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Although selected configuration interaction (SCI) algorithms can tackle much larger Hilbert spaces than the conventional full CI method, the scaling of their computational cost with respect to the system size remains inherently exponential. In addition, inaccuracies in describing the correlation hole at small interelectronic distances lead to the slow convergence of the electronic energy relative to the size of the one-electron basis set. To alleviate these effects, we show that the non-Hermitian, transcorrelated (TC) version of SCI significantly compactifies the determinant space, allowing us to reach a given accuracy with a much smaller number of determinants. Furthermore, we note a significant acceleration in the convergence of the TC-SCI energy as the basis set size increases. The extent of this compression and the energy convergence rate are closely linked to the accuracy of the correlation factor used for the similarity transformation of the Coulombic Hamiltonian. Our systematic investigation of small molecular systems in increasingly large basis sets illustrates the magnitude of these effects. [ABSTRACT FROM AUTHOR]

The objective of this paper is to investigate the heat transfer mechanism while considering the attributes of viscous dissipation, Joule heating, and nonlinear thermal radiations in the three-dimensional steady incompressible flow of Carreau liquid on an extendable rotating disk. By using the similarity transformation, the governed equations were converted into the nonlinear coupled ordinary differential equations. The essential characteristics of various variables like Prandtl number, Lewis number, Carreau liquid parameter, Brownian motion, thermophoresis parameter, radiation parameter, Eckert number and Hartmann number on velocity, thermal, and concentration are discussed through graphs and tables. The presented investigation divulges that the thermal and mass transfer rates enhance when Brownian motion and thermophoresis processes extended and manifest as opposing features on the concentration field. [ABSTRACT FROM AUTHOR]

In the present work, we turn our attention to ferrofluid flow over an expandable sheet in a porous medium. In this flow, the magnetic dipole is kept in $ y $ y axis at a fixed length from the center. Using similarity transformation, the governing equations of the model are transformed into a non-dimensional form. The non-dimensional coupled differential equations are solved numerically through the finite element procedure in COMSOL Multiphysics. Velocity, temperature, and concentration distributions are demonstrated for different values of non-dimensional parameters. In the presence of magnetic dipole, some of the non-dimensional parameters favor the velocity, temperature, and concentration distributions and some of them inhibit the velocity, temperature, and concentration distributions. Escalating the ratio of the stretching sheet enhances the velocity and heat transfer in the fluid and decreases the concentration in the fluid. The position of magnetic dipole from the sheet has an important role in the optimization of velocity distribution and heat transfer in the fluid. [ABSTRACT FROM AUTHOR]

This study investigates the various uses of density of motile microorganisms in the context of the flow of a binary base fluid with double diffusion past a vertical surface. The research aims to comprehend the interactions between motile microorganisms and the fluid dynamics, as well as the heat and mass transport mechanisms in this system. The analysis involves mathematically constructing the governing equations, transforming them into dimensionless nonlinear ordinary differential equations using similarity transformations, and numerically solving them using the MATLAB bvp4c solver. An analysis of the influence of several parameters on the profiles of velocity, temperature, concentration, nanoparticle concentration, and density of motile microorganisms is conducted using graphical representation. The findings demonstrate that boosting the thermophoresis parameter intensifies the temperature profile. In addition, an increase in the nanofluid Schmidt number results in a larger concentration of nanoparticles, whereas a higher bioconvection Lewis number reduces the density of the motile microorganism profile. These findings may find use in biomedical engineering as well as industrial processes that include enhancing the efficiency of mass transfer and bioconvection. Numeric simulation prophesies 99.9% for both shear stress and heat transfer rate intensification for Prandtl values are noticed. [ABSTRACT FROM AUTHOR]

This study conducts a computational analysis to explore how magnetic fields, radiation, heat, and mass transfer collectively influence a horizontal stretching sheet within a porous medium. The research focuses on elucidating the dynamics of thin film flow through the formulation of time‐dependent equations and subsequent transformation of fluid flow equations into ordinary differential equations via similarity transformation. The numerical solution is attained employing the Runge–Kutta fourth‐order method coupled with a shooting technique. MATLAB software is utilized to generate graphs and numerical values, offering a detailed representation of engineering‐relevant physical quantities in tabular form. The investigation revealed notable trends associated with varying parameters. Increasing unsteadiness parameters lead to a reduction in velocity, temperature, and concentration fields, while the temperature distribution demonstrates a positive correlation with radiation parameters. Moreover, elevated Prandtl numbers and unsteadiness parameters correspond to augmented heat and mass flux, respectively. Of particular significance is the observed heightened heat transfer rate during the transition from a Prandtl number of 1 (representing air) to 2 (representing oil), alongside an increased mass transfer rate with the escalation in Schmidt number from 0.62 (representing hydrogen) to 0.78 (representing ammonia). A comparative analysis of the numerical findings with existing literature demonstrates excellent agreement, affirming the validity and relevance of the present study. These insights offer valuable implications for understanding and optimizing heat and mass transfer processes in porous media, with potential applications in various engineering and scientific domains. [ABSTRACT FROM AUTHOR]

This article uses a finite-element approximation approach for solving a three-dimensional flow problem of a nanofluid influenced by heat transfer due to nanoparticles over a non-linearly stretching sheet within an unbounded domain. Utilising similarity transformations, a well-posed coupled system of nonlinear ordinary differential equations is derived from the governing partial differential equations describing the flow and heat transfer processes. The resulting system is then solved by using quadratic Lagrange polynomials as basic functions over a mesh of different finite elements through the Galerkin finite element (GFE) technique. This implementation is based on a regular grid utilising Lagrange polynomials for solving the converted equations. The effects of various parameters of interest are efficiently discussed with the help of graphs and numeric tables. Both numerical and exact solutions are compared favourably, demonstrating a high level of accuracy. It is noteworthy that the GFE method emerges as a much more stable numerical technique than the other existing analytic and semi-analytical methods. Furthermore, the adopted finite-element method reduces the dimensionality of Sobolev's space's finite-dimensional subspace and also improves the solution's convergence rate. Moreover, the velocity is negative, and its magnitude increases as the stretching rates ratio increases due to the downward flow in the vertical direction. The temperature and heat transmission from the sheet are barely impacted by Brownian motion due to the dominance of other forces and length scales involved in the heat transfer process. [ABSTRACT FROM AUTHOR]

In current work, the unsteady stagnation point's flow on a special third-grade fuzzy hybrid (Al2O3 + Cu/SA) nanofluid (HNF) through a permeable convective shrinking/stretching sheet has been scrutinized. In addition, the adverse consequences of heat source, viscous dissipation, nonlinear thermal radiation, and fuzzy nanoparticle volume fraction are likewise taken into consideration. Non-linear coupled partial differential equations (PDEs) get transformed into ordinary differential equations (ODEs) using an effective similarity transformation. After that, the ODEs are numerically solved using the bvp4c algorithm. Regarding validation, the present results align with earlier published research. The effects of heat distribution, flow rate, Nusselt number, and skin friction coefficient on hybrid nanofluid dynamics are explored using graphical and tabular forms. The nanoparticle volume fraction is considered a triangular fuzzy number (TFN) [0, 5%, 10%]. With the use of TFNs, ODEs are transformed into fuzzy differential equations (FDEs). The TFNs are controlled using a widely used ζ - cut technique and ζ - cut ∈ [0, 1], which requires minimal computational effort to examine their dynamical performance. Also, the comparison of Al2O3/SA, Cu/SA and Al2O3 + Cu/SA through the fuzzy membership functions (MFs). The fuzzy MFs show that the hybrid nanofluid (Al2O3 + Cu/SA) in terms of rate of heat transfer is better than both Cu/SA and Al2O3/SA nanofluids. [ABSTRACT FROM AUTHOR]

In this work, computational intelligence methodologies are used to investigate the trihybrid nanofluid, a new theoretical model with remarkable thermal transmission properties to enhance liquid thermal performance. The nanostructure Cu, Al2O3, and TiO2 were immersed in the base liquid (C2H6O2) to produce (Cu + Al2O3 + TiO2/C2H6O2) trihybrid nanofluid. In a Darcy-Forchheimer porous medium over a stretching Riga sheet, this study examines the electromagnetic ternary hybrid nanofluid flow under various slip situations. The study takes into account the complex interactions between a number of variables, including as viscous dissipation, radiation, heat sources, and chemical reactions. Similarity transformations are used to convert complex partial differential equations for flow, energy, and concentration into nonlinear ordinary differential equations. The highly nonlinear equations of the problem are solved numerically with the use of techniques from the bvp4c approach. The results of the bvp4c method produce the reference dataset required for the Levenberg-Marquardt backpropagation of neural networks (LMBNN). The neural network performance is validated using regression analysis, mean square errors, and error histogram data. The model problem's consistency and precision are evaluated using the absolute error, which is given for each model instance at around 10-06 - 10-08, 10-05 - 10-10 and 10-06 05-10-09. In order to reduce mean square error, the nonlinear fluid dynamics system's numerical solutions have been taken into consideration. Using the comparative configurations of MSE, error histograms, state transitions, correlation, and regression, the reliability and competence of the stochastic technique are verified. [ABSTRACT FROM AUTHOR]

This study reports both MagnetoHydroDynamics (MHD) and heat generation aspects of a water-based hybrid nanofluid flow with various shapes of the nanoparticles involving Nimonic 80A and Fe 3 O 4 , over a moving wedge. Similarity transformations were adapted to obtain non-dimensional equations and solved using MATLAB bvp4c code. All the results and graphs were formulated after a positive outcome of our results with that available in existing literature. Nusselt number, which signifies the heat transfer rate in a flow, increased with an increase in empirical shape factors of the nanoparticle with a contrasting decrease in the drag experienced during the flow, represented by the skin friction coefficient. The velocity profile decreased at a rate of 0.75% for M = 0. 6 to M = 0. 8 due to the augmenting Lorentz forces while it augmented by 18.9% for an augmenting velocity ratio parameter from R = 0. 0 to R = 0. 5 due to the no-slip boundary conditions. Both the Nusselt number and skin friction coefficients decreased with an increase in magnetic parameter. An increase in the nanoparticle concentration resulted in an incrementing streamline value along with increasing temperature profile due to increasing thermal conductivity of the fluid flow system. The physical significance of the study involves in its applications in nuclear, steel industries, MRI scanning for its anti-corrosive and high thermal conductivity properties. [ABSTRACT FROM AUTHOR]

The transport phenomena of Casson nanofluid flow between two parallel disks subject to convective boundary conditions are analyzed in this paper. The mathematical model incorporates the impact of thermophoresis and Brownian motion since the Buongiorno's nanoliquid model is adopted to characterize the nanoliquid's transport features. The appropriate similarity transformations are applied to obtain the resulting nondimensional ordinary differential equations from the basic governing equations. The resulting ordinary differential equations and the associated boundary conditions are solved analytically by adopting the homotopy perturbation technique. Further, a statistical experiment is conducted to identify notable flow parameters which cause significant impact on the heat transfer rate. The characteristics of critical pertinent parameters on the flow field are graphically manifested. It is worth noting that the Casson nanofluid velocity escalates by augmenting the magnetic field parameter in the case of injection near the disks. Nanoparticle concentration is considerably diminished with an increment in thermophoresis parameter. In the cases of equal and unequal Biot numbers, the heat transfer rate is promoted with higher values of the Brownian motion parameter. Among the Casson fluid parameter, squeezing parameter and magnetic field parameter, the heat transfer rate discloses the highest positive sensitivity with the lowest value of the Casson fluid parameter. [ABSTRACT FROM AUTHOR]

This research addresses the complex dynamics of hybrid Casson nanoliquids in flow and heat transfer applications, focusing on the interaction between fluid dynamics and thermal phenomena in the presence of magnetohydrodynamics (MHD), viscous dissipation, and Joule heating. The motivation behind this study stems from the need to enhance the efficiency of heat transfer processes in various engineering applications, such as cooling systems and electronic devices, where hybrid nanofluids can offer superior thermal performance compared to conventional fluids. The novelty of this work lies in its comprehensive numerical investigation of a hybrid Casson nanoliquid over a moving permeable surface, incorporating a detailed analysis of MHD effects, viscous dissipation, and Joule heating. Using the Tiwari and Das model to formulate the governing equations, the study employs similarity transformations to convert these equations into a system of ordinary differential equations (ODEs). MATLAB is then used to derive numerical solutions, with a stability analysis ensuring the physical dependability of these solutions. Key findings reveal that the temperature distribution of the hybrid nanoliquid shows a positive correlation with both Prandtl and Hartmann numbers. Additionally, a positive relationship between temperature and the Eckert number is observed. These insights offer valuable guidance for engineers aiming to optimize heat transfer processes using hybrid nanofluids, highlighting their potential for improved thermal management in practical applications. [ABSTRACT FROM AUTHOR]

Theoretical research has been done on the hydromagnetic three-dimensional nanofluid flow across an inclined stretching sheet in the presence of Brownian motion and thermophoresis. It is taken into account that there are two different kinds of water-based nanofluids that contain copper and alumina. Three-dimensional nonlinear-type similarity transformations are used to convert the governing boundary-layer equations into a collection of similarity equations, which are then numerically solved by MATLAB. Further, results obtained in some limiting cases are compared to some results that have already been published, and it is found that there is good agreement. The problem is controlled by a number of physical factors, and the impact of these factors on different flow distributions is thoroughly examined with the help of graphs and tables. It has been observed that the nanofluid has better heat transfer conductivity than the ordinary base fluid. [ABSTRACT FROM AUTHOR]

In this work, entropy generation is optimized through the application of the second law of thermodynamics. The slip mechanisms, Brownian diffusions, and thermophoresis are elaborated using the tangent hyperbolic nanomaterial model. Magnetohydrodynamic (MHD) fluid is taken into consideration. To characterize the impact of activation energy, a unique model involving the binary chemical reaction is deployed. The effects of mixed convection that is nonlinear in nature, bioconvection, and Joule effect are all taken into consideration. The key partial differential equations (PDEs) are reduced into ordinary differential equations (ODEs) by utilizing appropriate similarity transformations and then solved numerically with the help of a built-in 'bvp4c' technique of MATLAB software. Varied flow parameters' impacts on the nanoparticle volume concentration, entropy number, microorganism concentration, temperature, and velocity fields are analyzed using graphs. Various flow variables are taken into consideration to calculate the total rate of entropy generation. The obtained results show that concentration irreversibility, Joule effect irreversibility, viscous dissipation, and heat irreversibility all influence the entropy. The numerical outcomes were observed by fixing the physical parameters as 0.1 < α < 4.0 , 0.1 < M < 1.2 , 0.1 < N r < 2.2 , 0.1 < L e < 2.2 , 0.1 < N b < 0.4 , 0.1 < N t < 1.0 , 2.0 < ⁡ Pr ⁡ < 5.0 , and 0.1 < L b < 2.0 , as well as their impact on the momentum, thermal, concentration, and microorganism density profiles. From results, an increasing estimate of the variable representing chemical reaction indicates a decline in the concentration. The higher the chemical reaction variable, Hartmann number, and Weissenberg number, the higher the entropy number, while the Bejan number has a contrary behavior. Subsequently, all the outcomes are plotted in graphs and discussed in detail, when subjected to the involving physical quantities. [ABSTRACT FROM AUTHOR]

Exponential space‐based heat source with shear‐thinning/thickening behavior offers innovative insights into the optimization of thermal transport process in complex systems, such as in the cooling of microelectronics, energy storage technologies, and biomedical devices, where accurate thermal control is critical. This study explores the investigation of an exponential space‐based heat source with effects of shear thinning/thickening behavior of a ternary infinite shear rate viscosity‐dependent Carreau water‐based nanofluid [Cu, Fe3O4, SiO2] over a three‐dimensional wedge in a magnetized environment. The interaction between heat transport and magnetic fields is explored through the behavior of the ternary nanofluid by classifying the both shear‐thinning and shear‐thickening effects. The incorporation of physical assumptions in the model gives the set of partial differential equations (PDEs) and similarity transformations are launched to convert them into ordinary differential equations (ODEs). Furthermore, bvp4c scheme is used to fetch the numerical solution. Temperature profile is increasing with exponential‐based source heat parameter due to a reduction in the rate of heat absorption by the fluid. Ternary nanofluids exhibit the highest rate of temperature increment due to the effects of multiple nanoparticles as compared to hybrid or single‐nanoparticle nanofluids. Rate of velocity decrement in ternary nanofluids compared to bi‐hybrid nanofluids and single‐particle nanofluids. [ABSTRACT FROM AUTHOR]

Unlike the simplification of individual lines, the generalization of contour clusters oriented to geographical features is a structured generalization behavior that extracts knowledge of geographical features form the perspective of spatial cognition. In decision level, terrain generalization is essentially a similarity transformation between the geomorphic structures corresponding to multi‐scale contour cluster. However, the multi‐scale structural similarity relations are not directly connected with the application of contour generalization. Therefore, this paper presents an automated method for terrain contour structured generalization considering multi‐scale structural similarity. Firstly, a drainage tree structure is constructed from contour lines to establish associations between valley branches and contour bends. Then, the quantitative relationships between multi‐scale structural similarity and map scale changes are explored using an indirect quantitative expression method. Finally, the contour structural generalization is fully automated through iterative optimization principle based on the multi‐scale structural similarity relations. The experiment results demonstrate the rationality and feasibility of fully automating the contour generalization process based on multi‐scale geomorphic structural similarity relations. And the proposed method not only overcomes the challenge of determining "how much to select" in map generalization, but also is valuable for enriching the content of spatial similarity relations and map generalization, thereby providing a theoretical method system and support for the construction of national basic vector databases. [ABSTRACT FROM AUTHOR]

The rising use of 3D digital products has increased the demand for copyright protection. In this paper, we propose a novel and robust 3D watermarking method with high imperceptibility based on EMD (empirical mode decomposition) on surfaces. It first defines a normalized modulus signal on a 3D host model so as to involve EMD into 3D watermarking effectively. And then, it extracts different scale features of the defined signal by using EMD to locate the proper embedding positions. After this, the watermark signal is embedded repeatedly and cyclically into the 3D host model to enhance the robustness. The embedding strength is optimized according to a predefined fidelity parameter to control the imperceptibility of the watermark. Many experiment results show that the proposed method can obtain good results against various attacks while maintaining high invisibility, such as pseudo-random noise, Laplacian smoothing, simplification, subdivision, cropping, and similarity transformation. Furthermore, it is very competitive with the current state-of-the-art 3D watermarking techniques in terms of robustness and invisibility. [ABSTRACT FROM AUTHOR]

Purpose: The current work investigates an unsteady squeezed flow of hybrid-nanofluid between two parallel plates in occurrence with a uniform transverse magnetic field. Water is used as base fluid mixed with Graphene Oxide (GO) and Copper (Cu) nanoparticles. The flow considered here is under slip boundary conditions. Design/methodology/approach: The governing PDEs are transmuted into ODEs by applying an appropriate similarity transformation and then solved numerically using the 4th order R-K method with shooting technique. Graphical illustrations for velocity, temperature, entropy generation (NG), Bejan number (Be), streamline etc. are presented and discussed in detail from the physical point of view. The nature of the Nusselt number is also studied numerically through contour plots for different flow parameters. Findings: There is no funding obtained for the research work. Social implications: This kind of study may be used in various fields including polymer processing, lubrication apparatus, compression including hydrodynamical machines compression, food processing etc. Originality/value: It is observed that very little investigation has yet been made about the movement of hybrid nanofluid between two analogous plates. [ABSTRACT FROM AUTHOR]

This study focuses on investigating the effects of viscous dissipation, magnetohydrodynmaics (MHD) and mixed convection on Casson nanofluid thin film flow over a vertical stretching surface, considering its unsteady, two‐dimensional nature. The problem is formulated by assuming incompressible flow and employing boundary layer approximations, leading to a system of partial differential equations (PDEs). These PDEs are then transformed into nonlinear ordinary differential equations (ODEs) using similarity transformations. Numerical techniques, facilitated by computational software such as Mathematica, are employed to solve these nonlinear ODEs. The investigation probes into the mathematical analysis of various physical parameters, presenting their effects through graphical representations. The impact of parameters such as concentration Grashof number (Gc), thermal Grashof number (Gr), magnetic parameter (M), unsteadiness parameter (S), dimensionless film thickness (β), and Casson fluid parameter (γ) are examined. The velocity profile f′(η)$f^{\prime}( \eta )$ exhibits an increase with rising values of Gc and Gr, while it decreases with increasing values of M, S, β, and γ. The results are further elucidated through tabular representations, providing insights into the variations of skin‐friction coefficient, Sherwood number, and Nusselt number with respect to the aforementioned parameters. [ABSTRACT FROM AUTHOR]

This research leads to carrying out the productivity and the efficiency of the carbon nanotubes (CNTs) that have extensive applications in solar collectors. Due to the superior thermal as well as electrical properties, the use of CNTs has an important contribution to the nanotechnology revolution. Therefore, owing to the aforementioned vital points, this investigation intended to put forth the thermophysical properties of both single and multi-walled CNT nanofluids past a stretching surface. Additionally, an electrically conducting nanofluid flow phenomenon enriches due to the inclusion of dissipation (Ohmic heating) and external heat source/sink. The dimensional form of the three-dimensional fluid flow phenomena is transformed to a non-dimensional form with the use of similarity transformation and further numerical procedure is implemented to solve the nonlinear governing equations. The substantial significance of the characterizing parameters is presented briefly via figures and the comparative analysis with the earlier investigation is deployed through the table. However, the main findings of this study are as follows: A significant attenuation in the shear rate is marked for the enhanced inertial drag but it augments for the augmented values of the magnetization; further, particle concentrations of both the CNTs favor accelerating the fluid momentum as well as temperature distribution. [ABSTRACT FROM AUTHOR]

The boosting of base fluid thermal transport is a remarkable significance in the current research era, and numerous types of techniques are being utilized to achieve this goal. The mixture of nanoparticles inside the host fluid is responsible to improve base fluid thermal performance. The modified Buongiorno's nanofluid model is explored in the current study along with the significant trihybrid nanoparticle ((TiO2+Al2O3+MoS2)−Water)$( {( {{\mathrm{TiO}}_{\mathrm{2}}{\mathrm{ + A}}{{\mathrm{l}}}_{\mathrm{2}}{{\mathrm{O}}}_{\mathrm{3}}{\mathrm{ + Mo}}{{\mathrm{S}}}_{\mathrm{2}}} ){\mathrm{ - Water}}} )$ effect. The fundamental equations of the chosen flow model are transformed using a similarity transformation, and the succeeding equations are then resolved numerically using the discretization of Keller‐Box in MATLAB. The primary velocity profile is directly raised with large values of the Hartman number, unsteady, and Ellis's fluid parameters, while an inverse curves trend is reported in secondary velocity. The primary speed of fluid is significantly greater compared to di and mono‐hybrid cases, and this study reveals that optimal thermal transport is achieved against tri‐hybrid cases. The tri‐hybrid model has 9% improvement in Nusselt number when compared to single and two‐type nanoparticle fluid models. [ABSTRACT FROM AUTHOR]

This study presents a comprehensive numerical computation of heat‐mass transfer characteristics of single‐walled carbon nanotube (SWCNT)/multi‐walled carbon nanotube (MWCNT)‐water suspension flow over a porous stretching sheet with an inclined magnetic field. The governing equations for fluid flow characteristics are formulated using the Sisko fluid model to capture the Newtonian and non‐Newtonian behavior of the nanotube‐water mixture. The nonlinear coupled partial differential equations are converted into nonlinear dimensionless coupled ordinary differential equations using suitable similarity transformations. These equations are solved using MATLAB by implementing the four‐stage Lobatto IIIa formula. The comprehensive set of computations is performed to explore the influence of pertinent parameters, including Sisko fluid parameters, concentration of nanotubes, stretching sheet velocity, and porous medium characteristics on the flow, heat, and mass transfer profiles. From the graphs and statistical analysis, it is clear that the volume fraction of SWCNT and MWCNTs are strongly correlated. The investigation reveals that increasing the inclination angle affects the fluid velocity. The variation in all flow features is negligible for volume fractions of CNTs between 0% and 10% but a significant effect is observed only beyond 10%. Higher volume fractions of CNTs result in enhanced local heat transfer coefficient. This can be attributed due to the outstanding heat transfer capabilities of CNTs owing to their high thermal conductivity. However, Shear thickening fluids exhibit high heat transfer phenomena when compared to shear‐thinning and Newtonian fluids. This research provides valuable insights into the optimization of CNT‐based nanofluids for efficient heat and mass transfer applications in electronics cooling, heat exchangers, and solar energy systems, offering opportunities to enhance energy efficiency and device performance. [ABSTRACT FROM AUTHOR]

We consider seven-vertex two-dimensional integrable statistical model. With the help of intertwining vector method we construct its counterpart integrable model of SOS type. More general models of both types are constructed by means of fusion procedure. For SOS models we calculate the Boltzmann weights in terms of terminating hypergeometric series 9F8. Then using the similarity transformation for R-operators we construct a new family of vertex models containing the 11-vertex model as a simplest representative. For this new set of models the vertex-SOS correspondence is constructed: we find the intertwining vectors and show that they do not depend on spectral parameter and the SOS statistical weights are similar to those obtained from the 7-vertex model. [ABSTRACT FROM AUTHOR]

As a means of influencing technological advancements in engineering applications and various fluid products, the generalized Fourier's and Fick's models have proven to be of great importance. Industries such as power station engineering, high thermal material processing, and bio-heat elements apply the concept of anomalous heat and mass transfer mechanism. The objective of this study is to stimulate the flow of a radiative magnetohydrodynamics Jeffery fluid over an expanding surface with anomalous heat and mass transfer dynamics subjected to nth order reaction and variable thermophysical properties. A set of similarity transformations is used to neutralize the governing equations into a nondimensionless form. To obtain the model parametric analysis, a numerical tool via the spectral local linearization method (SLLM) is deployed after transformation of the governing flow equation from a two-unknown partial differential equations to a one-variable ordinary differential equation. It is observed that the thermal boundary layer thickness is found to be enhanced with increasing parametric values of magnetic, Eckert and radiation parameters. For the radiation parameter R ∈ [ 0. 5 0 , 2. 5 0 ] , the skin drag force, Nusselt and Sherwood number increase by 0. 6 1 % , 4 8. 0 0 % and 0. 9 1 % , respectively. Additionally, a 2 0 0 % increment in the nth order parameter boosts the rate of heat transfer by 0. 7 8 %. while it downsizes the Sherwood number by 1 4. 3 2 %. [ABSTRACT FROM AUTHOR]

The study has been carried out to analyze the Magnetohydrodynamic (MHD) boundary layer flow, heat and mass transfer of the two-dimensional viscoelastic Oldroyd-B fluid over a vertical stretching sheet in the presence of thermal radiation and chemical reaction with suction/injection in a steady state. The governing equations of the system are partial differential equations, which then give rise to a set of highly nonlinear coupled ordinary differential equations using similarity transformations. The nonlinearity in the differential equations is dealt with quasilinearization technique. The resultant equations are numerically solved using Chebyshev wavelet collocation method. The effects of magnetic field, radiation, chemical reaction and buoyancy parameters are investigated. The numerical values of local skin friction coefficient, local Nusselt number and local Sherwood number are also tabulated and analyzed. We observe that the increase in buoyancy parameters enhances the velocity profiles and larger values of magnetic field decrease the velocity profiles but increases the temperature and concentration profiles. Error analysis has been done to check the convergence of the numerical scheme. [ABSTRACT FROM AUTHOR]

This article focuses on the effect of buoyancy on the bioconvective micropolar fluid flow over a curved stretching surface under the slip boundary condition. Mass and heat transfer analysis has been analysed using double stratification, linear heat source, chemical reaction and Joule dissipation. The calculation of entropy formation in a fluid flow is also illustrated. Using similarity transformations, the system of partial differential equations is transformed into a set of ordinary differential equations through reduction in the flow equations and then solved using the numerical methodology of the Runge‐Kutta‐Fehlberg 4th‐5th order method. The mathematical data obtained for velocity, temperature, concentration, and bio‐convection profiles with different parameters are presented on graphs. The velocity profile exhibits consistent behaviour near the buoyancy parameter, with a decrease at the boundary followed by an increase. Notably, the velocity profile experiences a decrease under first‐order slip conditions but grows when subjected to second‐order slip. Micro‐rotation intensifies as the material parameter increases. Conversely, temperature and concentration has declined as the stratification parameter rises. Additionally, the concentration of motile microorganisms reduces with increasing Lewis number and Peclet number. As the material parameter rises, entropy decreases while the Bejan number increases. [ABSTRACT FROM AUTHOR]

The present investigation examines the circulation of TiO2−H2O${\mathrm{TiO}}_{2} - {{\mathrm{H}}}_{2}{\mathrm{O}}$ and Ti6Al2V−H2O${\mathrm{Ti}}_{6}{\mathrm{Al}}_{2}{\mathrm{V}} - {{\mathrm{H}}}_{2}{\mathrm{O}}$ based nanofluids while considering the concentration of waste discharge. An innovative stacking regressor model is used to increase prediction accuracy. Using Shooting and Runge Kutta Fehlberg's fourth and fifth‐order schemes, the governing equations are converted into ordinary differential equations using similarity transformation and then numerically solved. The findings are represented graphically, and the model's correctness is assessed using Gaussian Process Regression, Categorical Boost, Extreme Gradient Boosting, and Random Forest, with linear regression acting as a meta‐model. The closely related testing and training data show the model's consistency and stability. Magnetic field and inclination angle will decline the velocity, space, and temperature‐dependent internal heat generation factors will enhance the temperature. Raising the pollutant external source parameter raises concentration. In all the cases, Ti6Al2V−H2O${\mathrm{Ti}}_{6}{\mathrm{Al}}_{2}{\mathrm{V}} - {{\mathrm{H}}}_{2}{\mathrm{O}}$ shows better performance than TiO2−H2O${\mathrm{TiO}}_{2} - {{\mathrm{H}}}_{2}{\mathrm{O}}$ based nanofluid. The work's application ranges from fluid dynamics to waste management. By offering precise forecasts of nanofluid concentration, the proposed prediction model may aid in designing and optimizing waste discharge systems. [ABSTRACT FROM AUTHOR]

In this article, two-dimensional unsteady incompressible viscous nanofluids magneto-hydrodynamic (MHD) flow among two parallel plates extended infinitely is investigated. The equations that results from the use of similarity transformations for non-linear partial differential system are solved by the new algorithm. The important key to this construct is the derivatives that appear as coefficients in the power series. The effects of apparent physical parameters on velocity concentration and temperature distributions are described using a schematic diagram and interpreted physically. The effects of apparent physical parameters on concentration, temperature, and velocity distributions are described by graphs. For the flow of nanofluids, the results indicate that it is inversely proportional between the rate of mass and heat transfer with nanoparticle size fraction and magnetic parameter. Over time, squeeze number and schmidt number lead to increase the rate of mass transfer. This problem is dissolved numerically by using the Runge-Kutta scheme of fourthorder (RK4S) . [ABSTRACT FROM AUTHOR]

This study investigates the effects of activation energy and chemical reactions on the boundary layer flow around a wedge that is moving in a nanofluid. To represent the problem, nonlinear partial differential equations are utilized. These equations can be reduced to nonlinear coupled ordinary differential equations using similarity transformations. These equations are numerically solved using the Keller Box technique, and then their numerical and pictorial solutions are studied using MATLAB. The study looks at the relationship between the velocity, temperature, and concentration profiles and important factors such as the Prandtl number, constant moving parameter, activation energy, and reaction rate. The parametric range of factors such as 0.1 ≤ λ ≤ 1.0, 0.1 ≤ Le ≤ 3.0, 0.1 ≤ E ≤ 2.0, 0.1 ≤ Pr ≤ 7.0, 0.1 ≤ Nt ≤ 0.5, 0.1 ≤ Nb ≤ 1.0, 0.1 ≤ σ ≤ 3.4, 0.1 ≤ δ ≤ 2.5, and 0.1 ≤ β ≤ 2.0 is utilized. Furthermore, a comprehensive investigation is conducted into the remedies for skin friction and heat transmission rate. It is deduced that a growing magnitude in moving fluid velocity is noted for lower Prandtl, moving factor, reaction factor, and greater activation energy. It is depicted that the maximum enhancing magnitude in temperature and concentration with good distributions is examined for each pertinent factor. The growing magnitude of heat transport is noted for lower Lewis and temperature-difference factors but increases as pressure-gradient and Brownian factor rise. [ABSTRACT FROM AUTHOR]

The current research is based on the impact of thermal and solutal slip in the boundary layer nanofluid flow through a moving accelerating wedge. The present investigation is considered with the influence of Brownian motion and thermophoresis. Thermal insulation, geothermal engineering, crude oil extraction, and heat exchangers are very important applications of nanofluid movement over a wedge surface with thermal and concentration slip. The suggested mathematical analysis is expressed in terms of partial differential equations (PDEs). These PDEs are transformed into ordinary differential equations via similarity transformation. The Keller Box technique is used to integrate the resultant non-similar equations. The set of discretized and first order differential equations is formed with the help of central difference and the Newton–Raphson technique. The graphical and numerical results are extracted with the help of MATLAB. The numerical results with the influence of the Prandtl factor (Pr), constant moving factor (λ), thermal slip factor (S2), and concentration slip parameter (S2) are interpreted visually and numerically. Graphical representations of velocity, thermal, and mass concentration profiles are analyzed in depth. The solution for skin friction coefficient, heat transport rate, and mass transport rate is calculated. The moving velocity function increases as Pr increases. The rate of slip temperature and slip concentration rate is enhanced for a lower Prandtl factor. The maximum slip behavior in temperature function and fluid concentration slip is deduced for each value of thermal-slip and concentration-slip factors. For high Prandtl and Brownian motion factors, the rate of Nusselt number is enhanced significantly. [ABSTRACT FROM AUTHOR]

The incorporation of three distinct nanoparticles in blood within the context of cubic autocatalysis holds significant potential for enhancing biomedical applications, particularly in targeted drug delivery and therapeutic interventions. The increased reaction rate improves the efficiency of catalytic processes within the bloodstream. This research investigates the thermal transport characteristics of a trihybrid Carreau nanofluid (blood) containing copper (Cu), titanium dioxide (TiO2), and aluminum oxide (Al2O3), nanoparticles in the context of a wedge‐shaped artery under the influence of autocatalytic cubic autocatalysis. Effects of thermal radiation, and heat generation are used for heat transport analysis, heterogeneous‐homogeneous chemical process included for blood concentration, and an inclined magnetic field is imposed for securitization of blood velocity. Also, the generated PDEs from the physical model are handled through similarity transformations and converted into ODEs. Bvp4c, a numerical technique is used to get the solution and then Levenberg‐Marquardt neural network (LM‐NN), a multilayer neural network scheme is used to train and predict the solution for each parameter. In addition, the numerical values of volumetric friction of coefficients enhance the thermal conductivity, and the heat transport rate is increased. The magnetic parameter, radiation and chemical processes enhance the rate of heat transport while the Weissenberg number reduces the velocity profile. [ABSTRACT FROM AUTHOR]

This article investigates the effect of activation energy on Carreau fluid flow in the presence of variable thermal conductivity, inclined magnetic field, melting heat transfer, and Soret and Dufour phenomena. A set of suitable similarity transformations is applied for transforming the governing partial differential equations (PDEs) considered for the physical phenomena into non-linear ordinary differential equations (ODEs). We obtained the results by solving the non-linear ODEs numerically which describe the behavior of the velocity, temperature, and concentration profiles of the fluid against the governing parameters and illustrated these graphically. The velocity distribution decreases for angle of inclination while it is increasing against higher melting parameter. The temperature distribution enhances with higher modified Dufour parameter and Prandtl number while it declines for thermal conductivity, activation energy, and melting parameters. The concentration distribution increases for melting parameter, Soret number, and activation energy parameter while decreasing for temperature difference parameter, Schmidt number, and reaction rate parameter. Skin friction, Nusselt and Sherwood numbers are evaluated numerically against the various governing parameters. Accuracy of the present work is illustrated and established through comparison carried out for skin friction versus magnetic parameter with existing results in the literature. [ABSTRACT FROM AUTHOR]

The magnetohydrodynamics (MHD) Williamson fluid model close to a moving surface is thoroughly analysed in this work, taking into account the effects of changing thermal conductivity, and diffusion. The overall dynamics of flow are affected by the major influence of thermal conductivity variations on heat transfer. The nonlinear partial differential equations governing the system are converted into ODEs by similarity transformations, taking into consideration the effects of porous media using the Darcy model. The Runge–Kutta fourth‐order (RK4) method is used to numerically solve these equations, making it easier to examine incompressible fluid flow on the moving surface. The findings provide important new understandings of the intricate flow patterns and the development of shear layers brought about by the fluid‐surface interaction at varied thermal conductivity levels. These results improve our understanding of fluid dynamics in geophysical and atmospheric environments and are essential for the design and optimisation of engineering applications with changeable thermal characteristics. [ABSTRACT FROM AUTHOR]

In the present investigation, influence of the chemical reaction, magnetic field and slip on micropolar fluid flow via a porous wedge in the existence of Hall and ion-slip are examined. The pertinent highly non-linear PDEs are changed into an arrangement of non-linear coupled ODEs by utilizing similarity transformation. The equations were calculated using the 'Keller Box Method' (KBM). The numerical data for skin-friction coefficients, Nusselt number, Sherwood number, velocities, thermal and concentration fields are portrayed by graphs for various existing parameters and analyzed in detail. The heat transfer characteristics of working magnetic fluid escalated with acceleration in slip and power-law parameters. Moreover, the mass transfer function escalated with material and chemical reaction parameters. [ABSTRACT FROM AUTHOR]

Designing guidance mechanisms using bistable mechanisms with two stable positions is a common low-power solution for maintaining the guidance position without continuous external energy input. However, the coupling between kinematics and statics in compliant bistable mechanisms poses a challenge for their application in mechanism synthesis. To address this issue, this paper introduces the pole similarity transformation theory into the synthesis of compliant mechanisms and proposes a general synthesis method for planar serial-based compliant bistable mechanisms. This method models the compliant mechanism using the strain energy method and analyzes the bistable characteristics of the mechanism within its motion plane using the saddle point searching method. By doing so, the proposed method can identify stable positions without predetermined motion trajectories, making it more suitable for designing compliant bistable mechanisms with general planar motion. Additionally, this method utilizes the pole map to describe the stable positions of the rigid components in the compliant mechanism and establishes an information database for compliant bistable mechanisms. Through leveraging the pole similarity transformation, the pole maps of the mechanisms in the information database are matched with the pole map of the motion task, thus achieving the synthesis of planar serial-based compliant bistable mechanisms for the rigid-body guidance problem. The paper provides a detailed explanation of the mechanism synthesis process and demonstrates its application through a case study. [ABSTRACT FROM AUTHOR]

In order to truly describe the dynamic characteristics of bottom-hole pressure in the reservoir, in this paper, the elastic outer boundary condition is introduced to replace the three kinds of traditional outer boundary conditions (infinity, constant pressure, closed), and a spherical nonlinear seepage model is established for the dual-porosity reservoir, which takes into account wellbore storage, effective well diameter and quadratic gradient term. The solution of the model in the Laplace space is found, and the similar structural formula of the solution is obtained by combining the Laplace transformation with the similarity construction method. Subsequently, by the Stehfest numerical inversion method, the well test curve is drawn, and the influence of main reservoir parameters on bottom-hole pressure dynamics is analyzed. The introduction of the elastic outer boundary not only breaks the traditional fixed form of the ideal outer boundary condition, but also improves the interpretation accuracy of the reservoir boundary. At the same time, a more general representation of the model is put forward, which provides a more effective theoretical basis for further exploration of the seepage law of the reservoir. Simultaneously, the similarity construction method simplifies the complex calculation process of solving the model and provides a new idea for solving the more complicated percolation model of oil and gas reservoirs. The similar construction method simplifies the complicated calculation process of solving the model and provides a new idea for solving the more complicated percolation model of oil and gas reservoirs. [ABSTRACT FROM AUTHOR]

The current study investigates the effects of thermal radiation and Lorentz's force on heat and mass flow in a nanofluid with a magnetic field and free convection, as it passes over a vertical permeable sheet. The dominant PDEs are turned into linked nonlinear ODEs using an appropriate similarity transformation. Using the MATLAB ODE45 tool, dimensionless ODEs are numerically computed using the finite difference procedure. Four different water-based nanofluids are considered, including copper, titanium dioxide, aluminum oxide, and silver. The influence of emerging dimensionless numbers and other parameters, such as the magnetic force parameter, the radiation parameter, the suction parameter, the Prandtl number, the Schmidt number, the Dufour number, as well as for constant values of the modified local Grashof number and local Grashof number on the concentration, velocity, and temperature profiles is emphasized and mentioned. Moreover, the visual representation of the effects of a volume percentage of up to 4% copper nanoparticles on the distributions of concentration, temperature, and velocity is also shown. The temperature profile, concentration profile, and velocity profile all grow with an increase in the volume percent of copper nanoparticles between 0.00 and 0.04. Furthermore, numerous scenarios are investigated for the distributions of the local Sherwood number, the local Nusselt number, and the local skin friction coefficient. The local Nusselt number decreases, and the local skin friction coefficient and Sherwood number increase about by 30 %, 45 %, and 60 % respectively due to increasing the value of volume fraction from 0 % to 4 %. The local skin friction coefficient increases and the local Nusselt number decreases by about 15 % and 39 % respectively for rising values of the thermal radiation number from 0.5 to 3.5. In addition, for magnetic force parameter values between 0.5 and 4.0, the local skin friction coefficient drops by about 13 %. [ABSTRACT FROM AUTHOR]

The current study aims to investigate the heat generation/absorption, radiation, and chemical reaction impacts on a laminar flow, with an upward half-space three-dimensional, incompressible permeable, stretchable, rotating hybrid nanofluid (Al2O3-Cu/H2O). Using appropriate similarity transformations, leading nonlinear governing equations were taken into account and were converted into ordinary differential equations. These equations were evaluated by deploying MATLAB's bvp5c feature. The resulting graphs assess velocity, temperature, and concentration for a range of effects. Additionally, Sherwood and Nusselt numbers and skin friction results were obtained. The findings were compared with previously published research. [ABSTRACT FROM AUTHOR]

Research Problem: The importance of improving the temperature properties of commonly used fluids in industrial processes is being addressed in this research. Nanofluids, which are composed of extremely small particles dispersed in common liquids such as water or petrol, are the main subject of this area of study. Using a vertically stretchable surface subjected to thermal radiation, the study examines the heat transfer behavior and efficiency of nanofluids.Methodology: Nanofluids that convey heat are studied by applying the fundamental rules of fluid physics to the variables that control their motion. To measure the amount of energy transferred, a nanofluid model is used. Similarity transformations are used to convert the system’s differential equations into ordinary differential equations (ODEs). The subsequent set of nonlinear ODEs is solved using numerical methods. Utilizing graphical analysis, patterns of velocity and temperature may be seen, and their responses to changes in other parameters can be investigated.Implications: This research has important implications for our knowledge of how nanofluids act in heat transfer applications, especially when exposed to thermal radiation and working with vertically stretchy surfaces. The effects of flow direction and thermal conductivity on distributions of velocity and temperature were elucidated, among other important results. More effective heating and cooling systems may be possible as a result of these findings, which have consequences for improving heat transfer processes in industrial environments.Future Work: To better understand how nanofluids behave in heat transfer applications, future studies might investigate more complicated situations and boundary circumstances. It may be possible to optimize nanofluid formulations by studying the impact of various nanoparticle kinds and concentrations on heat transfer efficiency. Research could be more applicable to real-world industrial processes if the numerical results were experimentally validated. [ABSTRACT FROM AUTHOR]

There have been a lot of claims made in the literature recently regarding the physical characteristics of nanofluids in different flow systems, especially the laminar flow regimes. The goal of this study is to investigate the two‐dimensional laminar flow of Jeffrey liquid that describes the characteristics of heat and mass transfer towards a stagnation point over a radial moving disc through the Buongiorno nanofluid model. The study also aims to investigate the impact of mass transpiration velocity, magnetic field, and zero mass flux incorporated in a Jeffrey fluid. The study reduces complicated partial differential equations to a collection of ordinary differential equations using the similarity transformation, which makes it easier to compute dual numerical solutions using the bvp4c solver. A particular value of the shrinking parameter yields dual solutions. The findings of the current research demonstrate that the suction constraint amplifies the friction factor phenomenon in the second solution, while in the first solution, an annulment tendency is noted. Additionally, the first solution exhibits a monotonic behavior whereas the second solution shows a fall in both the friction factor and the rate of heat transfer by increasing the Deborah number. Finally, the results of this analysis with the available data matched the limiting situations very well. [ABSTRACT FROM AUTHOR]

Due to their widespread use in engineering, hybrid nanofluids have been the primary focus of mathematical and physical research. Only the improvement of hybrid nanofluids’ variable heat conductivity and viscosity has been considered so far. Hybrid nanofluid flow across an inclined cylinder has many potential uses, including heat transfer and cooling in electrical devices, energy storage, refrigerants, and the automobile industry. Examining the effects of buoyant force, variable viscosity, variable thermal conductivity, mass suction, convective thermal conditions, and a magnetic field on the stagnation point flow of a Al2O3–Cu/H2O hybrid nanofluid in an inclined cylinder is our objective in this work. In order to find solutions to boundary-condition flow-describing partial differential equations, we turn them into ordinary differential equations using similarity transformations. We achieve this by employing a numerical strategy known as the fourth-order Runge–Kutta technique, which incorporates shooting techniques. A graphical representation of the findings emphasizes the influence of many physical parameters on flow dynamics. In addition, we address the influence of drag force and rate of heat transfer on various elements, such as the Biot parameter, magnetic variable, viscosity variable, and thermal conductivity variable. The mixed convection and magnetic parameters cause the velocity profile to rise while the temperature profile falls. The research’s results elucidate the cause behind the rise in thermal contour of hybrid nanofluids, which is seen when there is an increment in thermal conductivity, radiation parameter, and Biot number. The heat transfer rate exhibits a significant increase of 36.87% in the aiding flow scenario when a 2.0 mass suction is applied in conjunction with a 0.01 hybrid nanofluid, as compared to the conventional fluid. In the scenario of opposing flow, the heat transfer rate exhibits a significant increase of 36.96% when compared to that of ordinary fluid. Heat transfer increases 43.00% when Rd increases from 0.1 to 0.5 for both assisting and opposing flow. [ABSTRACT FROM AUTHOR]

This study investigates the mass and heat transfer properties of Ag-H2O nanofluid MHD Forchheimer flows and Ag-MoS2/H2O hybrid nanofluid over two-dimensional linear stretching surfaces in aligned magnetic fields with absorption of radiation. The fluid experiences rotational motion around the vertical axis at a consistent angular speed. The system of nonlinear ODEs is derived from the set of nonlinear PDEs by use of similarity transformations. The BVP-5C shooting approach in MATLAB is then employed to solve the associated system of ODEs. As the Forchheimer number, porosity parameter, rotation parameter and aligned magnetic field exhibit an ascent, the velocity profile along the x-axis and y-axis experiences a decrement. Simultaneously, an augmentation in the magnetic parameter, thermal radiation and rotation parameter induces a heightened temperature profile. Additionally, greater values of the Forchheimer number, rotation parameter and magnetic parameters correspond to an increase in concentration profile. Furthermore, the results indicated an increased temperature profile in the Ag-MoS2/H2O hybrid nanofluid compared to that in the Ag-H2O nanofluid for magnetic, rotation and radiation parameters. Also, the concentration profile of magnetic and rotation parameters along with the Forchheimer number were noted to be higher in the Ag-MoS2/H2O hybrid nanofluid compared to that in the Ag-H2O nanofluid. [ABSTRACT FROM AUTHOR]

This study addresses the applications of non-uniform heat source/sink and viscous dissipation in the magnetohydrodynamic (MHD) flow of Casson nanoparticles toward a porous stretchable sheet. The free convective flow for the inclusion of thermal buoyancy along with dissipative heat encourages the flow phenomena. The governing equations of the flow model are presented in terms of partial differential equations and then transformed into a system of ordinary differential equations using similarity transformations. These systems of equations are solved numerically by using the Runge–Kutta fourth-order method with a very efficient shooting technique. The effects of various parameters such as the Casson parameter, elastic parameter, porosity parameter, Prandtl number, non-uniform heat source/sink constant, Eckert number, skin fraction and Nusselt number on the flow area are computed and represented graphically. The present results reflect that the velocity of nanoparticles declined effectively with the porosity parameter and nanoparticle volume fraction. The temperature profile is increased with the elastic parameter and heat source parameter while decreasing with the Eckert number and Casson fluid parameter. Moreover, it is observed that when the Hartmann number is maximum, a retardation in wall shear force against nanoparticles volume fraction is marked. [ABSTRACT FROM AUTHOR]

THE STAGNATION POINT FLOW OF AN INCOMPRESSIBLE VISCOUS electrically conducting fluid impacting orthogonally on a heated rotating disk is studied with internal volumetric heat generation/absorption in the presence of a uniform magnetic field. A uniform suction or injection is applied through the surface of the disk. Appropriate similarity transformations are used to reduce the governing differential equations of the problem into a system of nonlinear ordinary differential equations and then solved numerically using the fourth-order Runge-Kutta method. In the second step, the work is oriented towards linear stability analysis by considering infinitesimally small disturbances within the boundary layer. Using normal mode decomposition in the Görtler-Hammerlin framework, the resulting eigenvalue problem is then solved numerically by means of the pseudo-spectral method using Laguerre's polynomials. As a result, the critical conditions for the onset of thermal instability are described and discussed in detail using multiple configurations. It is found that the presence of a magnetic field and suction/injection act to increase the stability of the basic flow. However, the rotation parameter and the internal heat generation/absorption contribute significantly to destabilizing the basic flow. [ABSTRACT FROM AUTHOR]

The current study focuses on the flow actions of two-dimensional hybrid nanofluids when they pass through a stretching sheet with viscous dissipation. The hybrid nanomaterials under consideration are Ag + Al,03 and Cu + TiO2, having H:zO functioning as the base fluid. A similarity transformation is utilized to simplify the governing model by switching the partial differential equations (PDEs) into a non-dimensional ordinary differential equation (ODE) system. The study explores changes in volume fraction (0), velocity power index (m), wall thickness parameter (a), and Eckart number (Ec) through graphical representations of entropy generation, thermal and velocity profiles. Remarkably, the velocity field exhibits a substantial increase when these relevant parameters are promoted. In this investigation, the Homotopy Perturbation method is employed to solve the nonlinear ODEs resulting from the study. This technique offers a direct and efficient approach to tackling the problem. The numerical data for the Nusselt number and skin friction coefficient of hybrid nanofluids are shown in a table. [ABSTRACT FROM AUTHOR]

The theme of this study is to investigate the theoretical and numerical simulation of heat and mass transfer of magneto hydrodynamic power-law nanofluid flow over a stretching sheet with surface heat flux and Soret/Dufour effects. The mass flux and energy flux increase with temperature and concentration differences using the Soret/Dufour impact. The similarity transformations were used to transform a physical problem into a non-linear differential equation, and the non-linear equations were solved by the Keller box technique. The Soret/Dufour and magnetic field are incorporated into a nanofluid model. The similarity transformation was used to reduce thermal energy, mass, and momentum in algebraic systems. The impact of nanofluid factors, such as generalized Brownian motion parameter Nb, Dufour parameter Df, Soret parameter Sr, Le, and Pr, are generalized Lewis and Prandtl numbers; the thermophoresis parameter Nt and magnetic parameter on dimensionless stretching surface functions are shown numerically and graphically. The quantitative relationship between heat transfer and skin friction is shown by using Keller box and MATLAB. The skin friction coefficient Cf, Sherwood number Shx, and Nusselt number Nux values were also computed and displayed on the graph. The increment in slip temperature, fluid velocity, and fluid concentration is enhanced with a high Dufour parameter. The temperature variation and fluid concentration are decreased with applied-magnetic effects because the magnetic field acts like an insulating material in heat transfer systems. The enhancement in the Nusselt number and Sherwood number is increased with Soret and Dufour effects. [ABSTRACT FROM AUTHOR]