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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.

The contribution of nanoparticles is important to enhance energy resources and improve the efficiency of solar management systems. Owing to impressive thermal consequences, various applications of nanoparticles are observed in engineering processes, chemical and mechanical industries, thermal systems and many more. It is further emphasized that the decomposition of nanoparticles with non-Newtonian materials is more dynamic from an application point of view. The current research communicates the improvement in thermal transportation phenomenon due to interaction of nanoparticles along with decomposing of third-grade base fluid. The nanofluid is immersed with microorganism to justify the applications of bioconvection. The thermal observations are carried out with the existence of some extra thermal consequences like activation energy and radiative phenomenon with nonlinear approach. The modified relations of Fourier and Fick theories have been used to entertain the thermal results. The confined flow is due to the accelerated regime with stretching characteristics. The dynamical system is formulated with the attention of partial differential equations. The physical impact of parameters is addressed for specific range of parameters like 0. 3 ≤ M ≤ 0. 9 , 0. 2 ≤ α ≤ 0. 8 , 0. 1 ≤ Pr ≤ 1. 0 , 0. 3 ≤ Rb ≤ 0. 9 , 0. 2 ≤ δ T ≤ 1. 0 , 0. 2 ≤ Rd ≤ 1. 0 , 0. 2 ≤ Nr ≤ 1. 0 , 0. 2 ≤ Nb ≤ 1. 0 , 0. 3 ≤ β ≤ 1. 0 , 0. 2 ≤ S ≤ 0. 6 , 0. 2 ≤ Nt ≤ 1. 0 , 0. 2 ≤ θ w ≤ 0. 6. The analytical outcomes are listed via homotopy analysis scheme. The role of parameters fluctuating in the various profiles is graphically observed. The results conveyed via the current model are effective in enhancing the thermal processes, solar systems, heat transfer, control of cooling and heating phenomenon, biofuels, fertilizers, etc. [ABSTRACT FROM AUTHOR]

With advances in the use of nanomaterials for heat transfer, various attributes have been recognized by researchers, paving the way for more dynamic and interdisciplinary applications. The assessment of heat and mass transfer facilitated by nanomaterials, especially in the context of sliding phenomena, plays a crucial role in manufacturing, industrial operations and the petroleum sector, among others. Driven by such considerations, the present study introduces bioconvective patterns into nanofluid flow, taking into account several sliding conditions. These multiple sliding conditions, related to speed, temperature, concentration and microorganisms, were examined to study the synergistic effects on heat and mass transfer. The flow examined is influenced by a porous stretchable surface, incorporating suction and injection mechanisms, while the fluid itself is electrically conductive. A firing method was designed to tackle the proposed model. The impact of various parameters is analyzed visually, revealing that the velocity profile is diminished by the velocity slip constant and the permeability of the porous medium. Furthermore, the interaction of multiple sliding effects distinctly enhances thermal processes. [ABSTRACT FROM AUTHOR]

The improved thermal assessment of nano‐particles in presence of magnetic force, thermal radiation and activation energy involve dynamic applications in thermal engineering, industrial processes, and modern technologies. The bioconvection pattern in various nanoparticles attributes novel bio‐technology applications like bio‐fuels petroleum engineering, enzymes, bio‐sensors, and many more. On this end, present theoretical analysis endeavors to examine the thermal characteristics of time dependent Williamson nanofluid confined by an unsteady stretched radioactive Riga plate. Here, nanofluid bioconvection is developed by the combined aspects of buoyancy forces and magnetic field with collaboration of motile microorganisms and nanoparticles. Present analysis is further carried out in presence of activation energy, nonlinear thermal radiation and chemical reaction. The whole exploration is exposed to convective Nield constraints on boundary. The dimensionless form of formulated nonlinear system is achieved with utilization of apposite transformations and then approximate solution is elucidated by shooting technique. The graphical interpretation for numerous relevant parameters on velocity, concentration, temperature and motile microorganism profiles are displayed. The results reveal that an increasing variation in velocity is noticed with modified Hartmann. An increasing nanofluid temperature is associated with Williamson parameter and temperature ratio constant. Moreover, the motile microorganism distribution enhances with bioconvected Lewis and mixed convection constant. [ABSTRACT FROM AUTHOR]

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.

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 fourpointed star enhance the bioconvection flow in a hexagonal cavity. [ABSTRACT FROM AUTHOR]

The bioconvection aspect for the rate type nanomaterial under dynamic of induced magnetic force has been numerically worked out. The Oldroyd-B nonlinear model is incorporated to inspect the interesting rheological dynamic of rate type classifications. Following nonlinear models, the relaxation and retardation features are observed. The numerical proposed data is fundamentally achieved via the shooting method. After developing the dimensionless problem expressions, the shooting numerical algorithm is followed for the computations. The physical onset of parameters is graphically listed with interesting applications. It is observed that a more strong induced magnetic field profile has been observed due to the presence of bio-convective Lewis number and Rayleigh number. An enriched profile of thermal phenomenon due to Grashof number is observed. The composed reflected outcomes present importance in thermal management systems, extrusion systems, plasma physics, chemical processes, nuclear systems, extrusion mechanism, biofuels, etc. [ABSTRACT FROM AUTHOR]

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.

Present research deals with the study of time-dependent pulsatile MHD (Magnetohydrodynamics) hybrid nanofluid with entropy optimization and electrokinetic force in a channel. The current mathematical model is formulated as the Cu − Au − blood (Casson fluid) hybrid nanofluids flow between the bottom and wavy top walls. The pulsatile flow is subjected to an inverse magnetic field of uniform force to study the effect of the resulting Lorenz force. Exact solutions for velocity, temperature, heat transfer rate, and streamlines are constructed by employing the perturbation approach to evaluate coupled nonlinear partial differential equations (PDEs). The velocity (u s) of the blood-based Cu − Au hybrid nanofluid increases with increasing values of the electro-osmotic parameter. The higher values of copper-gold nanoparticle volume fraction increase the entropy generation (N G) . This theoretical investigation helps estimate entropy in systems biology, which is used to treat cancer and improve the function of medical devices. [ABSTRACT FROM AUTHOR]

Recently, nanoengineering has evolved to utilize nanoparticles along with base liquids to enhance the thermal attributes of pure liquids. The industry today also highly relies upon thermal machine performances, and the use of nanomaterials is the key to serve this purpose. In this research, the applications of the slip phenomenon are addressed for bioconvection applications in a non-Newtonian "Eyring–Powell" nanofluid model confined by a stretching sheet. The activation energy and nonlinear thermal radiation are taken as novel impacts during the study. The flow has been saturated by Darcy–Forchheimer porous space. The fundamental laws are attributed to formulate the governing expressions. The numerical simulations are continued employing a shooting scheme to obtain the solutions. The executive and novel physical importance of parameters that governs the flow is addressed for nanofluid velocity, temperature, concentration, and microorganisms' profiles. The observations reveal that presence of slip parameter control the velocity but improve the heat and mass transportation phenomenon. The nanoparticles concentration increases with inertial forces and activation energy. Moreover, the bioconvection Lewis number declines the microorganism profile while increasing trend is noted for higher values of slip parameter. [ABSTRACT FROM AUTHOR]

Using incompressible smoothed particle hydrodynamics (ISPH), this study examines the bioconvection flow of oxytactic microorganisms in a porous annulus populated by nano-encapsulated phase change material (NEPCM). Artificial neural network (ANN) is joined with the ISPH method to accurately predict the values of average N u ‾. Between the outside hexagonal-shaped domain and the embedded wavy cylinder, a new annulus is produced. The ranges of the pertinent parameters are wave amplitude of an embedded cylinder A = 0.1 − 0.5 , Hartmann number H a = 0 − 80 , a radius of the cylinder R c y l d = 0.05 − 0.5 , Darcy number D a = 10 − 2 − 10 − 5 , undulation number K u n d = 2 − 32 , bioconvection Rayleigh number R a b = 1 − 1000 , Rayleigh number R a = 10 3 − 10 6 , and Lewis number L e = 1 − 20. The regulated geometric characteristics of an embedded wavy cylinder, such as wavy amplitude, cylinder radius, and undulation numbers, have been found to contribute significantly to widening the cooling region and minimizing the oxytactic microorganisms. Hence, the embedded wavy cylinder can be applied for various thermal uses including cooling devices and heat exchangers. The average N u ‾ is enhanced under an increment in the geometric parameters of the embedded cylinder. Increasing Rayleigh/bioconvection Rayleigh numbers enhances the buoyancy forces that accelerate the velocity field. [ABSTRACT FROM AUTHOR]

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 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. [ABSTRACT FROM AUTHOR]

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.

In this study, the flow parameters of Reiner–Philippoff nanofluid flow with high‐order slip properties, activation energy, and bioconvection have been analyzed using artificial neural networks (ANNs). Local Nusselt number (LNN), local Sherwood number (LSN), and motile density number (MDN) are considered as flow parameters. Numerical values have been obtained by numerical methods using flow equations. To estimate the flow parameters, three different ANN models have been designed. The Levenberg–Marquardt training algorithm is used in multilayer perceptron network models with 10 neurons in the hidden layers. In all, 70% of the data set has been used for training the models, 15% for validation, and 15% for testing. The performance analysis of the network models has been made by calculating the determined performance parameters. The R values for the LNN, LSN, and MDN parameters have been calculated as 0.99261, 0.98769, and 0.99102, respectively, and the average deviation values are −0.65%, 0.06%, and −0.11%, respectively. The attained outcomes showed that the ANNs can predict the LNN, LSN, and MDN, which are the flow parameters of the Reiner–Philippoff nanofluid flow, with high accuracy. [ABSTRACT FROM AUTHOR]

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.

The ultra-high significances of thermal radiation, magnetic field and activation energy in thermal enhancement processes allow significant applications in chemical and mechanical engineering, modern technology and various thermal engineering eras. The improvement in energy resources and production became one of the major challenges for researchers and scientists for sustained development in industrial growths. Beside this, the bioconvection assessment in nanomaterials conveys prestigious applications in biotechnology like bio-sensors, enzymes, petroleum industry, bio-fuels and many more. In view of such renewable applications, present exploration discloses unsteady two-dimensional flow of third-grade nanomaterial accommodating gyrotactic microorganisms induced by unsteady stretched Riga sheet in porous medium. The formulated flow problem is further scrutinized by utilizing the chemical reaction, activation energy, thermal radiation and magnetic aspects. The convective Nield constraints are further subjected in the current investigation. Apposite transformations are used to condense the nonlinear developed problem into dimensionless ordinary form. The numerical solution of such similar flow problem is presented via shooting technique. The detailed graphical illustrations of the dimensionless temperature, nanoparticles concentration, velocity and motile microorganisms for physical significance of diverse relevant parameters are deliberated. Furthermore, numerical data of local Sherwood, Nusselt and motile density numbers is designated in tabular form. Study accentuated that velocity increases for higher modified Hartmann and material constants, while the effects of buoyancy ratio and bioconvected Rayleigh numbers are rather opposite. The temperature, microorganism and concentration distributions were enhanced for unsteady parameter. It is also acknowledged that the concentration distribution is enhanced for activating the energy number. Moreover, the microorganism distribution enhances for concentration difference and magneto-porous constants, while bioconvected Lewis and Peclet numbers show conflicting trend. [ABSTRACT FROM AUTHOR]

In the era of nano-engineering, the decomposition of nanoparticles with base liquids enhances the thermal performances of such base materials. Owing to the tremendous demand for high thermal performances in industries, the use of nanoparticles becomes more fascinating. In most nanofluid analyses, the thermal inspection of non-Newtonian is based on the assumption of constant viscosity. However, considering viscosity as a function of temperature is more beneficial to improve the transportation of mass and heat transfer phenomenon. This theoretical analysis addresses the narrative role of partial slip and temperature-dependent viscosity in the bioconvection assessment of Maxwell nanofluid confined by a stretched surface. The nonlinear thermal radiation and activation energy applications are encounter as a novel impact. The formulated set of coupled and nonlinear flow problems is numerically presented with proper execution of shooting algorithm. The comparative task for verifications is done against previous investigations with excellent confirmation claim. The graphical exploration because of flow parameters is reported for the nanofluid velocity, temperature, concentration, and microorganisms. The observations are summarized in the conclusion part. [ABSTRACT FROM AUTHOR]

Here theoretical analysis of heat, mass and motile microorganisms transfer rates in Casson fluid flow over stretched permeable surface of cylinder is studied. Investigated is carried out in the presence of suspended nanoparticles and self-propelled gyrotactic microorganisms. The effects of buoyancy forces, magnetic field and thermal radiation are considered. The nanoparticles with suitable suspension are stabilized through mutual effects of buoyancy forces and bioconvection. Furthermore, activation energy and Darcy- Forchheimer effects on bio nanofluid flow are accounted. The constitutive theories are executed to develop the model formulation. The obtained model is made dimensionless trough appropriate transformations. The dimensionless flow model is tackled by built-in algorithm of shooting technique. Impact of flow controlling constraints parameters is physically elaborated by making graphical illustrations. The outcomes based on numerical data against essential engineering formulations like surface drag force, Nusselt, density and Sherwood numbers are tabulated. Main outcomes are successfully summarized in terms of closing remarks. [ABSTRACT FROM AUTHOR]

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.

As part of the growing evolution in nanotechnology and thermal sciences, nanoparticles are considered as an alternative solution for the energy depletion due to their ultra-high thermal effectives. Nanofluids reflect inclusive and broad-spectrum significances in engineering, industrial and bio-engineering like power plants, energy source, air conditioning systems, surface coatings, evaporators, power consumptions, nano-medicine, cancer treatment, etc. The present study describes the bio-convective peristaltic flow of a third-grade nanofluid in a tapered asymmetric channel. Basic conservation laws of mass, momentum, energy, and concentration as well as the microorganism diffusion equation are utilized to model the problem. The simplified form of the modeled expressions is accounted with long wavelength assumptions. For solving the resulting coupled and nonlinear equations, a well-known numerical method implicit finite difference scheme has been utilized. The graphical results describe the velocity, temperature and concentration profiles, and the density of motile microorganisms at the nanoscale. Furthermore, microorganism concentration lines are analyzed. [ABSTRACT FROM AUTHOR]

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.

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. [ABSTRACT FROM AUTHOR]

Owing to the growing interest of bioconvection flow of nanomaterials, many investigations on this topic have been performed, especially in this decade. The bioconvection flow of nanofluid includes some novel significance in era of biotechnology and bio-engineering like bio-fuels, microbial enhanced oil recovery, enzymes, pharmaceutical applications, petroleum engineering, etc. The current analysis aims to explore the various thermal properties of Sutterby nanofluid over rotating and stretchable disks with external consequences of variable thermal conductivity, heat absorption/generation consequences, activation energy and thermal radiation. The considered flow problem is changed into dimensionless form with convenient variables. The numerical structure for the obtained non-dimensional equations is numerically accessed with built-in shooting technique. The consequences of various physical parameters are observed for enhancement of velocity, temperature, concentration and motile microorganism. It is noted that both axial and tangential velocity components decrease with Reynolds number and buoyancy ratio parameter. The nanofluid concentration improves with activation energy and concentration Biot number. Moreover, an improved microorganisms profile is noticed with microorganism Biot number and bioconvection Rayleigh number. [ABSTRACT FROM AUTHOR]

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. [ABSTRACT FROM AUTHOR]

A numerical analysis is performed to analyze the bioconvective double diffusive micropolar non-Newtonian nanofluid flow caused by stationary porous disks. The consequences of the current flow problem are further extended by incorporating the Brownian and thermophoresis aspects. The energy and mass species equations are developed by utilizing the Cattaneo and Christov model of heat-mass fluxes. The flow equations are converted into an ordinary differential model by employing the appropriate variables. The numerical solution is reported by using the MATLAB builtin bvp4c method. The consequences of engineering parameters on the flow velocity, the concentration, the microorganisms, and the temperature profiles are evaluated graphically. The numerical data for fascinating physical quantities, namely, the motile density number, the local Sherwood number, and the local Nusselt number, are calculated and executed against various parametric values. The microrotation magnitude reduces for increasing magnetic parameters. The intensity of the applied magnetic field may be utilized to reduce the angular rotation which occurs in the lubrication processes, especially in the suspension of flows. On the account of industrial applications, the constituted output can be useful to enhance the energy transport efficacy and microbial fuel cells. [ABSTRACT FROM AUTHOR]

This paper investigates the bioconvection in rotating system between two rotating plates immersed in a nanofluid with temperature dependent viscosity and thermal conductivity. The passively controlled model is introduced to characterize the nanoparticle concentration on the upper plate. By means of the similarity transformation, the proposed governing equations are reduced to a class of coupled ODEs with boundary conditions and then the numerical solutions are obtained by the Matlab bvp4c ODE solver. Some important characteristics of velocity, temperature, nanoparticle concentration and density of the motile microorganisms are displayed graphically and discussed in detail. Results show that the viscosity variation parameter has remarkable influence on the local skin friction coefficient and Sherwood number, while local Nusselt number and wall motile microorganisms flux are more sensitive to the thermal conductivity variation parameter. Higher bioconvection Péclet number leads to the aggregation of the motile microorganisms in the middle of the two plates. Moreover, the aggregation of motile microorganisms is weakened by the intense Brownian motion, but improved by the thermophoresis effect. [ABSTRACT FROM AUTHOR]

The present work focuses on the numerical investigations of the existence of oxytactic microorganisms on the bioconvection flow of nano-encapsulated phase change material (NEPCM) inside an annulus. The novel geometry of an annulus contains an inner wavy cylinder and an outer circular cylinder considering a rotational circular velocity of an inner wavy cylinder. The incompressible smoothed particle hydrodynamics (ISPH) method solved the dimensionless form of controlling equations. The novel annulus between the embedded circular cylinder and the outer circular cylinder can be applied in the tube bundles in heat exchangers. Further, rotation of an inner wavy cylinder in a circular cavity can be used in thermal fin's vibration and cooling of the electric devices. The effects of pertinent parameters such as a rotational frequency number ω , bioconvection Rayleigh number Ra b , thermal radiation Rd , Lewis number Le , and Hartmann number Ha on the contours of oxygen concentration ϕ , temperature θ , heat capacity ratio Cr , oxytactic microorganisms N , and velocity field V as well as the average Nusselt & Sherwood numbers Nu ¯ and Sh ¯ are conducted. Increasing ω enhances the maximum of V by 56.6% and lowers Nu ¯. The variations of Ra b are enhanced the contours of N and maximized the velocity field from 0.86 at Ra b = 1 to 8.22 at Ra b = 100 due to the power in bioconvection flow. Increasing Le diminishes the strength of oxygen concentration ϕ and microorganisms N. Increasing Ha from 0 to 50 slows down the velocity field's maximum by 47.2 % and enhances the value of Nu ¯. [ABSTRACT FROM AUTHOR]

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., Competing Interests: 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., (© 2023 Published by Elsevier Ltd.)

[Display omitted] • Here three-dimensional radiative Maxwell nanoparticles is addressed. • Bio-convection is considered. • Non-uniform heat source and sink is inspected for heat transfer phenomenon improvement. • Porous impact and inertial forces are encountered via Darcy-Forchheimer law. The three-dimensional analysis for radiative Maxwell nanoparticles in presence of microorganisms due to rotating frame in numerically addressed numerically. The novel impact of non-uniform heat source and sink is inspected for heat transfer phenomenon improvement. The porous impact and inertial forces are also encountered via Darcy-Forchheimer law. The convective boundary conditions are utilized for the simulated problem. The modified version of Buongiorno nano-model is followed for inspecting the thermophoretic behavior and Brownian movement of nanoparticles. The shooting numerical technique is employed for simulation procedure. The fluctuated pattern of velocity, heat transfer rate, concentration change and microorganism profile is noticed. The results claimed that the presence of inertial parameter declined the velocity but enhanced the nanofluid temperature and concentration profiles. The non-uniform heat source parameters significantly improve the heat transfer rate. The change in rotation parameter reduces the velocity while reverse observations are noted for temperature and concentration profiles. [ABSTRACT FROM AUTHOR]

Velocity profile for (a) parameter M and K (b) Rb and Nr. (c) β m and factor β 1 [Display omitted] • Here Brinkman type micropolar nanoparticles over a stretched surface. • Bio-convection with gyrotactic microorganismss is considered. • Non-uniform heat source and sink is accounted. • Thermo-diffusion aspects of nano-materials are visualized for heat and mass transfer phenomenon. The thermal consequences of the Brinkman type micropolar nanoparticles are inspected theoretically in presence of microorganisms. The impact of non-uniform heat source and sink is also observed. The thermo-diffusion aspects of nano-materials are visualized for heat and mass transfer phenomenon. The appropriate transformations successfully convert the flow problem into dimensionless form. The shooting numerical computations are performed to access the solution. The accuracy of numerical data is predicted via making comparison with already performed continuations. The graphical significances for the desired parameters is addressed with aims for graphs and tables. The findings are summarized with practical applications. The novel outcomes show that velocity of fluid reduces with inclination factor and Brinkman parameter. The nanofluid temperature is enhanced with non-uniform heat source sink parameters and Brinkman parameter. The nanofluid concentration reduces with viscosity constraint. The obtained results presents applications in the era of thermal engineering, energy production, cooling and heat systems, enzymes etc. [ABSTRACT FROM AUTHOR]

A three-dimensional (3-D) investigation of micropolar nanofluid has been presented under the novel impact of nonlinear thermal radiation, activation energy and magnetohydrodynamic features. The induced flow is reflected by a rotating disk which rotates with uniform velocity along z -directions. The fundamental features of Brownian diffusion and thermophoretic assessment is determined by following Buongiorno's nanofluid model. The nanofluid contains gyrotactic microorganisms for which bioconvection pattern is examined for stability assessment. The model flow problem under the certain flow assumptions are retained into the set of dimensionless eqs. A numerical procedure is employed to achieve the solution of such equations. The prime features of parameters against velocity, temperature, concentration and microorganism profiles are graphically examined with justified physical consequences. The numerical computations for wall shear stress, effective local Nusselt number, local Sherwood number and local motile density number are elaborated in terms of numerical data. The simulated theoretical results yield dynamic applications in era of thermal engineering and bio-technology area [ABSTRACT FROM AUTHOR]

The aim of current attempt is to visualize the flow of ('modified') second-grade nanofluid with heat, motile microorganisms and mass transfer rates over stretching surface. The modified second grade fluid is utilized to analyze the rheological behavior. The energy equation is modified with presence of heat absorption and generation effects. In order to stabilize the suspension of nanoparticles, the concept of microorganisms has been introduced. Further present flow analysis is performed with Nield boundary conditions. The formulated equations are first reduced in to dimensionless form by using similarity variables. The approximate solution of these locally similar nonlinear ordinary differential equations is calculated by using shooting method through computational software MATLAB. The calculated results are carefully compared with earlier studies and found an excellent agreement. The ascendancy of interesting parameters like generalized second-grade parameter Brownian motion, thermophoresis effects, Peclet number are examined for multiple values of power law index. It is found that velocity profile declined effectively by buoyancy ratio parameter and bioconvection Rayleigh number. The temperature and concentration profiles enhanced with thermophoretic parameter. It is further observed that motile microorganism profile depressed with Brownian movement parameter and Prandtl number. A prominent demising temperature profile has been noted for shear thickening case as compared to shear thinning. • Modified second-grade nanofluid with motile microorganisms is studied. • Present flow analysis is performed with Nield boundary conditions. • The flow is considered over a stretching surface in two-dimensional channel. • MATLAB software is used to execute the numerical shooting algorithm. • A numerical comparison is also presented for the governing parameters. [ABSTRACT FROM AUTHOR]

On account of fabrication of nano bio-materials applications in various industrial and technological manufacturing systems, bioconvection in nanofluid has become famous in recent years. This investigation is made by adopting bioconvected flow of Oldroyd-B nanofluid over stretched sheet which assumed to be oscillatory. The periodically moving sheet generates the flow. The thermal radiations effects are also encountered in the energy equation. Three independent variables governed by the flow equations are diminished into two independent variables. The series solution for transformed ordinary differential equations is calculated by homotopy analysis method. In present investigation, thermal radiation for linearized Rosseland's assumption is studied in one parametric approach instead of two parametric approaches. Here, the temperature profile does not depend upon Prandtl number and radiation parameter but combination of these two which is termed as effective Prandtl number. Significance of flow parameters on effective local Nusselt number, local Sherwood number and local motile density number is evaluated in tabular form. It is noted that the temperature of nanoparticles effectively enhanced by increasing buoyancy ratio and Rayleigh number. The concentration profile increases with buoyancy ratio and bioconvected Rayleigh number. The higher values of bio-convected Peclet number lead to be decrement of motile microorganism profile. The results presented here can play effective role for enhancement of efficiency of heat transfer devices and microbial fuel cells. • Bioconvected flow of Oldroyd-B nanofluid over stretched sheet is considered. • The periodically moving sheet generates the flow. • The thermal radiations effects are also encountered in the energy equation. • Local Nusselt number, local Sherwood number and local motile density number are evaluated in tabular form. [ABSTRACT FROM AUTHOR]