Artificial neural network scheme to solve the hepatitis B virus model

This article aims to describe the simulation studies of the hepatitis B virus non-linear system using supervised neural networks procedures supported by Levenberg-Marquardt back propagation methodology. The proposed strategy has five distinct quantities: susceptible X(t), symptomatic infections Y(t), chronic infections W(t), recovered population R(t), and a population that has received vaccinations Z(t). The reference data set for all three distinct cases has been obtained utilizing the ND-Solver and Adams method in Mathematica software. The outcomes have been validated with performance plots for all cases. To check the accuracy and effectiveness of proposed methodology mean square error has are presented. State transition, and regression plots are illustrated to elaborated the testing, training, and validation methodology. Additionally, absolute errors for different components of hepatitis B virus model are demonstrated to depict the error occurring during distinct cases. Whereas the data assigned to training is 81%, and 9% for each testing and validation. The mean square error for all three cases is 10−12 this show the accuracy and correctness of proposed methodology

Mass and Heat Transport Assessment and Nanomaterial Liquid Flowing on a Rotating Cone: A Numerical Computing Approach

In the present study, we explore the time-dependent convectional flow of a rheological nanofluid over a turning cone with the consolidated impacts of warmth and mass exchange. It has been shown that if the angular velocity at the free stream and the cone’s angular velocity differ inversely as a linear time function, a self-similar solution can be obtained. By applying sufficient approximation to the boundary layer, the managed conditions of movement, temperature, and nanoparticles are improved; afterward, the framework is changed to a non-dimensional framework utilizing proper comparability changes. A numerical solution for the obtained system of governing equations is achieved. The effect of different parameters on the velocity, temperature, and concentration profiles are discussed. Tangential velocity is observed to decrease with an increase in the Deborah number, whereas tangential velocity increases with increasing values of the angular velocity ratio, relaxation to the retardation time ratio, and buoyancy parameter. Expansion in the Prandtl number is noted to decrease the boundary layer temperature and thickness. The temperature is seen to decrease with an expansion in the parameters of lightness, thermophoresis parameter, and Brownian movement. It is discovered that the Nusselt number expands by expanding the lightness parameter and Prandtl number, whereas it increases by decreasing the Deborah number. We also noticed that the Sherwood number falls incrementally in Deborah and Prandtl numbers, but it upsurges with an increase in the buoyancy parameter

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

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 α1 and buoyancy effect γ1 on velocities F′G and temperature Θ 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

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

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 α1 and buoyancy effect γ1 on velocities F′G and temperature Θ 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

A neural network computational structure for the fractional order breast cancer model

Abstract The current study provides the numerical performances of the fractional kind of breast cancer (FKBC) model, which are based on five different classes including cancer stem cells, healthy cells, tumor cells, excess estrogen, and immune cells. The motive to introduce the fractional order derivatives is to present more precise solutions as compared to integer order. A stochastic computing reliable scheme based on the Levenberg Marquardt backpropagation neural networks (LMBNNS) is proposed to solve three different cases of the fractional order values of the FKBC model. A designed dataset is constructed by using the Adam solver in order to reduce the mean square error by taking the data performances as 9% for both testing and validation, while 82% is used for training. The correctness of the solver is approved through the negligible absolute error and matching of the solutions for each model’s case. To validates the accuracy, and consistency of the solver, the performances based on the error histogram, transition state, and regression for solving the FKBC model

Thermophoresis and Brownian Effect for Chemically Reacting Magneto-Hydrodynamic Nanofluid Flow across an Exponentially Stretching Sheet

This comparative research investigates the influence of a flexible magnetic flux and a chemical change on the freely fluid motion of a (MHD) magneto hydrodynamic boundary layer incompressible nanofluid across an exponentially expanding sheet. Water and ethanol are used for this analysis. The temperature transmission improvement of fluids is described using the Buongiorno model, which includes Brownian movement and thermophoretic distribution. The nonlinear partial differential equalities governing the boundary layer were changed to a set of standard nonlinear differential equalities utilizing certain appropriate similarity transformations. The bvp4c algorithm is then used to tackle the transformed equations numerically. Fluid motion is slowed by the magnetic field, but it is sped up by thermal and mass buoyancy forces and thermophoretic distribution increases non-dimensional fluid temperature resulting in higher temperature and thicker boundary layers. Temperature and concentration, on the other hand, have the same trend in terms of the concentration exponent, Brownian motion constraint, and chemical reaction constraint. Furthermore, The occurrence of a magnetic field, which is aided by thermal and mass buoyancies, assists in the enhancement of heat transmission and wall shear stress, whereas a smaller concentration boundary layer is produced by a first-order chemical reaction and a lower Schmidt number

Comparative dynamics of mixed convection heat transfer under thermal radiation effect with porous medium flow over dual stretched surface

Abstract Due to enhanced heat transfer rate, the nanofluid and hybrid nanofluids have significant industrial uses. The principal objective of this exploration is to investigate how thermal radiation influences the velocity and temperature profile. A water-based rotational nanofluid flow with constant angular speed $${\Omega }$$ Ω is considered for this comparative study. A similarity conversion is applied to change the appearing equations into ODEs. Three different nanoparticles i.e., copper, aluminum, and titanium oxide are used to prepare different nanofluids for comparison. The numerical and graphical outputs are gained by employing the bvp-4c procedure in MATLAB. The results for different constraints are represented through graphs and tables. Higher heat transmission rate and minimized skin friction are noted for triple nanoparticle nanofluid. Skin coefficients in the x-direction and y-direction have reduced by 50% in trihybrid nanofluid by keeping mixed convection levels between the range 3 <\upepsilon \le 11 3 < ϵ ≤ 11 . The heat transmission coefficient with raising the levels of thermal radiation between 0.5 < {\uppi } \le 0.9 0.5 < π ≤ 0.9 and Prandlt number $$7 < {\text{Pr}} \le 11$$ 7 < Pr ≤ 11 has shown a 60% increase