Neuro-intelligent mappings of hybrid hydro-nanofluid Al2O3–Cu–H2O model in porous medium over rotating disk with viscous dissolution and Joule heating

https://doi.org/10.1016/j.ijhydene.2021.06.065Get rights and content

Highlights

  • Neuro-intelligent mappings computing for viscous dissolution and Joule heating.

  • A computing backpropagation networks was found working for hydro-nanofluidic system.

  • Designed technique is implemented to measure the dynamics of different scenarios.

  • Study the dynamics of velocities and temperature profiles.

  • Determination and stability of scheme are validated on rigorous analysis.

Abstract

The aim of study is to investigate the mass and heat transfer phenomena in hybrid hydro-nanofluidic system involving Al2O3–Cu–H2O over the rotating disk in porous medium with viscous dissolution and Joule heating through the stochastic solver by way of Levenberg-Marquardt backpropagation neural networks. The mathematical model in system of PDEs describes the physical phenomena of the hybrid hydro-nanofluid flow problem are converted into set of ODEs by means of scaling group transformations. The datasets are constructed by utilizing the power of explicit Runge-Kutta numerical method that help to the develop a continuous neural networks mapping. The validation, training and testing processes are utilized to learn the neural network mapping to estimate the solution of various scenarios with cases that are constructed by varying different values of physical constraints such as porosity factor, inertia coefficient, Prandtl number, Brinkman number, radiation parameter, mgnetic parameter, concentration of nanoparticles on the velocities and temperature profiles. Determination, convergence, verification and stability of Levenberg-Marquardt backpropogation neural network mappings are validated on the assessment of achieved accuracy through regression based statistical analysis, mean squared error and error histograms for hybrid hydro-nanofluidic model.

Introduction

Enhancement in rate of fluid heat transfer has gained several attention for engineers and scientists due to its enormous applications in industrial, electronic, chemical, engineering fields. Most common fluids including oil, ethylene glycol, water, kerosene and many more are used in electric and engineering appliances, they have less heat transfer capability because of low thermal conductivity rate. Chi [1] developed a new type of fluid to overcome the problem by boosting up thermal conductivity of fluid by means of adding nanoparticles. These nanoparticles are made of different materials such as nitrides, carbides, oxides, nonmetals, metal alumina with less than nanometers size. A while later, the numerous researches and studies are conducted on these nanofluids due to their applications in life science, fuel cell, imaging, medical, manufacturing, electronic cooling, medical, HVAC systems and food processing [[2], [3], [4]].

The thermal behaviour performance of trapezoidal, house and semi circle shaped channels are numerically compared for ZnO nanoparticles. Moreover, the effect of varying concentration of nanoparticles over heat transfer and pressure are examined and stated that trapezoidal channel have better thermal performance rather than other shapes [5]. The flow of different shaped EHD nanofluid inside an insertion with permeable wall is studied and the higher gradient values for temperature are achieved for platelet [6]. The heat transfer rate for base fluid water with Al2O3–H2O nanoparticle are numerically analyzed and it is observed that the temperature drop because of power efficiency and thermal resistance, which explains the improvement in applicability and reliability upto 70% of electronic chip [7]. Similarly, in Ref. [8] the heat transfer phenomena of Al2O3–H2O nanoparticle in heat sink microchannel in the existence of external magnetic field is examined and concluded that the applied magnetic field and Nusselt number have direct relation. The MWCNT-paraffin liquid nanofluid thermal conductivity at various temperature and concentrations are numerically studied through applying artificial neural networks [9]. The comparative study on the base of different micropolar nanofluids are numerically studied to analysis the effects on the heat transfer and flow over the shrinking/stretching sheet [10]. The different properties of nanoparticles along with various significance are numerically investigated by enormous researchers including: thermal conductivity [11,12], heat transfer flow [[13], [14], [15], [16]], thermo-physical characteristics and fractional volume [17], heat sink [18], photocatalytic activity [19,20] and flow rate [[21], [22], [23], [24], [25], [26]]. MHD flow, and heat and mass transfer phenomena of nanofluid flowing over the vertical plate are numerically studied through novel spectral relaxation method [27]. Keller Box method is applied for numerically investigate the effects of involved parameters on the nanofluid flow that is flow over the stretching sheet [27,28].

The thermophysical properties of ordinary nanofluids by introducing new kind of fluid that is mixture or compound of base fluid with atleast two different nanoparticles known as hybrid nanofluids (HNF). Due to improved surface area, specific heat, particle rearrangements, structure, type and thermal conductivity HNF are fascinated the more researchers, scientists and engineers now a days to exploit HNF for particle problems. HNF have better performance over ordinary nanofluids by this reason HMF extensively used in industrial and engineering fields including, nuclear system cooling, solar heating system, microscopic chips and HVAC systems. Now a days, comparative analysis based on their performance of HNFs and nanofluids are investigated by very few researchers [[29], [30], [31]]. HNFs are numerically discussed to illustrates the flow behavior by varying parameter values over various surfaces including; stagnation region [32,33], shrinking sheet [34], stretching plate [[35], [36], [37]], saddle/nodal stagnation point [38]. Moreover, rotating effect of the plate on fluid have many applications in fluid dynamics as, crystal growth processes, medical equipment, rotor-stator system, food processing, disk cleaner, computer storage devices, rotating machinery, etc. The first time the rotating plate effect on fluid is analytically analyzed by Van Karman through momentum-integrated approach [39]. The rotational effect of plate with different physical effects and flow configuration are studied by many researchers and scientist few of them are [[40], [41], [42]]. The other name of Joule heating is “Ohmic heating”, it is a procedure of create resistive heat in the material during passage of electric current through a conducting material. Furthermore, Ohmic heating effect is widely practically applicable in various kinds of the electronics and electric appliances.

Now a days the artificial neural networks (ANNs) based numerical approaches are extensively used to solve differential equations appears in various fields application including material science, biomedical, welding, engineering, finance, medicine and geology. ANNs has a significant and good performance model with the independence of various data sets, moreover it is suitable for solving various applications of real-world problems. ANNs working based on the human brain with similar features including remembering, learning, making and deciding without receiving any assist. Few recent potential applications of ANNs including, nonlinear reactive transport model [43], Thomas-Fermi equation [44], porous fin [45], muti-paragraph equation [46], Emden-Fowler equation [47], blood flow [48], Blasious equation [49], Lane-Emden system [50], dust density model [51], COVID-19 [52], reactive power planing [53], heartbeat dynamics model [54], astrophysics [55], control autoregressive systems [56], energy [57], wind power [58], Line Echo Cancellation [59]. The idea of using hybrid nanofluids is to further improvement of heat transfer system due to the thermal characteristics of hybrid nanofluid and it is more efficient in thermal conduction. Hybrid nanofluids have efficient heat transfer property and pressure drop characteristics. The heat transfer properties of conventional liquids are quite poor, but they have many applications in heating and cooling processes, chemical processes, power generation and other usages make the reprocessing of these fluids necessary, so that they can have improved heat transfer property. The recent studies have shown that the inclusion of nanoparticles to different liquids can affect the suspension viscosity and can upgrade the thermal conductivity. The thermophysical properties of nanoliquids depend on the nanoparticle shape, concentration, material and base fluid type. In recent researches of nanofluids, the research workers use hybrid nanoliquid, which contain suspended dissimilar nanosized particles. The main advantage to use hybrid nanoliquids is the upgradation of heat transfer characteristics [[60], [61], [62]]. So the conclusion is that the thermal conductivity can be improved by using the hybrid nanoliquids carrying the composite nanosized particles. But the considerable challenges in back of the practical applications is production procedure, long-term stability, choosing the appropriate nanomaterials combination and the cost of nanoliquids. As the discussion the hybrid nanofluids have vast applications that is the reason why authors studied the studied the hybrid nanofluid. Moreover, as per above mentioned literature the neural networks through Levenberg-Marquardt algorithm based on backpropagation not yet applied on the rotating disk with hybrid nanofluid problem along porous medium. This motive the authors to investigate the proposed nanofluid problem through NN-MBP solver. The innovative aspects are listed for proposed investigation as follows:

  • A new artificial intelligence application based on stochastic computing is designed to examine the dynamics of velocities and temperature profiles in the hybrid hydro-nanofluidic system involving Al2O3–Cu–H2O over the rotating disk in porous medium with viscous dissolution and Joule heating.

  • The design continuous mapping based networks are developed effectively by exploiting multi-layer hidden neurons structure trained with Levenberg-Marquardt algorithm for hybrid hydro-nanofluidic model.

  • The designed intelligent computing is implemented to measure the dynamics of the system by varying values of porosity factor, inertia coefficient, Prandtl number, Brinkman number, radiation parameter, mgnetic parameter, concentration of nanoparticles on the velocities and temperature profiles.

  • Determination, convergence, verification and stability of Levenberg-Marquardt backpropogation neural network mappings are validated on the assessment of achieved accuracy through regression based statistical analysis, mean squared error and error histograms for hybrid hydro-nanofluidic model.

The paper is organized as: in Section Problem formulation the problem formulation of the hybrid hydro-nanofluidic model is explained. Learning and designed methodology of the designed solver is described in Section Learning and designed methodology, where the results and their simulation are illustrated in Section Results and simulation. Moreover, the conclusion is elaborated in section Conclusion.

Section snippets

Problem formulation

Consider hybrid nanofluid with steady and incompressible flow over rotation disk with porous medium in 3-dimension under viscose dissipation effects and Ohmic heating. The (r, φ, z) cylindrical coordinates system is straight in such a way that the surface placed in plane and the z > 0 region for fluid flow, moreover the z-axis is perpendicular to surface. The disk is rotating with constant angular velocity ω around the z-axis. Heat source/sink and nonlinear radiation are explained as heat

Learning and designed methodology

The system of ODEs define in Eq. (9), (10), (11), (12) are numerically solved through neural network Levenberg Marquardt Backpropagation (NN-LMBP) solver by means of MATLAB neural network time series app. The neural networks is trained through Levenberg Marquardt activation function with 80 hidden neurons, 2 delays, 5% of testing and validation each, along with 90% of training of the target data sets. The data set trained until desire output data is obtained through satisfying any one of

Results and simulation

The system of ODEs define in Eq. (9), (10), (11), (12) are numerically solved through neural network Levenberg Marquardt Backpropagation (NN-LMBP) solver by means of MATLAB neural network time series app. The designed solver is applied on the different scenarios and cases of the problem to elaborate the effects of varying involved physical parameters on the velocities and temperature profiles (F, F′, G, θ), where these are constructed through changing values of parameters define in Eq. (14).

Conclusion

The hybrid hydro-nanofluid Al2O3–Cu–H2O problem over the rotating disk in porous medium with viscous dissolution and Joule heating is numerically solved through designed NN-LMBP solver. The Al2O3 and Cu nanoparticles are used with water base fluid to analysis the flow behaviour of different scenarios and cases constructed on various parameters values through numerically and graphically with detailed description. The results obtained through NN-LMBP solver for the hybrid hydro-nanofluid problem

Declaration of competing interest

The authors declare that they have no known competing financial interests or personal relationships that could have appeared to influence the work reported in this paper.

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