In this paper, the Levenberg-Marquardt backpropagation scheme is used to develop a neural network model for the examination of the fluid flow on a magnetized flat surface with slip boundaries. The tangent hyperbolic fluid is considered along with heat generation, velocity, and thermal slip effects at the surface. The problem is modelled in terms of a non-linear differential system and Lie symmetry is used to get the scaling group of transformation. The order reduction of differential equations is done by using Lie transformation. The reduced system is solved by the shooting method. The surface quantity, namely skin friction, is evaluated at the surface for the absence and presence of an externally applied magnetic field. A total of 88 sample values are estimated for developing an artificial neural network model to predict skin friction coefficient (SFC). Weissenberg number, magnetic field parameter, and power law index are considered three inputs in the first layer, while 10 neurons are taken in the hidden layer. 62 (70%), 13 (15%), and 13 (15%) samples are used for training, validation, and testing, respectively. The Levenberg-Marquardt backpropagation is used to train the network by entertaining the random 62 sample values. Both mean square error and regression analysis are used to check the performance of the developed neural networking model. The SFC is noticed to be high at a magnetized surface for power law index and Weissenberg number.
Citation: Khalil Ur Rehman, Wasfi Shatanawi, Zead Mustafa. Artificial intelligence (AI) based neural networks for a magnetized surface subject to tangent hyperbolic fluid flow with multiple slip boundary conditions[J]. AIMS Mathematics, 2024, 9(2): 4707-4728. doi: 10.3934/math.2024227
In this paper, the Levenberg-Marquardt backpropagation scheme is used to develop a neural network model for the examination of the fluid flow on a magnetized flat surface with slip boundaries. The tangent hyperbolic fluid is considered along with heat generation, velocity, and thermal slip effects at the surface. The problem is modelled in terms of a non-linear differential system and Lie symmetry is used to get the scaling group of transformation. The order reduction of differential equations is done by using Lie transformation. The reduced system is solved by the shooting method. The surface quantity, namely skin friction, is evaluated at the surface for the absence and presence of an externally applied magnetic field. A total of 88 sample values are estimated for developing an artificial neural network model to predict skin friction coefficient (SFC). Weissenberg number, magnetic field parameter, and power law index are considered three inputs in the first layer, while 10 neurons are taken in the hidden layer. 62 (70%), 13 (15%), and 13 (15%) samples are used for training, validation, and testing, respectively. The Levenberg-Marquardt backpropagation is used to train the network by entertaining the random 62 sample values. Both mean square error and regression analysis are used to check the performance of the developed neural networking model. The SFC is noticed to be high at a magnetized surface for power law index and Weissenberg number.
| [1] |
B. Manvi, J. Tawade, M. Biradar, S. Noeiaghdam, U. Fernandez-Gamiz, V. Govindan, The effects of MHD radiating and non-uniform heat source/sink with heating on the momentum and heat transfer of Eyring-Powell fluid over a stretching, Results Eng., 14 (2022), 100435. https://doi.org/10.1016/j.rineng.2022.100435 doi: 10.1016/j.rineng.2022.100435
|
| [2] |
H. Shahzad, Q. U. Ain, A. A. Pasha, K. Irshad, I. A. Shah, A. Ghaffari, et al., Double-diffusive natural convection energy transfer in magnetically influenced Casson fluid flow in trapezoidal enclosure with fillets, Int. Commun. Heat Mass, 137 (2022), 106236. https://doi.org/10.1016/j.icheatmasstransfer.2022.106236 doi: 10.1016/j.icheatmasstransfer.2022.106236
|
| [3] |
A. A. Pasha, M. M. Alam, T. Tayebi, S. Kasim, A. S. Dogonchi, K. Irshad, et al., Heat transfer and irreversibility evaluation of non-Newtonian nanofluid density-driven convection within a hexagonal-shaped domain influenced by an inclined magnetic field, Case Stud. Therm. Eng., 41 (2023), 102588. https://doi.org/10.1016/j.csite.2022.102588 doi: 10.1016/j.csite.2022.102588
|
| [4] |
C. N. Guled, J. V. Tawade, P. Kumam, S. Noeiaghdam, I. Maharudrappa, S. M. Chithra, et al., The heat transfer effects of MHD slip flow with suction and injection and radiation over a shrinking sheet by optimal homotopy analysis method, Results Eng., 18 (2023), 101173. https://doi.org/10.1016/j.rineng.2023.101173 doi: 10.1016/j.rineng.2023.101173
|
| [5] |
G. Dharmaiah, J. L. R. Prasad, K. S. Balamurugan, I. Nurhidayat, U. Fernandez-Gamiz, S. Noeiaghdam, Performance of magnetic dipole contribution on ferromagnetic non-Newtonian radiative MHD blood flow: An application of biotechnology and medical sciences, Heliyon, 2 (2023). https://doi.org/10.1016/j.heliyon.2023.e13369 doi: 10.1016/j.heliyon.2023.e13369
|
| [6] |
T. Sajid, W. Jamshed, M. R. Eid, S. Algarni, T. Alqahtani, R. W. Ibrahim, et al., Thermal case examination of inconstant heat source (sink) on viscous radiative sutterby nanofluid flowing via a penetrable rotative cone, Case Stud. Therm. Eng., 48 (2023), 103102. https://doi.org/10.1016/j.csite.2023.103102 doi: 10.1016/j.csite.2023.103102
|
| [7] |
M. Waqas, Y. J. Xu, M. Nasir, M. M. Alam, A. A. Pasha, K. Irshad, et al., Darcy-Forchheimer mangetized flow based on differential type nanoliquid capturing Ohmic dissipation effects, Propuls. Power Res., 12 (2023), 443−455. https://doi.org/10.1016/j.jppr.2023.08.003 doi: 10.1016/j.jppr.2023.08.003
|
| [8] |
N. S. Akbar, S. Nadeem, T. Hayat, A. A. Hendi, Effects of heat and mass transfer on the peristaltic flow of hyperbolic tangent fluid in an annulus, Int. J. Heat Mass., 54 (2011), 4360−4369. https://doi.org/10.1016/j.ijheatmasstransfer.2011.03.064 doi: 10.1016/j.ijheatmasstransfer.2011.03.064
|
| [9] |
S. Akram, S. Nadeem, Consequence of nanofluid on peristaltic transport of a hyperbolic tangent fluid model in the occurrence of apt (tending) magnetic field, J. Magn. Magn. Mater., 358 (2014), 183−191. https://doi.org/10.1016/j.jmmm.2014.01.052 doi: 10.1016/j.jmmm.2014.01.052
|
| [10] |
M. Naseer, M. Y. Malik, S. Nadeem, A. Rehman, The boundary layer flow of hyperbolic tangent fluid over a vertical exponentially stretching cylinder, Alex. Eng. J., 53 (2014), 747−750. https://doi.org/10.1016/j.aej.2014.05.001 doi: 10.1016/j.aej.2014.05.001
|
| [11] |
S. A. Gaffar, V. R. Prasad, O. A. Bég, Numerical study of flow and heat transfer of non-Newtonian tangent hyperbolic fluid from a sphere with Biot number effects, Alex. Eng. J., 54 (2015), 829−841. https://doi.org/10.1016/j.aej.2015.07.001 doi: 10.1016/j.aej.2015.07.001
|
| [12] |
T. Hayat, M. Shafique, A. Tanveer, A. Alsaedi, Magnetohydrodynamic effects on peristaltic flow of hyperbolic tangent nanofluid with slip conditions and Joule heating in an inclined channel, Int. J. Heat Mass, 102 (2016), 54−63. https://doi.org/10.1016/j.ijheatmasstransfer.2016.05.105 doi: 10.1016/j.ijheatmasstransfer.2016.05.105
|
| [13] |
T. Hayat, S. Qayyum, A. Alsaedi, S. A. Shehzad, Nonlinear thermal radiation aspects in stagnation point flow of tangent hyperbolic nanofluid with double diffusive convection, J. Mol. Liq., 223 (2016), 969−978. https://doi.org/10.1016/j.molliq.2016.08.102 doi: 10.1016/j.molliq.2016.08.102
|
| [14] |
K. U. Rehman, A. A. Malik, M. Y. Malik, N. U. Saba, Mutual effects of thermal radiations and thermal stratification on tangent hyperbolic fluid flow yields by both cylindrical and flat surfaces, Case Stud. Therm. Eng., 10 (2017), 244−254. https://doi.org/10.1016/j.csite.2017.07.003 doi: 10.1016/j.csite.2017.07.003
|
| [15] |
K. G. Kumar, B. J. Gireesha, M. R. Krishanamurthy, N. G. Rudraswamy, An unsteady squeezed flow of a tangent hyperbolic fluid over a sensor surface in the presence of variable thermal conductivity, Results Phys., 7 (2017), 3031−3036. https://doi.org/10.1016/j.rinp.2017.08.021 doi: 10.1016/j.rinp.2017.08.021
|
| [16] |
V. Nagendramma, A. Leelarathnam, C. S. K. Raju, S. A. Shehzad, T. Hussain, Doubly stratified MHD tangent hyperbolic nanofluid flow due to permeable stretched cylinder, Results Phys., 9 (2018), 23−32. https://doi.org/10.1016/j.rinp.2018.02.019 doi: 10.1016/j.rinp.2018.02.019
|
| [17] |
S. M. Atif, S. Hussain, M. Sagheer, Heat and mass transfer analysis of time-dependent tangent hyperbolic nanofluid flow past a wedge, Phys. Lett. A, 383 (2019), 1187−1198. https://doi.org/10.1016/j.physleta.2019.01.003 doi: 10.1016/j.physleta.2019.01.003
|
| [18] |
Z. Ullah, G. Zaman, A. Ishak, Magnetohydrodynamic tangent hyperbolic fluid flow past a stretching sheet, Chinese J. Phys., 66 (2020), 258−268. https://doi.org/10.1016/j.cjph.2020.04.011 doi: 10.1016/j.cjph.2020.04.011
|
| [19] |
W. Khan, I. A. Badruddin, A. Ghaffari, H. M. Ali, Heat transfer in steady slip flow of tangent hyperbolic fluid over the lubricated surface of a stretchable rotatory disk, Case Studi. Therm. Eng., 24 (2021), 100825. https://doi.org/10.1016/j.csite.2020.100825 doi: 10.1016/j.csite.2020.100825
|
| [20] |
S. Sindhu, B. J. Gireesha, Scrutinization of unsteady non-Newtonian fluid flow considering buoyancy effect and thermal radiation: Tangent hyperbolic model, Int. Commun. Heat Mass, 135 (2022), 106062. https://doi.org/10.1016/j.icheatmasstransfer.2022.106062 doi: 10.1016/j.icheatmasstransfer.2022.106062
|
| [21] |
A. Hussain, N. Farooq, A. Ahmad, L. Sarwar, Impact of double diffusivity on the hyperbolic tangent model conveying nano fluid flow over the wedge, Int. Commun. Heat Mass, 145 (2023), 106849. https://doi.org/10.1016/j.icheatmasstransfer.2023.106849 doi: 10.1016/j.icheatmasstransfer.2023.106849
|
| [22] |
M. A. Elogail, Peristaltic flow of a hyperbolic tangent fluid with variable parameters, Results Eng., 17 (2023), 100955. https://doi.org/10.1016/j.rineng.2023.100955 doi: 10.1016/j.rineng.2023.100955
|
| [23] |
N. S. Akbar, S. Nadeem, R. U. Haq, Z. H. Khan, Numerical solutions of magnetohydrodynamic boundary layer flow of tangent hyperbolic fluid towards a stretching sheet, Indian J. Phys., 87 (2013), 1121−1124. https://doi.org/10.1007/s12648-013-0339-8 doi: 10.1007/s12648-013-0339-8
|
| [24] |
K. U. Rehman, N. U. Saba, M. Y. Malik, A. A. Malik, Encountering heat and mass transfer mechanisms simultaneously in Powell-Erying fluid through Lie symmetry approach, Case Stud. Therm. Eng., 10 (2017), 541−549. https://doi.org/10.1016/j.csite.2017.10.011 doi: 10.1016/j.csite.2017.10.011
|
| [25] |
K. U. Rehman, M. Y. Malik, I. Zehra, M. S. Alqarni, Group theoretical analysis for MHD flow fields: A numerical result, J. Braz. Soc. Mech. Sci., 41 (2019), 1−9. https://doi.org/10.1007/s40430-019-1662-6 doi: 10.1007/s40430-019-1662-6
|
| [26] |
Z. Ullah, G. Zaman, A. Ishak, Magnetohydrodynamic tangent hyperbolic fluid flow past a stretching sheet, Chinese J. Phys., 66 (2020), 258−268. https://doi.org/10.1016/j.cjph.2020.04.011 doi: 10.1016/j.cjph.2020.04.011
|
| [27] |
H. Sadaf, Z. Asghar, N. Iftikhar, Cilia-driven flow analysis of cross fluid model in a horizontal channel, Comput. Part. Mech., 9 (2022), 1−8. https://doi.org/10.1007/s40571-022-00539-w doi: 10.1007/s40571-022-00539-w
|
| [28] |
S. Arulmozhi, K. Sukkiramathi, S. S. Santra, R. Edwan, U. Fernandez-Gamiz, S. Noeiaghdam, Heat and mass transfer analysis of radiative and chemical reactive effects on MHD nanofluid over an infinite moving vertical plate, Results Eng., 14 (2022), 100394. https://doi.org/10.1016/j.rineng.2022.100394 doi: 10.1016/j.rineng.2022.100394
|
| [29] |
Y. Nawaz, M. S. Arif, K. Abodayeh, M. Mansoor, Finite difference schemes for MHD mixed convective Darcy-Forchheimer flow of Non-Newtonian fluid over oscillatory sheet: A computational study, Front. Phys., 11 (2023), 16. https://doi.org/10.3389/fphy.2023.1072296 doi: 10.3389/fphy.2023.1072296
|
| [30] |
Y. Nawaz, M. S. Arif, K. Aboda, Predictor-corrector scheme for electrical magnetohydrodynamic (MHD) Casson nanofluid flow: A computational study, Appl. Sci., 13 (2023), 1209. https://doi.org/10.3390/app13021209 doi: 10.3390/app13021209
|
| [31] |
C. S. Liu, The Lie-group shooting method for boundary-layer problems with suction/injection/reverse flow conditions for power-law fluids, Int. J. Nonlin. Mech., 46 (2011), 1001−1008. https://doi.org/10.1016/j.ijnonlinmec.2011.04.016 doi: 10.1016/j.ijnonlinmec.2011.04.016
|
| [32] | W. M. K. A. D. Zaimi, B. Bidin, N. A. A. Bakar, R. A. Hamid, Applications of Runge-Kutta-Fehlberg method and shooting technique for solving classical Blasius equation, World Appl. Sci. J., 17 (2012), 10−15. |
| [33] |
K. U. Rehman, W. Shatanawi, U. Firdous, A comparative thermal case study on thermophysical aspects in thermally magnetized flow regime with variable thermal conductivity, Case Stud. Therm. Eng., 44 (2023), 102839. https://doi.org/10.1016/j.csite.2023.102839 doi: 10.1016/j.csite.2023.102839
|
| [34] | A. Usman, M. Rafiq, M. Saeed, A. Nauman, A. Almqvist, M. Liwicki, Machine learning computational fluid dynamics, In: 2021 Swedish Artificial Intelligence Society Workshop (SAIS), IEEE, Sweden, 2021. https://doi.org/10.1109/SAIS53221.2021.9483997 |
| [35] |
D. Drikakis, F. Sofos, Can artificial intelligence accelerate fluid mechanics research?, Fluids, 8 (2023), 212. https://doi.org/10.3390/fluids8070212 doi: 10.3390/fluids8070212
|
| [36] |
Z. Said, P. Sharma, R. M. Elavarasan, A. K. Tiwari, M. K. Rathod, Exploring the specific heat capacity of water-based hybrid nanofluids for solar energy applications: A comparative evaluation of modern ensemble machine learning techniques, J. Energy Storage, 54 (2022), 105230. https://doi.org/10.1016/j.est.2022.105230 doi: 10.1016/j.est.2022.105230
|
| [37] |
A. Shafiq, A. B. Çolak, T. N. Sindhu, T. Muhammad, Optimization of Darcy-Forchheimer squeezing flow in nonlinear stratified fluid under convective conditions with artificial neural network, Heat Transf. Res., 53 (2022). https://doi.org/10.1615/HeatTransRes.2021041018 doi: 10.1615/HeatTransRes.2021041018
|
| [38] |
K. U. Rehman, W. Shatanawi, Non-Newtonian mixed convection magnetized flow with heat generation and viscous dissipation effects: A prediction application of artificial intelligence, Processes, 11 (2023), 986. https://doi.org/10.3390/pr11040986 doi: 10.3390/pr11040986
|
| [39] |
M. Adamu, A. B. Çolak, Y. E. Ibrahim, S. I. Haruna, M. F. Hamza, Prediction of mechanical properties of rubberized concrete incorporating fly ash and nano silica by artificial neural network technique, Axioms, 12 (2023), 81. https://doi.org/10.3390/axioms12010081 doi: 10.3390/axioms12010081
|
| [40] |
M. Fathizadeh, M. Madani, Y. Khan, N. Faraz, A. Yıldırım, S. Tutkun, An effective modification of the homotopy perturbation method for MHD viscous flow over a stretching sheet, J. King Saud Univ.-Sci., 25 (2013), 107−113. https://doi.org/10.1016/j.jksus.2011.08.003 doi: 10.1016/j.jksus.2011.08.003
|
Figures(11) / Tables(9)
Khalil Ur Rehman, Wasfi Shatanawi, Zead Mustafa. Artificial intelligence (AI) based neural networks for a magnetized surface subject to tangent hyperbolic fluid flow with multiple slip boundary conditions[J]. AIMS Mathematics, 2024, 9(2): 4707-4728. doi: 10.3934/math.2024227
DownLoad: