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In the current study, we numerically analyze the significance of motile microbes on the magnetohydrodynamic steady convective streams of tangent hyperbolic (TH) nanofluid flow across an elastic nonlinearly stretching surface of an irregular thickness. The consequences of an external magnetic field, thermal radiation, and thermal conductivity are also examined on the TH nanofluid. The governing system of equations (nonlinear set of partial differential equations) is transfigured into a system of ordinary differential equations (ODEs) by using the similarity variable conversions. Furthermore, the reduced form of nonlinear ODEs is numerically computed through the parametric continuation method (PCM) using MATLAB software. The relative evaluation is carried out to authenticate the numerical outcomes. It has been observed that the energy field accelerates with the Rayleigh number, Weissenberg number, and Brownian motion. The mass propagation ratio improves with the effect of activation energy and decreases with the influence of chemical reactions. Furthermore, the motile microbes’ profile declined with the outcome of the Peclet and Lewis numbers. The skin friction increases up to 7.3% with various magnetic values ranging from 0.5 to 1.5. However, the energy transfer rate declines to 5.92%. The thermal radiation boosts the energy propagation rate and flow velocity by up to 11.23 and 8.17%, respectively.

The steady two-dimension (2D) ternary nanofluid (TNF) flow across an inclined permeable cylinder/plate is analyzed in the present study. The TNF flow has been examined under the consequences of heat source/sink, permeable medium and mixed convection. For the preparation of TNF, the magnesium oxide (MgO), cobalt ferrite (CoFe2O4) and titanium dioxide (TiO2) are dispersed in water. The rising need for highly efficient cooling mechanisms in several sectors and energy-related processes ultimately inspired the current work. The fluid flow and energy propagation is mathematically described in the form of coupled PDEs. The system of PDEs is reduced into non-dimensional forms of ODEs, which are further numerically handled through the Matlab package (bvp4c). It has been observed that the results display that the porosity factor advances the thermal curve, whereas drops the fluid velocity. The effect of heat source/sink raises the energy field. Furthermore, the plate surface illustrates a leading behavior of energy transport over cylinder geometry versus the variation of ternary nanoparticles (NPs). The energy dissemination rate in the cylinder enhances from 4.73 to 11.421%, whereas for the plate, the energy distribution rate boosts from 6.37 to 13.91% as the porosity factor varies from 0.3 to 0.9. [ABSTRACT FROM AUTHOR]

This study enlightens the magnetohydrodynamic Jeffery-Hamel flow under an inclined Lorentz force through a non-uniform conduit having slip at walls, which is frequently applied in geothermal applications, electronic cooling devices, and modern energy systems, etc. Therefore, the performance of a two-dimensional purely radial flow inside a converging-diverging channel is explored from the perspective of second law of thermodynamics for Carreau nanofluids. The intersecting walls of conduit are inclined with horizontal plane to construct a converging flow for negative angle (α < 0) and a diverging flow for positive angle (α > 0). Additionally, second law thermodynamic evaluation offers an effective method for improving thermal performance by reducing entropy production. To accomplish the main objective, rigorous physical theories and assumptions are implemented based on the passive control approach of Buongiorno's model. By applying distinctive modifications, the governing equations are renovated into a system of ordinary differential equations, which are solved numerically by a collocated technique based on finite difference code. Simple shear near the wall influences the flow configurations allow compression in a local flow topology in regions of divergent channel. The temperature profiles increase with sophisticated heat source and Brinkman number. Entropy is minimum and uniform with optimum channel angle and velocity slip. [ABSTRACT FROM AUTHOR]

Due to enhanced heat transfer rate, the nanofluid and hybrid nanofluids have significant industrial uses. The principal objective of this exploration is to investigate how thermal radiation influences the velocity and temperature profile. A water-based rotational nanofluid flow with constant angular speed Ω is considered for this comparative study. A similarity conversion is applied to change the appearing equations into ODEs. Three different nanoparticles i.e., copper, aluminum, and titanium oxide are used to prepare different nanofluids for comparison. The numerical and graphical outputs are gained by employing the bvp-4c procedure in MATLAB. The results for different constraints are represented through graphs and tables. Higher heat transmission rate and minimized skin friction are noted for triple nanoparticle nanofluid. Skin coefficients in the x-direction and y-direction have reduced by 50% in trihybrid nanofluid by keeping mixed convection levels between the range 3 < ϵ ≤ 11 . The heat transmission coefficient with raising the levels of thermal radiation between 0.5 < π ≤ 0.9 and Prandlt number 7 < Pr ≤ 11 has shown a 60% increase. [ABSTRACT FROM AUTHOR]

In this study, the mixed convective stagnation-point flow of a Al 2 O 3 - C u / H 2 O hybrid nanofluid towards a stretched disc with a convective boundary and zero mass flux condition is described with mass suction and viscous dissipation effects. The process is accomplished by using thermophoretic and Brownian motion physical phenomena. After performing a similarity transformation on the PDEs in order to convert them into an ODE system, the bvp4c solver is then employed in order to carry out a numerical solution. In the study that was described above, the flow, heat, and mass transfer characteristics were investigated with the assistance of the Buongiorno model and the Devi and Devi model. The following characteristics were brought up as points of contention: ϕ 1 , ϕ 2 , λ , S , N t , N b , L e , E c , B i and B. There is a very good consonance among the existing and antecedent results in undeniable cases, as well as a connection error of approximately 0%. The velocity and temperature profiles upsurge with the increment of the nanoparticle volume fraction and mixed convection parameter, while the velocity increases with the addition of the suction parameters. As a result of this study, we are able to estimate the flow and thermal behavior of Al 2 O 3 - C u / H 2 O when the physical parameters are embedded. [ABSTRACT FROM AUTHOR]

The purpose of this work is to investigate the Darcy-Forchheimer flow of a hybrid nanofluid within two parallel discs. We combine gold Au , silver Ag , copper Cu , and iron oxide Fe 3 O 4 nanoparticles with base fluid blood in this framework. An appropriate similarity variables technique is implemented to transform partial differential systems into ordinary systems. In the results validation section, the numerical result is evaluated using a higher-order precise algorithm (bvp4c), and determined to the analytical result is by making use of the firing approach. Pictorial judgments revealed the estimates of several physical variables that arise over the momentum distribution and thermal distribution profiles. As compared to nanofluid, hybrid nanofluid significantly improves heat transfer rate. The thermal profile is improved when the Brinkman number increases in value. As the porosity parameter is increased, the velocity profile decreases. As the amplitude of the rotation parameter increases, so does the pressure profile. The Darcy-Forchheimer medium investigation of a hybrid nano-fluid streaming through the middle of two parallel disks is addressed, taking into account viscous dissipation and heat radiation for various nanoparticles. Additionally, enough agreement is observed when the numerical findings are compared to previously reported and analytical data. As compared to simple nanofluids, hybrid nanofluids have shown higher thermal properties and stability, making them attractive candidates for thermal applications such as solar thermal systems, automotive cooling systems, heat sinks, engineering, medical fields, or thermal energy storage. [ABSTRACT FROM AUTHOR]

This research analyzes the three-dimensional magneto hydrodynamic nanofluid flow through chemical reaction and thermal radiation above the dual stretching surface in the presence of an inclined magnetic field. Different rotational nanofluid and hybrid nanofluids with constant angular velocity ω ∗ for this comparative study are considered. The constitutive relations are used to gain the equations of motion, energy, and concentration. This flow governing extremely non-linear equations cannot be handled by an analytical solution. So, these equations are transformed into ordinary differential equalities by using the similarity transformation and then handled in MATLAB by applying the boundary values problem practice. The outcomes for the considered problem are accessed through tables and graphs for different parameters. A maximum heat transfer amount is observed in the absence of thermal radiation and when the inclined magnetic field and axis of rotation are parallel. [ABSTRACT FROM AUTHOR]

The utilization of hybrid nanofluids (HNs) to boost heat transfer is a promising area of study, and thus, numerous scientists, researchers, and academics have voiced their admiration and interest in this area. One of the main functions of nanofluids is their dynamic role in cooling small electrical devices such as microchips and associated gadgets. The major goal of this study is to perform an analysis of the buoyancy flow of a shrinking/stretching sheet, whilst considering the fascinating and practical uses of hybrid nanofluids. The influence of a nonlinear heat source/sink induced by a micropolar fluid is also inspected. Water-based alumina and copper nanoparticles are utilized to calculate the fine points of the fluid flow and the features of heat transfer. The governing equations are framed with acceptable assumptions and the required similarity transformations are used to turn the set of partial differential equations into ordinary differential equations. The bvp4c technique is used to solve the simplified equations. Dual solutions are presented for certain values of stretching/shrinking parameters as well as the mixed convective parameter. In addition, the shear stress coefficient in the first-branch solution (FBS) escalates and decelerates for the second-branch solution (SBS) with the superior impact of the magnetic parameter, the mass transpiration parameter, and the solid nanoparticles volume fraction, while the contrary behavior is seen in both (FB and SB) solutions for the larger values of the material parameter. [ABSTRACT FROM AUTHOR]

Heat transfer in a symmetrical cavity with two semi-cylinders was explored in this study. Several parameters, such as ( 10 3 ≤ R a ≤ 10 6 ), ( 10 − 5 ≤ D a ≤ 10 − 2 ), ( 0.02 ≤ ϕ ≤ 0.08 ), ( 0.2 ≤ ε ≤ 0.8 ), and ( 0 ≤ H a ≤ 100 ) were selected and evaluated in this research. The outcome of the magnetic field and the temperature gradient on the nanofluid flow is considered. The geometric model is therefore described using a symmetry technique. The flow issue for the governing equations has been solved using the Galerkin finite element method (G-FEM), and these solutions are presented in dimensionless form. The equations for energy, motion, and continuity were solved using the application of the COMSOL Multiphysics® software computer package. According to the results, there is a difference in the occurrence of the magnetic parameter and an increase in heat transmission when the right wall is recessed inward. The heat transmission is also significantly reduced when the right wall is exposed to the outside. The number of Nusselt grows directly proportional to the number of nanofluids in the environment. In contrast, all porous media with low Darcy and Hartmann numbers, high porosity, and low volume fraction have high Nusselt numbers. It is found that double streamlines for the hot side and single cooling for Darcy, Rayleigh, and Hartmann numbers. A cold isotherm at various physical parameters is needed in the top cavity. Rayleigh's number and a solid volume fraction raise Darcy's number, increasing heat transmission inside the cavity and thermal entropy determines entropy components. [ABSTRACT FROM AUTHOR]

In many industries, extremely high-performance cooling is a crucial requirement. However, the fundamental challenge to developing energy-efficient heat transfer fluids required for cooling is insufficient thermal conductivity. In this case, the utilization of nanofluid is effective to overcome these challenges. The current study aims to examine the two-dimensional (2D) stretching wall jet heat transfer fluid flow induced by a water-based alumina nanofluid embedded in a porous medium with buoyancy force. In addition, irregular heat sink/source and slip effects are assessed. The leading partial differential equations are changed into ordinary differential equations by incorporating similarity variables, then these equations are computationally or numerically worked out via the boundary-value problem of fourth-order (bvp4c) technique. The pertinent factors influencing the symmetry of the hydrothermal performance including friction factor, velocity, and temperature profiles, are illustrated using tables and graphs. The symmetrical outcomes reveal that the velocity declines in the presence of nanoparticles, whereas the temperature uplifts both assisting and opposing flows. Moreover, the friction factor augments due to porosity while the heat transfer rate declines. [ABSTRACT FROM AUTHOR]

"The author (Z. Raizah) extends her appreciation to the Deanship of Scientific Research at King Khalid University, Abha, Saudi Arabia, for funding this work through the Research Group Project under Grant Number (RGP.1/334/43)." now reads: "The author (Z. Raizah) extends her appreciation to the Deanship of Scientific Research at King Khalid University, Abha, Saudi Arabia, for funding this work through the Research Group Project under Grant Number (RGP.1/300/44)." Correction to: I Scientific Reports i https://doi.org/10.1038/s41598-023-37973-6, published online 03 July 2023 The original version of this Article contained an error in the Acknowledgements section. [Extracted from the article]