Investigation of Mixed Convection in Spinning Nanofluid over Rotating Cone Using Artificial Neural Networks and BVP-4C Technique

Ali Hassan, Qusain Haider, Najah Alsubaie, Fahad M. Alharbi, Abdullah Alhushaybari and Ahmed M. Galal
Additional contact information
Ali Hassan: Department of Mathematics, University of Gujrat, Gujrat 50700, Pakistan
Qusain Haider: Department of Mathematics, University of Gujrat, Gujrat 50700, Pakistan
Najah Alsubaie: Department of Computer Sciences, College of Computer and Information Sciences, Princess Nourah bint Abdulrahman University, P.O. Box 84428, Riyadh 11671, Saudi Arabia
Fahad M. Alharbi: Department of Mathematics, Al-Qunfudah University College, Umm Al-Qura University, Mecca, Saudi Arabia
Abdullah Alhushaybari: Department of Mathematics, College of Science, Taif University, P.O. Box 11099, Taif 21944, Saudi Arabia
Ahmed M. Galal: Department of Mechanical Engineering, College of Engineering in Wadi Alddawasir, Prince Sattam Bin Abdulaziz University, Saudi Arabia

Mathematics, 2022, vol. 10, issue 24, 1-20

Abstract: The significance of back-propagated intelligent neural networks (BINs) to investigate the transmission of heat in spinning nanofluid over a rotating system is analyzed in this study. The buoyancy effect is incorporated along with the constant thermophysical properties of nanofluids. Levenberg–Marquardt intelligent networks (ANNLMBs) are employed to study heat transmission by using a trained artificial neural network. The system of highly non-linear flow governing partial differential equations (PDEs) is transformed into ordinary differential equations (ODEs) which is taken as a system model. This achieved system model is utilized to generate data set using the “Adams” method for distinct scenarios of heat transmission investigation in a spinning nanofluid over a rotating system for the implementation of the proposed ANNLMB. Additionally, with the help of training, testing, and validation, the approximate solution of heat transmission in a spinning nanofluid in a rotating system is obtained using a BNN-based solver. The generated reference data achieved employing the proposed artificial neural network based on a Levenberg–Marquardt intelligent network is distributed in the following manner: training at 82%, testing at 9%, and validation at 9%. Furthermore, MSE, histograms, and regression analyses are performed to depict and discuss the impact of the varying influence of key parameters, such as unsteadiness “s” in spinning flow, Prandtl number effect “pr”, the rotational ratio of nanofluid and cone ? 1 and buoyancy effect ? 1 on velocities F ? G and temperature ? profiles. The mean square error confirms the accuracy of the achieved results. Prandtl number and unsteadiness decrease the temperature profile and thermal boundary layer of the rotating nanofluid.

Keywords: neural networks; Levenberg–Marquardt neural network; heat transmission; spinning nanofluid; rotating system (search for similar items in EconPapers)
JEL-codes: C (search for similar items in EconPapers)
Date: 2022
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