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The research on entropy generation in a mechanical system is quite imperative owing to its immense applications in the production of advanced cooling devices and medical appliances. The basic need on this research is how to optimize the irreversibilities within the systems and channelize that energy towards the benefit. This study elucidates the entropy generation analysis of a Casson nanofluid near a stagnation point over a lubricated vertical wall. A thin film of shear-thinning liquid with power law index of 0.5 is employed on the wall to ensure the lubrication. The effect of induced magnetic field and the chemical reaction stimulated by the activation energy is also incorporated within the flow. The non-linear PDEs of the substantive problem along with the compatible interfacial and boundary conditions are reverted into ODEs with the aid of suitable similarity transformation, and then cracked numerically using the sixth-order Runge Kutta method assisted with Nachtsheim–Swigert shooting practice. One of the significant findings reveals that the fluid friction irreversibilities in the entropy generation are diminished with the magnetic parameter and the Casson parameter, whereas the thermal irreversibility predominates over the total entropy generation for the escalating values of the activation energy parameter. [ABSTRACT FROM AUTHOR]

This study examines the effect of heat production and radiation absorption on the magnetohydrodynamic Casson fluid flow at the stagnation point in a porous medium. We convert the group of fluid flow equations, which are non-linear partial differential equations with suitable boundary constraints, into a set of non-linear ordinary differential equations using similarity transformations. The homotopy analysis method (HAM) solves the converted system of ordinary differential equations. We draw graphs for numerous values of non-dimensional parameters and tables of surface drag force, rates of heat transfer, and mass transfer to analyze the relationship between velocity field, temperature field, concentration field, and other essential parameters involved in the study. We have proven that the Dufour number, radiation parameter, and heat generation parameter elevate the fluid temperature, whereas the magnetic parameter lowers it. The Casson fluid parameter, buoyancy force parameter, and mixed convection parameter all promote fluid movement throughout the flow field. The presented tabular data allows us to see the trend of heat and mass transfer rates, as well as drag force rates, against important parameters, enhancing our understanding of these rates. [ABSTRACT FROM AUTHOR]

The current study presents the stagnation point of tetra-hybrid nanofluid blood flow over a vertical stretching cylinder. Stratification phenomenon and thermal radiation effects are considered and filled with porous structure of tissues. Adding motile microorganisms to the blood flow to examine the bioconvection phenomenon is a key part of this study. Ag, MoS2, SWCNT, and MWCNT are considered for enhancing thermal transmission rate, and comparisons are done for di-hybrid, tri-hybrid and tetra-hybrid nanofluids flowing in the blood stream. Numerical results are computed using the fifth-order Runge-Kutta-Fehlberg method. The impacts of non-dimensional parameters are figured out graphically in velocity, energy, concentration, and density of microorganism profiles and explained in detail. Validation of current result with distinct values of the curvature parameter and volume fraction is found to be in excellent agreement. Heat transfer, mass transfer rate, and drag force are discussed via bar graphs for important physical parameters such as Hartmann number, Prandtl number, and Schmidt number, and their results are investigated. Sensitivity analysis is done for design optimization and parameters results are discussed to fix good-to-fit data. The measured outcomes demonstrate that the thermal radiation parameter has the maximum heat transfer rate, and the major results of the current study are that sphere-shaped nanoparticles have an efficient heat transfer rate 16.3% higher than other geometry. Tetra-hybrid nanofluids have efficient heat transfer rate 2.99% higher than hybrid nanofluid. The discussed results have significant applications in atherosclerosis treatment, drug delivery, deep tissue penetration for targeted treatment, and neurotherapy. [ABSTRACT FROM AUTHOR]

Investigation of ternary nanofluids piqued the interest of researchers and engineers more specifically in chemical and applied thermal engineering. The improved characteristics of ternary nanoliquid are dominant over the previous classes Thus, the analysis of nanofluids through elastic surface is common from engineering and industrial applications which is important to report. This research purely emphasized on the study of ternary nanoliquids through the permeable elastic surface. The enhanced thermal conductivity, density, heat capacitance, and viscosity were estimated using the supporting correlations. Further, different physical constraints like thermal slip, radiation, suction/injection, uniform surface convection, and stretching/shrinking effects were added to enhance the model's novelty. Then, the model was analyzed numerically, and the physical results were furnished. It is investigated that the concentration of Al2O3 in the range of 0.02 to 0.2 reduced the movement to about a stagnant point, and also, a quick decrease in the velocity is observed for the suction case. The thermal performance of the problem is enhanced in the presence of stronger convection (B1 = 0.2, 0.4, 0.6, 0.8) provided from the surface, and the optimum temperature of ternary nanofluid is noticed near the stagnant surface. Further, the existence of viscous dissipation (Ec1 = 0.01, 0.02, 0.03, 0.04) and nanoparticle amount (Φ3 = 0.02, 0.08, 0.14, 0.20) highly contributes in the temperature for both stretching and shrinking cases. The significant effects of heating source (Q1 = 0.1, 0.2, 0.3, 0.4) and imposed thermal radiation effects (Rd = 0.1, 0.2, 0.3, 0.4) potentially enhanced the temperature performance of the ternary nanofluidic system. Thus, the added physical constraints are good physical tools to augment the model performance. [ABSTRACT FROM AUTHOR]

Recent advancements in nanofluid technology have emphasized the potential of ternary hybrid nanofluids (THNFs) to significantly enhance thermal and hydrodynamic properties. The implementation of a wavy sinusoidal cylinder is proposed as a novel approach to optimize heat transfer in a variety of engineering applications. This study focuses on analysing the flow and thermal behaviour of TiO2-Al2O3-MoS2/Kerosene oil a THNF around a circular cylinder with a sinusoidal radius, demonstrating enhanced heat conduction capabilities compared to conventional hybrid nanofluids. The governing equations, formulated as partial differential equations, are solved using the bvp4c solver. The study reveals that the shape of nanoparticles plays a crucial role in heat transfer efficiency. Specifically, when the solid volume fraction increases from 1% to 3%, brick-shaped particles exhibit the lowest heat transfer enhancement of 25.80%, while blade-shaped particles achieve the highest enhancement of 68.24%. Additionally, the heat transfer coefficient improves from 1.5% to 1.8% across different nanoparticle shapes under varying dissipation parameters. Similar trends are observed in the reduction of drag force with changes in the velocity slip parameter. These findings underscore the significant impact of nanoparticle shape and volume fraction on the thermal performance of THNFs, offering valuable insights for optimizing heat transfer systems in engineering applications. [ABSTRACT FROM AUTHOR]

Thermal transmission is very significant in the industrial and engineering sectors. This research aims to investigate the MHD stagnation point movement of methanol and water-driven Cu −Al2O3 hybrid nanofluid flow via an exponentially extending cylinder. An inclined magnetic field’s control, suction or injection and viscous dissipation impacts are used and considered in the flow paradigm, as no prior research has been performed on it. This motivated the authors to perform a computational analysis of the distinct base fluid (water and methanol)-driven hybrid nanofluid flow with the aforementioned impacts, which gives distinctiveness to the flow model. The basic partial differential equation flow mechanism has been streamlined to nondimensional ordinary differential equations by the inclusion of distinct dimensionless factors, which are simulated employing the BVP4c methodology. The impacts of dimensionless variables, namely the Eckert factor, suction/injection term, Biot factor, velocity ratio term and magnetic factor, on the flow speed, thermal distribution, rate of shearing stress and thermal transmission are delineated in figures and demonstrated with tables. The major findings specify that methanol-based hybrid nanofluid (Cu −Al2O3/methanol) has a significantly higher thermal transmission rate when compared with the water-based hybrid nanofluid (Cu −Al2O3/water). Furthermore, it has been shown that the methanol-based hybrid nanofluid has an absolute friction drag that is up to 26.5% larger than that of nanofluid. The thermal gradient reduces with the enhancement of Ec and M. Moreover, the fluid temperature upsurges as Ec and Bi elevate. These outcomes significantly advance fluid dynamics and nanofluid research, offering opportunities for improved thermal transmission in numerous industrial and engineering sectors. A noteworthy validation with previously published work has also been performed. [ABSTRACT FROM AUTHOR]

This study aims to discover the application of bioconvection and heat absorption or omission aspect of 2D incompressible MHD Oldroyd-B nanofluid over the stagnation region. Directed by suitable similarity transformations, the system of PDEs is transformed into a system of coupled nonlinear ODEs. The results were made by using Runge–Kutta shooting technique. The Buongiorno model is capitalized while Oldroyd-B model is employed for portraying the viscoelastic behavior of the flow. In order to visualize the impact of relevant parameters on momentum boundary layer, temperature, concentration and microorganism profiles are computed graphically. Numerical outcomes for the local Nusselt number, Sherwood number, microorganism number and local skin friction number are calculated for different parametric situations to provide interesting features of the examination. Furthermore, it has been also observed from statistical point that the correlation coefficient of the local Nusselt number, Sherwood number, microorganism number and local skin friction number with various parametric situations are highly significant at the α = 0. 0 1 level of significance (p < 0. 0 0 0 1 for a two-tailed test). [ABSTRACT FROM AUTHOR]

This research delves into evaluating thermal radiative flux and energy in a micropolar nanofluid undergoing stagnation point flow. Its primary objective is to better understand heat transfer characteristics and energy distribution within the flow field. The study comprehensively analyses the nanofluid's thermal behavior, specifically exploring the influence of relevant factors on energy distribution. Through graphical representations of the results and in-depth discussions, valuable insights are gleaned regarding the thermal performance of micropolar nanofluids in stagnation point flows. The partial differential equations for the developed model altered into a system of nonlinear ordinary differential equations of dimensional free statements. These are numerically solved using the Runge–Kutta–Fehlberg integration schema and shooting technique. The obtained results are visually presented through graphs and extensively discussed. As observed, the velocity field decreases with various values of porosity and Prandtl terms and temperature distribution is raised by about 0.25%, correspondingly with increasing values of thermophoresis and radiation. [ABSTRACT FROM AUTHOR]

This study is focused on examining how solar radiation, thermal convection, and viscous dissipation impact the stagnation point flow in a variable porous space. The colloidal nanoparticles of TiO 2 (titanium oxide) have dispersed in different base fluids taken as H2O (water) and C2H6O2 (ethylene glycol). Boosting heat transfer is made possible by the porous space in hybrid nanofluid flow. The use of porous media leads to increased surface area for heat transfer, which in turn improves heat exchange between the nanofluid and the solid matrix. A suitable set of transformable variables is employed to convert the leading equations in dimensionless form. This set of new equations has been evaluated by employing Mathematica and artificial neural network (ANN). It has been noticed in this work that, the thermal panels have augmented with escalation in volume fractions of solid nanoparticles as well as with positive and negative growth in Eckert number. The range of the parameter Rd , S , Da , Gr , ϕ is considered between 0 and 1. While Ec number range is taken out of this range for better performance. [ABSTRACT FROM AUTHOR]

This study examines the effect of heat production and radiation absorption on the magnetohydrodynamic Casson fluid flow at the stagnation point in a porous medium. We convert the group of fluid flow equations, which are non-linear partial differential equations with suitable boundary constraints, into a set of non-linear ordinary differential equations using similarity transformations. The homotopy analysis method (HAM) solves the converted system of ordinary differential equations. We draw graphs for numerous values of non-dimensional parameters and tables of surface drag force, rates of heat transfer, and mass transfer to analyze the relationship between velocity field, temperature field, concentration field, and other essential parameters involved in the study. We have proven that the Dufour number, radiation parameter, and heat generation parameter elevate the fluid temperature, whereas the magnetic parameter lowers it. The Casson fluid parameter, buoyancy force parameter, and mixed convection parameter all promote fluid movement throughout the flow field. The presented tabular data allows us to see the trend of heat and mass transfer rates, as well as drag force rates, against important parameters, enhancing our understanding of these rates.

In recent times, the interaction of nanoparticles has significantly enhanced the thermal association of heat transport. This phenomenon plays a crucial role in hydraulic systems, particularly in the context of lubrication and its associated consequences on mass and heat transport. Current studies have focused on investigating the thermal effects of a third-order nanofluid on a lubricated stretched surface near an analytical stagnation point. The lubrication process involves the use of a thin, adjustable coating of lubricant fluid. To analyze this complex system, we employ the Buongiorno model and explore thermophoresis and the Brownian motion phenomenon. For deriving analytical results of updated boundary layer ordinary differential equations, we rely on the dependable and effective hybrid homotopy analysis method (HHAM). To exhibit the effectiveness of our study, we provide a numerical comparison. Based on theoretical flow assumptions, we establish a range of flow parameters. In the presence of lubrication, we physically examine how these parameters affect temperatures, velocities, concentration, and other relevant quantities of thermal interest. These new findings have practical applications in polymer production, heat transmission, and hydraulic systems. [ABSTRACT FROM AUTHOR]

Industrial applications in domains such as warm rolling, crystal development, thermal extrusion and optical fiber illustration are seeing a significant increase. These applications specifically focus on addressing the challenge of a cylinder in motion inside a fluid environment. Elevated temperatures may affect the viscosity and thermal conductivity of fluids. Understanding the relationship between temperature and the properties of fluids is crucial. In light of these presumptions, the primary goal of this study is to examine, under transverse magnetic field, shape factor, velocity, thermal slip conditions and viscous dissipation, how temperature-dependent fluid properties could enhance the heat transfer efficiency and performance evolution of ternary hybrid nanofluid. In order to study flow fluctuations, the impact of nanoparticle addition and improvements in heat transfer, a variable Prandtl number is also included. The use of similarity variables converts the controlling flow model from partial differential equations (PDEs) to ordinary differential equations (ODEs). Mathematica’s shooting strategy solves ODEs using the fourth-order Runge–Kutta (RK-IV) method. Numerical calculations were done after setting parameters to acquire the desired results. Analytical data are provided in tables and graphs for convenient usage. The results showed that the velocity profile increases as the values of ϕ3, Pr, M, Re and S grow, and decreases when the values of θr decrease. Re, Pr and S lower the temperature profile, whereas ϕ3, θr and Ec raise it. The skin friction profile steepens as ϕ3, S, Re and M increase relative to the stretched cylinder, and flattens as θr and ω decrease. The Nusselt number profile rises as θr, Pr, S and Re decrease with ϕ3, Ec and δ. When the Prandtl number goes from 3.0 to 6.2 in a ternary hybrid nanofluid with brick-shaped nanoparticles, the Nusselt number goes up by around 55.7%. [ABSTRACT FROM AUTHOR]

AbstractThe main purpose of this article is to optimize the thermal performance of system involving stagnation point flow of Al2O3+ water based nanofluid over a nonlinearly stretching surface. The mathematical model for the problem under consideration utilizes the Tiwari and Das’s single phase flow model for the nanofluid. The aim is to find a similar solution of the problem using some suitable similarity variables. The partial differential equations dictating the flow situation are converted into dimensionless ordinary differential equations. Numerical solution of the system of dimensionless ordinary differential equations has been obtained with the help of MATLAB’s inbuilt bvp4c package. Further, Taguchi analysis along with ANOVA and regression analysis have been performed against the variable like Pr,γ,n and ϕ corresponding to response variable to predict the optimal heat transfer of the system. Outcomes of ANOVA indicate that Pr has maximum and ϕ has minimum influence over the Nusselt number. [ABSTRACT FROM AUTHOR]

This study examines the rheological effects of a hybrid nanofluid and the swimming behavior of gyrotactic microorganisms in an unsteady flow over an expandable Riga wedge. A stagnation point region, suspended with hybrid nanofluid and microorganisms, is considered, subject to velocity slip at the boundary. The study investigates the bio-convection fluid flow phenomenon and considers the effects of chemical reaction, heat source/sink, mass suction, and activation energy. A precise similarity transformation is used to convert the governing partial differential equations into ordinary differential equations. These are then numerically solved using the shooting technique in MATLAB, specifically with the BVP4C solver. The study scrutinizes the effects of various relevant parameters on the dimensionless profiles of velocity, temperature, concentration, and microorganisms. Furthermore, the surface drag force, heat transfer rate, Sherwood number, and motile microorganism density are calculated. To validate the accuracy of the adopted numerical scheme, a tabular comparison is made between the current results and those from the literature in a limiting case. It is observed that adding Al2O3 nanoparticles decreases the fluid velocity, while adding Cu nanoparticles increases it; however, in both cases, the fluid temperature decreases. Increasing the wedge angle parameter enhances the fluid temperature and motile density. The heat transfer coefficient decreases with increasing nanoparticle concentration and wedge angle parameter, whereas the opposite behavior is observed for the Biot number. [ABSTRACT FROM AUTHOR]

Abstract Owing to enhanced thermal characteristics of nanomaterials, multidisciplinary applications of such particles have been utilized in the industrial and engineering processes, chemical systems, solar energy, extrusion processes, nuclear systems etc. The aim of current work is to suggests the thermal performances of thixotropic nanofluid with interaction of magnetic force. The suspension of microorganisms in thixotropic nanofluid is assumed. The investigation is further supported with the triple diffusion flow. The motivations for considering the triple diffusion phenomenon are associated to attaining more thermal applications. The flow pattern is subject to novel stagnation point flow. The convective thermal constraints are incorporated. The modeled problem is numerically evaluated by using shooting technique. Different consequences of physical parameters involving the problem are graphically attributed. The insight analysis is presented for proposed problem with different engineering applications. It is claimed that induced magnetic field enhanced due to magnetic parameter while declining results are observed for thixotropic parameter. The heat transfer enhances due to variation of Dufour number. Furthermore, low profile of nanoparticles concentration has been observed for thixotropic parameter and nano-Lewis number.

Abstract This project covers the investigation of the boundary layer flow of a hybrid nanofluid past a biaxial stretching/shrinking sheet. The hybrid nanofluid consists of copper (Cu) and alumina ( $${Al}_{2}{O}_{3}$$ Al 2 O 3 ) nanoparticles, which are diluted into water to form $$Cu-{Al}_{2}{O}_{3}-$$ C u - Al 2 O 3 - water hybrid nanofluid. The governing partial differential equations (PDEs) are derived from Navier-Stokes equations. The system of PDEs is reduced to a system of ordinary differential equations using an appropriate similarity transformation. MATLAB’s bvp4c function is used to numerically solve the resulting system of governing ordinary differential equations. The aim of this study is to gain a comprehensive understanding of the intricate behavior displayed by hybrid nanofluids on the stagnant directed flow of extended/shrunk flat surfaces, considering the effects of Brownian motion, thermophoresis, and various nanoparticles. The generated numerical results of flow profiles, skin friction coefficient, and Nusselt number have been presented graphically and discussed in the relevance of the governing parameters contributing to the flow. The outcomes reveal that the velocity components are reduced with increasing $${Al}_{2}{O}_{3}-$$ Al 2 O 3 - water nanofluid volume fraction. A monotonical increase in the parameters stretching/shrinking and suction/injection with a corresponding rise in both nanoparticles volume fraction propels heat gradient rate. An increase in the Schmidt numbers encourages a mass transfer field due to an enhanced boundary viscosity. The validation of numerical results is done with previously published results. Through our results, we have found that the performance of a hybrid nanofluid is more significant than other fluids. In addition, this study enhances the progress of theoretical comprehension by endeavoring to resolve the intricate interplay between fluid dynamics and thermal characteristics through the utilization of numerical approaches.

The industrial sector has shown a growing interest in hybrid nanofluids affected by magnetohydrodynamics (MHD) owing to their wide range of applications, including photovoltaic water heaters and scraped surface heat exchangers. The main purpose of this study is to look at how entropy is created in a hybrid nanofluid of |${\rm{A{{l}_2}{{O}_3}{-}Cu}}$| mixed with |${\rm{{{H}_2}O}}$| at a non-axisymmetric stagnation point flow with Joule heating and viscous dissipation. By using appropriate non-similarity transformations, the partial differential equations (PDEs) governing the boundary layer region of this issue are transformed into a set of non-linear PDEs. The BVP4c MATLAB program, which uses local non-similarity and additional truncation, may fix the problem. The velocity profiles in both directions grow when the values of |${{\phi }_2},\ M,\lambda $|⁠ , and A parameters increase. The temperature profile rises as the values of A and |$Ec$| grow and lowers as |${{\phi }_2}$| and M increase. The obtained numerical findings demonstrate significant impacts on both the heat transfer rate and fluid flow parameters of the hybrid nanofluid. When the concentration of nanoparticles and the magnetic parameter are heightened, there is an enhancement seen in the skin friction coefficient and decline in heat transfer rate. In addition, the entropy production profile shows an increasing tendency as a function of the parameters |${{\phi }_2},\ M,$| and |$Br,$| while demonstrating a decreasing tendency of function of the parameter |$\alpha $|⁠. The Bejan number profile has a positive correlation with the parameter |$\alpha $| but shows a negative correlation with the variables |${{\phi }_2},\ M,$| and |$Br$|⁠. [ABSTRACT FROM AUTHOR]

The capture of individual cells using microfluidic chips represents a widely adopted and efficient approach for investigating the biochemical microenvironment of singular cells. While conventional methods reliant on boundary effects pose challenges in precisely manipulating individual cells, single-cell capture grounded in the principle of stagnation point flow offers a solution to this limitation. Nevertheless, such capture mechanisms encounter inconsistency due to the instability of the flow field and stagnation point. In this study, a microfluidic device for the stable capture of single cells was designed, integrating the principle of fluid mechanics by amalgamating stagnation point flow and boundary effects. This innovative microfluidic chip transcended the limitations associated with single methodologies, leveraging the strengths of both stagnation point flow and boundary effects to achieve reliable single-cell capture. Notably, the incorporation of capture ports at the stagnation point not only harnessed boundary effects but also enhanced capture efficiency significantly, elevating it from 31.9% to 83.3%, thereby augmenting capture stability. Furthermore, computational simulations demonstrated the efficacy of the capture ports in entrapping particles of varying diameters, including 9 μm, 14 μm, and 18 μm. Experiment validation underscored the capability of this microfluidic system to capture single cells within the chip, maintaining stability even under flow rate perturbations spanning from 60 μL/min to 120 μL/min. Consequently, cells with dimensions between 8 μm and 12 μm can be reliably captured. The designed microfluidic system not only furnishes a straightforward and efficient experimental platform but also holds promise for facilitating deeper investigations into the intricate interplay between individual cells and their surrounding microenvironment. [ABSTRACT FROM AUTHOR]

This study investigates two-dimensional time-dependent stagnation point nanofluid flow over a permeable stretching or sinking sheet. The electrically conducting fluid allows for the interaction of a transverse magnetic field along with magnetic dissipation and thermal radiation to enrich the flow phenomena. The use of nanofluids is becoming increasingly important in a variety of industrial applications, as well as in engineering and biomedicine. The process of peristaltic pumping, the flow of blood in the artery, the drug delivery process, and besides that, the cooling of electronic devices for the better shape of the product at the final stage of production, the use of nanofluid, are all important. The transformed dimensionless governing equations are obtained by the implementation of various transformation rules, and the model is designed by using different thermophysical properties such as viscosity, conductivity, etc. Finally, the numerical technique RK-fourth-order method is deployed to solve the set of equations and the iteration process is continued up to the desired accuracy of 10 − 5 . The validation of the current result is shown with the earlier investigation in particular cases, and further, the behavior of the physical parameters is presented through graphs. It is observed that the particle concentration has a greater impact in enhancing the velocity distribution for the variation of suction/injection. The behavior of the magnetic parameter vis-à-vis the unsteadiness parameter and the thermal buoyancy presents their greater contribution in enhancing the magnitude of nanofluid velocity. [ABSTRACT FROM AUTHOR]

The axisymmetric stagnation point flow of brick and blade-shaped Silver and Copper nanoparticles immersed in an ethylene glycol base fluid under the influence of an induced magnetic field over an unsteady radial stretching surface is investigated in this study. The unsteady phenomenon is considered because most flow issues in practice are unsteady. The fundamental laws of mass, momentum, and energy conservation are used to present the physical model. Heat transmission is also examined under the effects of magnetohydrodynamics, Joule heating, viscous dissipation, and convective boundary conditions to give a realistic physical investigation. Scaling analysis transforms the flow-governing issue into a collection of higher-order nonlinear ODEs. These are, then, solved numerically using the fourth-order Runge–Kutta and shooting techniques. Moreover, the numerical technique is validated by calculating residual error. It is concluded that, compared to the Ag–EG nanofluid, the Cu–EG nanofluid had the highest IMF, lowest temperature, minimum surface drag, and maximum heat flux, making it the ideal choice for creating a radial module. [ABSTRACT FROM AUTHOR]

This research communication scrutinizes the time-dependent radiated stagnation point flow by a movable Riga surface in the presence of porous medium, mixed convection, viscous dissipation and radiative heat flux. Both electro-magneto effects are accounted for. The considered flow problem comprises Copper (Cu) as a nanoparticle in a continuous phase fluid water (H2O). The mathematical modeling depends on two main expressions, i.e., momentum equation of Navier-Stokes equation under certain conditions and temperature expression. The coupled system is further simplified via similarity transformations. Computational outcomes are computed by implementing bvp4c technique with the shooting concept. The obtained results are displayed graphically. It is noticed from the computations that both Nusselt number (NN) and skin friction coefficient (SFC) declined subject to increasing estimations of the unsteady variable. The final outcomes and main key points are listed in the conclusion section. [ABSTRACT FROM AUTHOR]

This research highlights the physical significance of nanoparticle in magnetohydrodynamics (MHD) stagnation point flow (SPF) over a stretchable surface with porosity effect and boundary slip phenomenon. The nanoliquid and its advanced thermal activity are shown extra auspicious results when the flow is considered over a permeable (porous) medium. In addition, the nanoparticles of radius size play an important role in the thermal performance of nanofluid. In this work, copper is accounted as a nanoparticle and water as a base fluid. Nanomanufacturing, surface engineering, coatings, nanofabrication and tribology are some of the important and special mechanical characteristics of nanoparticles [D. Guo, G. Xie and J. Luo, J. Phys. D, Appl. Phys.  47, 013001 (2014)]. The flow is electrically conducted in the presence of applied magnetic field. Mixed convection, Joule heating and viscous dissipation effects are accounted in the mathematical modeling. Appropriate similarity variables are used to convert the couple governing system of PDEs into ordinary ones and results are computed through bvp4c via shooting concept. From the obtained results, it is divulged that the velocity field increases against higher estimations of unsteady parameter, while it declines versus larger magnetic parameter and radius of nanoparticles. The engineering interest like skin friction and Nusselt number is mathematically calculated and results are computed in a tabular form, and their obtained outcomes show that the magnitude of skin friction rises against unsteadiness parameter and radius of nanoparticles. This study is an extended work of [Verma et al.Chem. Eng. J. Adv.12, 100366 (2022)] with some extra flow assumptions like MHD, SPF, Joule heating, heat generation/absorption and viscous dissipation. Obtained results are compared with [Grubka and Bobba J. Heat Transf.  107, 248 (1985)], Verma et al. [Chem. Eng. J. Adv.  12, 100366 (2022)] and [Elbashbeshy and Emam Therm. Sci.15,  477 (2011)] found 100% accuracy with them. The most important result of the conducted study is that the skin friction coefficient immensely augments subject to larger estimations of radius of nanoparticles when permeability of porosity is less. [ABSTRACT FROM AUTHOR]

In this study, we examine the boundary layer flow of magnetohydrodynamic single-wall carbon nanotubes combined with human blood as the base fluid approaching a stretchable surface. Nonlinear governing equations turned into nonlinear ordinary differential equations by employing some similarity conversions and the resulting equations with associated boundary conditions are solved numerically by applying the perturbation technique. Profiles of velocity and temperature as well as shear stress and heat flux at the wall under the influence of several controlling parameters are examined in detail and the results are represented in graphical and tabular forms. Results show how these variables are influenced by various controlling parameters, demonstrating the intricate interplay between nanotube, magnetic field strength and fluid properties. A correlation with the earlier published data is also shown to validate the results and a brilliant concurrence can be seen, and so reliable results are being introduced. The outcomes of our model provide a foundation for designing efficient drug delivery systems and biomagnetic applications. The understanding of how nanotubes interact with blood flow under magnetic fields can lead to improved strategies for manipulating and guiding nanoparticles within the body, enhancing the precision of medical interventions. [ABSTRACT FROM AUTHOR]

This study investigates the influence of quadratic (nonlinear) convection in transient magnetohydrodynamic (MHD) combined convection over a two‐dimensional stretching sheet. It explores the effects of thermal radiation, suction, and heat sources or sinks. The Crank–Nicholson implicit finite difference method is employed for numerical computations. The significance lies in considering secondary convection, which is crucial in understanding nonlinear convective effects affecting flow and heat transfer properties. The study aims to advance our comprehension of how secondary convection impacts the overall system behavior. Through numerical calculations validated against existing literature, strong agreement is demonstrated. The study evaluates secondary convection effects, magnetic, buoyancy, gravitational parameters, Prandtl number, and radiation parameters. Notably, strong quadratic convection alters flow patterns, affecting velocity and temperature profiles. Moreover, it is observed that when increasing the nonlinear (quadratic) convective factors, the temperature profile increases for λ<1 $\lambda \lt 1$ and decreases for λ>1 $\lambda \gt 1$. The prevalence of nonlinear or second‐order convection highlights magnetic dominance. In essence, this research enhances our understanding of complex convection interactions in MHD flow, shedding light on the role of secondary convection in shaping system behavior. [ABSTRACT FROM AUTHOR]

Nanofluids represent a novel heat transfer liquid, making them an efficient medium for enhancing energy transmission. Nevertheless, significant knowledge gaps still exist concerning current strategies for improving heat transfer in nanofluids, underscoring the necessity for comprehensive research on these fluid systems. Therefore, this study considered theoretical analysis retrieves the influence of radiative two‐dimensional stagnation point flow of second‐grade micropolar fluid flow about an elongated channel surface implanted in porous media with magnetic effect, and modified heat and mass flux is under consideration. The major novel effect of the current study is to analyze the activation energy and thermal aspect of the system in the presence of nonlinear radiation effects that are considered in the revised mathematical framework by utilizing the boundary layer theory. The resulting set of coupled partial differential equations is further reduced and transformed into a dimensionless system of ordinary differential equations through appropriate scaling invariants. We initiate the RKF‐45 investigation scheme to numerically analyze the transformed dimensionless system, considering relevant parameters. The computational algorithm is implemented using MATLAB programming syntax. Plotted visuals are revealed for leading parameters against pertinent flow profiles graphically and with numerical data. Additionally, the convergence analysis of the numerical results for various flow profiles of the fluids were compared to establish the authenticity of the proposed flow problem. These research findings play a significant role in controlling heat transfer rates and fluid velocities in diverse manufacturing processes and industrial applications, ultimately aiding in achieving the desired product quality. [ABSTRACT FROM AUTHOR]

This research is focused on the examination of an unsteady flow of an electromagnetic nanofluid close to a stagnation point over an expanded sheet kept horizontally. Buongiorno's nanofluid model is revised with the combined influence of the externally applied electric and magnetic fluxes. Moreover, the underneath surface offers multiple slips into the nanofluid flow. The leading partial differential equations (PDE) are renovated to the nonlinear ordinary differential equations (ODE) with the assistance of similarity transformations. Thus, the outcomes are received numerically by using the RK-6 with Nachtsheim–Swigert shooting technique. The enlistment of the outcomes for the momentum, energy and concentration profiles along with the skin-friction coefficient (C f x ∗) , Nusselt number (Nu x ∗) and Sherwood number (Sh x ∗) for several parametric values are presented in a graphical and tabular form and discussed in detail. The variation of streamlines with respect to the unsteadiness parameter is also recorded. Statistical inspection reveals that the flow parameters are highly correlated with the wall shear stress, wall heat and mass fluxes. Findings indicate that the escalation of electric flux tries to intensify the hydrodynamic boundary layer meanwhile the magnetic flux assists to stabilize the growth by reducing it for both the steady and unsteady flow patterns. Influence of velocity slip parameter ξ from 0.0 to 1.5 causes the reduction in Nu x ∗ by 16.98% for steady flow while 60.27% for time-dependent flow case. Moreover, we expect that these theoretical findings are very much helpful for several engineering and industrial applications such as polymer sheet productions, manufacturing automobile machines, cooling microelectronic chips, etc. [ABSTRACT FROM AUTHOR]

This investigation explores the convective MHD stagnation point flow of Casson nanofluid over a stretching sheet in a porous medium with higher-order chemical reactions and multiple slips. The examination of heat transmission is carried out in the presence of radiation, Joule heating, viscous dissipation, and heat source. The system of governing equations was simplified by using appropriate transformations. The transformed equations are tackled numerically by a Runge-Kutta-based shooting technique with the bvp5c MATLAB package. The graphical and numerical results for different parametric values are discussed and presented through figures and tables. It is observed that an increase in the magnetic field, porosity, and Casson fluid parameter reduces the velocity whereas the opposite trend is seen in the case of the thermal Grashof number and the solutal Grashof number. Increasing values of radiation and Joule heating parameters, and the Eckert number, lead to an increase in the temperature. The chemical reaction, suction, and solutal slip were found to reduce the concentration. The friction factor was reduced due to the higher values of the thermal Grashof number, solutal Grashof number, and the velocity ratio parameter. Also, an increase in the Brownian motion and thermal slip parameters decreases the heat transfer rate. The computational results of the Nusselt number have been validated with published results in the literature and found good agreement. The results obtained in this investigation have applications to biomedical, engineering, and industrial sectors such as food processing, polymer manufacturing, glass, and fiber production, improving oil recovery, and material processing. [ABSTRACT FROM AUTHOR]

This project covers the investigation of the boundary layer flow of a hybrid nanofluid past a biaxial stretching/shrinking sheet. The hybrid nanofluid consists of copper (Cu) and alumina ( Al 2 O 3 ) nanoparticles, which are diluted into water to form C u - Al 2 O 3 - water hybrid nanofluid. The governing partial differential equations (PDEs) are derived from Navier-Stokes equations. The system of PDEs is reduced to a system of ordinary differential equations using an appropriate similarity transformation. MATLAB's bvp4c function is used to numerically solve the resulting system of governing ordinary differential equations. The aim of this study is to gain a comprehensive understanding of the intricate behavior displayed by hybrid nanofluids on the stagnant directed flow of extended/shrunk flat surfaces, considering the effects of Brownian motion, thermophoresis, and various nanoparticles. The generated numerical results of flow profiles, skin friction coefficient, and Nusselt number have been presented graphically and discussed in the relevance of the governing parameters contributing to the flow. The outcomes reveal that the velocity components are reduced with increasing Al 2 O 3 - water nanofluid volume fraction. A monotonical increase in the parameters stretching/shrinking and suction/injection with a corresponding rise in both nanoparticles volume fraction propels heat gradient rate. An increase in the Schmidt numbers encourages a mass transfer field due to an enhanced boundary viscosity. The validation of numerical results is done with previously published results. Through our results, we have found that the performance of a hybrid nanofluid is more significant than other fluids. In addition, this study enhances the progress of theoretical comprehension by endeavoring to resolve the intricate interplay between fluid dynamics and thermal characteristics through the utilization of numerical approaches. [ABSTRACT FROM AUTHOR]

Using the power of numerical computation through Levenberg Marquardt backpropagation ($LMB$LMB), the fluidic issue in the present study has features of heat transfer by convection in the hybrid nanofluid suspension of magnesium oxide and gold nanoparticles. The influence of slip effects on boundary layer flow with viscous dissipation at the nodal/saddle stagnation point is examined using a mathematical model. The current study considers water to be the base fluid, $MgO$MgO and $Au$Au as nanoparticles, and the circular cylinder to be the medium’s surface. Non-linear partial differential equations are converted into ordinary differential equations via similarity transformations. The dataset for Levenberg Marquardt backpropagation is generated in Mathematica software using an explicit RK-4 approach by varying different parameters such as the slip parameter ($\lambda $λ), convective parameter ($Bi$Bi), Eckert number ($E{c^*}$Ec∗) and volume fraction (${\phi _2}$ϕ2), Bi with Ec. Validation, training, and testing are utilized for network modeling through the Levenberg-Marquardt backpropagation approach for various scenarios of the fluidic model. The result shows that the base fluid’s thermal behavior is quickly increased by the $MgO - Au$MgO−Au/water hybrid nanofluid. The reliability of the findings is evaluated using autocorrelation, regression, mean square error, absolute error, and error histogram analyses. [ABSTRACT FROM AUTHOR]

Several strategies are used to increase the heat transmission capabilities of ordinary fluid. Using metallic nanomaterials the thermal conductivity is modified which can improve the energy transport mechanism. Our primary goal is to observe the dual diffusion and volumetric friction of injected nanoparticles in blood flow simultaneously. The Eyring–Powell fluid is speculated as blood on the basis of shear thinner behavior. The entropy formation in the region of stagnation in MHD Eyring–Powell nanofluid flow is scrutinized. The flow is produced by stretchable surface. The impacts of slip mechanism viscous dissipation and melting heating are included in the current analysis. The single and two phase model are used as coupled model to inquire the effects of nanomaterials. System of PDEs are achieved and reduced to ODEs using appropriate variables. The reduced ODEs are solved using RK-4 methodology. It is evident that blood flow is greatly influenced by Lorentz forces and fluid primary parameter. On the other hand, the secondary and increased volumetric rate encourage the flow of blood. The blood temperature is rising function of thermophoresis, Eckert and magnetic parameter. Similar trend for solutal profile was noted against Brownian and Lewis number. The system irreversibility are rising with Brinkman, magnetic and diffusion variable. The coefficient of energy transport rate and frictional drag are rising function of material parameters and volumetric concentration of injected nanomaterial. It is interesting to see that nearly all profile show comparable trend with higher concentration of nanomaterials.

This study explores using hybrid nanofluids to improve water quality by enhancing heat transfer and substance decomposition. Nanofluids effectively remove pollutants, optimise heat transfer, control pollution sources, and regulate fluid dynamics, which can lead to efficient pollution management in water systems. Thus, the present research examines the flow of an unsteady hybrid Al2O3–Cu/water nanofluid near the stagnation region in a porous medium, considering the discharge concentration and convective boundary conditions. Governing equations in ordinary differential equations are obtained using similarity transformations. The BVP4C solver in MATLAB is employed to expose dual solutions. The volume fraction of copper φa2, the suction/injection parameter (S), and the unsteadiness parameter (A), collectively contribute to the delay of the boundary layer separation. Increasing the values of φa2,A, and S enhances convective heat transfer. When the sheet shrunk between the range of −16.2 and −13, hybrid nanofluid has higher convective thermal transfer than nanofluid. Moreover, an increment in φa2 and S raises the skin friction coefficients and mass diffusion rates. Stability analysis reveals that the first solution is stable while the second one is unstable.

Owing to current evolution in nanotechnology, the idea of nanomaterials has been developed to improve the heat transfer phenomena. In order to obtain diverse significance of nanomaterials in engineering systems, applications of different thermal sources are contributed. The aim of current analysis is to presents the induction of induced magnetic force for couple stress nanofluid due to moving stretched surface. For prediction of heat and mass phenomenon, variable role of thermal conductivity and mass diffusivity of nanofluid is assumed. Furthermore, the heat transfer rate is further influenced by nonlinear radiated phenomenon. The convective boundary constraints are taken to enhance the thermal pattern. The problem modeled via governing equations is numerically solved with shooting method. Simulations are captured with physical explanations. It is claimed that the interaction of magnetic number leads to decrement in the velocity. The enhancement in heat and mass transfer have been exhibited due to magnetic number. Current results attribute applications in plasma physics, thermal systems and electromagnetism. Moreover, summarize observations preserve biomedical applications like magnetic resonance imaging (MRI).

The graphene oxide–molybdenum disulfide (GO–MoS2) exhibited the performance of photocatalytics under solar light radiation and the problem is more significant during Marangoni convection. In this scenario, the thermosolutal Marangoni stagnation point flow over a stretching sheet where the GO–MoS2 nanoparticles are embedded in a base fluid water are taken into consideration. The inclined magnetic field with the Joule heating effect, thermal radiation, chemical reaction and Soret and Dufour effect is introduced in the system. The leading equations are simplified by applying the proper similarity transformation and then solved numerically with the help of the MATLAB bvp4c routine. The impact of several parameters on the velocity, temperature and concentration with other physical properties such as skin friction, local Nusselt number and local Sherwood number has been displayed. Moreover, the results of this paper demonstrate a brief equivalency between nanofluid and hybrid nanofluid. It is experimented that the Marangoni effect arises due to a fluctuation in temperature as well as a chemical reaction. Surface tension refers to mean temperature and mean concentration restricts the fluid velocity. GO–MoS2 exhibits the increase in antimicrobial effects with enhancement in the glutathione oxidation and it is also used for DNA detection. The impact of GO and MoS2 in the flow of hybrid nanofluid shows significance with a huge application in medical science. [ABSTRACT FROM AUTHOR]

This paper proposes a mathematical modeling approach to examine the two-dimensional flow stagnates at x = 0 over a heated stretchable sheet in a porous medium influenced by nonlinear thermal radiation, variable viscosity, and MHD. This study’s main purpose is to examine how thermal radiation and varying viscosity affect fluid flow motion. Additionally, we consider the convective boundary conditions and incorporate the gyrotactic microorganisms equation, which describes microorganism behavior in response to fluid flow. The partial differential equations (PDEs) that represent the conservation equations for mass, momentum, energy, and microorganisms are then converted into a system of coupled ordinary differential equations (ODEs) through the inclusion of nonsimilarity variables. Using MATLAB’s built-in solver bvp4c, the resulting ODEs are numerically solved. The model’s complexity is assessed by plotting two-dimensional graphics of the solution profiles at various physical parameter values. The physical parameters considered in this study include skin friction coefficient, local Nusselt number, local Sherwood number, and density of motile microorganisms. These parameters measure, respectively, the roughness of the sheet, the transformation rate of heat, the rate at which mass is transferred to it, and the rate at which microorganisms are transferred to it. Our study shows that, depending on the magnetic parameter M, the presence of a porous medium causes a significant increase in fluid velocity, ranging from about 25% to 45%. Furthermore, with an increase in the Prandtl number Pr, we have seen a notable improvement of about 6% in fluid thermal conductivity. Additionally, our latest findings are in good agreement with published research for particular values. This study provides valuable insights into the behavior of fluid flow under various physical conditions and can be useful in designing and optimizing industrial processes. [ABSTRACT FROM AUTHOR]

Abstract Improving heat transmission is a modern difficulty faced in a multitude of areas, incorporating but not limited to electronics, heat exchangers, biochemical reactors, and other similar areas. In their capacity as cutting-edge heat transfer fluids, nanofluids have the promise of becoming a useful instrument in the pursuit of greater energy transfer efficiency. So, the focus of this work is on how it is possible to enhance heat transmission by using nanofluids. Using a stretched exponentially accelerating surface, this analysis investigates the effect that nanoparticle aggregation with thermal radiation has on the T i O 2 − C 2 H 6 O 2 nanofluid of mixed convective stagnation point flow through Darcy-Forchheimer porous surfaces. The aggregation of nanoparticles may be assessed using modified Krieger-Dougherty and Maxwell-Bruggeman models. By using the right similarity transformations, the controlling equations of this problem were turned into a numerical model that can be unraveled. Mathematica was used to resolve the issue numerically by using the shooting with Runge-Kutta (RK-IV) procedure. T i O 2   nanoparticles with base fluid C 2 H 6 O 2 under aggregation effect boost heat transfer performance. A diversity of parameter estimates, including the mixed convection, mass suction, solid volume fraction of nanoparticles, thermal radiation, and stretching, were used to provide solutions for heat transfer and lower skin friction coefficients, as well as velocity and temperature curves. In addition to the findings, there were graphs and tables with explanations. The increase in heat transfer rates was 6.7021% when the suction parameters were set between 2.0 to 2.5 with ϕ =0.01. When the amount of nanoparticles volume fraction went from 0% to 1% by volume, the ineptitude of heat transfer went by an average of 4.249%. Aggregation models are often favored over non-aggregation models due to their ability to provide more accurate velocity and skin fraction profiles. Because of their superior precision, they are often used in situations where accuracy is paramount. [ABSTRACT FROM AUTHOR]

Nanofluid comprising nanometer sized materials, called nanoparticles. These liquids are built colloidal suspensions of nanomaterials in a continuous phase liquid. The nanomaterials utilized in nanoliquids are typically made of carbon nanotubes, oxides and metals. In this research, communication, the impact of Brownian diffusion and thermophoresis is addressed in flow of non‐Newtonian fluid towards shrinking/stretching the surface. The energy equation is developed subjesct to dissipation, radiative flux (nonlinear) and Ohmic heating. The activation energy is further considered for chemical reaction. The nonlinear flow expressions are transformed into ordinary differential equations with the help of similarity transformations. The obtained systems of ordinary differential equation's are numerically solved through Shooting method (bvp4c). The concentration, temperature and velocity profiles are determined graphically. Mass transfer, surface drag force and heat transfer rate are shown by tables. At last, entropy and Bejan number are discussed through graphs in which entropy showed increasing behavior for magnetic, radiation, Brinkman and diffusivity parameter but Bejan number showed opposite behavior for them. [ABSTRACT FROM AUTHOR]

This article employs an artificial neural network technique to approximate the solution for the stagnation point flow with velocity and thermal slip effects, as well as radiative heat transfer. The PDE governing system is transformed into a set of coupled ordinary differential systems by incorporating similarity variables. The shooting method is used to obtain a dataset in Mathematica. To test the precision of the suggested model, the operations of training, testing, and validation are performed, and the results are compared to a reference dataset. The Levenberg-Marquardt backpropagation neural network model is utilized to solve the system of equations under different scenarios, and its output is evaluated using mean square error, state transition dynamics, error histograms analysis, and regression illustrations. The findings indicate that the neural network approach achieves a high level of accuracy when predicting thermal analysis. Moreover, the current Artificial Neural Network model has an advantage over other numerical techniques in that it can handle more intricate mathematical models while minimizing the resources required for problem-solving.

An experimental study was made on burning velocity in powder-gas hybrid combustion in order to investigate the determination factor to alter the burning velocity caused by the addition of power in the premixed gas. A burner system was newly developed to visualize the dynamic flame behavior originally stabilized in a stagnation point flow field. Using the system, the instantaneous burning velocity and burning area by powder loading were obtained and analyzed. It was found that the burning velocity and burning area varied substantially in accordance with the powder loading amount. Data analyses exhibited that a positive correlation was found between them, suggesting that wrinkling shall be a major cause to alter the burning velocity. To understand the mechanism of wrinkle formation, the change of the flow field ahead of the flame with powder loading was measured. It is suggested that the wrinkles could be attributed to the pyrolysis gases evolved in the preheating zone, which could both increase the local burning velocity by increasing the local equivalence ratio and change the flow field due to the divergence flow generated by each powder. Further study would be needed to confirm the suggested mechanism.

Investigation of heat transfer is a potential research area to acquire the targets in engineering and various industries. Although, conventional liquids are good for many such applications but their heat transfer rate is limited and thus it is essential to study new fluids which meet the requirements. Therefore, a new ternary nanofluid model acquired using enhanced thermal conductivity, electrical conductivity, heat capacity, basic governing laws and similarity transforms. The model comprises the motivational aspects of thermal slip, convective condition, radiative flux and viscous dissipation and predict the parametric ranges for excellent heat transfer results. The nanoparticles (Al2O3, CuO and Cu) amount is kept up to 0.04. For the results simulation, the numerical technique based on shooting scheme is implemented and solved the model. It is scrutinized that induction of aforementioned physical quantities significantly improved thermal transport performance of ternary nanoliquid. These are an excellent sources to acquire the preferred amount of heat for industrial applications. Further, higher B1 near surface boosted the temperature with increasing B1 in the range of 0.1–0.4. The heat transfer rate at the surface effectively enhanced for thermal slip (α1), radiation number (Rd) and Biot number (B1) in the range of 0.1,0.3,0.5,0.7.

Abstract Nanotechnology is progressively being used to increase heat transfer rates by employing an efficient homogenous combination of nanoparticles. Inspired by these developments, a simulation investigation of porous media subjected to stagnation point flow under the effects of dissipation and uneven thermal sink/generation boundary layer is performed. Dimensionless forms of the governing equations are obtained by adopting a model of Tiwari–Das nanofluid to study the fluid flow considering water-based Cu and Cuo nanoparticles. A coupled ordinary derivative invariant model is obtained from the transformed partial differentiation equations. A computational shooting method with a fourth-order Runge–Kutta scheme is used to offer solutions to the ODEs (Ordinary Differential Equations). This study was done to understand the impacts of pertinent physical terms on the flow characteristics in porous media. Additionally, the wall quantities, thermal, and concentration diffusion are examined and discussed, and the output is presented in plots and tables. The limiting cases are considered and briefly addressed as compared with the existing results. The solution outputs revealed that the heat propagation is momentously influenced by the volume and size of the nanoparticles. The fluid molecular bond is strengthened by the rising induced magnetic field. This investigation is treasured in extensive applications that are not restricted to the physical sciences and engineering. [ABSTRACT FROM AUTHOR]

Stagnation point flow defines the fluid motion near the stagnation point of a solid surface and has utilization in the process of polymer extrusion, electronic gadgets cooling, nuclear reactor, etc. Furthermore, the main theme of this work is to analyze the heat transfer characteristics of stagnation point flow of Casson nanofluid over stretching sheet using induced magnetic field and Cattaneo-Christov model. The Casson fluid is a non-Newtonian fluid model; and in the current work the working fluid consists of nanoparticles of Au (Gold) and blood (Casson fluid). In the existing model, temperature of the surface depends on the distance from the stagnation point. Therefore, Darcy-Forchheimer porous model is incorporated. The solution of coupled nonlinear PDEs is obtained by bvp4c. The heat transfer and flow characteristics of Au-blood based Casson nanofluid are discussed graphically. The dual behavior is observed in the profiles of induced magnetic field with increase in the value of reciprocal magnetic Prandtl number, however the velocity outlines of Au-blood nanofluid declined. A comparison is presented with previous article and is found to be in good agreement. [ABSTRACT FROM AUTHOR]

This study investigates the suction and magnetic field effects on the two-dimensional nanofluid flow through a stretching/shrinking sheet at the stagnation point in the porous medium with thermal radiation. The governing partial differential equations (PDEs) are converted into ordinary differential equations (ODEs) using the similarity transformation. The resulting ODEs are then solved numerically by using the bvp4c solver in MATLAB software. It was found that dual solutions exist for the shrinking parameter values up to a certain range. The numerical results obtained are compared, and the comparison showed a good agreement with the existing results in the literature. The governing parameters' effect on the velocity, temperature and nanoparticle fraction fields as well as the skin friction coefficient, the local Nusselt number and the Sherwood number are represented graphically and analyzed. The variation of the velocity, temperature and concentration increase with the increase in the suction and magnetic field parameters. It seems that the thermal radiation effect has increased the local Sherwood number while the local Nusselt number is reduced with it. [ABSTRACT FROM AUTHOR]

This article inspects the quantitative aspects of stagnation point flow of MHD nanofluid. The novelty of the present numerical investigation is to consider bioconvective MHD stagnation point flow of nanofluid in non-Darcy porous ambience. The mathematical model comprehends bioconvection phenomenon caused by motile gyrotactic micro-organisms, thermal radiation and buoyancy effects, and fluid flow is encased in Darcy Forchheimer porous environment. The governing non-linear partial differential equations of the fluid flow are established in accordance with aforesaid presumptions and are reduced into ordinary differential equations with significant similarity transformation. Numerical solutions of the mathematical model are solved using Fifth order Runge–Kutta-Felhberg method with shooting technique and exhibited with graphical description for pertinent parameters on velocity, temperature, nanoparticle concentration and density of micro-organisms. Major outcome of present study shows velocity profiles decline for porous parameter and inertia co-efficient whereas bioconvection Lewis number, Peclet number and micro-organism difference parameter exhibits a weakening response for density of micro-organism profile. Comparison of numerical outcomes for Nusselt number with erstwhile published research results are attempted and presented. [ABSTRACT FROM AUTHOR]

The current research endows the mathematical modeling for the stagnation point flow along with melting nonlinear radiative heat transfer for cross fluid. It has many applications such as synthesis of polymer solutions, plastic manufacturing, food processing, preparation of synthesis, adhesives, etc. A radially stretching sheet has started the flow keeping the assumption of rotational symmetry. Transformation approach is adopted to attain the nonlinear ordinary differential equations based on standard conservation laws of mass, linear momentum and also energy. Numerical solutions of the governing problem are computed via the shooting technique. Characteristics of the parameters appearing in modeling like the melting parameter, power–law index, local Weissenberg number, nonlinear radiation parameter, temperature ratio parameter and Prandtl number are comprehensively analyzed through graphical behavior. In addition, comparative analysis is presented for the cases when the value of free stream velocity overtops the stretching velocity and vice versa. Results are authenticated by taking special cases and excellent compatibility is achieved with the existing literature. The detailed analysis anticipates that the boundary layer structures could be strengthened by growing the melting parameter. Elevation in Weissenberg number caused velocity along with temperature profiles to demonstrate for A > 1. Further, the temperature behaves oppositely analogous to development in nonlinear radiation parameter besides the temperature ratio parameter. [ABSTRACT FROM AUTHOR]