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This study offers a numerical assessment of unsteady laminar flow, heat and mass transfer of conventional hybrid nanofluid considering activation energy which is noticed in chemical processes. Further, non linear radiation and bioconvection flow with first order slip is also accounted. Nanoparticles as Cu and Al2O3 in the base fluid H2O are included in this analysis. Similarity transformation is applied to the governing model equations to reduce dimensionless form and ''bvp4c'' a MATLAB solver, is applied to get numerical outputs of flow problem. Validation of numerical outcomes is done by an analytical approach optimal auxiliary function method (OAFM). This analysis reports better thermal characteristics when volume fractions 0.0 ≤ φ1 ≤ 0.5 and 0.0 ≤ φ2 ≤ 0.5 of both nanoparticles Cu and Al2O3 are enhanced. Results for present analysis are interpreted numerically and graphically for distinct enhanced values of dimensionless parameters and physical quantities. The high resistance offered by velocity slip (0 ≤ Sv1 ≤ 1.0) and Forchheimer parameter (0 ≤ Fr ≤ 10) cause a drop in velocity profiles. It is noticed that bioconvection Peclet number (0 ≤ Pe ≤ 0.7) leading to a drop (χ(η) = 0.139972 to χ(η) = 0.0817063, at η = 1) in density distribution of motile microorganisms.

A novel treatment of fractional-time derivative using the incompressible smoothed particle hydrodynamics (ISPH) method is introduced to simulate the bioconvection flow of nano-enhanced phase change materials (NEPCM) in a porous hexagonal cavity. The fractional-time derivative is based on the Caputo style, which reflects the fractional order behavior in complex systems. In this work, the circular rotation of the embedded four-pointed star and the motion of oxytactic microorganisms in a hexagonal cavity are conducted. Due to the significance of fractional derivatives in handling real physical problems with more flexibility than conventional derivatives, the present scheme of the ISPH method is developed to solve the fractional-time derivative of the bioconvection flow in a porous hexagonal cavity. This study implicates the variations of a fractional-time derivative, a parametric of an inner four-pointed star, and the pertinent physical parameters on the behavior of a bioconvection flow of a nanofluid in a hexagonal-cavity containing oxytactic microorganisms. The presence of microorganisms has a significant role in many biological, engineering, and medical phenomena. From the present numerical investigation, it is well mentioned that the computational time of the transient processes can be reduced by applying a fractional-time derivative. The variable sizes of an inner four-pointed star enhance the bioconvection flow in a hexagonal cavity.

In this article, we investigate the bioconvection flow of Casson nanofluid by a rotating disk under the impacts of Joule heating, convective conditions, heat source/sink and gyrotactic microorganisms. When Brownian diffusion and thermophoretic effects exist, the Casson fluid is examined. The existing physical problem of Casson nanofluid flow with energy transports is demonstrated under the above considerations in the form of partial differential equations (PDEs). Using the appropriate transformations, the PDEs are converted into non-linear ordinary differential equations (ODEs). The mathematical results are calculated through MATLAB by using the function bvp4c. The problem's results are rigorously examined graphically and described with physical justifications. Velocity fields decrease as the bioconvection Rayleigh parameter rises. The thermal profile and soluteal field of species also magnify with an upsurge in thermophoresis number estimations. The microorganism's fields are decayed by larger microbes Biot number.

The entropy generation phenomenon is important in thermodynamic systems, chemical engineering, industrial systems, reducing the energy consumptions and optimizing the resource utilization. Owing to such motivated applications, aim of current research is to present the applications entropy generation phenomenon in double diffusion flow Carreau-Yasuda nanofluid due to bidirectional stretched surface. The rheology of non-Newtonian fluid is observed by using the Carreau-Yasuda (CY) nonlinear model. The analysis is further supported with suspension of microorganisms with Carreau-Yasuda nanofluid. The formulated model is extended by entertaining the viscous dissipation, thermal radiation and activation energy consequences. The inertial effects are supported with Darcy Forchheimer approach. Additionally, non-Fourier and Fick theories are implanted to observe the thermal phenomenon. The equations resulted from the given model are analytically entertained via homotopy analysis scheme. The physical insight of thermal model is graphically presented. Moreover, the streamlines are plotted for flow model. An enhancing outcomes for entropy generation phenomenon are noted due to diffusion parameter and magnetic parameter. Moreover, the optimized phenomenon also increases due to Brinkman number.

The current study proposes the technique of intelligent numerical computing using back-propagated neural networks (BNNs) for the numerical treatment of a magnet cross-bioconvection flow analysis of nanofluid modal (MHDBC-NFM) including gyrotactic microorganisms with activation energy. Utilizing efficient information, the original system model MHDBC-NFM in partial differential equations (PDEs) is remade into non-linear ordinary differential equations (ODEs). Using the computational capability of the Lobatto IIIA technique, these generated non-linear ODEs are then bettered to provide a dataset of Levenberg Marquardt algorithm-based backpropagated neural networks (LMA-BNNs) for twelve scenarios of this proposed model. The validation, training, and testing processes are carried out simultaneously to acclimate the neural networks. Levenberg-Marquardt backpropagation is used to lower the mean square error (MSE) function, which is then used to derive the estimated solution for MHDBC-NFM for various scenarios. The comparative investigations and performance assessments using correlation, error histograms, MSE, and regression results illustrate the efficacy of the suggested BNNs methodology. The observed diminishing behavior of the nondimensional gyrotactic microorganism field is correlated with the bioconvection Lewis number. Additionally, the results show that temperature profiles become more intense for higher radiation parameter values.

Owing to the admirable thermal features of nanofluids, different applications of nanomaterials are reported in thermal engineering, solar systems, industrial processes, cooling processes etc. The aim of this research is to communicates the thermal impact of cross nanofluid with applications of bioconvection phenomenon. The additional thermal impact of radiated phenomenon, activation energy and viscous dissipation is endorsed. The stretching cylinder induced the flow. The interaction of new variables presents the dimensionless form of the problem. The numerical simulations are performed with implementation of finite difference method by using bvp4c code. The graphical framework for flow parameters is evaluated. It is observed that velocity profile increase for curvature index and curvature parameter. The velocity profile reduces with interaction of first order slip parameter. The enhanced thermal impact of heat transfer due to Biot number is noticed.

The role of nanofluids in the development of many electronic devices at the industrial level is very significant. This investigation describes the thermal exploration for a bioconvective flow of Maxwell nanoparticles over stretching and revolving the cylinder placed in a porous medium. The fluid flow is in contact with chemically reactive activation energy. The swirling flow is induced by the stretching rotary cylinder. The magnetic effect of constant strength B0 is practiced to the flow system in combination with thermally radiative effects and a heat source/sink for controlling the thermal effects upon the flow system. The thermophoretic and Brownian motion characteristics, due to the nanofluid flow, are captured by implementing the Buongiorno model. The central focus of this study is to explore the thermal and mass transfer for the flow problem accompanied by motile microorganisms. The governing equations have been converted to the dimensionless form with similar variables, and the homotopy analysis method (HAM) has then been applied for solution. It has been concluded in this investigation that fluid flow decays for escalation in the Maxwell, porosity, and magnetic parameters, and Forchheimer and bioconvection Rayleigh numbers, while upsurges with the augmenting values of the Buoyancy factor. With the increasing values of the Brownian number, thermophoretic and radiation factors upsurge the thermal profiles and decline the concentration profiles. Moreover, the density of motile microorganisms declines with the expansion in the Peclet number. The range for η is taken from 0 to seven to get the convergence of the graph.

This research communicates the thermal assessment of Sutterby nanofluid containing the gyrotactic microorganisms with solutal and Marangoni boundaries. The applications of melting phenomenon and thermal conductivity are also considered. The flow is confined by a stretched cylinder. The prospective of Brownian motion and thermophoresis diffusions are also taken account via Buongiorno nanofluid model. The problem is formulated with help of governing relations and equations which are altered into dimensionless form via appropriate variables. The numerical scheme based on shooting scheme is employed to access the solution. A comparative analysis is performed to verify the approximated solution. The observations reveal that the velocity profile enhanced with the Marangoni number while a declining velocity profile has been observed with Sutterby nanofluid parameter and Darcy resistance parameter. The nanofluid temperature get rise with thermal conductivity parameter and thermal Biot number. An arising profile of nanofluid concentration is observed for concentration conductivity parameter and buoyancy ratio parameter.

Owing to the magnified thermal performances of nanoparticles and essential applications in various industrial and engineering processes like heat exchangers, cooling systems, boilers, MEMS, chemical engineering, laser diode arrays and cool automobile engines, variety of research is presented in this topic. On this end, current investigation deals with the unsteady flow of Williamson nanofluid containing the gyrotactic microorganisms over a rotating cylinder. The additional features like activation energy, chemical reaction and variable thermal conductivity are also composed in the current flow problem. The whole flow model is subjected to the second order slip from which results two slip parameters that effectively control the associated boundary layers. The formulated problem is based on the utilization of governing equations which are converted into dimensionless form with help of appropriate transformation. The self similar solution of constituted equations is followed by using shooting technique. The obtained results are confirmed by comparing already reported investigations with convincible agreement. The graphical analysis for involved parameters is comprehensively presented for both circular cylinder and flat plat as a liming case. The physical aspects of each flow parameter are discussed. The numerical illustration for local Nusselt number, local Sherwood number and motile density number are also presented in tabular form. The results show that temperature ratio parameter and slip constant increase the nanofluid temperature which is more prominent in case of circular cylinder. The concentration and microorganism distributions enhances with unsteady parameter. Moreover, a declining microorganism distribution is observed with mixed convection parameter, Peclet number and bioconvection Lewis number.

The thermal mechanism of nanofluids due to advanced features is the most interesting research area owing to the applications in heat transmit devices, cooling procedure, energy production, etc. The nanofluids with motile microorganisms signify their importance in bio-medical engineering and biotechnology. This research communicates the accessed dynamic feature of Reiner–Philippoff nanofluid with applications of the bioconvection phenomenon. The magnetic force impact and activation energy features are also intended to perform the radiative analysis of Reiner–Philippoff nanomaterial. The slip features higher-order relations are incorporated to analyze the flow. The modifications in the energy equation are suggested by using thermal radiation with nonlinear relationship. The flow equations, which in turn to non-dimensionless form, are numerically tackled with a shooting scheme. A comprehensive thermal analysis for the endorsed parameters is presented. The numerical data is achieved to examine the fluctuation in heat, mass, and motile density function. The simulated results show that the velocity profile improves with Philippoff fluid parameter while a declining change is noticed for the slip parameter. With increase of Philippoff fluid parameter, both temperature and concentration profile declined. The consideration of higher order slip is more effective for increasing the temperature, concentration and microorganisms’ profiles.

The research communicates the melting applications of viscoelastic nanoparticles with microorganisms due to wedge-shaped configuration. The important features of activation energy, thermophoresis diffusion characteristics and Brownian motion are also highlighted. The analysis is performed in view of Melting process. The flow process is represented mathematically using partial differential equations. For the optimization technique using MATLAB computer-based tools, the Labotto IIIa formulation has utilized. In the velocity equation, the temperature profile, concentration profile and microorganisms' profile, the reporting of the main parameters are fully defined and discussed through figures. The speed can be enhanced by means of a mixed convection appearance is determined. Furthermore, nanoparticles are decreasing in temperature and concentration profiles and the high number of Peclet decreases the profile of microorganisms. This article's research includes a wide range of applications in nanotechnology, electrical and biomedical, biotechnology, medication delivery, chemotherapy, food processing, and other sectors. The claimed results reflect that increasing change in velocity is associated to the higher values of second grade fluid parameter and Marangoni ratio constant. The increase in wedge constant enhanced the velocity. Moreover, the concentration profile and microorganism field reduces with increasing Marangoni ratio constant.

The bioconvective flow of non-Newtonian fluid induced by a stretched surface under the aspects of combined magnetic and porous medium effects is the main focus of the current investigation. Unlike traditional aspects, here the viscoelastic behavior has been examined by a combination of both micropolar and second grade fluid. Further thermophoresis, Brownian motion and thermodiffusion aspects, along with variable thermal conductivity, have also been utilized for the boundary process. The solution of the nonlinear fundamental flow problem is figured out via convergent approach via Mathematica software. It is noted that this flow model is based on theoretical flow assumptions instead of any experimental data. The efficiency of the simulated solution has been determined by comparing with previously reported results. The engineering parameters’ effects are computationally evaluated for some definite range.

Recently, the thermal prospective of nanofluids has been studied extensively by researchers due to motivating thermal applications of such nano-materials. The most fascinating applications associated to the nano-materials included the heat transfer enhancement, solar applications, energy resources, extrusion systems, medical and bio-medical applications, cooling and heating of many devices etc. The collective transport nanoparticles with microorganisms ensure the stability and nanofluids and improve the thermal efficiencies. This research presents the novel applications of induced magnetic force impact on the bio-convective transport of non-Newtonian nanoparticles when the thermal radiation and activation energy consequences become more dominant. The nonlinear thermal relations have been introduced to improve the thermal process. The Maxwell nanofluid model is selected to improve the thermal transportation phenomenon. The consideration of microorganisms is effective to ensure the stability of nano-materials. The stretched surface induced the flow with assumptions of stagnation point. The model is presented in terms of coupled and nonlinear equations which are solved with aim of shooting algorithm. The physical outcomes are carefully observed and presented via graphs and tables. A decrement change in velocity is observed due to velocity ratio parameter. The nanofluid temperature improved with increasing and velocity ratio parameter and Biot constant. Moreover, the presence of reciprocal magnetic Prandtl number increases the nanofluid temperature, concentration and microorganisms profiles.

Recently, nanofluids are an effective source of enhancing the thermal transportation systems associated with industrial and engineering phenomena. With the nanoscale size and effective thermal properties, the nanomaterials convey exclusive beneficial applications in heat exchanges, coolant processes, medical treatment, electronic cooling systems, energy production, etc. Keeping all such motivating significances of nanoparticles in mind, this research presents the thermal aspects of Oldroyd-B nanofluid with applications of bioconvection phenomenon over a convectively heated configuration when the slip effects are more dominant. The bio-convective nanofluid model is further extended by incorporating the thermal radiation relations in nonlinear form and activation energy. The modifications in heat and mass equations are suggested in view of modified Cattaneo-Christov theories. The magnetic force and porous medium applications are also entertained. The convective conditions are imposed on accessing the flow dynamically. The numerical simulations via shooting technique by using MATLAB software are performed with convincing solution accuracy. The physical objective in view of all parameters that govern the flow model is presented in graphs and tables. The obtained theoretical results reflects applications in thermal extrusion processes, power plants, enhancing the heat/mass process, information technology, chemical processes, pharmacological processes, cooling and heating systems, solar energy production, bio-technolgy applications like enzymes, biofules etc.