Search

The investigation of heat and mass transfer between two porous disks containing porous media is the focus of this paper. In this research, (Ag–Al2O3/water)-based hybrid nanofluid is used. Governing partial differential equations are converted to nonlinear ordinary differential equations by similarity transformations. Numerical solutions to nonlinear systems of equations are achieved using the shooting technique. It is examined how the particle's diameter and nanolayer thickness affect the thermal conductivity of a hybrid nanofluid. Due to the increment of nanolayer thickness, the Nusselt number increases and vice versa for the radius of the particle. Tables and graphs show how the governing parameters influence velocity, temperature, and mass concentration profiles, as well as physical quantities such as skin friction coefficient and Nusselt number. As the values of the porous medium parameters ( P m = 7 –13) and nanolayer thickness (h = 4 –12) elevate, the flow of skin friction coefficient and Nusselt number escalate in both porous disks. Moreover, as the values of the particle radius (r = 9 % to 12%) and Reynolds number (Re = − 1 to 2) amplify, the flow of heat transfer rate is diminished in the lower disk. Porous materials have a high surface area, which increases the contact area between the nanofluids and the porous medium. Porous materials can enhance the permeability of the fluid, reducing the pressure drop in the system. This can be advantageous in applications where high flow rates and low-pressure drops are desired, such as in heat exchangers or cooling systems. Porous materials can provide trapping sites or adhesion points for the nanoparticles, enhancing their dispersion and stability within the hybrid nanofluids. The porosity of the flow medium can therefore influence the purification and filtration efficiency of the hybrid nanofluids, ensuring their cleanliness and functionality. Understanding and controlling the porosity can help optimize the flow characteristics of the nanofluids in various applications. Overall this field will focus on refining hybrid nanofluid compositions, improving modeling techniques, validating experimental findings, optimizing system designs, and exploring new applications. [ABSTRACT FROM AUTHOR]

The use of renewable energy sources is leading the charge to solve the world's energy problems, and non-Newtonian nanofluid dynamics play a significant role in applications such as expanding solar sheets, which are examined in this paper, along with the impacts of activation energy and solar radiation. We solve physical flow issues using partial differential equations and models like Casson, Williamson, and Prandtl. To get numerical solutions, we first apply a transformation to make these equations ordinary differential equations, and then we use the MATLAB-integrated bvp4c methodology. Through the examination of dimensionless velocity, concentration, and temperature functions under varied parameters, our work explores the physical properties of nanofluids. In addition to numerical and tabular studies of the skin friction coefficient, Sherwood number, and local Nusselt number, important components of the flow field are graphically shown and analyzed. Consistent with previous research, this work adds important new information to the continuing conversation in this area. Through the examination of dimensionless velocity, concentration, and temperature functions under varied parameters, our work explores the physical properties of nanofluids. Comparing the Casson nanofluid to the Williamson and Prandtl nanofluids, it is found that the former has a lower velocity. Compared to Casson and Williamson nanofluid, Prandtl nanofluid advanced in heat flux more quickly. The transfer of heat rates are 25.87 % , 33.61 % and 40.52 % at R d = 0.5 , R d = 1.0 , and R d = 1.5 , respectively. The heat transfer rate is increased by 6.91 % as the value of Rd rises from 1.0 to 1.5. This study is further strengthened by a comparative analysis with previous research, which is complemented by an extensive table of comparisons for a full evaluation. [ABSTRACT FROM AUTHOR]

The present analysis is to investigate the potential applications of nanomaterial suspensions in various contexts, particularly in biomedical rheological models. Nanofluids, which are suspensions of nanoparticles in a base fluid, have been identified as an important material for cooling microelectronic devices such as microchips. In this study, we focus on the transport rates of mass, thermal, and motile microorganisms in the permeable stretching surface flow of tangent hyperbolic nanofluid, which contains gyrotactic microorganisms. Our goal is to analyze the behavior of the nanofluid and microorganisms under these conditions, which could have important practical applications. This study also investigates the behavior of aligned magneto nanofluid through buoyancy forces and stratification. The collective impacts of buoyancy forces and Darcy–Forchheimer porous medium result in the phenomenon of bioconvection, which helps to stabilize the nanofluid. To analyze the system, a set of partial differential equations is transmuted to ordinary differential equations via similarity variables. Numerical results are obtained by employing Runge–Kutta along shooting technique via an efficient MATLAB code. The code's implementation involves using the shooting method to achieve accurate numerical solutions. This study utilizes graphical representation to analyze and explain the effect of different parameters on the distribution of velocity, temperature, concentration, and bioconvection. Various factors are investigated to determine their effects. In order to validate the proposed model, the comparison table serves as evidence for the validity and accuracy of the proposed model. [ABSTRACT FROM AUTHOR]

The flow and heat transfer induced by an exponentially shrinking sheet with hybrid nanoparticles are investigated comprehensively in this paper. Nanoparticles are considered due to their unusual characteristics such as extraordinary thermal conductivity, which is significant in advanced nanotechnology, heat exchangers, material sciences, and electronics. The main objective of this research is to enhance heat transportation. The flow model is first transformed and simplified to a system of ordinary differential equations utilizing non-dimensional quantities and similarity functions. Then, the desired system is solved with the help of the Runge–Kutta numerical method and the shooting technique in MATLAB script. The results show that a stronger porosity parameter raises the temperature while diminishing the velocity. Additionally, they emphasize that augmentations in the magnetic parameter, Eckert number, radiation parameter, and the volume fractions of titanium dioxide and silver nanoparticles are all proportional to the temperature profile. [ABSTRACT FROM AUTHOR]

This study considered the Cattaneo–Christov heat flux for examining the nanofluid flow with heat transfer towards a stretching sheet involving thermal and solutal buoyancy, activation energy, thermal radiation, and microorganism concentration. It is suggested that the model of Buongiorno nanofluid can be used to sync the influences of thermophoresis and Brownian motion. The 2D boundary layer with non-Fourier PDEs is converted into 1D nonlinear ODEs. Using the RK-4 method, the acquired equations were analyzed numerically. In this regard, the relevant engineering quantities are extensively computed with a higher degree of precision and then tabulated. The motile concentration, temperature, nanoparticles concentration, and velocity decline for numerous values of involved parameters such as slips of microorganism concentration, thermal, solutal, and hydrodynamic, respectively. The temperature field decreased when the parameter of thermal relaxation was imposed, while the reverse behavior was shown for thermophoresis, radiation parameter, and Brownian motion. The current results manifest a reasonable assessment of their existing counterparts. [ABSTRACT FROM AUTHOR]

Due to high-ultra thermic significances, the nanosize materials are used in various chemical and mechanical engineering, modern technology and thermic engineering eras. For industrial growth of a country, one of the biggest challenges for engineers and scientists is improvement in thermal production and resources. In this study we analyzed the momentum and thermic aspects of MHD Ellis ternary nano material embedded with dust particles via stretchable Riga plate including volume concentration of dust material. The flow generating PDE's for two phase models are minimized into dimensionless nonlinear ODE's by using the right modification. To acquire the graphical results the BVP4c method was adopted in MATLAB software. Fundamental aspects affecting velocity and temperature have investigated through graphs. Additionally Nusselt number and skin friction have also been evaluated. Compared it with previous literature to check the validity of results. Finding reveals that as compared to dusty phase the performance of trihybrid nano phase thermal transport is improved. Moreover, the temperature profile increases for rotational and volume fraction dust particles parameter. Dusty fluids are used in numerous manufacturing and engineering sectors, like petroleum transport, car smoke emissions, caustic granules in mining and power plant pipes. [ABSTRACT FROM AUTHOR]

This communication briefings the roles of Lorentz force and nanoparticles aggregation on the characteristics of water subject to Titanium dioxide rotating nanofluid flow toward a stretched surface. Due to upgrade the thermal transportation, the nanoparticles are incorporated, which are play significance role in modern technology, electronics, and heat exchangers. The primary objective of this communication is to observe the significance of nanoparticles aggregation to enhance the host fluid thermal conductivity. In order to model our work and investigate how aggregation characteristics affect the system's thermal conductivity, aggregation kinetics at the molecular level has been mathematically introduced. A dimensionless system of partial-differential equations is produced when the similarity transform is applied to a elaborated mathematical formulation. Thereafter, the numerical solution is obtained through a well-known computational finite element scheme via MATLAB environment. When the formulation of nanoparticle aggregation is taken into consideration, it is evident that although the magnitude of axial and transverse velocities is lower, the temperature distribution is enhanced by aggregation. [ABSTRACT FROM AUTHOR]

This communication studies the importance of varying the radius D p of Copper nanoparticles for microgravity-modulated mixed convection in micropolar nanofluid flux under an inclined surface subject magnetic field and heat source. In the current era, extremely pervasive modernized technical implementations have drawn attention to free convection governed by g-jitter force connected with microgravity. Therefore, fixed inter-spacing of nanoparticles and effects of g-jitter on the inclined surface are taken into consideration. A mathematical formulation based on conservation principles was non-dimensionalized by enforcement of similarity transformation, yielding a related set of ODEs. The convective non-linearity and coupling, an FE discretization, was implemented and executed on the Matlab platform. The numerical process' credibility was ensured for its acceptable adoption with the defined outcomes. Then, the computational endeavor was continued to elucidate the impacts of various inputs of D p , the amplitude of modulation ϵ , material parameter β , mixed convection parameter λ , inclination angle γ , and magnetic parameter M. The enlarging size of nanoparticles accelerated the nanofluid flow due to the depreciation of viscosity and receded the fluid temperature by reducing the surface area for heat transportation. The modulated Nusselt number, couple stress, and skin friction coefficient are significantly affected by the variation of D p , M, β , λ , and ϵ. These results would benefit experts dealing with upper space transportation and materials' performance, such as the effectualness of chemical catalytic reactors and crystals. [ABSTRACT FROM AUTHOR]

The time-independent performance of a micropolar nanofluid under the influence of magneto hydrodynamics and the existence of a porous medium on a stretching sheet has been investigated. Nano-sized particles were incorporated in the base fluid because of their properties such as their extraordinary heat-enhancing ability, which plays a very important role in modern nanotechnology, cooling electronic devices, various types of heat exchangers, etc. The effects of Brownian motion and thermophoresis are accounted for in this comprehensive study. Using similarity conversion, the leading equations based on conservation principles are non-dimensionalized with various parameters yielding a set of ODEs. The numerical approach boundary value problem fourth-order method (bvp4c) was implemented as listed in the MATLAB computational tool. The purpose of this examination was to study and analyze the influence of different parameters on velocity, micro-rotation, concentration, and temperature profiles. The primary and secondary velocities reduced against the higher inputs of boundary concentration, rotation, porosity, and magnetic parameters, however, the base fluid temperature distribution grows with the increasing values of these parameters. The micro-rotation distribution increased against the rising strength of the Lorentz force and a decline is reported against the growing values of the micropolar material and rotational parameters. [ABSTRACT FROM AUTHOR]

Boosting the heat transfer rate in a base fluid is of interest to researchers; many traditional methods have been utilized to do this. One significant way is using nanofluid to boost thermal performance. This investigation sought to improve the transmission of a thermal above-stretching inclined surface over an upper surface to be influenced by the magnetic field B 0 along the microgravity g * (τ) = g 0 (1 + a cos (π ω t)) . The G-jitter impacts were analyzed for three colloidal fluids flow; the mono micropolar nanofluid (alumina/water), micropolar hybrid nanofluid (alumina–titanium)/water, and micropolar trihybrid nanofluid (alumina–titanium–silicon)/water. Using suitable transformation, the governing formulation was changed into an ordinary differential equation. In a Matlab script, a computational code was composed to evaluate the impacts of the involved parameters on fluid dynamics. The fluid flow motion and thermal performance for the trihybrid case were greater than the mono and hybrid nanofluid cases subject to a microgravity environment. The fluid velocity and microrotation function decreased in opposition to the magnetic parameter's increasing strength, but with an increasing trend in the fluid temperature function. Fluctuations in the velocity gradient and heat flow gradient increased as the modulation amplitude increased. [ABSTRACT FROM AUTHOR]

The movement of biological fluids in the human body is a premium field of interest to overcome growing biomedical challenges. Blood behavior shows different behavior in capillaries, veins, and arteries during circulation. In this paper, a new mathematical relation for the nano-layer of biological fluids flows with the effect of TiO2 and Ag hybrid nanoparticles was developed. Further, we explain the engineering phenomena of biological fluids and the role of hybrid nanoparticles in the blood vessel system. The improvement of drug delivery systems by using low seepage Reynolds number was associated with expansion/contraction and was discussed in detail through the rectangular domain. Using similarity transformation, the governing equations were converted into non-linear ordinary differential equations, and the mathematical problem was solved by employing the numerical shooting method. Plots of momentum, temperature, skin friction coefficient, as well as the Nusselt number on different non-dimensionless parameters are displayed via lower/upper porous walls of the channel. It was analyzed that the walls of the channel showed different results on magnetized physical parameters. Values of thermophoresis and the Brownian motion flow of the heat transfer rate gradually increased on the upper wall and decreased on the lower wall of the channel. The important thing is that the hybrid nanoparticles, rather than nano, were more useful for improving thermal conductivity, heat transfer rate, and the nano-layer. [ABSTRACT FROM AUTHOR]

The objective of this study is to explore the heat transfer properties and flow features of an MHD hybrid nanofluid due to the dispersion of polymer/CNT matrix nanocomposite material through orthogonal permeable disks with the impact of morphological nanolayer. Matrix nanocomposites (MNC) are high-performance materials with unique properties and design opportunities. These MNC materials are beneficial in a variety of applications, spanning from packaging to biomedical applications, due to their exceptional thermophysical properties. The present innovative study is the dispersion of polymeric/ceramic matrix nanocomposite material on magnetized hybrid nanofluids flow through the orthogonal porous coaxial disks is deliberated. Further, we also examined the numerically prominence of the permeability (A*) function consisting of the Permeable Reynold number associated with the expansion/contraction ratio. The morphological significant effects of these nanomaterials on flow and heat transfer characteristics are explored. The mathematical structure, as well as empirical relations for nanocomposite materials, are formulated as partial differential equations, which are then translated into ordinary differential expressions using appropriate variables. The Runge-Kutta and shooting methods are utilized to find the accurate numerical solution. Variations in skin friction coefficient and Nusselt number at the lower and upper walls of disks, as well as heat transfer rate measurements, are computed using important engineering physical factors. A comparison table and graph of effective nanolayer thermal conductivity (ENTC) and non-effective nanolayer thermal conductivity are presented. It is observed that the increment in nanolayer thickness (0.4-1.6), enhanced the ENTC and thermal phenomena. By the enhancement in hybrid nanoparticles volume fraction (2% to 6%), significant enhancement in Nusselt number is noticed. This novel work may be beneficial for nanotechnology and relevant nanocomponents. [ABSTRACT FROM AUTHOR]

Three-dimensional flow via swirling porous disks and an annular sector is carried out using fully developed hybrid nanofluids. Here, a single-phase simulation based on thermophysical characteristics using various nanoparticle sizes and shapes is taken into account. A regression function connected with the permeable Reynolds number for injection and suction was created. We used the well-known and accurate "shooting approach" to apply to the governing, nonlinear, ordinary differential equation systems to obtain numerical results. Additionally, parametric research was employed to control the impact of embedded flow factors on concentration, velocity, and temperature. While the physical features of the bottom and upper disks, such as the skin friction coefficient and Nusselt number, are provided in a table, their characterization of the flow of several regulatory flow parameters, such as fluid velocity and temperature, is depicted graphically. The experimental range of nanoparticle fractions of 1% to 4% is considered with the Nusselt number having notable effects at φ = 4%. Both walls demonstrate the effects of an increase in injection factor, shear stress, and tensile stress. As the Eckert number rises at the lower wall, the rate of heat transfer dramatically increases, and the opposite is true for the upper wall. The rate of heat transmission is significantly impacted by the addition of different base fluids containing various kinds of nanoparticles. The aforementioned research created a solid foundation for the development of electronic computers with an emphasis on nanotechnology and biomedical devices. [ABSTRACT FROM AUTHOR]

This study briefings the roles of Coriolis, and Lorentz forces on the dynamics of rotating nanofluids flow toward a continuously stretching sheet. The nanoparticles are incorporated because of their unusual qualities like upgrade the thermal transportation, which are very important in heat exchangers, modern nanotechnology, electronics, and material sciences. The primary goal of this study is to improve heat transportation. Appropriate similarity transformations are applied for the principal PDEs to transform into nonlinear dimensionless PDEs. A widely recognized Numerical scheme known as the Finite Element Method is employed to solve the resultant convective boundary layer balances. Higher input in the solvent fraction parameter has a rising effect on the primary velocity and secondary velocity magnitude, and decreasing impact on the distributions of temperature. It is seen that growing contributions of the Coriolis, and Lorentz forces cause to moderate the primary and secondary velocities, but the temperature and concentration functions show opposite trend. The concentration, temperature, and velocities distributions for suction case is prominently than that of injection case, but inverse trend is observed for local Nusselt and Sherwood numbers. These examinations are relevant to the field of plastic films, crystal growing, paper production, heat exchanger, and bio-medicine. [ABSTRACT FROM AUTHOR]

In this study, the relevance of Lorentz and Coriolis forces on the kinetics of gyratory Maxwell nanofluids flowing against a continually stretched surface is discussed. Gyrotactic microbes are incorporated to prevent the bioconvection of small particles and to improve consistency. The nanoparticles are considered due to their valuable properties and ability to enhance thermal dissipation, which is important in heating systems, advanced technology, microelectronics, and other areas. The main objective of the analysis is to enhance the rate of heat transfer. An adequate similarity transformation is used to convert the primary partial differential equations into non-linear dimensionless ordinary differential equations. The resulting system of equations is solved using the finite element method (FEM). The increasing effects of the Lorentz and Coriolis forces induce the velocities to moderate, whereas the concentration and temperature profiles exhibit the contrary tendency. It is observed that the size and thickness of the fluid layers in the axial position increase as the time factor increases, while the viscidity of the momentum fluid layers in the transverse path decreases as the time factor decreases. The intensity, temperature, and velocity variances for the suction scenario are more prominent than those for the injection scenario, but there is an opposite pattern for the physical quantities. The research findings are of value in areas such as elastomers, mineral productivity, paper-making, biosensors, and biofuels. [ABSTRACT FROM AUTHOR]

We examine thermal management in the heat exchange of compact density nanoentities in crude base liquids. It demands the study of the heat and flow problem with non-uniform physical properties. This study was conceived to analyze magnetohydrodynamic Eyring–Powell nanofluid transformations due to slender sheets with varying thicknesses. Temperature-dependent thermal conductivity and viscosity prevail. Bioconvection due to motivated and dynamic microorganisms for Eyring–Powell fluid flow is a novel aspect herein. The governing PDEs are transmuted into a nonlinear differential structure of coupled ODEs using a series of viable similarity transformations. An efficient code for the Runge–Kutta method is developed in MATLAB script to attain numeric solutions. These findings are also compared to previous research to ensure that current findings are accurate. Computational activities were carried out with a variation in pertinent parameters to perceive physical insights on the quantities of interest. Representative outcomes for velocity, temperature, nanoparticles concentration, and bioconvection distributions as well as the local thermal transport for different inputs of parameters are portrayed in both graphical and tabular forms. The results show that the fluid's velocity increases with mixed convection parameters due to growing buoyancy effects and the fluid's temperature also increased with higher Brownian motion N b and thermophoretic N t . The numerical findings might be used to create efficient heat exchangers for increasingly challenging thermo-technical activities in manufacturing, construction, and transportation. [ABSTRACT FROM AUTHOR]

In this article, numerical simulations of the rotational flow of water-based magnetohydrodynamic (MHD) nanofluid containing single-wall carbon nanotube (SWCNT) and hybrid nanofluid containing single- and multiple-wall carbon nanotube (SWCNT-MWCNT) over a stretching sheet are performed. The primary goal is to improve thermal transport efficiency due to CNTs extraordinary thermal conductivity. The 3D governing equations for microorganism concentration, energy, momentum, concentration, and mass conservation are transformed into 1D ordinary differentiation via similarity transformations. In a MATLAB environment, the resultant system of equations (ODEs) are then solved using Runge–Kutta fourth order with the shooting process. Tables and graphs were used to show the results of physical parameters. According to our findings, enhancing the rotational parameter λ and the magnetic field M reduce the base fluid velocity along the x-axis, and on the other hand, the opposite tendency is shown along the y-axis. Furthermore, the velocities, temperature, and microorganism concentration profiles of hybrid nanofluid ( S W C N T − M W C N T /H2O) are found to be higher than those of mono nanofluid ( H 2 O + S W C N T ), while the concentration profile is found to be lower. [ABSTRACT FROM AUTHOR]

The mathematical modeling of the activation energy and binary chemical reaction system with six distinct types of nanoparticles, along with the magnetohydrodynamic effect, is studied in this paper. Different types of hybrid nanofluids flowing over porous surfaces with heat and mass transfer aspects are examined here. The empirical relations for nanoparticle materials associated with thermophysical properties are expressed as partial differential equations, which are then interpreted into ordinary differential expressions using appropriate variables. The initial shooting method converts the boundary condition into the initial condition with an appropriate guess and finally finds out an accurate numerical solution by using the Runge–Kutta method with numerical stability. Variations in nanoparticle volume fraction at the lower and upper walls of porous surfaces, as well as the heat transfer rate measurements, are computed using the controlling physical factors. The effects of the flow-related variables on the axial velocity, radial velocity, temperature, and concentration profile dispersion are also investigated. The Permeable Reynolds number is directly proportional to the regression parameter. The injection/suction phenomenon associated with the expanding/contracting cases, respectively, have been described with engineering parameters. The hybrid nanoparticle volume fraction (1–5%) has a significant effect on the thermal system and radial velocity. [ABSTRACT FROM AUTHOR]

This work aims to offer a mathematical model for two-phase flow that investigates the interaction of Casson nanofluid and dust particles across a stretching surface. MHD Darcy–Forchheimer porous medium and Fourier's law through Cattaneo–Christove thermal flux are also considered. The governing equations for the two phases model are partial differential equations later transmuted into ordinary ones via similarity transforms. The Runge–Kutta method with the shooting tool is utilized numerically to solve the boundary layer equations computed in MATLAB to obtain numerical results for various pertinent parameters. The numerical outcomes of momentum, temperature, and concentration distribution are visible for both phases. The results of the skin friction, heat transfer coefficients, and the Sherwood number are also visible in the graphs. Furthermore, by comparing the current findings to the existing literature, the validity of the results is confirmed and found to be in good agreement. The fluid velocity is reduced against increasing strength of Casson fluid parameter, enhanced the fluid phase and dust phase fluid temperature. The temperature declines against the growing values of the relaxation time parameter in both phases. Dusty fluids are used in various engineering and manufacturing sectors, including petroleum transportation, car smoke emissions, power plant pipes, and caustic granules in mining. [ABSTRACT FROM AUTHOR]

In this study, the significance of the Coriolis force on the dynamics of Carreau—Yasuda flow toward a continuously stretched surface subject to the Darcy–Forchheimer law is investigated. The nanoparticles are incorporated due to their unusual characteristics (e.g., extraordinary thermal conductivity), which are significant in heat exchangers and advanced nanotechnology. To avoid possible sedimentation of tiny particles, the gyrotactic microorganisms must be incorporated. The goal of this research was to find out the dynamics of three-dimensional rotational flow for nanofluids under the influence of Darcy–Forchheimer with the thermophoresis effect and motile microorganisms. The equations governing mass, momentum, and energy equations are formalized using partial derivatives, which may subsequently be transformed into dimensionless differential shapes using the personifications of apposite similarity transformations. The MATLAB application bvp4c was used in conjunction with a shooting technique to solve a nonlinear mathematical model based on ordinary differential equations. It was observed that the base fluid velocities decreased against higher input of rotation and porosity parameters; moreover, the Brownian motion and thermophoresis increased the temperature profile. [ABSTRACT FROM AUTHOR]

This article addresses the dynamic of three-dimensional rotating flow of Maxwell nanofluid across a linearly stretched sheet subject to a water-based fluid containing copper nanoparticles. Nanoparticles are used due to their fascinating features, such as exceptional thermal conductivity, which is crucial in modern nanotechnology and electronics. The primary goal of this comprehensive study is to examine the nanoparticles size and shape factors effect on the base fluid temperature. The mathematical model contains the governing equations in three dimensional partial differential equations form, and these equations transformed into dimensionless ordinary dimensional equations via suitable similarity transformation. The bvp4c technique is harnessed and coded in Matlab script to obtain a numerical solution of the coupled non-linear ordinary differential problem. It is observed that the greater input of rotating, Deborah number, and magnetic parameters caused a decline in the fluid primary and secondary velocities, but the nanoparticles concentration enhanced the fluid temperature. Further, a substantial increment in the nanofluid temperature is achieved for the higher nanoparticle's diameter and shape factors. [ABSTRACT FROM AUTHOR]

This numerical investigation effectively establishes a unique computing exploration for steady magnetohydrodynamic convective streams of tangent hyperbolic nanofluid traveling across a nonlinearly elongating elastic surface with a variable thickness. In addition, the importance of an externally imposed magnetic field of tangent hyperbolic nanofluid is comprehensively analyzed by considering the substantial impact of thermal conductivity and thermal radiation consequences. The governing PDEs (partial differential equations) are transmuted into a nonlinear differential structure of coupled ODEs (ordinary differential equations) using a series of variable similarity transformations. Furthermore, these generated ODEs (ordinary differential equations) are numerically set using a novel revolutionary Runge-Kutta algorithm with a shooting approach constructed in a MATLAB script. In this regard, extensive comparison studies are carried out to validate the acquired numerical results. The interactions between the associated profiles and the relevant parameters are rationally explored and shown using graphs and tabular forms. The velocity distribution declined with improving Weissengberg number W e and power-law index m, while the reverse performance can be observed for temperature. As enhancement in Brownian motion, Thermophoretic and radiation parameters significantly rise in temperature distribution. The use of many different technological and industrial systems, including nano-bioconvective systems, nano-droplet evaporation, nano-ink jet printing, and microbial fuel cells, would benefit this research study. [ABSTRACT FROM AUTHOR]

This study aims to determine the heat transfer properties of a magnetohydrodynamic Prandtl hybrid nanofluid over a stretched surface in the presence of bioconvection and chemical reaction effects. This article investigates the bio-convection, inclined magnetohydrodynamic, thermal linear radiations, and chemical reaction of hybrid nanofluid across stretching sheets. Also, the results are compared with the nanofluid flow. Moreover, the non-Newtonian fluid named Prandtl fluid is considered. Microfluidics, industry, transportation, the military, and medicine are just a few of the real-world applications of hybrid nanofluids. Due to the nonlinear and convoluted nature of the governing equations for the problem, similarity transformations are used to develop a simplified mathematical model with all differential equations being ordinary and asymmetric. The reduced mathematical model is computationally analyzed using the MATLAB software package's boundary value problem solver, Runge-Kutta-fourth-fifth Fehlberg's order method. When compared to previously published studies, it is observed that the acquired results exhibited a high degree of symmetry and accuracy. The velocity profiles of basic nanofluid and hybrid nanofluid are increased by increasing the Prandtl parameters' values, which is consistent with prior observations. Additionally, the concentration and temperature of simple and hybrid nanofluids increase with the magnetic parameter values. [ABSTRACT FROM AUTHOR]

Free convective flow in a cubical cavity loaded with copper-water nanofluid was examined numerically by employing a non-homogeneous dynamic model, which is physically more realistic in representing nanofluids than homogenous ones. The cavity was introduced to a horizontal magnetic field from the left sidewall. Both the cavity's vertical left and right sidewalls are preserved at an isothermal cold temperature (Tc). The cavity includes inside it four isothermal heating blocks in the middle of the top and bottom walls. The other cavity walls are assumed adiabatic. Simulations were performed for solid volume fraction ranging from (0 ≤ ϕ ≤ 0.06), Rayleigh number varied as (103 ≤ Ra ≤ 105), the Hartmann number varied as (0 ≤ Ha ≤ 60), and the diameter of nanoparticle varied as (10 nm ≤ dp ≤ 130 nm). It was found that at (dp = 10 nm), the average Nusselt number declines when Ha increases, whereas it increases as (Ra) and (ϕ) increase. Furthermore, the increasing impact of the magnetic field on the average Nusselt number is absent for (Ra = 103), and this can be seen for all values of (ϕ). However, when (dp) is considered variable, the average Nusselt number was directly proportional to (Ra) and (ϕ) and inversely proportional to (dp). [ABSTRACT FROM AUTHOR]

The two-dimensional boundary layer flow of a Prandtl nanofluid was explored in the presence of an aligned magnetic field over an inclined stretching/shrinking sheet in a non-Darcy permeable medium. To transform the PDEs of the leading equations into ODEs, a coupled boundary value problem was formed and suitable similarity functions were used. To obtain numerical answers, an efficient code for the Runge–Kutta technique with a shooting tool was constructed with a MATLAB script. This procedure is widely used for the solution of such problems as it is efficient and cost-effective with a fifth-order accuracy. The significance of immersed parameters on the velocity, temperature, concentration, and bioconvection is shown through figures. Furthermore, the physical parameters of the skin friction coefficient and the Nusselt numbers are demonstrated in tables. The declining behavior of the flow velocity against the porosity parameter K p and the local inertia co-efficient F r is shown, and the both parameters of the Darcy resistance and Darcy–Forchheimer resistance are responsible for slowing the fluid speed. The increasing values of the Schmidt number S c decrease the concentration of the nano entities. [ABSTRACT FROM AUTHOR]

The numerical analysis of MHD-free convective heat transfer and its interaction with the radiation over a heated flame inside a porous semicircular cavity loaded with SWCNTs–water nanofluid was explored for the very first time in the present work. The two circular arcs of the upper wall of the enclosure were preserved at a constant cold temperature, whereas the middle region of it was considered adiabatic. The midland region of the lower wall was heated partially, while other regions were also assumed adiabatic. An internal hot flame was included inside the cavity, while the cavity was exposed to a magnetic field. The results were illustrated for Hartmann number (0 ≤ Ha ≤ 100), Rayleigh number (104 ≤ Ra ≤ 106), heated region length (0.1 ≤ L ≤ 0.3), solid volumetric fraction (0 ≤ φ ≤ 0.04), Darcy number (10−3 ≤ Da ≤ 10−5) and radiation parameter (0 ≤ Rd ≤ 1). It was found that decreasing L is the best option for enhancing natural convection. Moreover, it was noted that (Nuout) is directly proportion to (Ra), (ϕ), (Rd) and (Da) increase. In contrast, it was in reverse proportion to (Ha). Furthermore, the results showed that augmentation of about (4%) and a decrement of (56.55%) are obtained on the average (Nu) on the heated length by increasing the radiation and the Hartmann number, respectively. Moreover, raising the radiation number from (0 to 1) causes an augmentation of about (73%) in the average (Nu) of the heated flame. Results also indicated that increasing the Hartmann number will cause a decrement of about (82.4%) of the maximum velocity profile in the vertical direction. [ABSTRACT FROM AUTHOR]

• The microorganisms and nanoparticles concentration increased along with the melting parameter. • The thermal efficiency increases directly as thermophoresis and thermal relaxation parameters increased. • The enhancement in the magnetic field and β reduces the nanoparticle's concentration. • Sherwood numbers continue to rise against Brown motion parameter and Lewis number. An investigation for fluctuating temperature with Cattaneo–Christov features and self-motive bioconvective microbes immersed in the water based nanofluid has been observing with excision/accretion of the leading edge. A set of partial differential equations is transferring by implementing the similarity measures to an ordinary differential pattern. A finite element technique is employed to establish the numerical results of the set of non-linear system of equations via Matlab programming. The numerical solution's reliability and validity are determined by ascertaining convergence specifications and comparing them to established novel solutions. The formulation of boundary layer configurations for microbes propagation, fluid temperature, the volume fraction of nano-inclusions, and the fluid velocity with varying persuasive parameters have discussed. The main findings of the prevailing assessment are that an increasing trend in the ablation/slash accretion in leading-edge declines in the non-dimensional melting factor of fluid velocity and temperature, while a decreasing trend has seen with the enhancing impact of ablation/slash accretion at the leading edge that represents the flow velocity deceleration. Furthermore, a significant result is that an increase in the non-dimensional melting factor enhances the density of the liquid. [ABSTRACT FROM AUTHOR]

A report is prepared for the free convection of micropolar nanofluid past a continuously moving plate. Free convection of polar fluid is obtained due to the interaction of thermal buoyancy acted against the gravitational force. In addition to that, the novelty of the current investigation is to carry over the coupling impact of the governing equations arises because of the inclusion of dissipative heat energy, and the variation of heat source/sink in the presence of suction/blowing. The governing equations are distorted into their ordinary form by the suitable choice of similarity transformation. Furthermore, the homotopy perturbation method (HPM) is employed for the solution of the set of transformed equations. The behavior of the contributing parameters is presented via graphs and the comparison between the analytical HPM and the conventional numerical technique using the in‐built code bvp5c is presented in tabular form. The numerical simulation shows its good concurrency between the methodologies employed. In few major outcomes, it is seen that the shear rate enriches with an increase in nanoparticle volume fraction. Furthermore, the rate of heat transfer decelerates significantly for the enhanced value of thermal radiation whereas the coupling parameter is favorable for the enhancement. [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 examines the transport phenomenon in which host fluid completely mixed with three different nanoparticles types (ternary hybrid nanofluid) has attract scientist's attention for considering of its significance. The primary reason for the rising interest in tri-hybrid nanofluid is its unique ability to improve thermal performance, which is really useful in various heat exchangers. In the present analysis, the main objective of this article is to examining the laminar, time-dependent, incompressible and two dimensional (2D) trihybrid magnetized squeezing flow of a Boger-micropolar nanofluid between non-porous and porous disk to observe the thermal performance of fluid. This model describes the way to attain a more appropriate heat conductor as compared to bi-hybrid, mono nanofluid. The ternary nanofluid is formulated by adding three types of nano size particles with distinct chemical and physical bonds into water as a base liquid. This mixture helps in purification of environment, decomposing destructive substance and other devices that required cooling. At z = − H (1 − a t) 1 / 2 the lower disk is fixed and the liquid is squeezing due to movement of top disk with axial direction. At the lower surface a homogeneous suction/injection is imposed. Energy and velocity slip impacts are also considered at the fixed bottom disk. Appropriate similarity functions are imposed to transform the governs equations into non-linear ordinary differential equations (ODE's) and then numerically solved by bvp4c technique in MATLAB environment. The outcomes are then displayed in graphically to investigate the microrotation, velocity and temperature profiles. The temperature profile decreased against tri-hybrid case in the lower disk case and then are enhanced near to the top disk in tri-hybrid case, so finally, we conclude that ternary nano size particles have an excellent thermal conductivity as compared to single and hybrid nanoparticles. The present results are found to be good agreement with existence literature for limited cases. • Significance of tri-hybrid nanoparticles in thermal management is modeled. • Tiwari and Das model for nanoparticles is taken into account for modeling. • Ternary hybrid nanofluid have an excellent thermal conductivity. • Higher inputs of magnetic field cause to twisting behavior between disk. [ABSTRACT FROM AUTHOR]

In this article, ethylene glycol (EG) + waterbased Maxwell nanofluid with radiation and Soret effects within two parallel plates has been investigated. The problem is formulated in the form of partial differential equations. The dimensionless governing equations for concentration, energy, and momentum are generalized by the fractional molecular diffusion, thermal flux, and shear stress defined by the Caputo–Fabrizio time fractional derivatives. The solutions of the problems are obtained via Laplace inversion numerical algorithm, namely, Stehfest's. Nanoparticles of silver (Ag) are suspended in a mixture of EG + water to have a nanofluid. It is observed that the thermal conductivity of fluid is enhanced by increasing the values of time and volume fraction. The temperature and velocity of water-silver nanofluid are higher than those of ethylene glycol (EG) + water (H2O)-silver (Ag) nanofluid. The results are discussed at 2% of volume fraction. The results justified the thermo-physical characteristics of base fluids and nanoparticles shown in the tables. The effects of major physical parameters are illustrated graphically and discussed in detail. [ABSTRACT FROM AUTHOR]

The original article can be found online at https://doi.org/10.1038/s41598-023-41141-1.Correction to: Scientific Reportshttps://doi.org/10.1038/s41598-023-41141-1, published online 31 August 2023The original version of this Article contained an error in the spelling of the author Mohammed Sallah which was incorrectly given as Muhammed Sallah.The original Article has been corrected.By Humaira Sharif; Bagh Ali; Imran Siddique; Iqra Saman; Mohammed M. M. Jaradat and Mohammad SallahReported by Author; Author; Author; Author; Author; Author [Extracted from the article]

• G-jitter micropolar hybrid nanofluid flow persuaded by heat source is modeled. • The non-linear systems of ordinary differential equations is solved by finite element technique. • The fluid temperature rises up with increasing strength of magnetic field. • The reduced skin friction becomes stronger for higher inputs of amplitude parameter. An exploration is sought for improved thermal transportation across an extending inclined sheet in the upper space to be influenced by periodic micro gravity g * (τ) = g 0 (1 + a cos (π ω t)) and magnetic field B 0. The mixed convection induced by g-jitter effects is studied for the flow of two colloidal liquids; the alone micropolar nano fluid (copper/ water) and micropolar hybrid nano fluid (alumenia-copper/ water). The leading formulation in its transformed form as ordinary differential format is manipulated via finite-element discretization. A computational code is coded in Matlab script to assess the impacts of involved parameters on dynamic of fluid. The differentiated enhanced performance of hybrid naofluids is observed in this upper space g-jitter influenced flow. The fluid velocity is slowed against growing strength of Hartmann number, but it becomes faster against micropolar material quantity. Both velocity and temperature distribution for hybrid nanofluid flow attains higher values in comparison with those of alone mono-nanofluid. The fluctuation of skin-friction factor and heat flux gradient improves with larger inputs of amplitude of modulation. [ABSTRACT FROM AUTHOR]

Thermal management is a crucial task in the present era of miniatures and other gadgets of compact heat density. This communication presents the momentum and thermal transportation of nanofluid flow over a sheet that stretches exponentially. The fluid moves through a porous matrix in the presence of a magnetic field that is perpendicular to the flow direction. To achieve the main objective of efficient thermal transportation with increased thermal conductivity, the possible settling of nano entities is avoided with the bioconvection of microorganisms. Furthermore, thermal radiation, heat source dissipation, and activation energy are also considered. The formulation in the form of a partial differential equation is transmuted into an ordinary differential form with the implementation of appropriate similarity variables. Numerical treatment involving Runge–Kutta along with the shooting technique method was chosen to resolve the boundary values problem. To elucidate the physical insights of the problem, computational code was run for suitable ranges of the involved parameters. The fluid temperature directly rose with the buoyancy ratio parameter, Rayleigh number, Brownian motion parameter, and thermophoresis parameter. Thus, thermal transportation enhances with the inclusion of nano entities and the bioconvection of microorganisms. The findings are useful for heat exchangers working in various technological processors. The validation of the obtained results is also assured through comparison with the existing result. The satisfactory concurrence was also observed while comparing the present symmetrical results with the existing literature. [ABSTRACT FROM AUTHOR]

Bioconvection phenomena for MHD Williamson nanofluid flow over an extending sheet of irregular thickness are investigated theoretically, and non-uniform viscosity and thermal conductivity depending on temperature are taken into account. The magnetic field of uniform strength creates a magnetohydrodynamics effect. The basic formulation of the model developed in partial differential equations which are later transmuted into ordinary differential equations by employing similarity variables. To elucidate the influences of controlling parameters on dependent quantities of physical significance, a computational procedure based on the Runge–Kutta method along shooting technique is coded in MATLAB platform. This is a widely used procedure for the solution of such problems because it is efficient with fifth-order accuracy and cost-effectiveness. The enumeration of the results reveals that Williamson fluid parameter λ , variable viscosity parameter Λ μ and wall thickness parameter ς impart reciprocally decreasing effect on fluid velocity whereas these parameters directly enhance the fluid temperature. The fluid temperature is also improved with Brownian motion parameter N b and thermophoresis parameter N t . The boosted value of Brownian motion N b and Lewis number L e reduce the concentration of nanoparticles. The higher inputs of Peclet number P e and bioconvection Lewis number L b decline the bioconvection distribution. The velocity of non-Newtonian (Williamson nanofluid) is less than the viscous nanofluid but temperature behaves oppositely. [ABSTRACT FROM AUTHOR]

In this paper, a mathematical model is established to examine the impacts of Stefan blowing on the unsteady magnetohydrodynamic (MHD) flow of an electrically conducting nanofluid over a stretching sheet in the existence of thermal radiation, Arrhenius activation energy and chemical reaction. It is proposed to use the Buongiorno nanofluid model to synchronize the effects of magnetic and electric fields on the velocity and temperature fields to enhance the thermal conductivity. We utilized suitable transformation to simplify the governing partial differential equation (PDEs) into a set of nonlinear ordinary differential equations (ODEs). The obtained equations were solved numerically with the help of the Runge–Kutta 4th order using the shooting technique in a MATLAB environment. The impact of the developing flow parameters on the flow characteristics is analyzed appropriately through graphs and tables. The velocity, temperature, and nanoparticle concentration profiles decrease for various values of involved parameters, such as hydrodynamic slip, thermal slip and solutal slip. The nanoparticle concentration profile declines in the manifestation of the chemical reaction rate, whereas a reverse demeanor is noted for the activation energy. The validation was conducted using earlier works published in the literature, and the results were found to be incredibly consistent. [ABSTRACT FROM AUTHOR]

An analysis for magnetic dipole with stagnation point flow of micropolar nanofluids is modeled for numerical computation subject to thermophoresis, multi buoyancy, injection/suction, and thermal radiation. The partial derivative is involved in physical consideration, which is transformed to format of ordinary differential form with the aid of similarity functions. The variational finite element procedure is harnessed and coded in Matlab script to obtain the numerical solution of the coupled non-linear ordinary differential problem. The fluid temperature, velocity, tiny particles concentration, and vector of micromotion are studied for two case of buoyancy (assisting 0 < λ , and opposing 0 > λ ) through finite-element scheme. The velocity shows decline against the rising of ferromagnetic interaction parameter (β) (assisting 0 < λ and opposing 0 > λ ), while the inverse behaviour is noted in micro rotation profile. Growing the thermo-phoresis and microrotation parameters receded the rate of heat transfer remarkable, and micromotion and fluid velocity enhance directly against buoyancy ratio. Additionally, the rate of couple stress increased against rising of thermal buoyancy (λ) and boundary concentration (m) in assisting case, but opposing case shows inverse behavior. The finite element scheme convergency was tested by changing the mesh size, and also test the validity with available literature. [ABSTRACT FROM AUTHOR]

The main objective of this investigation is to reveal the effects of nanoparticle aggregation aligned to thermal radiation with the prescribed heat flux. The Cattaneo–Christov heat flux (non-Fourier) and mass flux (non-Fick's) approaches in the optimized Buongiorno's model have been used to analyze the nanofluid magneto-transport mechanisms over the surface impacted by the gyrotactic behavior of microbe dispersion. The partial differentials are transformed into the set of nonlinear differential equations through boundary layer estimations and similarity substitutions, then computed by applying a variational finite element strategy. Researchers are looking into tiny nanoparticles because they have amazing properties, such as excellent thermal conduction, which are needed in advanced nanotechnology, heat exchangers, materials engineering, and technologies. The significance of this extensive study is to enhance the heat transition. Various aspects of the aggregation parameters on nanofluid velocity and temperature patterns are investigated and visually illustrated concerning the involved physical parameters. The effect of nanoparticle aggregation on the boundary is descending by the including parameters causes an increment in heat transfer rate. A significant correlation has been observed between the sets of results, which represents the accuracy of the finite element method used herein. The computations have been done by reducing the size of the mesh so that the numerical analysis can be used to ascertain convergence in the results. [ABSTRACT FROM AUTHOR]

The below work comprises the unsteady flow and enhanced thermal transportation for Carreau nanofluids across a stretching wedge. In addition, heat source, magnetic field, thermal radiation, activation energy, and convective boundary conditions are considered. Suitable similarity functions use to transmuted partial differential formulation into the ordinary differential form, which is solved numerically by the finite element method and coded in Matlab script. Parametric computations are made for faster stretch and slowly stretch to the surface of the wedge. The progressing value of parameter A (unsteadiness), material law index ϵ , and wedge angle reduce the flow velocity. The temperature in the boundary layer region rises directly with exceeding values of thermophoresis parameter Nt, Hartman number, Brownian motion parameter Nb, ϵ , Biot number Bi and radiation parameter Rd. The volume fraction of nanoparticles rises with activation energy parameter EE, but it receded against chemical reaction parameter Ω , and Lewis number Le. The reliability and validity of the current numerical solution are ascertained by establishing convergence criteria and agreement with existing specific solutions. [ABSTRACT FROM AUTHOR]

Numeric simulations are performed for a comparative study of magnetohydrodynamic (MHD) rotational flow of hybrid nanofluids (MoS2-Ag/ethyleneglycol-water (50–50%) and MoS2-Go/ethyleneglycol-water (50–50%)) over a horizontally elongated plane sheet. The principal objective is concerned with the enhancement of thermal transportation. The three-dimensional formulation governing the conservation of mass, momentum, energy, and concentration is transmuted into two-dimensional partial differentiation by employing similarity transforms. The resulting set of equations (PDEs) is then solved by variational finite element procedure coded in Matlab script. An intensive computational run is carried out for suitable ranges of the particular quantities of influence. The primary velocity component decreases monotonically and the magnitude of secondary velocity component diminishes significantly when magnetic parameter, rotational parameter, and unsteadiness parameter are incremented. Both the primary and secondary velocities are smaller in values for the hybrid phase Ag-MoS2 than that of hybrid phase Go-MoS2 but the nanoparticle concentration and temperature are higher for hybrid phase Ag-MoS2. The increased values of parameters for thermophoresis, Brownian motion, shape factor, and volume fraction of ϕ 2 made significant improvement in the temperature of the two phases of nano liquids. Results are also computed for the coefficients of skin friction(x, y-directions), Nusselt number, and Sherwood number. The present findings manifest reasonable comparison to their existing counterparts. Some of the practical engineering applications of the present analysis may be found in high-temperature nanomaterial processing technology, crystal growing, extrusion processes, manufacturing and rolling of polymer sheets, academic research, lubrication processes, and polymer industry. [ABSTRACT FROM AUTHOR]

In this mathematical study, magnetohydrodynamic, time-independent nanofluid flow over a stretching sheet by using the Cattaneo–Christov heat flux model is inspected. The impact of the thermal, solutal boundary and gravitational body forces with the effect of double stratification on the mass flow and heat transfer phenomena is also observed. The temperature-dependent viscosity impact on heat transfer through a moving sheet with capricious heat generation in nanofluids have studied, and the viscosity of the fluid is presumed to deviate as the inverse function of temperature. With the appropriate transformations, the system of partial differential equations is transformed into a system of nonlinear ordinary differential equations. By applying the variational finite element method, the transformed system of equations is solved. The properties of the several parameters for buoyancy, velocity, temperature, stratification, and Brownian motion parameters have examined. The enhancement in the concentration and thermal boundary layer thickness of the nanofluid sheet due to the increment in the viscosity parameter, also increased the temperature and concentration of nanoparticles. Moreover, the fluid temperature declined with the increasing values of thermal relaxation parameter. This displays that the Cattaneo–Christov heat flux model provides a better assessment of temperature distribution. Moreover, confirmation of the code and precision of the numerical method has inveterate with the valuation of the presented results with previous studies. [ABSTRACT FROM AUTHOR]

The present study investigated the unsteady magnetohydrodynamic (MHD) nanofluid flow over a radially nonlinear stretching sheet along with the viscosity dependent on temperature, convective boundary condition, thermo-diffusion, and the radiation effects. Moreover, the nanofluid's viscous effects were considered dependent on temperature and the exponential Reynolds model was considered in this context. It was additionally assumed that a uniform suspension of nanoparticles is present in the base fluid. The Buongiorno model, which involves the thermophoresis and Brownian motion effects, was considered. For the sake of a solution, the variational finite element method was selected with coding in MATLAB and the numerical results were contrasted with the published articles. The influence of various physical parameters on the velocity, temperature, and concentration profiles are discussed by the aid of graphs and tables. It was detected that the nanofuid viscosity parameter declines the fluid flow velocity, while, for the temperature and the concentration profiles, it accomplished the reverse phenomenon. [ABSTRACT FROM AUTHOR]

The present study investigated the steady magnetohydrodynamics of the axisymmetric flow of a incompressible, viscous, electricity-conducting nanofluid with convective boundary conditions and thermo-diffusion over a radially stretched surface. The nanoparticles' volume fraction was passively controlled on the boundary, rather than actively controlled. The governing non-linear partial differential equations were transformed into a system of nonlinear, ordinary differential equations with the aid of similarity transformations which were solved numerically, using the very efficient variational finite element method. The coefficient of skin friction and rate of heat transfer, and an exact solution of fluid flow velocity, were contrasted with the numerical solution gotten by FEM. Excellent agreement between the numerical and exact solutions was observed. The influences of various physical parameters on the velocity, temperature, and solutal and nanoparticle concentration profiles are discussed by the aid of graphs and tables. Additionally, authentication of the convergence of the numerical consequences acquired by the finite element method and the computations was acquired by decreasing the mesh level. This exploration is significant for the higher temperature of nanomaterial privileging technology. [ABSTRACT FROM AUTHOR]

The current research investigates the effects of Brownian motion, thermophoresis, and multi buoyancy forces on MHD Prandtl fluid as it flows through a stretched cylinder with convective boundary conditions. Linear thermal conductivity is included in the energy equation's development. The nanofluid flows are important in cooling systems, modern nano-technology, electronic parts and heat exchangers. The primary objective of this research is to enhance heat transportation. The problem consists of nonlinear PDEs and these equations are transformed into ODEs by incorporating suitable similarity transformations. The shooting strategy is used to solve the problem numerically after converting the non-dimensional ordinary differential equations to a system of first-order ODEs. A comparison is made between the MATLAB-generated findings and those that have already been published. The numerical results of various parameters have been systematically organized into tabular representations. Graphs show how significant parameters affect the given velocity, temperature, concentration, and motile microorganism measurements. When the buoyancy ratio and bio-convective Rayleigh number increase, the velocity profile drops; however, the temperature profile shows increasing behavior for the thermal radiation parameter. The concentration profiles are enhanced for the higher inputs in curvature parameter, magnetic parameter, and activation parameter while the density of motile microbes' decay for enhanced inputs of bio-convective Lewis number. [ABSTRACT FROM AUTHOR]

Improving the thermo-physical characteristics of water by the simple process of suspending nano-size particles may enhance the performance of solar distillation systems. More solar energy can be absorbed by the nanofluid and condensing cover of the solar still, thanks to the enhanced characteristics that magnify the temperature differential between the two. To systematically evaluate the latest progress in using nanofluids in a solar still energy system, this review intends to cover the most recent published studies between 2020 and 2024.Examining the impact of integrated hybrid nanofluid with solar still energy systemson water productivity is the primary focus of this review. The analysis also highlights different key aspects, including the system layout, type and concentration of nanoparticles, as well as water productivity. The findings demonstrate that by adding Al 2 O 3 at concentrations of0.1 %,0.2 %, and 0.3 %, traditional solar still productivity can be enhanced to 4.9, 5.47, and 6.12 L/m2, respectively. In addition, as compared to a standard solar still devoid of nanoparticles, the cumulative productivity of a modified solar still using a hybrid nanofluid may be elevated by 11.6 %. Additionally, hybrid nanofluids may increase daily water production by 27.2 % in the summer and 21.7 % in the winter, all because of their differing operating temperatures. To further promote the use of nanofluids in solar still energy systems and guarantee an increase in total efficiency, this investigation provides a number of research recommendations for future studies. Seemingly, this has the potential to increase the utilisation of hybrid nanofluids in solar distillationsystems with the aim of boosting the absorbed energy. [ABSTRACT FROM AUTHOR]

This article analyzes the time-independent performance of two-dimensional non-Newtonian nanofluid flow on a circular stretching cylinder. The Casson-Sutterby nanofluid is considered under the application of magnetic effects acting in the direction normal to the flow. Impacts of Brownian motion and thermophoresis are accounted for in this study. The governing PDEs are transformed into ODEs by invoking an adequate similarity transformation. The solution of reduced equations is obtained by applying the numerical technique bvp4c. A detailed graphical examination of the fluid flow is provided, and the dependence of velocity, temperature, and concentration profiles on different critical physical constraints is studied. The flow's velocity increases with increasing curvature values and Sutterby nanofluid parameters. However, it has an opposite reaction for magnetic, thermophoresis, sponginess, and Darcy resistance parameters. The flow temperature decreases with increasing curvature, magnetic field, and Sutterby nanofluid parameters, while it enhances the values of thermophoresis, sponginess, Darcy resistance, thermal relaxation time, and Brownian motion parameters. These findings play a significant role in industrial implementations like paper manufacturing, natural products, polymer industry, heating and cooling systems, 3D printer, biomedical flows, and mining industries. [ABSTRACT FROM AUTHOR]

The current research evaluates the thermophysical characteristics of a rotational Williamson hybrid nano-liquid in three dimensions with Darcy-Forchheimer, magnetic field, nonlinear thermal radiation, activation energy, dual stratifications, and suction/injection effects on a stretched surface. The heat transmission enhancement is primary focus of the current study. Single-wall and multi-wall carbon nanotubes are combined with the base fluid C 2 H 6 O 2 - H 2 O to form a hybrid fluid. Tiny particles are studied because of their unique characteristics, like excellent thermal conductivity, which is crucial in contemporary nanotechnology, cooling systems, cancer treatment, material sciences, and electrical components. Partial differential equations define flow models, and these equations are converted into ordinary differential equations by a workable similarity transformation due to the nonlinear nature of the resulting governing differential equations. The Runge–Kutta method is used to solve the mathematical structure numerically. The obtained results revealed a high degree of symmetry and precision compared to previously published studies. The primary velocity of hybrid nanofluid decreased and the secondary velocity of hybrid nanofluid increased for increasing the Williamson parameter values. The temperature as well as concentration profiles of hybrid nano-liquid are reduced for boosted values of stratification parameters. Moreover, Nusselt number, skin friction coefficient along y-axis and Sherwood number of Williamson hybrid nanofluid are declined with incremental in magnetic parameter. [ABSTRACT FROM AUTHOR]