Abstract
The present study introduces the simultaneous effects of local thermal non-equilibrium (LTNE), heat source and magnetic field on thermal instability to the onset of convection in electrically conducting Al\(_2\)O\(_3\)–Cu/water hybrid nanoliquid flowing through parallel plates with rough boundaries. The Saffman-interface condition is incorporated for non-neglecting surface roughness. Linear stability analysis in longitudinal mode is performed by constructing eigenvalue problem, which is solved numerically using finite difference code with three-stage Lobatto IIIa formula and compared with Runge Kutta shooting method. The present numerical code for limiting cases, i.e. free–free, rigid–rigid, rigid–free boundaries, is also compared with Galerkin method (number of terms, \(N_{\max }= 15\)). Increasing the values of roughness parameters (\(\lambda _1\), \(\lambda _2\)), LTNE parameter (\(N_{\text {H}}\)), Heat source/sink (\(S_{\text {bl}}, S_{\text {np}}\)) and Chandrashekar number (Q) favours the convection, thus destablizes the system whereas Lewis number (Le) follows the opposite trend. The artificial neural network with four input variables for predicting the critical Rayleigh number using Levenberg–Marquardt back propagation algorithm, is also presented. The optimal number of neurons in the hidden layer is selected on the basis of coefficient of determination (\(R^2\)), root mean square error and root mean relative error. Finally, the simulated and predicted results are compared and in good agreement.
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Adun H, Wole-Osho I, Okonkwo EC, Bamisile O, Dagbasi M, Abbasoglu S (2020) A neural network-based predictive model for the thermal conductivity of hybrid nanofluids. Int Commun Heat Mass Transf 119:104930
Agarwal S, Rana P (2015) Thermal stability analysis of rotating porous layer with thermal non-equilibrium approach utilizing \(Al_2O_3\)-EG oldroyd-b nanofluid. Microfluid Nanofluid 19(1):117–131
Agarwal S, Rana P (2016) Nonlinear convective analysis of a rotating oldroyd-b nanofluid layer under thermal non-equilibrium utilizing \(Al_2 O_3\)-EG colloidal suspension. Eur Phys J Plus 131(4):101
Agarwal S, Rana P, Bhadauria B (2014) Rayleigh-benard convection in a nanofluid layer using a thermal nonequilibrium model. J Heat Transf 136(12):122501
Ahmad S, Nadeem S (2020) Cattaneo-Christov-based study of SWCNT-MWCNT/EG Casson hybrid nanofluid flow past a lubricated surface with entropy generation. Appl Nanosci 10:5449–5458
Ahmad S, Nadeem S, Khan MN (2021) Enhanced transport properties and its theoretical analysis in two-phase hybrid nanofluid. Appl Nanosci. https://doi.org/10.1007/s13204-020-01634-1
Ahmadi MH, Ghazvini M, Maddah H, Kahani M, Pourfarhang S, Pourfarhang A, Heris SZ (2020) Prediction of the pressure drop for CuO/(Ethylene glycol-water) nanofluid flows in the car radiator by means of Artificial Neural Networks analysis integrated with genetic algorithm. Phys A Stat Mech Appl 546:124008
Ahmed J, Shahzad A, Farooq A, Kamran M, Khan SU-D, Khan SU-D (2020) Radiative heat transfer in Homann stagnation-point flow of hybrid nanofluid. Applied Nanoscience 10:5305–5314
Akbarzadeh P, Mahian O (2018) The onset of nanofluid natural convection inside a porous layer with rough boundaries. J Mol Liq 272:344–352
Albatati F, Rana P, Li Z (2021) External field impact on expedition of discharging including nanoparticles. J Mol Liq 335:116134
Asteris PG, Tsaris AK, Cavaleri L, Repapis CC, Papalou A, Di Trapani F, Karypidis DF (2015) Prediction of the fundamental period of infilled rc frame structures using artificial neural networks. Comput Intell Neurosci 2016:e510490
Barletta A, Celli M, Lagziri H (2015) Instability of a horizontal porous layer with local thermal non-equilibrium: effects of free surface and convective boundary conditions. Int J Heat Mass Transf 89:75–89
Bhadauria B, Hashim I, Siddheshwar P (2013) Effect of internal-heating on weakly non-linear stability analysis of rayleigh-bénard convection under g-jitter. Int J Non-Linear Mech 54:35–42
Bujurke N, Basti D, Kudenatti RB (2008) Surface roughness effects on squeeze film behavior in porous circular disks with couple stress fluid. Transp Porous Media 71(2):185–197
Buongiorno J (2006) Convective transport in nanofluids. J Heat Transf 128(3):240–250
Celli M, Kuznetsov AV (2018) A new hydrodynamic boundary condition simulating the effect of rough boundaries on the onset of rayleigh-bénard convection. Int J Heat Mass Transf 116:581–586
Celli M, Barletta A, Storesletten L (2013) Local thermal non-equilibrium effects in the darcy-bénard instability of a porous layer heated from below by a uniform flux. Int J Heat Mass Transf 67:902–912
Chamkha AJ, Aly A (2010) Mhd free convection flow of a nanofluid past a vertical plate in the presence of heat generation or absorption effects. Chem Eng Commun 198(3):425–441
Chandrasekhar S (1961) Hydrodynamic and hydromagnetic stability. Oxford University Press, New York
Chen S, Hassanzadeh-Aghdam M, Ansari R (2018) An analytical model for elastic modulus calculation of sic whisker-reinforced hybrid metal matrix nanocomposite containing sic nanoparticles. J Alloy Compd 767:632–641
Chen X, Wang D, Wang T, Yang Z, Zou X, Wang P, Luo W, Li Q, Liao L, Hu W et al (2019) Enhanced photoresponsivity of a gas nanowire metal-semiconductor-metal photodetector by adjusting the fermi level. ACS Appl Mater Interfaces 11(36):33188–33193
Chivers T (2002) The influence of surface roughness on fluid flow through cracks. Fatigue Fract Eng Mater Struct 25(11):1095–1102
Cho HW, Park YG, Seo YM, Ha MY (2020) Prediction of the heat transfer performance of mixed convection in a lid-driven enclosure with an elliptical cylinder using an artificial neural network. Num Heat Transf Part A Appl 78:29–47. https://doi.org/10.1080/10407782.2020.1777793
Choi SU, Eastman JA (1995) Enhancing thermal conductivity of fluids with nanoparticles. Tech. rep., Argonne National Lab., IL (United States)
Dierich F, Nikrityuk P (2013) A numerical study of the impact of surface roughness on heat and fluid flow past a cylindrical particle. Int J Therm Sci 65:92–103
Duan Z, Yin Q, Li C, Dong L, Bai X, Zhang Y, Yang M, Jia D, Li R, Liu Z (2020) Milling force and surface morphology of 45 steel under different al 2 o 3 nanofluid concentrations. Int J Adv Manuf Technol 107(3):1277–1296
Gao T, Li C, Zhang Y, Yang M, Jia D, Jin T, Hou Y, Li R (2019) Dispersing mechanism and tribological performance of vegetable oil-based cnt nanofluids with different surfactants. Tribol Int 131:51–63
Gao T, Li C, Jia D, Zhang Y, Yang M, Wang X, Cao H, Li R, Ali HM, Xu X (2020) Surface morphology assessment of cfrp transverse grinding using cnt nanofluid minimum quantity lubrication. J Clean Prod 277:123328
Gupta Y, Rana P (2021) MHD natural convection in inclined wavy annulus utilizing hybrid nanofluid with discrete wavy coolers. J Therm Anal Calorim 143:1303–1318
Haynes WM (2014) CRC handbook of chemistry and physics. CRC Press, Boca Raton
He W, Ruhani B, Toghraie D, Izadpanahi N, Esfahani NN, Karimipour A, Afrand M (2020) Using of artificial neural networks (ANNs) to predict the thermal conductivity of Zinc Oxide Silver (50%-50%)/Water hybrid Newtonian nanofluid. Int Commun Heat Mass Transf 116:104645
Holman JP (2008) Heat transfer. Tata Mcgraw Hill, Ninth Edition, New Delhi
Jama M, Singh T, Gamaleldin SM, Koc M, Samara A, Isaifan RJ, Atieh MA (2016) Critical review on nanofluids. J Nanomater 2016:26
Jambunathan K, Hartle SL, Ashforth-Frost S, Fontama VN (1996) Evaluating convective heat transfer coefficients using neural networks. Int J Heat Mass Transf 39:2329–2332
Khurana M, Rana P, Srivastava S (2016) Influence of the combined effect of magnetic field and rotation on the onset of a non-newtonian viscoelastic nanofluid layer: Linear and nonlinear analyses. The European Physical Journal Plus 131(12):437
Koo J, Kleinstreuer C (2005) Analysis of surface roughness effects on heat transfer in micro-conduits. Int J Heat Mass Transf 48(13):2625–2634
Kunert C, Harting J (2007) Roughness induced boundary slip in microchannel flows. Phys Rev Lett 99(17):176001
Kuznetsov A (2004) Numerical modeling of turbulent flow in a composite porous/fluid duct utilizing a two-layer k-\(\varepsilon\) model to account for interface roughness. Int J Therm Sci 43(11):1047–1056
Lilly T, Duncan J, Nothnagel S, Gimelshein S, Gimelshein N, Ketsdever A, Wysong I (2007) Numerical and experimental investigation of microchannel flows with rough surfaces. Phys Fluids 19(10):106101
Liu Y, Xu G, Sun J, Li H (2015) Investigation of the roughness effect on flow behavior and heat transfer characteristics in microchannels. Int J Heat Mass Transf 83:11–20
Nield DA, Kuznetsov AV (2003) Investigation of forced convection in an almost circular microtube with rough walls. Int J Fluid Mech Res 30(1)
Nield D, Kuznetsov A (2010) The effect of local thermal nonequilibrium on the onset of convection in a nanofluid. J Heat Transf 132(5):052405
Rabbi KM, Sheikholeslami M, Karim A, Shafee A, Li Z, Tlili I (2020) Prediction of MHD flow and entropy generation by Artificial Neural Network in square cavity with heater-sink for nanomaterial. Phys A Stat Mech Appl 541:123520
Rana P, Khurana M (2020) LTNE thermoconvective instability in newtonian rotating layer under magnetic field utilizing nanoparticles. J Therm Anal Calorimetry. https://doi.org/10.1007/s10973-020-10301-0
Rana P, Shehzad S, Ambreen T, Selim MM (2021) Numerical study based on CVFEM for nanofluid radiation and magnetized natural convected heat transportation. J Mol Liq 334:116102
Revathi G, Sajja VS, Babu MJ, Raju CSK, Shehzad SA, Bapanayya C (2021) Entropy optimization in hybrid radiative nanofluid (CH3OH+SiO2+Al2O3) flow by a curved stretching sheet with cross-diffusion effects. Appl Nanosci. https://doi.org/10.1007/s13204-021-01679-w
Rostami S, Toghraie D, Esfahani MA, Hekmatifar M, Sina N (2021) Predict the thermal conductivity of SiO2/water-ethylene glycol (50:50) hybrid nanofluid using artificial neural network. J Therm Anal Calorim 143:1119–1128
Safaei MR, Hajizadeh A, Afrand M, Qi C, Yarmand H, Zulkifli NWBM (2019) Evaluating the effect of temperature and concentration on the thermal conductivity of ZnO-\(TiO_2\)/EG hybrid nanofluid using artificial neural network and curve fitting on experimental data. Phys A 519:209–216
Saffman PG (1971) On the boundary condition at the surface of a porous medium. Stud Appl Math 50(2):93–101
Sajid MU, Ali HM (2019) Recent advances in application of nanofluids in heat transfer devices: a critical review. Renew Sustain Energy Rev 103:556–592
Santra AK, Chakraborty N, Sen S (2009) Prediction of heat transfer due to presence of copper-water nanofluid using resilient-propagation neural network. Int J Therm Sci 48:1311–1318
Seo YM, Luo K, Ha MY, Park YG (2020) Direct numerical simulation and artificial neural network modeling of heat transfer characteristics on natural convection with a sinusoidal cylinder in a long rectangular enclosure. Int J Heat Mass Transf 152:119564
Sheikholeslami M, Gerdroodbary MB, Moradi R, Shafee A, Li Z (2019) Application of Neural Network for estimation of heat transfer treatment of \(Al_2O_3\)-H2O nanofluid through a channel. Comput Methods Appl Mech Eng 344:1–12
Sheikholeslami M, Farshad SA, Ebrahimpour Z, Said Z (2021) Recent progress on flat plate solar collectors and photovoltaic systems in the presence of nanofluid: a review. J Clean Prod 293:126119
Shishkina O, Wagner C (2011) Modelling the influence of wall roughness on heat transfer in thermal convection. J Fluid Mech 686:568–582
Shukla N, Rana P, Pop I (2020) Second law thermodynamic analysis of thermo-magnetic Jeffery-Hamel dissipative radiative hybrid nanofluid slip flow: existence of multiple solutions. Eur Phys J Plus 135:849
Sukhatme SP (2006) Heat transfer. Universities Press
Tafarroj MM, Mahian O, Kasaeian A, Sakamatapan K, Dalkilic AS, Wongwises S (2017) Artificial neural network modeling of nanofluid flow in a microchannel heat sink using experimental data. Int Commun Heat Mass Transf 86:25–31
Taghavifar H, Taghavifar H, Mardani A, Mohebbi A, Khalilarya S, Jafarmadar S (2016) Appraisal of artificial neural networks to the emission analysis and prediction of CO2, soot, and NOx of n-heptane fueled engine. J Clean Prod 112:1729–1739
Taylor JB, Carrano AL, Kandlikar SG (2006) Characterization of the effect of surface roughness and texture on fluid flow-past, present, and future. Int J Therm Sci 45(10):962–968
Vadasz P (2006) Heat conduction in nanofluid suspensions. J Heat Transf 128(5):465–477
Vögler A, Shelyag S, Schüssler M, Cattaneo F, Emonet T, Linde T (2005) Simulations of magneto-convection in the solar photosphere-equations, methods, and results of the muram code. Astron Astrophys 429(1):335–351
Waini I, Ishak A, Pop I (2020) Hiemenz flow over a shrinking sheet in a hybrid nanofluid. Res Phys 19:103351
Wakif A, Boulahia Z, Sehaqui R (2016) Numerical study of a thermal convection induced by a purely internal heating in a rotating medium saturated by a radiating nanofluid. Int J Comput Appl 135(10):33–42
Wakif A, Boulahia Z, Sehaqui R (2018) A semi-analytical analysis of electro-thermo-hydrodynamic stability in dielectric nanofluids using buongiorno’s mathematical model together with more realistic boundary conditions. Res Phys 9:1438–1454
Wakif A, Chamkha A, Thumma T, Animasaun I, Sehaqui R (2020) 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 Calorimetry 143:1201–1220
Wang Q, Xie G, Zeng M, Luo L (2006) Prediction of heat transfer rates for shell-and-tube heat exchangers by artificial neural networks approach. J Therm Sci 15:257–262
Wang X, Li C, Zhang Y, Ding W, Yang M, Gao T, Cao H, Xu X, Wang D, Said Z et al (2020a) Vegetable oil-based nanofluid minimum quantity lubrication turning: academic review and perspectives. J Manuf Process 59:76–97
Wang P, Zhang X, Duan W, Teng W, Liu Y, Xie Q (2020b) Superhydrophobic flexible supercapacitors formed by integrating hydrogel with functional carbon nanomaterials. Chin J Chem. https://doi.org/10.1002/cjoc.202000543
Xie GN, Wang QW, Zeng M, Luo LQ (2007) Heat transfer analysis for shell-and-tube heat exchangers with experimental data by artificial neural networks approach. Appl Therm Eng 27:1096–1104
Yadav D, Kim C, Lee J, Cho HH (2015a) Influence of magnetic field on the onset of nanofluid convection induced by purely internal heating. Comput Fluids 121:26–36
Yadav N, Yadav A, Kumar M et al (2015b) An introduction to neural network methods for differential equations. Springer, Berlin
Yadav D, Wang J, Bhargava R, Lee J, Cho HH (2016) Numerical investigation of the effect of magnetic field on the onset of nanofluid convection. Appl Therm Eng 103:1441–1449
Yu C, Shih Y (1980) Thermal instability of an internally heated fluid layer in a magnetic field. Phys Fluids 23(2):411–412
Yu H, Wilamowski BM (2011) Levenberg-marquardt training. Ind Electron Handb 5(12):1
Zhang J, Wu W, Li C, Yang M, Zhang Y, Jia D, Hou Y, Li R, Cao H, Ali HM (2020) Convective heat transfer coefficient model under nanofluid minimum quantity lubrication coupled with cryogenic air grinding ti–6al–4v. Int J Precis Eng Manuf Green Technol. https://doi.org/10.1007/s40684-020-00268-6
Zhenjing D, Changhe L, Zhang Y, Lan D, Xiufang B, Min Y, Dongzhou J, Runze L, Huajun C, Xuefeng X (2021) Milling surface roughness for 7050 aluminum alloy cavity influenced by nozzle position of nanofluid minimum quantity lubrication. Chin J Aeronaut 34(6):33–53
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Rana, P., Gupta, V. & Kumar, L. LTNE magneto-thermal stability analysis on rough surfaces utilizing hybrid nanoparticles and heat source with artificial neural network prediction. Appl Nanosci 13, 819–838 (2023). https://doi.org/10.1007/s13204-021-01913-5
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DOI: https://doi.org/10.1007/s13204-021-01913-5