Computational modelling and thermophysical characterization of Kelvin–Voigt fluid flow: A neural network approach
V. Leela
Department of Science and Humanities, PES University, Bangalore, India
Search for more papers by this authorCorresponding Author
B. Shilpa
Department of Mathematics, Dayananda Sagar College of Engineering, Bangalore, India
Correspondence
B. Shilpa, Department of Mathematics, Dayananda Sagar College of Engineering, Bangalore 560078, India.
Email: [email protected]
Irfan Anjum Badruddin, Mechanical Engineering Department, College of Engineering, King Khalid University, Abha 61421, Saudi Arabia.
Email: [email protected]
Muhammad Nasir Bashir, Multi-Scale Fluid Dynamics Lab, Department of Mechanical Engineering, Yonsei University, Seoul 120–749, Republic of Korea.
Email: [email protected]
Search for more papers by this authorCorresponding Author
Irfan Anjum Badruddin
Mechanical Engineering Department, College of Engineering, King Khalid University, Abha, Saudi Arabia
Correspondence
B. Shilpa, Department of Mathematics, Dayananda Sagar College of Engineering, Bangalore 560078, India.
Email: [email protected]
Irfan Anjum Badruddin, Mechanical Engineering Department, College of Engineering, King Khalid University, Abha 61421, Saudi Arabia.
Email: [email protected]
Muhammad Nasir Bashir, Multi-Scale Fluid Dynamics Lab, Department of Mechanical Engineering, Yonsei University, Seoul 120–749, Republic of Korea.
Email: [email protected]
Search for more papers by this authorSarfaraz Kamangar
Mechanical Engineering Department, College of Engineering, King Khalid University, Abha, Saudi Arabia
Search for more papers by this authorCorresponding Author
Muhammad Nasir Bashir
Multi-Scale Fluid Dynamics Lab, Department of Mechanical Engineering, Yonsei University, Seoul, Republic of Korea
Correspondence
B. Shilpa, Department of Mathematics, Dayananda Sagar College of Engineering, Bangalore 560078, India.
Email: [email protected]
Irfan Anjum Badruddin, Mechanical Engineering Department, College of Engineering, King Khalid University, Abha 61421, Saudi Arabia.
Email: [email protected]
Muhammad Nasir Bashir, Multi-Scale Fluid Dynamics Lab, Department of Mechanical Engineering, Yonsei University, Seoul 120–749, Republic of Korea.
Email: [email protected]
Search for more papers by this authorMuhammad Mahmood Ali
Department of Mechatronic Engineering, Atlantic Technological University Sligo, Ash Lane, Sligo, Ireland
Search for more papers by this authorV. Leela
Department of Science and Humanities, PES University, Bangalore, India
Search for more papers by this authorCorresponding Author
B. Shilpa
Department of Mathematics, Dayananda Sagar College of Engineering, Bangalore, India
Correspondence
B. Shilpa, Department of Mathematics, Dayananda Sagar College of Engineering, Bangalore 560078, India.
Email: [email protected]
Irfan Anjum Badruddin, Mechanical Engineering Department, College of Engineering, King Khalid University, Abha 61421, Saudi Arabia.
Email: [email protected]
Muhammad Nasir Bashir, Multi-Scale Fluid Dynamics Lab, Department of Mechanical Engineering, Yonsei University, Seoul 120–749, Republic of Korea.
Email: [email protected]
Search for more papers by this authorCorresponding Author
Irfan Anjum Badruddin
Mechanical Engineering Department, College of Engineering, King Khalid University, Abha, Saudi Arabia
Correspondence
B. Shilpa, Department of Mathematics, Dayananda Sagar College of Engineering, Bangalore 560078, India.
Email: [email protected]
Irfan Anjum Badruddin, Mechanical Engineering Department, College of Engineering, King Khalid University, Abha 61421, Saudi Arabia.
Email: [email protected]
Muhammad Nasir Bashir, Multi-Scale Fluid Dynamics Lab, Department of Mechanical Engineering, Yonsei University, Seoul 120–749, Republic of Korea.
Email: [email protected]
Search for more papers by this authorSarfaraz Kamangar
Mechanical Engineering Department, College of Engineering, King Khalid University, Abha, Saudi Arabia
Search for more papers by this authorCorresponding Author
Muhammad Nasir Bashir
Multi-Scale Fluid Dynamics Lab, Department of Mechanical Engineering, Yonsei University, Seoul, Republic of Korea
Correspondence
B. Shilpa, Department of Mathematics, Dayananda Sagar College of Engineering, Bangalore 560078, India.
Email: [email protected]
Irfan Anjum Badruddin, Mechanical Engineering Department, College of Engineering, King Khalid University, Abha 61421, Saudi Arabia.
Email: [email protected]
Muhammad Nasir Bashir, Multi-Scale Fluid Dynamics Lab, Department of Mechanical Engineering, Yonsei University, Seoul 120–749, Republic of Korea.
Email: [email protected]
Search for more papers by this authorMuhammad Mahmood Ali
Department of Mechatronic Engineering, Atlantic Technological University Sligo, Ash Lane, Sligo, Ireland
Search for more papers by this authorAbstract
This research provides insight into the unsteady, fully developed natural convective flow and heat transfer of conducting viscoelastic Kelvin–Voigt zero order fluid in a vertical annulus with variable viscosity, induced and radial magnetic field. Quadratically and exponentially varying viscosity impacts on the flow field, magnetic and thermal fields are also analyzed. The nonlinear coupled governing PDEs are solved using an implicit Crank–Nicolson finite difference method and the Thomas algorithm to turn up the nonsimilar solutions. The effect of pertinent physical parameters on flow, magnetic, and thermal fields are discussed through graphs. In the course of numerical analysis, it is noted that enhancing the variations in viscosity parameters enhances skin friction and flow rate. The fluid velocity and local heat transport increase with buoyancy force. The artificial neural network model with the backpropagating Levenberg–Marquardt algorithm is adopted to analyze the heat transfer characteristics in quadratically and exponentially varying viscosity cases.
CONFLICT OF INTEREST STATEMENT
The authors have no conflicts to disclose.
Open Research
DATA AVAILABILITY STATEMENT
The data that supports the findings of this study are available within the article.
REFERENCES
- 1Shilpa, B., Leela, V.: Galerkin finite element analysis of heat and mass transfer of Jeffrey, Maxwell and Oldroyd-B nanofluids in a vertical annulus with an induced magnetic field and a non–uniform heat source/sink. Int. J. Ambient Energy 44(1), 1887–1903 (2023)
- 2Hindebu, B., Makinde, O.D., Guta, L.: Unsteady mixed convection flow of variable viscosity nanofluid in a micro-channel filled with a porous medium. Indian J. Phys. 96(6), 1749–1766 (2022). https://doi.org/10.1007/s12648-021-02116-y
- 3Hussain, Z., Alghamdi, M., Naeem Aslam, M., Muhammad, T.: Morlet-wavelet neural networks and sensitivity analysis in magnetized peristaltic flow subject to Soret–Dufour effects: An unsupervised approach. Int. Commun. Heat Mass Transfer 160, 108259 (2025)
- 4Shilpa, B., Leela, V., Rani, H.P.: Stability analysis of MHD radiative mixed convective flow in vertical cylindrical annulus: Thermal nonequilibrium approach. Heat Transfer 52(1), 707–733 (2023)
- 5Shilpa, B., Leela, V.: An artificial intelligence model for heat and mass transfer in an inclined cylindrical annulus with heat generation/absorption and chemical reaction. Int. Commun. Heat Mass Transfer 147, 106956 (2023)
- 6Badruddin, I.A., Zainal, Z.A., Aswatha Narayana, P.A., Seetharamu, K.N.: Thermal non-equilibrium modeling of heat transfer through vertical annulus embedded with porous medium. Int. J. Heat Mass Transfer 49(25-26), 4955–4965 (2006)
- 7Shilpa, B., Leela, V.: LTNE effect on non-linear radiative MHD mixed convective flow in an annular porous medium: Intelligent computing paradigm. Int. J. Ambient Energy 44(1), 1–16 (2023)
10.1080/01430750.2023.2180536 Google Scholar
- 8Badruddin, I.A., Zainal, Z.A., Khan, Z.A, Mallick, Z.: Effect of viscous dissipation and radiation on natural convection in a porous medium embedded within vertical annulus. Int. J. Therm. Sci. 46(3), 221–227 (2007)
- 9Gidde, R.R., Pawar, P.M.: On the effect of viscoelastic characterizations on polymers and on performance of micropump. Adv. Mech. Eng. 9, 1–12 (2017)
10.1177/1687814017691211 Google Scholar
- 10Jayabal, H., Dingari, N.N., Rai, B.: A linear viscoelastic model to understand the skin mechanical behaviour and for cosmetic formulation design. Int. J. Cosmetic Sci. 41, 292–299 (2019)
- 11Jozwiak, B., Orczykowska, M., Dziubinski, M.: Fractional generalizations of Maxwell and Kelvin-Voigt models for biopolymer characterization. PLoS One 10(11), e0143090 (2015). https://doi.org/10.1371/journal.pone.0143090
- 12Greco, R., Marano, G.C.: Identification of parameters of Maxwell and Kelvin-Voigt generalized models for fluid viscous dampers. J. Vibr. Control 21, 260–274 (2015)
- 13Xu, Z.D., Wang, D.X., Shi, C.F.: Model, tests and application design for viscous dampers. J. Vibr. Control 17, 1359–1370 (2010)
- 14Straughan, B.: Instability thresholds for thermal convection in a Kelvin–Voigt fuid of variable order. Rend. Circ. Mat. Palermo 2 71, 187–206 (2022). https://doi.org/10.1007/s12215-020-00588-1
- 15Straughan, B.: Competitive Double Diffusive Convection in a Kelvin–Voigt Fluid of Order One. Appl. Math. Opt. 84(Suppl 1), S631–S650 (2021). https://doi.org/10.1007/s00245-021-09781-9
- 16Shivakumara, I.S., Sureshkumar, S.: Convective instabilities in a viscoelastic-fluid-saturated porous medium with throughflow. J. Geophys. Eng. 4(1), 104–115, (2007).
- 17Shivakumara, I.S., Malashetty, M.S., Chavaraddi, K.B.: Onset of convection in a viscoelastic-fluid-saturated sparselypacked porous layer using a thermal nonequilibrium model. Can. J. Phys. 84(11), 973–990 (2006)
- 18Leela, V., Nagabhushana, P., Shilpa, B., Gangadhara Reddy, R.: Numerical investigation on effects of induced magnetic field and viscous dissipation on MHD mixed convection in a vertical micro-porous channel using the Brinkman–Forchheimer extended Darcy model. Int. J. Ambient Energy 43(1), 6950–6964 (2022)
10.1080/01430750.2022.2059006 Google Scholar
- 19Shilpa, B., Leela, V.: Integrated intelligent neuro computing technique for mixed convective flow and heat transfer in heterogeneous permeability media. Waves Random Complex Media 1–22 (2023)
10.1080/17455030.2023.2192809 Google Scholar
- 20Rani, H.P., Leela, V., B.S., Nagabhushana, P.: Numerical analysis of hydromagnetic mixed convective flow in an internally heated vertical porous layer using thermal nonequilibrium model. Heat Transfer 51(7), 6249–6273 (2023)
10.1002/htj.22590 Google Scholar
- 21Shilpa, B., Leela, V., Prasannakumara, B.C., Nagabhushana, P.: Soret and Dufour effects on MHD double-diffusive mixed convective heat and mass transfer of couple stress fluid in a channel formed by electrically conducting and non-conducting walls. Waves Random Complex Media 1–22 (2022). https://doi.org/10.1080/17455030.2022.2119491
- 22Anwar, M.S., Khan, M., Hussain, Z., Muhammad, T., Puneeth, V.: Investigation of heat transfer characteristics in MHD hybrid nanofluids with variable viscosity and thermal radiations. J. Radiation Res. Appl. Sci. 18(1), 101240 (2025)
- 23Hussain, Z., Hayat, T., Alsaedi, A., Anwar, M.S.: Mixed convective flow of CNTs nanofluid subject to varying viscosity and reactions. Sci. Rep. 11, 22838 (2021)
- 24Hussain, Z.: Heat transfer through temperature dependent viscosity hybrid nanofluid subject to homogeneous-heterogeneous reactions and melting condition: A comparative study. Phys. Scr. 96(1), 015210 (2021)
- 25Zanchini, E.: Mixed convection with variable viscosity in a vertical annulus with uniform wall temperatures. Int. J. Heat Mass Transfer 51, 30–40 (2008)
- 26Gbadeyan, J.A., Titiloye, E.O., Adeosun, A.T.: Effect of variable thermal conductivity and viscosity on Casson nanofluid flow with convective heating and velocity slip. Heliyon 6, e03076 (2020)
- 27Chin, K.E., Nazar, R., Arifin, N.M., Pop, I.: Effect of variable viscosity on mixed convection boundary layer flow over a vertical surface embedded in a porous medium. Int. Commun. Heat Mass Transfer 34, 464–473 (2007)
- 28Kishan, N., Amrutha, P.: Variable viscosity effects on mixed convection heat and mass transfer along a semi-infinite vertical plate in the presence of chemical reaction and viscous dissipation. Int. J. Eng., Sci. Technol. 7(2), 27–42 (2015)
10.4314/ijest.v7i2.3 Google Scholar
- 29Kefenea, M.Z., Makindeb, O.D., Enyadene, L.G.: MHD variable viscosity mixed convection of nanofluid in a microchannel with permeable walls. Indian J. Pure Appl. Phys. 58, 892–908 (2020)
- 30Prasad, K.V., Pal, D., Umesh, V., Prasanna Rao, N.S.: The effect of variable viscosity on MHD viscoelastic fluid flow and heat transfer over a stretching sheet. Commun. Nonlinear Sci. Numer. Simulat. 15, 331–344 (2010)
- 31Pakdaman, M., Ahmadian, A., Effati, S., Salahshour, S., Baleanu, D.: Solving differential equations of fractional order using an optimization technique based on training an artificial neural network. Appl. Math. Comput. 293, 81–95 (2017). https://doi.org/10.1016/j.amc.2016.07.021
- 32Cheema, T.N., Asif Zahoor Raja, M., Ahmad, I., Naz, S., Ilyas, H., Shoaib, M.: Intelligent computing withLevenberg-Marquardt artificial neural networks for a nonlinear system of COVID-19 epidemic model for future generation disease control. Eur. Phys. J. Plus. 135(11), 932 (2020). https://doi.org/10.1140/epjp/s13360-020-00910-x
- 33Ahmad, I., Ilyas, H., Urooj, A., Aslam, M.S., Shoaib, M., Asif Zahoor Raja, M.: Novel applications of intelligent computing paradigms for the analysis of nonlinear reactive transport model of the fluid in soft tissues and microvessels. Neural Comput. Appl. 31(12), 9041–9059 (2019). https://doi.org/10.1007/s00521-019-04203-y
- 34Hussain, Z., Fazia, Anwar, M.S.: Neural network approach to investigate heat transfer in SWCNTs nanofluid within trapezoidal cavity with varied corrugated rod amplitudes. Phys. Scr. 99(10), 105257 (2024)
- 35Shilpa, B., Leela, V., Anjum Badruddin, I., Kamangar, S., Ganesan, P., Khan, A.A.: Exploration of Arrhenius activation energy and thermal radiation on MHD double-diffusive convection of ternary hybrid nanofluid flow over a vertical annulus with discrete heating. Case Studies Thermal Eng. 65, 105593 (2025)
- 36Rani, H.P., Shilpa, B., Leela, V., Gangadhara Reddy, R.: Numerical simulation and neural network model for hydromagnetic nanofluid convection in a porous wavy channel with thermal non-equilibrium model. Phys. Scr. 99(11), 115219 (2024)
- 37Shilpa, B., Leela, V., Anjum Badruddin, I., Kamangar, S., Nasir Bashir, M., Ali, M.M.: Integrated neural network based simulation of thermo solutal radiative double-diffusive convection of ternary hybrid nanofluid flow in an inclined annulus with thermophoretic particle deposition. Case Studies Thermal Eng. 62, 105158 (2024)
- 38Shilpa, B., Anjum Badruddin, I., Gangadhara Reddy, R., Kamangar, S., Khan, A.A.: Exploration of linear and exponential heat source/sink with the significance of thermophoretic particle deposition on ZnO-SAE50 nano lubricant flow past a curved surface. Case Studies Thermal Eng. 61, 104883 (2024)
- 39Shilpa, B., Leela, V., Alsulami, M.D.: Artificial neural network approach for MHD mixed convection and entropy generation in a vertical annulus with time periodic thermal boundary conditions in the presence of radial and induced magnetic field. Numer. Heat Transf. B: Fundam. 85(8), 1–27 (2024)
- 40Shilpa, B., Singh Chohan, J., Beemkumar, N., Kulshreshta, A., Ghodhbani, R., Othman, N.A., Abdullaeva, B., Ijaz Khan, M.: A novel machine learning approach for numerical simulation on the hybrid nanofluid flow past a converging/diverging channel: Properties of tantalum and alumina nanoparticles. Partial Differ. Equ. Appl. Math. 13 101063 (2025)
10.1016/j.padiff.2024.101063 Google Scholar
- 41Jha, B.K., Aina, B., Jha, Z.R.B.K., Aina, B., Rilwanu, Z.: Steady fully developed natural convection flow in a vertical annular microchannel having temperature-dependent viscosity: An exact solution. Alexandria Eng. J. 55, 951–958 (2016)
- 42Weng, H.C., Chen, C.K.: Drag reduction and heat transfer enhancement over a heated wall of a vertical annular microchannel. Int. J. Heat Mass Transf. 52, 1075–1079 (2009)
