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In this paper, an innovative form of nanofluids is identified as tri-hybrid nanofluid, which is synthesized by dispersing three or more varieties of nanomaterials in the considered base fluid. So, in this study, we comparatively examined SiO2/H2O nanofluid, TiO2+Al2O3/H2O hybrid nanofluid and SiO 2 + TiO2+Al2O3/H2O ternary hybrid nanofluid. Stretching of the flat surface enables us to develop the nanofluids flow. Additional considerations include the impacts of MHD, viscid dissipation, nonlinear thermal convection and radiation, joule heating and the presence of a heat source. For transforming PDEs (continuity, motion, heat equation and boundary constraints) into ODEs, an appropriate transformation procedure is used. HAM technique is used to solve these nonlinear coupled ODEs. Graphs are used to evaluate and examine the effect of numerous describing variables on nano, hybrid and tri-hybrid nanofluids speed and heat distribution. Furthermore, the computed values of engineering-relevant parameters ( C f and Nu) are tabulated and analyzed. The velocity of nanofluids acquires enhancing tendency for nonlinear thermal and mix convection parameter, but reverse upshot is assured due to nanoparticle volume fraction, Weissenberg number and magnetic parameters. Thermal field gets intensified in nature for magnetic and Eckert number, heat generation, thermal radiation and nanoparticles volume fractions. The ternary hybrid nanofluid has the most efficient behavior according to the comparative examination of ternary, hybrid and nanofluids. [ABSTRACT FROM AUTHOR]

This work investigates the Maxwell fluid flow in the variable porous space of cone and disc influenced by double diffusion on a variable porous space. In this study, the heat and mass transfer is influenced by the combined effects of Fourier's and Fick's laws, leading to heat and mass flux assumptions proposed by Cattaneo-Christov to characterize these transfer phenomena. The modeled equations have been converted to dimensionless form by using a suitable set of appropriate variables. This set of dimensionless equations was then solved by using artificial neural networks (ANNs). For this, initially, HAM (homotopy analysis method) has been used for the evaluation of modeled equations, and then, to analyze the dynamics of flow, Levenberg Marquardt Scheme through Neural Network Algorithm (LMS-NNA) has been employed. The optimal performance of the fluid model is observed at the epoch 10, 08, 427, 164, 203, 146, 101, 130, 255, 298, 166, and 222. The proximity to unity is a pivotal observation in this work that has been signifying a high degree of precision in the LMS-NNA design for the proposed model. The porosity factor has opposed the primary velocity profiles and has supported the secondary velocity profiles. Moreover, primary velocity profiles have declined with growth in Maxwell factor while secondary velocity panels have retarded by the upsurge in the retardation time factor. Thermal distribution has been supported by progression in thermophoresis and Brownian motion factors and has been opposed by escalation in the Prandtl number. Concentration distribution has augmented with the upsurge in thermophoresis factor and has declined with the escalation in factor, Schmidt number, and concentration relaxation time factor. It has been also observed in this work that the variable porous space controls the fluid flow and maintains the stability of Maxwell fluid flow between the cone and disc apparatus. The maximum error for testing, training, and validation of the proposed model is achieved for all 12 cases and discussed numerically in tabular form. [ABSTRACT FROM AUTHOR]

Tuberculosis remains a major health challenge for the humans of the whole world, especially in developing countries including Pakistan. Despite being a preventable and curable disease, TB is still the world's top infectious killer and among the leading diseases causing morbidity and mortality. In this paper, we formulate a deterministic model to study the dynamics and possible control of TB disease. Initially, we develop the model without control variables and present the basic mathematical analysis of the model. The stability results of the model at the disease-free case are presented when R 0 < 1 , and further it is proven that the infection will persist uniformly when R 0 > 1 . The model biological parameters are estimated using the confirmed TB infected cases reported in Khyber Pakhtunkhwa, Pakistan, from 2002 to 2017. Based on the estimated and fitted parameters, we obtained that R 0 ≈ 1.2928 . The model stability is investigated graphically when R 0 is greater or less than one. Further, the sensitivity analysis of the threshold parameter is performed in order to formulate an appropriate optimal strategy for curtailing the TB infection. Furthermore, we develop the control model using three control variables. The existence of the optimal control problem and the necessary mathematical results for the control characterizations is obtained. Finally, the simulations are presented to highlight the importance and impact of suggested control interventions on the disease dynamics. The proposed set of controls can be used for the elimination of TB infection in a community. [ABSTRACT FROM AUTHOR]

The energy transmission through micropolar fluid have a broad range implementation in the field of electronics, textiles, spacecraft, power generation and nuclear power plants. Thermal radiation's influence on an incompressible thermo-convective flow of micropolar fluid across a permeable extensible sheet with energy and mass transition is reported in the present study. The governing equations consist of Navier–Stokes equation, micro rotation, temperature and concentration equations have been modeled in the form of the system of Partial Differential Equations. The system of basic equations is reduced into a nonlinear system of coupled ODE's by using a similarity framework. The numerical solution of the problem has been obtained via PCM (Parametric Continuation Method). The findings are compared to a MATLAB built-in package called bvp4c to ensure that the scheme is valid. It has been perceived that both the results are in best agreement with each other. The effects of associated parameters on the dimensionless velocity, micro-rotation, energy and mass profiles are discussed and depicted graphically. It has been detected that the permeability parameter gives rise in micro-rotation profile. [ABSTRACT FROM AUTHOR]

Purpose: (1) A mathematical model for the Hybrid nanofluids flow is used as carriers for delivering drugs. (2) The flow conditions are controlled to enable drug-loaded nanofluids to flow through the smaller gap between the two tubes. (3) Hybrid nanofluids (HNFs) made from silver (Ag) and titanium dioxide (TiO2) nanoparticles are analyzed for applications of drug delivery. (Ag) and (TiO2) (NPs) are suitable candidates for cancer treatment due to their excellent biocompatibility, high photoactivity, and low toxicity. (4) The new strategy of artificial neural networks (ANN) is used which is machine-based and more prominent in validation, and comparison with other techniques. Design/methodology/approach: The two Tubes are settled in such a manner that the gap between them is uniform. The Control Volume Finite Element Method; Rk-4 and Artificial Neural Network (ANN). Findings: (1) From the obtained results it is observed that the dispersion and distribution of drug-loaded nanoparticles within the body will be improved by the convective motion caused by hybrid nanofluids. The effectiveness and uniformity of drug delivery to target tissues or organs is improved based on the uniform flow and uniform gap. (2) The targeting efficiency of nanofluids is further improved with the addition of the magnetic field. (3) The size of the cylinders, and flow rate, are considered uniform to optimize the drug delivery. Research limitations/implications: (1)The flow phenomena is considered laminar, one can use the same idea through a turbulent flow case. (2) The gap is considered uniform and will be interesting if someone extends the idea as non-uniform. Practical implications: (1) To deliver drugs to the targeted area, a suitable mathematical model is required. (2) The analysis of hybrid nanofluids (HNFs) derived from silver (Ag) and titanium dioxide (TiO2) nanoparticles is conducted for the purpose of drug delivery. The biocompatibility, high photoactivity, and low toxicity of (Ag) and (TiO2) (NPs) make them ideal candidates for cancer treatment. (3) Machine-based artificial neural networks (ANN) have a new strategy that is more prominent in validation compared to other techniques. Social implications: The drug delivery model is a useful strategy for new researchers. (1) They can extend this idea using a non-uniform gap. (2) The flow is considered uniform, the new researchers can extend the idea using a turbulent case. (3) Other hybrid nanofluids flow, in the same model for other industrial usages are possible. Originality/value: All the obtained results are new. The experimental thermophysical results are used from the existing literature and references are provided. [ABSTRACT FROM AUTHOR]

Hybrid nanofluids are capable of being used as a carrier for delivering drugs to targeted areas in the body. For this purpose, the Casson hybrid nanofluids (HNFs) flow is suggested between the gap of two tubes. The study involves analyzing blood-based hybrid nanofluids (HNFs) that consist of silver (Ag) and titanium dioxide (TiO2) nanoparticles for applications of drug delivery. Titanium oxide nanoparticles, or TiO2 NPs, have strong photoactivity, low toxicity, and excellent biocompatibility, making them promising candidates for cancer treatment. The attractiveness of silver nanoparticles (AgNPs) for cancer therapy is due to their unique properties. Graphic representations are provided based on the simulations of non-dimensional velocity, temperature, and skin friction under physical parameter variations, for the applications of drug delivery are investigated and discussed. The control volume finite element method (CVFEM), is used to solve the problem. The new strategy of artificial neural networks (ANN) is also used to solve the transform equations. Nanoparticles increase drug stability and extend shelf life by protecting them from degradation or inactivation. [ABSTRACT FROM AUTHOR]

Fractional calculus characterizes a function at those points, where classical calculus failed. In the current study, we explored the fractional behavior of the stagnation point flow of hybrid nano liquid consisting of TiO2 and Ag nanoparticles across a stretching sheet. Silver Ag and Titanium dioxide TiO2 nanocomposites are one of the most significant and fascinating nanocomposites perform an important role in nanobiotechnology, especially in nanomedicine and for cancer cell therapy since these metal nanoparticles are thought to improve photocatalytic operation. The fluid movement over a stretching layer is subjected to electric and magnetic fields. The problem has been formulated in the form of the system of PDEs, which are reduced to the system of fractional-order ODEs by implementing the fractional similarity framework. The obtained fractional order differential equations are further solved via fractional code FDE-12 based on Caputo derivative. It has been perceived that the drifting velocity generated by the electric field E significantly improves the velocity and heat transition rate of blood. The fractional model is more generalized and applicable than the classical one. [ABSTRACT FROM AUTHOR]

In the current work, the unsteady thermal flow of Maxwell power-law nanofluid with Welan gum solution on a stretching surface has been considered. The flow is also exposed to Joule heating and magnetic effects. The Marangoni convection equation is also proposed for current investigation in light of the constitutive equations for the Maxwell power law model. For non-dimensionalization, a group of similar variables has been employed to obtain a set of ordinary differential equations. This set of dimensionless equations is then solved with the help of the homotopy analysis method (HAM). It has been established in this work that, the effects of momentum relaxation time upon the thickness of the film is quite obvious in comparison to heat relaxation time. It is also noticed in this work that improvement in the Marangoni convection process leads to a decline in the thickness of the fluid's film. [ABSTRACT FROM AUTHOR]

Due to its remarkable thermodynamic development in various engineering sciences, the dispersion of nanostructures in classical base liquids is receiving greater attention from researchers and scientists. In light of the aforementioned inspirations, the suggested research is associated with using a water-based ternary-hybrid nanofluid that contains three unique nanostructures, silicon dioxide, titanium dioxide and aluminum oxide to optimize the heating process in science and engineering. In this situation, the influence of a chemically reactive magneto-hydrodynamics (MHD) Darcy–Forchheimer ternary hybrid composites transport involving nonlinear radiation across an exponentially permeable stretched surface is highlighted with the model's physical initial and boundary constraints. The simulation of the heat expression also includes the impacts of nonlinear thermal radiations, energy supply, energy dissipation and magnetic force. Furthermore, the interpretation of Buongiorno's theory involves spontaneous and thermophoresis diffusions. Entropy analysis is explained using the second law of thermodynamics. We converted the model framework for fluid movement, energy and mass transfer (together with ternary hybrid nanofluid characteristics) into self-similar nondimensional differential equations, that were then further analytically evaluated by using the homotopy asymptotic method (HAM) technique via Mathematica software. The acquired results are illustrated numerically and graphically to study the behavior of fluid flow, heat, concentration distribution, drag force, rate of heat and mass transfer for various emergent components to gain scientific comprehension. With the growing values of magnetic, porosity and Forchheimer number, the nature of the velocity profile goes down. [ABSTRACT FROM AUTHOR]

This article focuses on discrete survival data analysis, employing a doubly Type-I censoring scheme (DT1SC) under a Bayesian framework for parameters estimation in a 3-component mixture geometric (3-CMG) distribution. The non-informative (uniform) prior is utilized under squared error, DeGroot, and precautionary loss functions. The time is considered as discrete in this paper, presenting a departure from continuous approaches in survival analysis. The methodology is tailored to address challenges that traditional survival analysis encounters when faced with limited or missing information. The proposed method effectively handles the complexities arising from incomplete or missing data, providing a robust mechanism for accurate parameter estimation. Through extensive simulations and application to real-world datasets, our approach demonstrates its effectiveness in managing uncertainties, particularly in scenarios involving sparse or missing data. This work represents a noteworthy contribution to methodological advancements in survival analysis, offering a valuable tool for researchers and practitioners navigating intricate dynamics within the 3-CMG under DT1CS with time being considered as discrete. [ABSTRACT FROM AUTHOR]

The numerical investigation of bioconvective nanofluid (NF) flow, which involves gyrotactic microbes and heat and mass transmission analysis above an inclined extending axisymmetric cylinder, is presented in this study. The study aims to investigate the bioconvection flow of nanofluid under the influence of heat sources/sinks. Through proper transformation, all partial differential equations are transformed into a non-linear ODE scheme. A new set of variables is presented in the directive to get the first-order convectional equations and then solved numerically using bvp4c MATLAB, embedded in the function. The proposed model is validated after calculating the error estimation and obtaining the residual error. The influence of various factors on the velocity, energy, concentration, and density of motile microorganisms is examined and studied. The analysis describes and addresses all physical measures of concentration such as Skin Friction (SF), Sherwood number, the density of motile microorganisms, and Nusselt number. To validate the present study, a comparison is conducted with previous studies, and excellent correspondence is found. In addition, the ND-Solve approach is utilized to confirm the bvp4c. The mathematical model is confirmed through error analysis. This study provides the platform for industrial applications such as cooling capacity polymers, heat exchange, and chemical production sectors. [ABSTRACT FROM AUTHOR]

This work explores the influence of double diffusion over thermally radiative flow of thin film hybrid nanofluid and irreversibility generation through a stretching channel. The nanoparticles of silver and alumina have mixed in the Maxwell fluid (base fluid). Magnetic field influence has been employed to channel in normal direction. Equations that are going to administer the fluid flow have been converted to dimension-free notations by using appropriate variables. Homotopy analysis method is used for the solution of the resultant equations. In this investigation it has pointed out that motion of fluid has declined with growth in magnetic effects, thin film thickness, and unsteadiness factor. Temperature of fluid has grown up with upsurge in Brownian motion, radiation factor, and thermophoresis effects, while it has declined with greater values of thermal Maxwell factor and thickness factor of the thin film. Concentration distribution has grown up with higher values of thermophoresis effects and has declined for augmentation in Brownian motion. [ABSTRACT FROM AUTHOR]

• This study focuses on the comprehensive analysis of thermal characterization of the ternary hybrid nanofluid flow within a continuously extending disk. • The characteristics of time-dependent magnetohydrodynamics tri-hybrid nanofluids consisting Molybdenum disulphide (MoS2), Silicon dioxide (SiO2), Multi-Walled Carbon Nanotubes (MWCNT), Water (H 2 O), hybrid (MWCNT + MoS 2 /H 2 O) and nanofluid (MWCNT/H 2 O) movement are analyzed for the thermal applications. • With the help of ohmic heating, quadratic convection, and a magnetic field the heat transmission mechanism and fluid dynamics are investigated.The significance of the study describe that tri-hybrid nanofluid has a higher energy transport rate than the traditional fluid at the surface of the disk. • The transformed coupled and nonlinear ordinary differential equations are solved analytically using Homotopy Analysis Method (HAM). • The impact of some important physical parameters on the fluid flow profile, temperature fields, drag force, and rate of heat transmission is depicted using plots. • The outcomes are validated by previous studies and a good degree of consistency is revealed. This study focuses on the comprehensive analysis of thermal characterization of the ternary hybrid nanofluid flow within a continuously extending disk. The characteristics of time-dependent magnetohydrodynamics tri-hybrid nanofluids consisting Molybdenum disulfide (MoS2), Silicon dioxide (SiO2), Multi-Walled Carbon Nanotubes (MWCNT), Water (H 2 O), hybrid (MWCNT + MoS 2 /H 2 O) and nanofluid (MWCNT/H 2 O) movement are analyzed for the thermal applications. With the help of ohmic heating, quadratic convection, and a magnetic field the heat transmission mechanism and fluid dynamics are investigated.The significance of the study describe that tri-hybrid nanofluid has a higher energy transport rate than the traditional fluid at the surface of the disk. The transformed coupled and nonlinear ordinary differential equations are solved analytically using Homotopy Analysis Method (HAM). The impact of some important physical parameters on the fluid flow profile, temperature fields, drag force, and rate of heat transmission is depicted using plots. The outcomes are validated by previous studies and a good degree of consistency is revealed. [ABSTRACT FROM AUTHOR]

In the pump of different machines, the vacuum pump oil (VPO) is used as a lubricant. The heat rate transport mechanism is a significant requirement for all industries and engineering. The applications of VPO in discrete fields of industries and engineering fields are uranium enrichment, electron microscopy, radio pharmacy, ophthalmic coating, radiosurgery, production of most types of electric lamps, mass spectrometers, freeze-drying, and, etc. Therefore, in the present study, the nanoparticles are mixed up into the VPO base liquid for the augmentation of energy transportation. Further, the MHD flow of a couple stress nanoliquid with the applications of Hall current toward the rotating disk is discussed. The Darcy-Forchheimer along with porous medium is examined. The prevalence of viscous dissipation, thermal radiation, and Joule heating impacts are also considered. With the aid of Cattaneo-Christov heat-mass flux theory, the mechanism for energy and mass transport is deliberated. The idea of the motile gyrotactic microorganisms is incorporated. The existing problem is expressed as higher-order PDEs, which are then transformed into higher-order ODEs by employing the appropriate similarity transformations. For the analytical simulation of the modeled system of equations, the HAM scheme is utilized. The behavior of the flow profiles of the nanoliquid against various flow parameters has discoursed through the graphs. The outcomes from this analysis determined that the increment in a couple-stress liquid parameter reduced the fluid velocity. It is obtained that, the expansion in thermal and solutal relaxation time parameters decayed the nanofluid temperature and concentration. Further, it is examined that a higher magnetic field amplified the skin friction coefficients of the nanoliquid. Heat transport is increased through the rising of the radiation parameter. [ABSTRACT FROM AUTHOR]

To enhance the surface properties of solids the mechanism of thin films is frequently used. Penetration, degradation, stiffness, illumination, diffusion, absorption, and electric performance are all characteristics of a bulk substance medium that a thin film can improve. In nanotechnology, thin film processing can be extremely useful. Therefore, the time-dependent nonlinearly convective stream of thin film nanoliquid over an inclined stretchable sheet with magnetic effect is investigated in current work. The features of mass and heat transport processes are explained using important factors like thermophoresis and Brownian movement. Nonlinear partial differential equations are obtained to model the time-dependent liquid film flow over an inclined surface, which are then turned into couple ordinary differential equations utilizing appropriate alterations. The results of the computation of the model problem are collected using an analytical approach Homotopy Analysis Method and presented the final finding numerically and graphically. During the flow assessment, the impact of individual flow factors such as magnetic, Brownian, and thermophoresis parameters on regular profiles (temperature, velocity, and concentration) are analyzed and found to be quite remarkable. Furthermore, the consequence of M and Nt factors on the velocity, concentration and thermal distribution leads to diminishing conduct. On the other hand, the thermal profile of the liquid film rises in response to the thermophoresis factor. The % wise variation in the skin friction, Nusselt number and Sherwood number versus physical parameters has been obtained and discussed. [ABSTRACT FROM AUTHOR]

In this paper, we consider a fractional COVID-19 epidemic model with a convex incidence rate. The Atangana–Baleanu fractional operator in the Caputo sense is taken into account. We establish the equilibrium points, basic reproduction number, and local stability at both the equilibrium points. The existence and uniqueness of the solution are proved by using Banach and Leray–Schauder alternative type theorems. For the fractional numerical simulations, we use the Toufik–Atangana scheme. Optimal control analysis is carried out to minimize the infection and maximize the susceptible people. [ABSTRACT FROM AUTHOR]

This work investigates numerically the solution of Darcy–Forchheimer flow for hybrid nanofluid by employing the slip conditions. Basically, the fluid flow is produced by a swirling disk and is exposed to thermal stratification along with non-linear thermal radiation for controlling the heat transfer of the flow system. In this investigation, the nanoparticles of titanium dioxide and aluminum oxide have been suspended in water as base fluid. Moreover, the Darcy–Forchheimer expression is used to characterize the porous spaces with variable porosity and permeability. The resulting expressions of motion, energy and mass transfer in dimensionless form have been solved by HAM (Homotopy analysis method). In addition, the influence of different emerging factors upon flow system has been disputed both theoretically in graphical form and numerically in the tabular form. During this effort, it has been recognized that velocities profiles augment with growing values of mixed convection parameter while thermal characteristics enhance with augmenting values of radiation parameters. According to the findings, heat is transmitted more quickly in hybrid nanofluid than in traditional nanofluid. Furthermore, it is estimated that the velocities of fluid f ′ ξ , g ξ are decayed for high values of ϕ 1 , ϕ 2 , F r and k 1 factors. [ABSTRACT FROM AUTHOR]

In this investigation, heat transportation together with irreversibility analysis for the flow of couple stress hybrid nanofluid past over a stretching surface is considered. The innovative characteristics and aims of this work are to note that the transportation heat couple stress model involves EMHD, viscous dissipation, Joule heating, and heat absorption, and omission. The hybrid nanofluid is prepared due to the suspension of the solid nanoparticles of the SWCNTs and MWCNTs in pure human blood. This mathematical model is an appropriate model for biological advantages including testing of human blood for drug deliveries to various parts of the human body. Particularly, the Prandtl number used for the blood is 21 and very large as compared to the other base fluids. Necessary modifications are used to translate the defining partial differential equations and boundary conditions into a layout that can be computed. To obtain mathematical approximations for the resulting scheme of nonlinear differential equations, the innovative homotopy analysis method (HAM) is used. The explanation for velocity, energy, and entropy are exposed and the flow against various influential factors ( E , M , k , Q , S and E c ) is discussed graphically. The numerical values are calculated and summarized for dimensionless C fx and N u x. In addition, the current study is compared for various values of Pr to that published literature and an impressive agreement in terms of finding is reported. It has also been noticed that the M and E factors retard the hybrid nanofluid flow, while the temperature of fluid becomes upsurges by the rise in these factors. 11.95% enhancement in the heat transfer rate has been attained using the hybrid nanofluids. [ABSTRACT FROM AUTHOR]

The current study focuses on the laminar flow of copper and copper oxide (Cu/blood and Cu + CuO/blood ) hybrid nanoliquid, considering blood as a carrier fluid in a rectangular domain between two permeable channels. This study may manipulate for the purpose such as the drug delivery process, flow dynamic mechanism of the micro-circulatory system. In the proposed model, MHD and heat source/sink on the flow pattern have been studied. Furthermore, the sides of each channel are permeable, allowing the nanoliquid to escape, filter, squeezing and dilating with a fixed velocity. Appropriate transformations are incorporated to convert the governing partial differential equations and the boundary conditions suitable for computation. The elegant homotopy analysis method (HAM) is used to obtain analytic approximations for the resulting system of nonlinear differential equations. The features of flow characteristics such as velocity, and temperature profiles in response to the variations of the emerging parameters are simulated and examined with a physical explanation. The magnetic field plays a vital role in the blood flow and therefore the existing literature has been extending with the addition of magnetic field. Among the many outputs of the study, it is found that the pressure distribution decline with the accumulated values of the magnetic parameter at the center of the flow regime. The augmentation in the temperature distribution estimates the pH values and electric conductivity. Therefore, the Cu and CuO hybrid nanofluids are used in this study for medication purposes. The magnetic field has an important role in the blood flow and therefore the extending study has been extending using the magnetic field. The heat emission/absorption term is added to the energy equation to maintain the homogeneous temperature for the blood flow. We expect that this work will provide efficient outputs for medical purposes such as drug delivery. [ABSTRACT FROM AUTHOR]

In this work, the thermal analysis for bio-convective hybrid nanofluid flowing upon a thin horizontally moving needle is carried out. The chemical reaction and viscous dissipation has also considered for flow system in the presence of microorganism. The hybrid nanoparticles comprising of Copper Cu and Alumina A l 2 O 3 are considered for current flow problem. Mathematically the flow problem is formulated by employing the famous Buongiorno's model that will also investigate the consequences of thermophoretic forces and Brownian motion upon flow system. Group of similar variables is used to transform the model equations into dimensionless form and have then solved analytically by homotopy analysis method (HAM). It has established in this work that, flow of fluid declines due to increase in bioconvection Rayleigh number, buoyancy ratio and volume fractions of nanoparticles. Thermal flow grows due to rise in Eckert number, Brownian, thermophoresis parameters and volume fraction of nanoparticles. Concentration profiles increase due to growth in Brownian motion parameter and reduces due to increase in thermophoresis parameter and Lewis number. Motile microorganism profile declines due to augmentation in Peclet and bioconvection Lewis numbers. Moreover, the percentage enhancement in the drag force and rate of heat transfer using conventional nanofluid and hybrid nanofluid are observed and discussed. The hybrid nanofluid increases the skin friction and heat transfer rate more rapidly and efficiently as compared to other traditional fluids. A comparison of the present study with the existing literature is also conducted with a closed agreement between both results for variations in thickness of the needle. [ABSTRACT FROM AUTHOR]

The magnetohydrodynamic hybrid second-grade nanofluid flow towards a stretching/shrinking sheet with thermal radiation is inspected in current work. Main concern of current investigation is to consider hybrid A l 2 O 3 - C u nanofluid which is perceived by hanging two dissimilar kinds of nanoparticles known as alumina and copper within the base fluid. The fluid motion is produced by non-linear stretching/shrinking sheet. The modeled equations which comprise of energy, motion and continuity equations are changed into dimensionless form using group of similar variables. To determine the solution of transformed problem, the Homotopy Analysis technique is used. The findings of this work revealed that the magnetic parameter improves the heat transfer rate. This work also ensures that there are non-unique solutions of modeled problem for shrinking case and a unique solution for stretching case. Higher values of Re x results in declining of flow field. Rise in M agrees to a decline in velocity distributions. Higher values of second order fluid parameter reduces the viscosity of fluid and accordingly velocity increases. Velocity profile is also a decreasing function of volume friction. [ABSTRACT FROM AUTHOR]

Figure: The graphical View of the flow model. [Display omitted] • Diffusion via random and thermophoresis and Darcy-Forchheimer effects is explored. • Energy Generation, Ohmic heating, MHD and radiation effects are incorporated with entropy generation. • Three kinds of nanocomposites (SiO 2 , TiO 2 and Al 2 O 3) are immersed in base fluid H 2 O. • The influence of a variety of developmental parameters on engineering quantities has been investigated in pictorial and tabular forms. • HAM is adopted to determine the solution of the model problem and validate with numerical technique. The proposed research is concerned with water-based ternary-hybrid nanofluid with nanostructures SiO 2 , TiO 2 and Al 2 O 3 for cooling purposes in engineering. A reactive MHD Darcy-Forchheimer liquid flow involving radiation effect across an exponentially permeable stretched surface is highlighted. Heat expression includes the impacts of nonlinear thermal radiations, energy supply, energy dissipation and magnetic force. The obtained results are demonstrated numerically and graphically to examine the behavior of fluid speed and temperature distribution for various emerging factors in order to gain a physical understanding. Entropy analysis is explained using the second law of thermodynamics. The values of C f , N u and S G are also calculated for the various parameters and physically explained. [ABSTRACT FROM AUTHOR]

Advanced techniques are used to enhance the efficiency of the energy assets and maximize the appliance efficiency of the main resources. In this view, in this study, the focus is paid to the solar collector to cover thermal radiation through optimization and enhance the performance of the solar panel. Hybrid nanofluids (HNFs) consist of a base liquid glycol (C 3 H 8 O 2 ) in which nanoparticles of copper (Cu) and aluminum oxide (Al 2 O 3 ) are doped as fillers. The flow of the stagnation point is considered in the presence of the Riga plate. The state of the solar thermal system is termed viva stagnation to control the additional heating through the flow variation in the collector loop. The inclusion of entropy generation and Bejan number formation are primarily conceived under the influence of physical parameters for energy optimization. The computational analysis is carried out utilizing the control volume finite element method (CVFEM), and Runge-Kutta 4 (RK-4) methods. (FEATool Multiphysics) software has been used to find the solution through (CVFEM). The results are further validated through a machine learning neural networking procedure, wherein the heat transfer rate is greatly upgraded with a variation of the nanoparticle's volume fraction. We expect this improvement to progress the stability of heat transfer in the solar power system., (© 2023. Springer Nature Limited.)

The present article examines the consequences of a magnetic field, Hall current, and thermal radiation on the spinning flow of hybrid nanofluid (HNF) across a revolving disc. The core objective of the study is to improve the energy transference rate through hybrid nano liquid for industrial and engineering operations. The HNFs have advanced thermophysical characteristics. Therefore, in the current study, a superior class of nanomaterials (carbon nanotubes (CNTs) and Al 2 O 3 ) are added to the base fluid. The modeled equations are demoted to a dimensionless set of Ordinary differential equations (ODEs) through similarity conversion and are analytically solved by engaging the homotopy analysis method. The physical constraints' effect on energy, velocity, motile microorganism, and mass profiles have been drawn and discussed. For accuracy, the results are compared to the published studies, which ensures the accuracy and reliability of the technique and results. It is observed that the energy communication rate lessens with the flourishing values of thermal radiation and for Hall current. Furthermore, it is noted that due to its carbon-carbon bonding in CNTs, it has a greater tendency for energy propagation than Al 2 O 3 nanoparticles., (© 2023 IOP Publishing Ltd.)

This study looks at the natural convections of Cu + Al 2 O 3 /H 2 O nanofluid into a permeable chamber. The magnetic field is also executed on the flow field and the analysis has been approached numerically by the control volume method. The study of hybrid nanofluid heat in terms of the transfer flux was supplemented with a wide range of parameters of hybrid nanofluid fractions, Rayleigh numbers Hartmann numbers and porosity factor. It's also determined that the flow and thermal distribution are heavily affected by the concentration of the nanoparticles. The concentration of nanoparticles increases the transport of convective energy inside the enclosure. The primary findings demonstrate that a rise in both the Rayleigh number and Darcy number leads to an improvement in convective heat transfer within the enclosure. However, the porosity has a negligible effect. Additionally, the rotation in a clockwise direction has a beneficial impact on the dispersion of heat transfer throughout the cavity. Furthermore, it is concluded that hybrid nanofluids are more reliable than conventional fluids in improving thermal properties., (© 2023. The Author(s).)

The current investigation employs a numerical simulation to demonstrate the impact of hall current on unsteady free convective flow caused by hybrid-nanofluid over a revolving sphere approaching the stagnation point. The prominent characteristics of Lorentz force as a result of magnetic field coupling with hybrid nanofluid is also explored. The process of energy and mass transmission is inspected with nonlinear thermal radiations, non-uniform energy supply, dissipation and nonlinear chemical reaction. In current flow model, a unique class of nanofluid known as the hybrid nanofluid is being used, which contain GO (graphene oxide) and MoS 2 (molybdenum disulfide) with water. The angular speed of both the sphere and free stream changes frequently with time. Employing adequate dimensionless variables, the partial-differential patterns strongly non-linear that represent the situational analysis are morphed into non-linear ordinary differential patterns. The analytical outcomes of ordinary differential pattern have been developed via OHAM technique. Utilizing tables and graphs, various aspects of such controllable physical characteristics have been highlighted and explored in depth. For varying values of M , φ , δ , S c and K n ,the variations in C f x , C f z , N u and S h in MoS 2 -GO/H 2 O are the greatest as contrasted to MoS 2 /H 2 O. The results are also compared to those reported existing literature and they are noticed to be in very close agreement., (©2023PublishedbyElsevierLtd.)

The current study provides a detailed analysis of steady two-dimensional incompressible and electrically conducting magnetohydrodynamic flow of a couple stress hybrid nanofluid under the influence of Darcy-Forchheimer, viscous dissipation, joule heating, heat generation, chemical reaction, and variable viscosity. The system of partial differential equations of the current model (equation of motion, energy, and concentration) is converted into a system of ordinary differential equations by adopting the suitable similarity practice. Analytically, homotopy analysis method (HAM) is employed to solve the obtained set of equations. The impact of permeability, couple-stress and magnetic parameters on axial velocity, mean critical reflux condition and mean velocity on the channel walls are discussed in details. Computational effects show that the axial mean velocity at the boundary has an inverse relation with couple stress parameter while the permeability parameter has a direct relation with the magnetic parameter and vice versa. The enhancement in the temperature distribution evaluates the pH values and electric conductivity. Therefore, the [Formula: see text] hybrid nanofluids are used in this study for medication purpose., (© 2021. The Author(s).)

This investigation describes the hydromagnetic flow of gravity-driven couple stress hybrid nanofluid past a heated plate. The carbon nanotubes (CNTs) are used to characterize the hybrid nanofluid. The heated plate is placed vertically with an application of homogenous-heterogeneous reactions to the assumed flow system. The homogeneous reaction governs by isothermal cubic autocatalytic kinetics while the heterogeneous reaction governs by the first order kinetics. For current study the couple stress hybrid nanofluid is presumed to be conducted electrically with impact of non-uniform magnetic effects. An appropriate set of dimensionless quantities has employed to governing equations and then has solved by homotopy analysis method. The influence of emerging parameters encountered in this work has discussed in detail with the help of graphs. In this study it has examined that, flow of fluid reduces with upsurge in magnetic parameter and volumetric concentrations, whereas thermal and concentration characteristics augment with increase in volumetric concentrations. Moreover, growth in Prandtl number leads to a reduction in thermal characteristics and growth in Schmidt number result a reduction in concentration profile. The impact of various emerging parameters has also studied numerically upon physical quantities. It has established that, with augmentation in values of buoyancy parameter there is a growth in the values of skin friction. A comparison has also carried out between current and established results with a fine agreement in both results., (© 2021. The Author(s).)

In this new world of fluid technologies, hybrid nanofluid has become a productive subject of research among scientists for its potential thermal features and abilities, which provides an excellent result as compared to nanofluids in growing the rate of heat transport. Our purpose here is to introduce the substantial influences of magnetic field on 2D, time-dependent and stagnation point inviscid flow of couple stress hybrid nanofluid around a rotating sphere with base fluid is pure blood, [Formula: see text] as the nanoparticles. To translate the governing system of partial differential equations and the boundary conditions relevant for computation, some suitable transformations are implemented. To obtain the analytical estimations for the corresponding system of differential expression, the innovative Optimal Homotopy Analysis Method is used. The characteristics of hybrid nanofluid flow patterns, including temperature, velocity and concentration profiles are simulated and analyzed in detail due to the variation in the evolving variables. Detailed research is also performed to investigate the influences of relevant constraints on the rates, momentum and heat transport for both [Formula: see text] and [Formula: see text]. One of the many outcomes of this analysis, it is observed that increasing the magnetic factor will decelerate the hybrid nanofluid flow velocity and improve the temperature profile. It may also be demonstrated that by increasing the Brownian motion factor, significant improvement can be made in the concentration field of hybrid nanofluid. The increase in the nanoparticle volume fraction from 0.01 to 0.02 in the case of the hybrid nanofluid enhances the thermal conductivity from 5.8 to 11.947% and for the same value of the nanoparticle volume fraction in the case of nanofluid enhance the thermal conductivity from 2.576 to 5.197%.

The thermal management of the flow of the hybrid nanofluid within the conical gap between a cone and a disk is analyzed. Four different cases of flow are examined, including (1) stationary cone rotating disk (2) rotating cone stationary disk (3) rotating cone and disk in the same direction and (4) rotating cone and disk in the opposite directions. The magnetic field of strength [Formula: see text] is added to the modeled problem that is applied along the z-direction. This work actually explores the role of the heat transfer, which performs in a plate-cone viscometer. A special type of hybrid nanoliquid containing copper Cu and magnetic ferrite Fe 3 O 4 nanoparticles are considered. The similarity transformations have been used to alter the modeled from partial differential equations (PDEs) to the ordinary differential equations (ODEs). The modeled problem is analytically treated with the Homotopy analysis method HAM and the numerical ND-solve method has been used for the comparison. The numerical outputs for the temperature gradient are tabulated against physical pertinent variables. In particular, it is concluded that increment in volume fraction of both nanoparticles [Formula: see text] effectively enhanced the thermal transmission rate and velocity of base fluid. The desired cooling of disk-cone instruments can be gained for a rotating disk with a fixed cone, while the surface temperature remains constant.

The main features of present numerical model is to explore and compare the behavior of simple and hybrid nanoparticles, which were allowed to move on a spreading sheet. The effect of magnetic dipole on hybrid nanofluid flow is considered. A magnetic dipole combined with hybrid nanofluid plays a vital role in controlling the momentum and thermal boundary layers. In view of the impacts of a magnetic dipole on the simple and hybrid nanofluids, steady, laminar and boundary layer flow of [Formula: see text] and [Formula: see text] are characterized in this analysis. The governing equations of flow problem are diminished to ordinary differential equation (ODE's) by using similarity approach. For the numerical solution of the nonlinear ODE's, Runge Kutta order 4 th technique has been executed. The impact of various physical constraints, such as volume friction, viscous dissipation, Prandtl number and so on have been sketched and briefly discussed for velocity and temperature profile. In this work, some vital characteristics such as skin friction, Curie temperature and local Nusselt number are chosen for physical and numerical analysis. It has been noted that the hybrid nanofluid is more efficient in thermal conduction due to its strong thermal characteristics as compared to simple nanofluid. From results, it is also observed that the turbulence of fluid flow can be controlled through magnetic dipole.

Here a new analytical scheme is presented to solve nonlinear boundary value problems (BVPs) of higher order occurring in nonlinear phenomena. This method is called second alternative of Optimal Homotopy Asymptotic Method. It converts a complex nonlinear problem into zeroth order and first order problem. A homotopy and auxiliary functions which are consisted of unknown convergence controlling parameters are used in this technique. The unknown parameters are determined by minimizing the residual. Many methods are used to determine these parameters. Here Galerkin's method is used for this purpose. It is applied to solve non-linear BVPs of order four, five, six, and seven. The Consequences are compared with other methods e.g., Differential Transform Method (DTM), Adomain Decomposition Method (ADM), Variational Iteration Method (VIM), and Optimal Homotopy Asymptotic Method (OHAM). It gives efficient and accurate first-order approximate solution. The achieved results are compared with the exact solutions as well as with other methods to authenticate the applied technique. This method is very simple and easy but more operative.