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This analysis explored the computational process of heat transfer analysis in a thin-film MHD flow embedded in the hybrid nanoparticles, which combine the spherical copper and alumina dispersed in ethylene glycol as the conventional heat transfer Newtonian fluid model over a stretching sheet. The nonlinear ordinary differential equations (ODEs) was attained by transforming partial differential equation (PDEs) as governing equations when implementing the similarity transformations technique. The resulting nonlinear ODEs have been utilized by using the Keller box method. The natures of the thin-film flow and heat transfer through the various values of the pertinent parameters: unsteadiness, nanoparticle volume fraction, thin-film thickness, magnetic interaction and intensity suction/injection are deliberated. The approximate results for velocity and temperature distributions and physical quantities in terms of local skin friction and Nusselt number have been obtained and analyzed via graphs and tables. As a consequence, the suction expresses a more prodigious effect on the hybrid nanofluid rather than injection fluid for all the investigation parameters. It is worth acknowledging that the existence of the nanoparticles and MHD in the viscous hybrid nanofluid tends to enhance the temperature profile but decay the particle movement in the thin-film flow. It is perceived that the velocity and temperature profiles decline for the growth of the unsteadiness, thin-film thickness and suction/injection parameters.

The dual solutions for the stagnation point flow in a cobalt–CeO2/kerosene hybrid nanofluid with melting heat transfer and thermal radiation are analyzed. The partial differential equations are solved by the conversion of the partial differential equations into nonlinear ordinary differential equations by utilizing suitable scaling group transformations. Numerical solutions are obtained by employing the built-in function in the MATLAB software (bvp4c). Physically recoverable solutions are found employing stability analysis. The factor variables of interest (melting parameter, the nanoparticle volume fraction of cobalt and CeO2) are then further analyzed by utilizing the sensitivity analysis (based on the response surface methodology model) for heat transfer rate, as well as the skin friction coefficient. It is found that the heat transfer and skin friction tend to be significantly higher in a hybrid nanofluid due to the radiation and melting heat transfer. The lower branch is found to be unstable, whereas the upper branch is found to be stable. Also, the heat transfer rate and skin friction coefficient are found to be negatively sensitive toward the melting parameter. The model in this study can be applied for microscopic propulsion systems and the nano-electromechanical systems integrated with a nano-based system.

In order to determine the effect of the divergent nozzle length on the single-hose nozzle geometry, the computational couple simulation approach was employed. Furthermore, a model was successfully provided for the two-way exchange of mass, momentum, and energy between two phases. The energy that was exchanged between two involved phases, the solid dry ice particle and a working medium of compressible air-fluid, was also obtained. The model was then coupled with the acoustic programming code solved using the Mump solver. The result revealed that the most extended divergent length showed the highest flow velocity across the nozzle cavity and induced the lowest turbulence flow. Thus, the acoustic sound pressure level was reduced. The shortest divergent nozzle length, equal to 200 mm, produced the highest sound pressure level equal to 85 dBA within the frequency range of 1000 to 1200 Hz. It also produced an average maximum of sound power level, which is 100 dB, across all frequency ranges. Therefore, this study is highly essential since the characteristics of the gas-particle flow within a nozzle cavity provide a deeper understanding of the multiphase flow in turbine and jet engine flow analysis.

Purpose The purpose of this study is to solve convective diffusion equation analytically by considering appropriate boundary conditions and using the Taylor-Aris method to determine the solute concentration, the effective and relative axial diffusivities. Design/methodology/approach >An analysis has been conducted on how body acceleration affects the dispersion of a solute in blood flow, which is known as a Bingham fluid, within an artery. To solve the system of differential equations analytically while validating the target boundary conditions, the blood velocity is obtained. Findings The blood velocity is impacted by the presence of body acceleration, as well as the yield stress associated with Casson fluid and as such, the process of dispersing the solute is distracted. It graphically illustrates how the blood velocity and the process of solute dispersion are affected by various factors, including the amplitude and lead angle of body acceleration, the yield stress, the gradient of pressure and the Peclet number. Originality/value It is witnessed that the blood velocity, the solute concentration and also the effective and relative axial diffusivities experience a drop when either of the amplitude, lead angle or the yield stress rises.

Heat transfer analysis in nanofluids is an active research field due to its extraordinary physical and chemical properties. In the current study, the focus lies on the effects of Stefan blowing when a non-Newtonian Casson base fluid flows over a surface which stretches linearly. A uniform transverse magnetic field is employed. The chemical reaction in the fluid with activation energy and radiation effects have also been engaging the attention. Fundamental laws of conservation are employed to model governing equations of flow. Similarity transform is introduced to reduce the said system of partial differential equations to ordinary differential equations which are in turn tackled analytically using Homotopy Analysis Method with genetic algorithms to optimise the series solution. The impact of pertaining parameters on the dimensionless velocity, temperature and concentration were presented explicitly. This study relevant to remedies for malign tissues, cells or clogged arteries of the heart.

The present work explored the heat transfer and boundary layer flow of a hybrid nanofluid or nanoparticles in an unsteady thin film flow over a stretching sheet. The similarity variables with techniques of the similarity transformations are introduced to reduce the governing equations of partial differential equations (PDEs) systems into a set of an ordinary differential equation (ODEs) system accompanying boundary conditions. The carbon nanotubes with single-wall, SWCNT and the multi-wall, MWCNT in kerosene base fluid are considered. The “bvp4c” function in the MATLAB software is used to solve the reduced form of the mathematical model numerically. The graphs and tables have been generated with the variations of the governing parameter. There exists a strong corelation between findings currently and published results. The rise of the nanoparticle for SWCNT and MWCNT volume fraction increases the local skin friction and the rate of heat transfer, but declines when the flow is decelerated.

This paper explores the mathematical model of thin-film flow and heat transfer utilizing hybrid nanofluid along with the two-dimensional time dependent stretching sheet. The influence of several parameters towards the model are discussed and solved by the method of collocation, namely bvp4c solver that can find in MATLAB software. In this paper, we focused on the effect of parameters are unsteadiness parameter λ, thermocapillarity number M, constant mass transfer parameter S, and concentration of towards the model. The numerical results have been obtained and shown in table and graph form. The effect of thermocapillarity number M and concentration of are explored and graphically portrayed through the velocity, temperature and concentration profile.

Nanofluid bioconvective channel flow is an essential aspect of the recent healthcare industry applications, such as biomedical processing systems. Thus, the present work examined the influence of nth order chemical reaction in an unsteady nanofluid bioconvective channel flow in a horizontal microchannel with expanding/contracting walls. The suitable form of the similarity transformation is exercised to transform the governing boundary layer equations into a more straightforward form of system to ease the computation process. The Runge–Kutta method of fifth-order integration technique solved the reduced boundary layer system and generated the numerical results as the governing parameters vary. It is found that the destructive second-order chemical reaction enhances the mass transfer rate at the lower wall but deteriorates the mass transfer rate at the upper wall. The upper channel wall has a better heat transfer rate than the lower wall when the Reynolds number increases.

The enhancement of heat transfer in a new kind of hybrid nanofluid is more than that of a single nanoparticle. Also, the thermal conductivity of diamond, silver and gold is more than that of copper, titanium oxide and alumina. Hence, an attempt is made to study the influence of hybrid nanoparticles (diamond and silica) with ethylene glycol as a base fluid in a diverging/converging channel. Using similarity analysis, the governing system of equations is transformed to a set of nonlinear ODEs. The resulting system is evaluated computationally by using the most powerful shooting procedure with the support of MATLAB software. The influence of (diamond and silica-ethylene glycol) hybrid nanomaterial on various thermofluidic parameters in a Jeffery–Hamel channel is investigated. The outcomes of this work conclude that (1) the fluid flow velocity decreases in divergent channels with increasing Reynolds number and nanoparticle volume fraction. (2) The skin friction coefficient is found to be a rising function of diamond nanoparticles in the presence of the ethylene glycol-based fluid for divergent channel.

The characteristics of Stefan blowing effects in a magneto-hydrodynamic flow of a Casson fluid past a stretching sheet are investigated. The effects of radiation, heat source/sink, Newtonian heating, Arrhenius activation energy and binary chemical reaction are considered for heat and mass transfer analysis. The homotopy analysis method (HAM) was utilised to solve the transformed non-dimensionalized equations analytically. The impact of various physical parameters affecting the flow are investigated. Further, the relationship of various parameters on the skin friction and rate of heat and mass transfer was explored using correlation and probable error. A sensitivity analysis was carried out based on the Response Surface Methodology to analyse the effect of Stefan blowing parameter, magnetic parameter and stretching/shrinking parameter on the reduced Nusselt number and reduced Sherwood number. A constant positive sensitivity for the reduced Nusselt number towards the Stefan blowing parameter for all levels of magnetic parameter and stretching/shrinking parameter was found. Further, the reduced Sherwood number indicated a negative sensitivity towards the Stefan blowing parameter.

One of the important parameters in developing dry ice blasting nozzle is the high-speed dry ice pellets. However, many studies focus primarily only on its performance without considering the noise emission that comes from an operating nozzle. In this method, the central composite optimization tool has been used. The two-way mass momentum and energy exchange are successfully modeled using the two-way mass momentum model. As an attempt to theoretically verify the model accuracy, a comparison is conducted on the density, pressure, temperature, as well as Mach number ratios corresponding to various ratios of nozzle area. In return, the smallest value of the convergent angle results in the highest velocity of 516.75 m s−1, as well as the highest level of the acoustic power level of 144.36 dB. Besides, one of the vital influencing factors on the emitted acoustic power level is the turbulence intensity, which can achieve a maximum of 1% intensity for an angle of 20° at the throat section. Besides, the same negative sensitivity of around − 0.99% is provided by the velocity and acoustic power level, which is highly responsive toward the convergent angle variation. Furthermore, the optimum nozzle convergent angle for the minimization of the acoustic power level and maximization of the velocity is 7.03°. The novelty of this research lies in the findings on the effective convergent angle of the dry ice blasting nozzle that accelerates the particle flow and minimizes the noise emission from the operating nozzle.

The present work investigated the unsteady stagnation-point flow and heat transfer of a nanofluid containing gyrotactic microorganisms past a permeable moving surface. The similarity transformations produced the mathematical model in the simpler form, which is in the form of ordinary differential equations, and the collocation method solved it numerically. The dual solutions are observable when the governing parameters vary. The decelerating flow and weak effect of suction at the shrinking sheet delays the boundary layer separation. Stability analysis showed that the upper branch solution is a solution with the stabilizing feature while the lower branch solution is an unstable solution which implies the flow with separation. This theoretical study is significantly relevant to microscopic biological propulsion integrated with the nano-based system.

The current and potential applications of bioconvection renewed drive for theoretical research on synthesis and process control in biofuel cells and bioreactors. Thus, this work devoted to solving the problem of free convection in micropolar boundary layer fluid flow and heat transfer past a vertical flat stretching plate within a porous medium. Scaling group of transformation was performed to achieve the appropriate similarity solutions, which was later applied to modify the governing boundary layer system to a nonlinear ordinary differential equations system. The Runge–Kutta method in association with the shooting technique in the Maple software exercised to attain the numerical solutions. There is a strong dependence of momentum transportation on the increment of the Darcy number, the suction/injection parameter and the Grashof number, respectively. The temperature distribution within the thermal boundary layer aided by augmenting the magnitude of the microrotation density.

In this paper, a numerical study was performed to examine the effect of divergent nozzle length of single-hose dry ice blasting on the development of acoustic power level. The active working medium is the mixture of solid dry ice particles and compressible air fluid at the inlet section. The two-dimensional planar model was solved using the finite volume method. The model has been verified theoretically by comparing to four different properties which are pressure ratio, density ratio, temperature ratio, and Mach number ratio over different nozzle area ratios (NARs). The results are presented in the quantitative and qualitative morphological views. The result shows that a more significant value of the NAR gives the highest value of velocity and acoustic power level along the nozzle cavity, of which 560 m s−1 and 146.2 dB, respectively. Besides, turbulence intensity is the most significant influencing factor for the acoustic power level development along the nozzle cavity since the trend of acoustic power level and turbulence intensity are the same. The characteristic of particle gas flow provides a novelty approach to determine the most significant influence factor of the performance and the noise emission.

A numerical simulation study was performed to examine the effect of nozzle geometry and divergent length on gas-particle flows in dual hose dry ice blasting. The simultaneous model of mass momentum and energy exchange between two phases was solved iteratively. The phases are solid dry ice particle and compressible air fluid as a working medium. The results were presented in the gas flow field along the nozzle centerline. The results showed that increasing divergent length decreases the gas-particle density along the centerline; and the density development along the nozzle centerline decreased along the length. Eddy viscosity of the nozzle cavity was steady for length of 0.25 m, but increased drastically for higher values. The substantial increase in eddy viscosity after that position is due to the mixing flow between dry ice pellet and compressed gas which is diverging out from the nozzle outlet area. Thus, the mixing flow experienced back pressure from the atmospheric pressure. The particle mass concentration decreased by increasing nozzle centerline coordinates. The pressure increased along the length; however, it dropped at the end due to the reverse pressure. The temperature increased steadily because of conversion of turbulence to internal thermal energy. The characteristics of gas-particle flow in the nozzle cavity provide better understanding of multiphase flow in turbine and jet engine flow analysis.

Microfluidic-related technologies and micro-electromechanical systems–based microfluidic devices have received applications in science and engineering fields. This article is the study of a mathematical model of steady forced convective flow past a rotating disc immersed in water-based nanofluid with microorganisms. The boundary layer flow of a viscous nanofluid is studied with multiple slip conditions and Stefan blowing effects under the magnetic field influence. The microscopic nanoparticles move randomly and have the characteristics of thermophoresis, and it is being considered that the change in volume fraction of the nanofluid does not affect the thermo-physical properties. The governing equations are nonlinear partial differential equations. At first, the nonlinear partial differential equations are converted to system of nonlinear ordinary differential equations using suitable similarity transformations and then solved numerically. The influence of relevant parameters on velocities, temperature, concentration and motile microorganism density is illustrated and explained thoroughly. This investigation indicated that suction provides a better medium to enhance the transfer rate of heat, mass and microorganisms compared to blowing. This analysis has a wide range engineering application such as electromagnetic micro pumps and nanomechanics.

In the present work, dynamical aspects of boundary layer flow of hydromagnetic fluid (suspended with microorganisms) are investigated near the stagnation region over a stretchable heated permeable sheet. Viscosity is taken as a linear function of temperature where the flow field accommodates diffusion processes due to temperature and concentration gradients (Soret/Dufour numbers). A system of partial differential equations is set up for the mathematical description of the related bio-physical phenomenon. Unit free conversions and analysis of symmetry are implemented to obtain nonlinear dimensional free differential equations setup which can be solved numerically via the Runge–Kutta–Fehlberg scheme. Results in the form of pictorial and tabulation representation reveal that velocity profile increases when viscosity is a function of temperature difference, but the velocity profile influences the fluid temperature in the opposite direction.

A theoretical study is presented for three-dimensional flow of bioconvection nanofluids containing gyrotactic microorganisms over a bi-axial stretching sheet. The effects of anisotropic slip, thermal jump and mass slip are considered in\ud the mathematical model. Suitable similarity transformations are used to reduce the partial differential equation system\ud into a nonlinear ordinary differential system. The transformed nonlinear ordinary differential equations with appropriate\ud transformed boundary conditions are solved numerically with the bvp4c procedure in the symbolic software, MATLAB.\ud The mathematical computations showed that an increase in Brownian motion parameter corresponds to a stronger\ud thermophoretic force which encourages transport of nanoparticles from the hot bi-axial sheet to the quiescent fluid. This\ud increases the nanoparticle volume fraction boundary layer. Fluid temperature and thermal boundary layer thickness\ud are decreased with increasing stretching rate ratio of the bi-axial sheet. The present simulation is of relevance in the\ud fabrication of bio-nanomaterials and thermally-enhanced media for bio-inspired fuel cells.

An effective recruitment evaluation plays an important role in the success of companies, industries and institutions. In order to obtain insight on the relationship between factors contributing to systematic recruitment, the artificial neural network and logic mining approach can be adopted as a data extraction model. In this work, an energy based k satisfiability reverse analysis incorporating a Hopfield neural network is proposed to extract the relationship between the factors in an electronic (E) recruitment data set. The attributes of E recruitment data set are represented in the form of k satisfiability logical representation. We proposed the logical representation to 2-satisfiability and 3-satisfiability representation, which are regarded as a systematic logical representation. The E recruitment data set is obtained from an insurance agency in Malaysia, with the aim of extracting the relationship of dominant attributes that contribute to positive recruitment among the potential candidates. Thus, our approach is evaluated according to correctness, robustness and accuracy of the induced logic obtained, corresponding to the E recruitment data. According to the experimental simulations with different number of neurons, the findings indicated the effectiveness and robustness of energy based k satisfiability reverse analysis with Hopfield neural network in extracting the dominant attributes toward positive recruitment in the insurance agency in Malaysia.

Unsteady three-dimensional laminar stagnation point forced convective boundary layer magnetohydrodynamic flow of a bionanofluid with variable transport properties is studied theoretically and numerically. Thermal convective and zero mass flux boundary conditions are incorporated in this study. The transport properties are assumed to be a function of nanoparticle volume fraction to get physically realistic results. The dimensional boundary layer equations along with the coupled boundary conditions are transformed via similarity transformations into a system of ordinary differential equations. The transformed equations are solved numerically using the Runge–Kutta–Fehlberg fourth-, fifth-order numerical method. The effect of selected governing parameters, namely, viscosity, thermal conductive, mass diffusivity, microorganism diffusivity, magnetic field and bioconvection Schmidt number, on the dimensionless velocity, temperature, nanoparticle volume fraction, microorganism, skin friction coefficient, heat transfer rate, mass transfer rate and microorganism transfer rate, is illustrated graphically and interpreted in detail. Comparisons with previous works are carried out for some limiting cases and found to be in good agreement.

In the development of dry ice blasting nozzle geometry, the critical process parameters depend on particle jet velocity. However, very few researchers have attempted sensitivity on the velocity flow area of specific nozzle geometric parameters. A numerical simulation approach was performed in this paper using Ansys Fluent to investigate different nozzle parameters on the velocity flow field. A two-dimensional model is solved iteratively using averaged Navier-Stokes under Eulerian flow description. It was found that the velocity value increases that reach 550 m/s with an increment of the nozzle area ratio of up to 20 without influencing convergent angle and the velocity magnitude drop linearly from 525 m/s to 505 m/s in with the rise of divergent length that swell up to 700 mm and with constant convergent angle and convergent length.

This research investigated the possibility of minimising airborne pathogen transmission in a mosque during congregational prayer by reducing air flow circulation within the space using the Computational Fluid Dynamics (CFD) simulation method. A three-dimensional model representing an internal mosque building and prayers congregation was created and meshed, using a numerical computational method. In contrast, an individual airborne pathogen transmission was modelled using a discrete particle model (DPM) to represent the particle flow characteristics. The model was validated using a piecewise approach, and the results were in good agreement with the experimental results. This demonstrated that fan deactivation could reduce pathogen transmission by 24.62%. The reason for this significant reduction is that droplets expelled by assailants during a prayer session lack the propagational energy required to cause infection of other members of the congregation due to disengagement of the fans. This research equally revealed that understanding the characteristics of particles adherence to surfaces and their directions of propagation can serve as a guide in epidemic prevention and transmission and control of infectious diseases.

Dry ice blasting plays an essential role in today’s cleaning industry, where many industry players have used it after realizing its advantages. The disadvantage of dry ice blasting is relatively small kinetic energy and offer less aggressive clean effect, especially for dual-hose nozzle geometry. This project was mainly to study the impact force of nozzle geometry of dry ice blasting concerning pressure and distance variation. The nozzle geometries with optimum size and shape are fabricated based on a recent literature study. The experimental research on the effect of the impact forces on different pressures and distances has been conducted to validate the simulation study. The result shows that the optimum nozzle design gives better performance than a based model. Besides, the optimum distance for dry ice blasting operation is less than 400 mm for the pressure range of 2 bars to 4 bars. This distance gives the maximum value of the impacted force for dry ice blasting operation in the industry.

Hopfield Neural Network (HNN) is a sort of neural network that is strongly dependent to energy minimization of solution. Although HNN managed to solve various optimization problem, the output of HNN suffered from a lack of interpretability and variation. This has severely limited the practical usability of HNN in doing logic programming. Inspired by random neuron perturbation, Estimation of Distribution Algorithm (EDA) has been proposed to explore various optimal neuron state. EDAs employs a probabilistic model to sample the neuron state in order to move toward the various optimal location of global minimum energy. In this paper, a new Mutation Hopfield Neural Network (MHNN) will be proposed to do k Satisfiability programming. Based on the experimental result, the proposed MHNN has outperformed conventional HNN in various performance metric.

Developing a data mining model for commodities price plays an important role in future investments and decisions for related companies. Viewed from this perspective, this paper proposes a logic mining model for accurately showcase the behavior of the commodities’ price from 2009 until 2018. This model utilizes 2 Satisfiability Reverse Analysis Method (2SATRA) integrated with Hopfield Neural Network (HNN). HNN is a single layered neural network that can be divided into learning and retrieval phase. In this case, the retrieved neuron state from HNN is an important component in 2SATRA. The inputs of the proposed model were realized by using the real commodities such as Palm oil, Latex, Gold, Crude Petroleum, Timber, Black & White Pepper and Cocoa Bean. This model discusses the implication of the 2SATRA model within the context of the discipline as well as practical application.

The dynamical behaviors of logic mining in real datasets are strongly dependent by its logical structure. In this case, logical rule that has been embedded to neural network has long suffered from a lack of interpretability and accuracy. This has severely limited the practical usability of logic mining. Logical permutation is a definitive finite arrangement of attributes that makes 2SAT became true. It was believed that the effect of permutation will increase the accuracy of the system. In this paper, we presented the effect of logical permutation in logic mining (2SATRA) integrated with recurrent Hopfield Neural Network (HNN). Several benchmark datasets will be used to validate the effect of logical permutation. It has been shown that 2SATRA with different permutation will results in improvement in terms of accuracy value. This finding will lead to a better understand of 2SATRA in doing real life datasets.

The study of laminar flow of heat and mass transfer over a moving surface in bionanofluid is of considerable interest because of its importance for industrial and technological processes such as fabrication of bio-nano materials and thermally enhanced media for bio-inspired fuel cells. Hence, the present work deals with the unsteady bionanofluid flow, heat and mass transfer past an impermeable stretching/shrinking sheet. The appropriate similarity solutions transform the boundary layer equations with three independent variables to a system of ordinary differential equations with one independent variable. The finite difference coupled with the Richardson extrapolation technique in the Maple software solves the reduced system, numerically. The rate of heat transfer is found to be higher when the flow is decelerated past a stretching sheet. It is understood that the state of shrinking sheet limits the rate of heat transfer and the density of the motile microorganisms in the stagnation region.

This paper studies the heat transfer in the blood fluid-based copper and alumina nanoparticles over an unsteady permeable stretching sheet. The model is governed by the governing equations consist of a series of ODEs that are reduced from PDEs by implementing the similarity transformations subjected to mixed boundary conditions. The results of the transformed equations has been obtained by using the Keller-box method in MATLAB software. This paper focuses on the characteristics of thin-film flow and heat transfer through the governing parameters; unsteadiness parameter, nanoparticles volume fraction, Casson parameter, and intensity of suction. From this study, it is observed that the behavior of both fields for nanofluid is lower than hybrid nanofluid under the suction effect. It is noticed that enhance the physical parameters increase the velocity field of the fluid. Further, increase the physical parameter also deteriorate the temperature field except for nanoparticles volume fraction.

Biological transport in nanofluid is an essential new focus in fluid dynamics since the suspensions of microorganisms and nanoparticles proved to enhance the thermal conductivity of the fluid, which benefits many industrial applications for instances, biofuel cells and bio-microfluidics devices. In this regard, the present work is dedicated to investigating the effects of magnetohydrodynamics (MHD) and chemical reaction in the boundary layer flow, heat, mass and living microorganism transfer past a permeable stretching surface in a dilatant nanofluid. At the surface of the stretching sheet, there are multiple kinds of slips which affect the mechanisms within the vicinity of the boundary layer. The scaling group analysis has been performed to produce the appropriate similarity solution specifically for the present model. The governing boundary layer model in the form of the partial differential equations are reduced to a system of ordinary differential equations via similarity solutions to ease the computational process. The transformed mathematical model is then solved numerically via the Blottner’s finite difference method (FDM). The presences of the velocity slip at the surface of the stretching sheet decelerated the fluid flow.

Radial Basis Function Neural Network (RBFNN) is a class of Artificial Neural Network (ANN) that contains hidden layer processing units (neurons) with nonlinear, radially symmetric activation functions. Consequently, RBFNN has extensively suffered from significant computational error and difficulties in approximating the optimal hidden neuron, especially when dealing with Boolean Satisfiability logical rule. In this paper, we present a comprehensive investigation of the potential effect of systematic Satisfiability programming as a logical rule, namely 2 Satisfiability (2SAT) to optimize the output weights and parameters in RBFNN. The 2SAT logical rule has extensively applied in various disciplines, ranging from industrial automation to the complex management system. The core impetus of this study is to investigate the effectiveness of 2SAT logical rule in reducing the computational burden for RBFNN by obtaining the parameters in RBFNN. The comparison is made between RBFNN and the existing method, based on the Hopfield Neural Network (HNN) in searching for the optimal neuron state by utilizing different numbers of neurons. The comparison was made with the HNN as a benchmark to validate the final output of our proposed RBFNN with 2SAT logical rule. Note that the final output in HNN is represented in terms of the quality of the final states produced at the end of the simulation. The simulation dynamic was carried out by using the simulated data, randomly generated by the program. In terms of 2SAT logical rule, simulation revealed that RBFNN has two advantages over HNN model: RBFNN can obtain the correct final neuron state with the lowest error and does not require any approximation for the number of hidden layers. Furthermore, this study provides a new paradigm in the field feed-forward neural network by implementing a more systematic propositional logic rule.

This paper studies heat transfer in a two-dimensional magnetohydrodynamic viscous incompressible flow in convergent/divergent channels. The temperature profile was obtained numerically for both cases of convergent/divergent channels. It was found that the temperature profile increases with an increase in Reynold number, Prandtl number, Nusselt number and angle of the wall but decreases with an increase in Hartmann number. A relatively new numerical method called the spectral homotopy analysis method (SHAM) was used to solve the governing non-linear differential equations. The SHAM 3rd order results matched with the DTM and shooting, showing that SHAM is feasible as a technique to be used.

An analysis is carried out to study the steady mixed convective boundary layer flow of a nanofluid in a Darcian porous media with microorganisms past a vertical stretching/shrinking sheet. Heat generation/absorption and chemical reaction effects are incorporated in the model. The partial differential equations are transformed into a system of ordinary differential equations by using similarity transformations generated by scaling group transformations. The transformed equations with boundary conditions are solved numerically. The effects of controlling parameters such as velocity slip, Darcy number, heat generation/absorption and chemical reaction on the skin friction factor, heat transfer, mass transfer and microorganism transfer are shown and discuss through graphs. Comparison of numerical solutions in the present study with the previous existing results in literature are made and comparison results are in very good agreement.

A mathematical model is presented for three-dimensional unsteady boundary layer slip flow of Newtonian nanofluids containing gyrotactic microorganisms over a stretching cylinder. Both hydrodynamic and thermal slips are included. By applying suitable similarity transformations, the governing equations are transformed into a set of nonlinear ordinary differential equations with appropriate boundary conditions. The transformed nonlinear ordinary differential boundary value problem is then solved using the Runge-Kutta-Fehlberg fourth-fifth order numerical method in Maple 18 symbolic software. The effects of the controlling parameters on the dimensionless velocity, temperature, nanoparticle volume fractions and microorganism motile density functions have been illustrated graphically. Comparisons of the present paper with the existing published results indicate good agreement and supports the validity and the accuracy of our numerical computations. Increasing bioconvection Schmidt number is observed to depress motile micro-organism density function. Increasing thermal slip parameter leads to a decrease in temperature. Thermal slip also exerts a strong influence on nano-particle concentration. The flow is accelerated with positive unsteadiness parameter (accelerating cylinder) and temperature and micro-organism density function are also increased. However nano-particle concentration is reduced with positive unsteadiness parameter. Increasing hydrodynamic slip is observed to boost temperatures and micro-organism density whereas it decelerates the flow and reduces nano-particle concentrations. The study is relevant to nano-biopolymer manufacturing processes.