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Interest in the thermal effects of nanofluid (NF) has increased recently due to the use of nanocomposites to magnify the thermal conductivity of conventional liquids and so boost the heat transit phenomena. Based on this fundamental concept, the current study inspects the thermal advanced third-grade fluid flow with nanocomposites with an extended surface and the inclusion of stratification, non-Fourier heat flux, mass flux, and radiation. Buongiorno’s NF model is employed to observe the thermophoresis and Brownian motion properties. The gyrotactic microorganisms, which are connected to the bioconvection phenomenon that intrigues most, are also considered to be present in the nanoparticles. The governing models are composed of partial differential equations; thereafter, the relevant transformations are applied to these equations to convert the structure into an ordinary differential model. These resultant models are solved by implementing the homotopy analysis method. It is explained in detail how the pertinent parameters are affecting the motion, temperature of fluid, nanocomposite volume, dynamic microbe density, skin friction rates, local Nusselt, and local Sherwood numbers. Applications for the flow of nanoparticles carrying gyrotactic microorganisms include enzyme biosensors, microfluidic devices, microbial fuel cells, and biotechnology.

The flow of carbon nanotubes (CNTs) via the Riga plate has a substantial influence, and it is used in the industrial sector, like fluid stirring, thermal reactors, semiconductors, tissue regeneration, gene delivery to organs, etc. However, the 3D Darcy–Forchheimer flow (DFF) of CNTs through the Riga plate with nonlinear thermal radiation and a non-uniform heat sink/source has not been investigated. As a consequence of this, the objective of this paper is to explore the impact of the nonlinear radiative DFF of water-based CNTs past a heated Riga plate with a non-uniform heat sink/source and homogeneous and heterogeneous reactions. In addition, the energy equation is constructed using the Cattaneo–Christov heat flux concept. By making use of appropriate variables, the governing flow models are mutated into a system of ordinary differential equations. These reduced equations are analytically and numerically computed by homotopy analysis method (HAM) and the bvp4c scheme. The brief discussion and visual depiction of the dominance of different factors on x- and y-direction velocities, thermal, nanoparticle concentration (NPC), surface drag coefficients, and local Nusselt number are presented in tables and figures. The growth of the Forchheimer number leads to a noticeable enrichment in the velocity profile in both directions. When the nanoparticle’s volume fraction and space-dependent heat source/sink parameters are increased, the thermal profile gets better. The NPC profile exhibits suppression as the intensity of both heterogeneous and homogeneous responses rises. [ABSTRACT FROM AUTHOR]

The aim of this study is to examine the Darcy–Forchheimer flow = of H 2 O -based A l − A l 2 O 3 / C u − A l 2 O 3 hybrid nanofluid past a heated stretchable plate including heat consumption/ generation and non-linear radiation impacts. The governing flow equations are formulated using the Naiver–Stokes equation. These flow equations are re-framed by using the befitted transformations. The MATLAB bvp4c scheme is utilized to compute the converted flow equations numerically. The graphs, tables, and charts display the vicissitudes in the hybrid nanofluid velocity, hybrid nanofluid temperature, skin friction coefficient, and local Nusselt number via relevant flow factors. It can be seen that the hybrid nanofluid velocity decreased as the magnetic field parameter was increased. The hybrid nanofluid temperature tended to rise as the heat absorption/generation, nanoparticle volume friction, and nonlinear radiation parameters were increased. The surface drag force decreased when the quantity of the magnetic parameter increased. The larger size of the radiation parameter led to enrichment of the heat transmission gradient. [ABSTRACT FROM AUTHOR]

The main goal of the current research is to investigate the numerical computation of Ag / Al 2 O 3 nanofluid over a Riga plate with injection/suction. The energy equation is formulated using the Cattaneo–Christov heat flux, non-linear thermal radiation, and heat sink/source. The leading equations are non-dimensionalized by employing the suitable transformations, and the numerical results are achieved by using the MATLAB bvp4c technique. The fluctuations of fluid flow and heat transfer on porosity, Forchheimer number, radiation, suction/injection, velocity slip, and nanoparticle volume fraction are investigated. Furthermore, the local skin friction coefficient (SFC), and local Nusselt number (LNN) are also addressed. Compared to previously reported studies, our computational results exactly coincided with the outcomes of the previous reports. We noticed that the Forchheimer number, suction/injection, slip, and nanoparticle volume fraction factors slow the velocity profile. We also noted that with improving rates of thermal radiation and convective heating, the heat transfer gradient decreases. The 40 % presence of the Hartmann number leads to improved drag force by 14 % and heat transfer gradient by 0.5 % . The 20 % presence of nanoparticle volume fraction leads to a decrement in heat transfer gradient for 21 % of Ag nanoparticles and 18 % of Al 2 O 3 nanoparticles. [ABSTRACT FROM AUTHOR]

The behavior of the Darcy–Forchheimer flow of a double-hybrid nanofluid toward a Riga plate with radiation and heat source/sink effects is investigated. The two different hybrid nanofluids, (Al 2 O 3 and Ag) and (Al 2 O 3 and TiO 2 ) with a base fluid (H 2 O), are considered. The governing flow models with accompanying boundary constraints are reshaped into non-linear ODEs by applying the symmetry variables. The reshaped ODEs are numerically computed using Bvp4c in Matlab and the ND solver in Mathematica. The impact of the emerging parameters on the heat transfer, surface shear stress, temperature and velocity profile is scrutinized and expressed in a tabular and graphical structure. It is noticed that the upsurge of the Hartmann number leads to an improvement in the velocity profile. The velocity declines when enriching the porosity parameter. The radiation and Biot number lead to strengthening the temperature profile. The surface shear stress exalts due to a larger modified Hartman number. The radiation and unsteady parameters are downturns in the heat transfer gradient. [ABSTRACT FROM AUTHOR]

This communication predominately discusses the rheological attributes of the Darcy–Forchheimer flow of a nanoliquid over a stretchy sheet with a magnetic impact. The present model considers the two diverse nanoparticles, such as C u and A g , and water as a base liquid. The heat equation accounts for the consequences of thermal radiation and a nonlinear heat sink/source when evaluating heat transmission phenomena. The current mechanical system is represented by higher-order PDEs, which are then remodeled into nonlinear higher-order ODEs that employ appropriate symmetry variables. The current mathematical systems are numerically computed by implementing the bvp4c technique. The characteristic attitudes of the related pertinent factors on the non-dimensional profiles are sketched via the figures, tables, and charts. The analysis predicts that the speed of the nanoliquid particles becomes slower when there is more presence of a magnetic field and injection/suction parameters. The growing amount of radiation is also pointed out, and the Eckert number corresponds to enriching the thermal profile. [ABSTRACT FROM AUTHOR]

This communication deliberates the time-reliant and Darcy–Forchheimer flow of water-based CNTs/gold nanoparticles past a Riga plate. In addition, nonlinear radiation, heat consumption and multiple slip conditions are considered. Entropy generation is computed through various flow parameters. A suitable transformation with symmetry variables is invoked to remodel the governing mathematical flow models into the ODE equations. The homotopy analysis scheme and MATLAB bvp4c method are imposed to solve the reduced ODE equations analytically and numerically. The impact of sundry flow variables on nanofluid velocity, nanofluid temperature, skin friction coefficient, local Nusselt number, entropy profile and Bejan number are computed and analyzed through graphs and tables. It is found that the nanofluid velocity is reduced by greater porosity and slip factors. The thickness of the thermal boundary layer increases with increasing radiation, temperature ratio, and heat consumption/generation parameters. The surface drag force is reduced when there is a higher Forchheimer number, unsteadiness parameter and porosity parameter. The amount of entropy created is proportional to the radiation parameter, porosity parameter and Reynolds number. The Bejan number profile increases with radiation parameter, heat consumption/generation parameter and the Forchheimer number. [ABSTRACT FROM AUTHOR]

This work performs a comparative investigation into Casson-Williamson fluid flow over a heated porous stretchy sheet. The energy and mass transfer equations are modeled by Cattaneo-Christov theory. The governing ow models are altered into an Ordinary Differential Equation (ODE) model through proper transformations. The Homotopy Analysis Method (HAM) scheme is applied to determine the series solutions. The responses of diverse ow variables to uid speed, uid warmness, liquid concentration, skin friction coefficient, local Nusselt number, local Sherwood number, local entropy generation number, and Bejan number are analyzed through graphs and charts. It was found that the uid speed would subside following an increase in values of the magnetic field, porosity, Casson uid, Williamson uid, and injection/suction parameters. The uid warmness is increased due to high-level radiation, convective heating, and heat generation/absorption parameters and it suppresses the previous highs when enriching the convective cooling parameter. The chemical reaction parameter causes an increase in the thickness of the solutal boundary layer. The larger skin friction coefficient occurs in Casson uid than Williamson uid. The local entropy generation is attenuated upon increase in the Casson and Williamson parameters and it aggravates when the Biot number rises. The Bejan number is elevated when the Reynolds, Brinkman, and Biot numbers experience an increase. [ABSTRACT FROM AUTHOR]

The nature of this prevailing inquisition is to scrutinize the repercussion of MHD mixed convective flow of CNTs/ A l 2 O 3 nanofluid in water past a heated stretchy plate with injection/suction, heat consumption and radiation. The Joule heating and viscous dissipation are included in our investigation. The Navier–Stokes equations are implemented to frame the governing flow expressions. These flow expressions are non-dimensioned by employing suitable transformations. The converted flow expressions are computed numerically by applying the MATLAB bvp4c procedure and analytically by the HAM scheme. The impacts of relevant flow factors on fluid velocity, fluid temperature, skin friction coefficient, and local Nusselt number are illustrated via graphs, tables and charts. It is unequivocally shown that the fluid speed declines when escalating the size of the magnetic field parameter; however, it is enhanced by strengthening the Richardson number. The fluid warmness shows a rising pattern when enriching the Biot number and heat consumption/generation parameter. The findings conclusively demonstrate that the surface drag force improves for a larger scale of Richardson number and is suppressed when heightening the unsteady parameter. In addition, it is evident from the outcomes that the heat transfer gradient decreases to increase the quantity of the Eckert number in the convective heating case; however, the opposite nature is obtained in the convective cooling case. Our numerical results are novel, unique and applied in microfluid devices such as micro-instruments, sleeve electrodes, nerve growth electrodes, etc. [ABSTRACT FROM AUTHOR]