021‐81747‐x |
| [51] | Schlichting, H., Gersten, K.: Boundary‐layer theory. Springer, Berlin, Heidelberg (2017) https://doi.org/10.1007/978‐3‐662‐52919‐5 · Zbl 1358.76001 · doi:10.1007/978‐3‐662‐52919‐5 |
| [52] | Blasius, H.: Boundary layers in fluids of small viscosity. Z Math Phys. 56, 1-37 (1908) · JFM 39.0803.02 |
| [53] | Hiemenz, K.: Die Grenzschicht an einem in den gleichformigen Flussigkeitsstrom eingetauchten geraden Kreiszylinder. Dinglers Polytech. J.326, 321-324 (1911) |
| [54] | Falkner, V.M., Skan, S.W.: Some approximate solutions of the boundary layer equations. Philos. Mag.12, 865-896 (1931) https://doi.org/10.1080/14786443109461870 · Zbl 0003.17401 · doi:10.1080/14786443109461870 |
| [55] | Sakiadis, B.C.: Boundary‐layer behavior on continuous solid surfaces: I. Boundary‐layer equations for two‐dimensional and axisymmetric flow. AIChE J.7, 26-28 (1961) https://doi.org/10.1002/aic.690070108 · doi:10.1002/aic.690070108 |
| [56] | Sakiadis, B.C.: Boundary‐layer behavior on continuous solid surfaces: II. The boundary layer on a continuous flat surface. AIChE J.7, 221-225 (1961) https://doi.org/10.1002/aic.690070211 · doi:10.1002/aic.690070211 |
| [57] | Sakiadis, B.C.: Boundary‐layer behavior on continuous solid surfaces: III. The boundary layer on a continuous cylindrical surface. AIChE J.7, 467-472 (1961) |
| [58] | Rasool, G., Wakif, A., Wang, X., Alshehri, A., Saeed, A.M.: Falkner‐Skan aspects of a radiating (50 · doi:10.1016/j.jppr.2023.07.001 |
| [59] | Sreenivasa, B.R., Faqeeh, A.J., Alsaiari, A., Alzahrani, H.A.H., Malik, M.Y.: Numerical study of heat transfer mechanism in the flow of ferromagnetic hybrid nanofluid over a stretching cylinder. Waves Random Complex Media1-17 (2022) https://doi.org/10.1080/17455030.2022.2061084 · doi:10.1080/17455030.2022.2061084 |
| [60] | Sowmya, G., Gamaoun, F., Abdulrahman, A., Varun Kumar, R.S., Prasannakumara, B.C.: Significance of thermal stress in a convective‐radiative annular fin with magnetic field and heat generation: application of DTM and MRPSM. Propuls. Power Res.11, 527-543 (2022) https://doi.org/10.1016/j.jppr.2022.11.001 · doi:10.1016/j.jppr.2022.11.001 |
| [61] | Varun Kumar, R.S., Alsulami, M.D., Sarris, I.E., Prasannakumara, B.C., Rana, S.Backpropagated neural network modeling for the non‐fourier thermal analysis of a moving plate. Mathematics11, 1-32 (2023) https://doi.org/10.3390/math11020438 · doi:10.3390/math11020438 |
| [62] | Krishnamurthy, M., Reddy, R.G., Alsulami, M.D., Prasannakumara, B.C.: Numerical investigation on the effect of electrical force and periodic force on neutrally buoyant spherical particles in a Newtonian fluid at low Reynolds numbers. Int. Commun. Heat Mass Transf.135, 106157 (2022) https://doi.org/10.1016/j.icheatmasstransfer.2022.106157 · doi:10.1016/j.icheatmasstransfer.2022.106157 |
| [63] | Gamaoun, F., Ullah, Z., Ameer Ahammad, N., Fadhl, B.M., Makhdoum, B.M., Abbas Khan, A.: Effects of thermal radiation and variable density of nanofluid heat transfer along a stretching sheet by using Keller Box approach under magnetic field. Therm. Sci. Eng. Prog.41, 101815 (2023) https://doi.org/10.1016/j.tsep.2023.101815 · doi:10.1016/j.tsep.2023.101815 |
| [64] | Buongiorno, J.: Convective transport in nanofluids. J. Heat Transfer128, 240-250 (2006) https://doi.org/10.1115/1.2150834 · doi:10.1115/1.2150834 |
| [65] | Hassan, M., Rizwan, M., Bhatti, M.M.: Investigating the influence of temperature‐dependent rheological properties on nanofluid behavior in heat transfer. Nanotechnology34, 505404 (2023) https://doi.org/10.1088/1361‐6528/acfb15 · doi:10.1088/1361‐6528/acfb15 |
| [66] | Hsu, C.‐Y., Satpathy, G., Al Kamzari, F.I., Manikandan, E., Ajaj, Y., Al Kindi, A.S.: Thermophysical characteristics of nanofluids: A review. In: Malik, J.A. (ed.), Sadiq Mohamed (ed.), M.J. (ed.) (eds.) Mod. Nanotechnol. Vol. 2 Green Synth. Sustain. Energy Impacts, pp. 337-362. Springer Nature Switzerland, Cham (2023) https://doi.org/10.1007/978‐3‐031‐31104‐8_15 · doi:10.1007/978‐3‐031‐31104‐8_15 |
| [67] | Estellé, P., Żyła, G.: Advances in rheological behavior of nanofluids and ion‐nanofluids—An editorial note. J. Mol. Liq.362, 119669 (2022) https://doi.org/10.1016/j.molliq.2022.119669 · doi:10.1016/j.molliq.2022.119669 |
| [68] | Alarifi, I.M., Alkouh, A.B., Ali, V., Nguyen, H.M., Asadi, A.: On the rheological properties of MWCNT‐TiO2/oil hybrid nanofluid: An experimental investigation on the effects of shear rate, temperature, and solid concentration of nanoparticles. Powder. Technol.355, 157-162 (2019) https://doi.org/10.1016/j.powtec.2019.07.039 · doi:10.1016/j.powtec.2019.07.039 |
| [69] | Yan, S.‐R., Kalbasi, R., Nguyen, Q., Karimipour, A.: Rheological behavior of hybrid MWCNTs‐TiO2/EG nanofluid: A comprehensive modeling and experimental study. J. Mol. Liq.308, 113058 (2020) https://doi.org/10.1016/j.molliq.2020.113058 · doi:10.1016/j.molliq.2020.113058 |
| [70] | Harchaoui, A., Mazouzi, R., Karas, A.: The rheology of nanolubricants based on Fe_2O_3, Al_2O_3, and ZnO oxide nanoparticles: A comparative study. Phys. Chem. Res.11, 181-189 (2023) https://doi.org/10.22036/pcr.2022.328709.2027 · doi:10.22036/pcr.2022.328709.2027 |
| [71] | Lamraoui, H., Mansouri, K., Saci, R.: Numerical investigation on fluid dynamic and thermal behavior of a non‐Newtonian Al_2O_3‐water nanofluid flow in a confined impinging slot jet. J. Nonnewton Fluid Mech.265, 11-27 (2019) https://doi.org/10.1016/j.jnnfm.2018.12.011 · doi:10.1016/j.jnnfm.2018.12.011 |
| [72] | Nobakht Hassanlouei, R., Jahangiri, M., Dawi, E.A., Vafaee, F., Salavati‐Niasari, M.: The new correlation for viscosity of synthesized viscoelastic‐based nanoliquid using functionalized MWCNT: Stability, thermal conductivity, and rheology. Alexandria Eng. J.72, 495-509 (2023) https://doi.org/10.1016/j.aej.2023.04.003 · doi:10.1016/j.aej.2023.04.003 |
| [73] | Hosseinzadeh, K., Mardani, M.R., Paikar, M., Hasibi, A., Tavangar, T., Nimafar, M., Ganji, D.D., Shafii, M.B.: Investigation of second grade viscoelastic non‐Newtonian nanofluid flow on the curve stretching surface in presence of MHD. Results Eng. 17, 100838 (2023) https://doi.org/10.1016/j.rineng.2022.100838 · doi:10.1016/j.rineng.2022.100838 |
| [74] | Abbas, N., Ali, M., Shatanawi, W.: Chemical reactive second‐grade nanofluid flow past an exponential curved stretching surface: Numerically. Int. J. Mod. Phys. B, 2450026 (2023) https://doi.org/10.1142/S0217979224500267 · doi:10.1142/S0217979224500267 |
| [75] | Tiwari, R.K., Das, M.K.: Heat transfer augmentation in a two‐sided lid‐driven differentially heated square cavity utilizing nanofluids. Int. J. Heat Mass Transf.50, 2002-2018 (2007) https://doi.org/10.1016/j.ijheatmasstransfer.2006.09.034 · Zbl 1124.80371 · doi:10.1016/j.ijheatmasstransfer.2006.09.034 |
| [76] | Shah, R.A., Rehman, S., Idrees, M., Ullah, M., Abbas, T.: Similarity analysis of MHD flow field and heat transfer of a second grade convection flow over an unsteady stretching sheet. Bound. Value Probl. 2017(162), 1-20 (2017) https://doi.org/10.1186/s13661‐017‐0895‐5 · Zbl 1379.35251 · doi:10.1186/s13661‐017‐0895‐5 |
| [77] | Mizerski, K.A.: The Oberbeck‐Boussinesq convection bt‐foundations of convection with density stratification. Springer International Publishing, Cham (2021) https://doi.org/10.1007/978‐3‐030‐63054‐6_2 · doi:10.1007/978‐3‐030‐63054‐6_2 |
| [78] | Rosseland, S.: Astrophysik und Atom‐Theoretische Grundlagen. Springer Verlag, Berlin (1931) · JFM 57.1616.05 |
| [79] | Wakif, A., Boulahia, Z., Mishra, S.R., Rashidi, M.M., Sehaqui, R.: Influence of a uniform transverse magnetic field on the thermo‐hydrodynamic stability in water‐based nanofluids with metallic nanoparticles using the generalized Buongiorno’s mathematical model. Eur. Phys. J. Plus133, 1-16 (2018) https://doi.org/10.1140/epjp/i2018‐12037‐7 · doi:10.1140/epjp/i2018‐12037‐7 |
| [80] | Wakif, A., Boulahia, Z., Ali, F., Eid, M.R., Sehaqui, R.: Numerical analysis of the unsteady natural convection MHD couette nanofluid flow in the presence of thermal radiation using single and two‐phase nanofluid models for Cu‐water nanofluids. Int. J. Appl. Comput. Math.4(81), 1-27 (2018) https://doi.org/10.1007/s40819‐018‐0513‐y · Zbl 1442.76155 · doi:10.1007/s40819‐018‐0513‐y |
| [81] | Wakif, A., Chamkha, A., Thumma, T., Animasaun, I.L., Sehaqui, R.: Thermal radiation and surface roughness effects on the thermo‐magneto‐hydrodynamic stability of alumina‐copper oxide hybrid nanofluids utilizing the generalized Buongiorno’s nanofluid model. J. Therm. Anal. Calorim.143, 1201-1220 (2021) https://doi.org/10.1007/s10973‐020‐09488‐z · doi:10.1007/s10973‐020‐09488‐z |
| [82] | Gholinia, M., Gholinia, S., Hosseinzadeh, K., Ganji, D.D.: Investigation on ethylene glycol Nano fluid flow over a vertical permeable circular cylinder under effect of magnetic field. Results Phys.9, 1525-1533 (2018) https://doi.org/10.1016/j.rinp.2018.04.070 · doi:10.1016/j.rinp.2018.04.070 |
| [83] | Nayak, M.K., Wakif, A., Animasaun, I.L., Alaoui, M.S.H.: Numerical differential quadrature examination of steady mixed convection nanofluid flows over an isothermal thin needle conveying metallic and metallic oxide nanomaterials: A comparative investigation, Arab. J. Sci. Eng.45, 5331-5346 (2020) https://doi.org/10.1007/s13369‐020‐04420‐x · doi:10.1007/s13369‐020‐04420‐x |
| [84] | Zhang, K., Shah, N.A., Alshehri, M., Alkarni, S., Wakif, A., Eldin, S.M.: Water thermal enhancement in a porous medium via a suspension of hybrid nanoparticles: MHD mixed convective Falkner’s‐Skan flow case study. Case Stud. Therm. Eng.47, 103062 (2023) https://doi.org/10.1016/j.csite.2023.103062 · doi:10.1016/j.csite.2023.103062 |
| [85] | Elboughdiri, N., Reddy, C.S., Alshehri, A., Eldin, S.M., Muhammad, T., Wakif, A.: A passive control approach for simulating thermally enhanced Jeffery nanofluid flows nearby a sucked impermeable surface subjected to buoyancy and Lorentz forces. Case Stud. Therm. Eng.47, 103106 (2023) https://doi.org/10.1016/j.csite.2023.103106 · doi:10.1016/j.csite.2023.103106 |
| [86] | Wakif, A., Shah, N.A.: Hydrothermal and mass impacts of azimuthal and transverse components of Lorentz forces on reacting Von Kármán nanofluid flows considering zero mass flux and convective heating conditions. Waves Random Complex Media1-22 (2022) https://doi.org/10.1080/17455030.2022.2136413 · doi:10.1080/17455030.2022.2136413 |
| [87] | Rasool, G., Shah, N.A., El‐Zahar, E.R., Wakif, A.: Numerical investigation of EMHD nanofluid flows over a convectively heated Riga pattern positioned horizontally in a Darcy‐Forchheimer porous medium: Application of passive control strategy and generalized transfer laws. Waves Random Complex Media1-20 (2022) https://doi.org/10.1080/17455030.2022.2074571 · doi:10.1080/17455030.2022.2074571 |
| [88] | Wakif, A., Sehaqui, R.: Generalized differential quadrature scrutinization of an advanced MHD stability problem concerned water‐based nanofluids with metal/metal oxide nanomaterials: A proper application of the revised two‐phase nanofluid model with convective heating and throug. Numer. Methods Partial Differ. Equ.38, 608-635 (2022) https://doi.org/10.1002/num.22671 · Zbl 1535.65240 · doi:10.1002/num.22671 |
| [89] | Wakif, A., Abderrahmane, A., Guedri, K., Bouallegue, B., Kaewmesri, P., Kaewthongrach, R., Channumsin, S., Sreesawet, S., Bumrungkit, A., Jirawattanapanit, P.: Importance of exponentially falling variability in heat generation on chemically reactive von kármán nanofluid flows subjected to a radial magnetic field and controlled locally by zero mass flux and convective heating conditions: A differential quadrature. Front. Phys.10, 1-17 (2022) https://doi.org/10.3389/fphy.2022.988275 · doi:10.3389/fphy.2022.988275 |
| [90] | Rasool, G., Ahammad, N.A., Ali, M.R., Shah, N.A., Wang, X., Shafiq, A., Wakif, A.: Hydrothermal and mass aspects of MHD non‐Darcian convective flows of radiating thixotropic nanofluids nearby a horizontal stretchable surface: Passive control strategy. Case Stud. Therm. Eng.42, 102654 (2023) https://doi.org/10.1016/j.csite.2022.102654 · doi:10.1016/j.csite.2022.102654 |
| [91] | Shu, C.: Differential quadrature and its application in engineering. Springer Science & Business Media, London (2012) |
| [92] | Ishak, A., Nazar, R., Pop, I.: Boundary layer flow and heat transfer over an unsteady stretching vertical surface. Meccanica.44, 369-375 (2009) https://doi.org/10.1007/s11012‐008‐9176‐9 · Zbl 1241.76355 · doi:10.1007/s11012‐008‐9176‐9 |
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