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In contemporary times, there has been a significant focus among researchers on hybrid nanofluids derived from oils, owing to their remarkable and substantial utility in the domains of engineering, mechanics, and industrial applications. The aim of this research is to determine the impact of incorporating tantalum and nickel nanoparticles in mineral oil on thermal characteristics and flow patterns, with the objective of predicting possible improvements. The dependence of the role of both nanoparticles on their shapes is evaluated for column, platelet, lamina, cylinder, and tetrahedron-type shapes. This work analyzes the thermal performance of two different nanofluids individually made of tantalum and nickel nanoparticles while also examining the synergistic effects produced due to the simultaneous suspension of these particles. A profound understanding of the intricate flow dynamics and thermal energy transfer phenomena along a vertical surface holds paramount importance in the pursuit of optimizing heat exchange procedures, formulating effective cooling systems, and designing thermally efficient devices. Furthermore, it contributes to the advancement of climate modeling, the precision of weather forecasting, and the refinement of the operational effectiveness of solar thermal systems. The basic mathematical model is formulated subject to free convection, time-dependent flow and heat conditions, and thermal radiation. This governing system is made non-dimensional to lessen the intricacy and provide the basis for the utilization of fractional operators. In order to assess the effectiveness of fractional modeling techniques, constant proportional Caputo (CPC) and Atangana–Baleanu (ABC) derivatives are operated for the model generalization. Most of the time, solving fractional models via an analytic method are not a feasible technique because it produces extremely complex and implicit mathematical expressions. However, in this study, the Laplace transform is served as a solution procuring technique, and series and integral form exact solutions are extracted for CPC and ABC derivative-based models, respectively. To interpret modifications in thermal and velocity patterns arising from diverse physical phenomena, numerous graphical depictions of exact solutions are communicated. Moreover, the implications of varying a number of critical factors, including the fractional parameter, nanoparticles' shapes and proportions, and radiation term, on shear stress and thermal productivity of the hybrid nanofluid are discussed using the tabulated findings. On comparing shape effects and individual suspensions of considered nanoparticles, it is observed that lamina shape and nickel nanoparticles are relatively more effective regarding the improvement of thermal performance. The model based on the CPC derivative yields lower profiles of temperature and flow functions as compared to the ABC derivative-based model. The results indicate that introducing homogeneous proportions of tantalum and nickel nanoparticles into mineral oil raises its heat-transferring capacity by up to 47.60%. These findings suggest that the examined hybrid nanofluid performs extremely well as a lubricant and a cooling agent. [ABSTRACT FROM AUTHOR]

During last decades the research of nanofluid is of great interest all over the World, particularly because of its thermal applications in engineering, and biological sciences. Although nanofluid performance is well appreciate and showed good results in the heat transport phenomena, to further improve conventional base fluids thermal performance an increasing number of researchers have started considering structured nanoparticles suspension in one base fluid. As to make an example, when considering the suspension of three different nanoparticles in a single base fluid we have the so called "ternary hybrid nanofluid". In the present study three different shaped nanoparticles are uniformly dispersed in blood. In particular, the three different shaped nanoparticles are spherical shaped ferric oxide Fe 3 O 4 , platelet shaped zinc Zn , and cylindrical shaped gold Au , which are considered in blood base fluid because of related advance pharmaceutical applications. Accordingly, we focused our attention on the sharp evaluation of heat transfer for the unsteady couple stress Casson tri-hybrid nanofluid flow in channel. In particular, we formulated the problem via momentum and energy equations in terms of partial differential equations equipped with realistic physical initial and boundary conditions. Moreover, we transformed classical model into their fractional counterparts by applying the Atangana–Baleanu time-fractional operator. Solutions to velocity and temperature equations have been obtained by using both the Laplace and the Fourier transforms, while the effect of physical parameters on velocity and temperature profiles, have been graphically analyzed exploiting MATHCAD. In particular, latter study clearly shows that for higher values of volume fraction ϕ hnf of the nanoparticles the fluid velocity declines, while the temperature rises for the higher values of volume fraction ϕ hnf of the nanoparticles. Using blood-based ternary hybrid nanofluid enhances the rate of heat transfer up-to 8.05%, spherical shaped Fe 3 O 4 enhances up-to 4.63%, platelet shaped Zn nanoparticles enhances up-to 8.984% and cylindrical shaped gold Au nanoparticles enhances up-to 10.407%. [ABSTRACT FROM AUTHOR]

The core devotion of this study is to develop a generalized model by means of a recently proposed fractional technique in order to anticipate the enhancement in the thermal efficiency of engine oil because of the dispersion of graphene and magnesia nanoparticles. In addition to investigating the synergistic attributes of the foregoing particles, this work evaluates shape impacts for column, brick, tetrahedron, blade, and lamina-like shapes. In the primary model, the flow equation is coupled with concentration and energy functions. This classical system is transmuted into a fractional environment by generalizing mathematical expressions of thermal and diffusion fluxes by virtue of the Prabhakar fractional operator. In this study, ramped flow and temperature slip conditions are simultaneously applied for the first time to examine the behavior of a hybrid nanofluid. The mathematical analysis of this problem involves the incorporation of dimension-independent parameters into the model and the execution of the Laplace transform for the consequent equations. By doing so, exact solutions are derived in the form of Mittag–Leffler functions. Multiple illustrations are developed by dint of exact solutions to chew over all aspects of temperature variations and flow dynamics. For the preparation of these illustrations, the details of parametric ranges are as follows: 0.00 ≤ Υ ≤ 0.04 , 2.0 ≤ G r 1 ≤ 8.0 , 0.5 ≤ S c ≤ 2.0 , 0.1 ≤ τ ≤ 4.0 , 0.1 ≤ d ≤ 0.6 , 0.2 ≤ λ 1 ≤ 1.5 , and 1.0 ≤ G r 2 ≤ 7.0 . The contribution of differently shaped nanoparticles, volume proportions, and fractional parameters in boosting the heat-transferring attributes of engine oil is also anticipated. In this regard, results for Nusselt number are provided in tabular form. Additionally, a brief analysis of shear stress is carried out for fractional parameters and various combinations of magnesia, graphene, and engine oil. This investigation anticipates that engine oil's hybridization with magnesia and graphene would result in a 33% increase in its thermal performance, which evidently improves its industrial significance. The enhancement in Schmidt number yields an improvement in the mass transfer rate. An increment in collective volume fraction leads to raising the profile of the thermal field. However, the velocity indicates a decreasing behavior. Nusselt number reaches its highest value ( N u = 8.1363 ) for the lamina shape of considered particles. When the intensity of the buoyancy force augments, it causes the velocity to increase. [ABSTRACT FROM AUTHOR]

An incredible eradication of thermal indulgence is required to enhance the flow and heat transfer enhancement in micro/nanofluidic devices. In addition, the rapid transport and instantaneous mixing of colloidal suspensions of metallic particles at nanoscale are exceptionally crucial at ascendency of inertial and surface forces. To address these challenges, the present work is intended to investigate the role of trimetallic nanofluid comprising of three kinds of nano-sized granules (titanium oxide, Silica and Aluminium dioxide) with pure blood through a heated micropump in the presence of inclined magnetic field and axially implemented electric field. To ensure rapid mixing in unidirectional flow, the pump internal surface is lined-up with mimetic motile cilia with slip boundary. The embedded cilia whip in pattern due to dynein molecular motion controlled by time and produce a set of metachronal waves along the pump wall. The shooting technique is executed to compute the numerical solution. In a comparative glance it is revealed that the trimetallic nanofluid exhibits 10% higher heat transfer efficiency as compared to bi-hybrid and mono nanofluids. Moreover, the involvement of electroosmosis results in almost 17% decrease in the heat transfer rate if it values jumps from 1 to 5. The fluid temperature in case of trimetallic nanofluid is higher and thus keeps the heat transfer entropy and the total entropy lower. Furthermore, involvement of thermal radiated and momentum slip significantly contribute in reducing heat losses. [ABSTRACT FROM AUTHOR]

This paper concentrated on the multiple generalized report of entropy generation of MHD Casson fluid via Caputo–Fabrizio (CF), Caputo (C), and Atangana–Baleanu (AB) fractional derivative. The ramped wall temperature on the plate while slipping condition on fluid velocity is considered. The mathematical model is made up of a collection of partial differential equations having physical boundaries. Triple fractional definitions are used to generalize the model and solve via joint Laplace and Zakian's numerical algorithm. The fractional results of entropy generation, velocity profile, temperature profile and Bejan number are also evaluated and compared for all three mentioned fractional operators as an objective of the present study. Entropy production can be maximize/ minimize through various physical parameters. The rate of heat transmission may be controlled by increasing the Prandtl number in isothermal temperature and boosting with the ramping wall temperature. It is indicated that Caputo model has maximum velocity and entropy generation in case of isothermal temperature besides Caputo–Fabrizio, and Atangana–Baleanu, while in case of ramped temperature, the phenomena is revised. The combined influence of slipping condition and ramped wall temperature rapidly boosts Casson fluid's velocity and entropy generation. [ABSTRACT FROM AUTHOR]

Electro-osmotic flow via a microchannel has numerous uses in the contemporary world, including in the biochemical and pharmaceutical industries. This research explores the electroosmotic flow of Casson-type nanofluid with Sodium Alginate nanoparticles through a vertically tilted microchannel. In addition, the transverse magnetic field is also considered. In this flowing fluid, the influence of heat and mass transmission is also explored. The aforementioned physical process is represented by partial differential equations. Utilizing suitable dimensionless variables for nondimensionalized. Furthermore, the non—dimensional classical system is fractionalized with the use of generalized Fourier and Fick's law. Generalizations are made using the Caputo derivative's description. The analytical solution of the velocity, temperature, and concentration profiles is obtained by combining the methods of Laplace and Fourier. Interestingly, the influence of several physical characteristics such as the fractional parameter, Casson fluid parameter, the thermal and mass Grashof numbers, and the zeta potential parameter is displayed. Moreover, the results show that the volume fractional of nanoparticles enhances the rate of heat transfer up to 39.90%, Skin friction up to 38.05%, and Sherwood number up to 11.11%. Also, the angle of inclination enhances the fluid velocity. [ABSTRACT FROM AUTHOR]

This article aims to study entropy generation and heat transfer due to free convection. Two types of base fluids (water and kerosene oil) are taken with a suspension of titanium alloy nanoparticles. An external magnetic field is applied in a perpendicular direction and the induced magnetic field is neglected. Scientific analysis is performed on magnetohydrodynamic flow through a Darcy medium. Free convection and the sudden motion of the heated plate cause the fluid to flow. The problem is formulated in terms of differential equations with associated physical conditions. Relations for entropy generation and Bejan numbers are also provided. The Laplace transform technique has been used for finding the exact solution to the problem. Results are plotted using Mathcad software and a comparison is made between water-titanium alloy and kerosene oil-titanium alloy nanoparticles for velocity, temperature, entropy generation, and Bejan number. It is concluded that kerosene oil base fluid has a greater velocity and temperature profile in all parametric studies as compared to water-based fluid. While in the case of entropy generation and Bejan number, near to the plate and for away the plate the behaver is distinct. Entropy generation and Bejan number are boosting up via using different base fluid. For larger estimation of Brinkman number, both Bejan number and entropy rate have the opposite effect. The volume fraction of nanofluid enhance the rate of heat transfer in case of both nanofluid. While the water base nanofluid enhance the rate of heat transfer up to 19.14% and kerosene oil base fluid is enhanced up to 30.01%. [ABSTRACT FROM AUTHOR]

In the present era of research, entropy generation is one of the most important topics, which is used to control the irreversibility phenomena during heat transfer. Due to the important application in engineering, atomic reactors and cooling process in different fields, this work aims to study the second law analysis of Casson fluid. Vertical plate geometry was considered, where the plate at the boundary exhibits arbitrary wall shear stress and the fluid lies above the plate. Exponential type heating was produced at the bounding plate whereas natural convection is caused because of buoyancy force. Magnetohydrodynamic (MHD) analysis was also considered perpendicular to the plate. The usual Darcy’s law of Newtonian fluid was modified to Darcy’s law for Casson fluid. The exact analysis was performed using the Laplace transform technique to establish exact solutions for the velocity field and temperature distribution. Results are interpreted physically using various plots and discussed in detail. [ABSTRACT FROM AUTHOR]

This article investigates graphite-aluminum oxide hybrid nanoparticles in water-base fluid with the addition of heat generation in the presence of a porous medium. The problem is formulated in terms of momentum and energy equations with sufficient initial and boundary conditions. The solution is investigated by using the Laplace transform method. It is observed that the velocity of the drilling fluid is controlled by adding hybrid nanoparticles as compared to simple nanofluids. In a similar way, the temperature of the fluid is reduced. Also, the heat transfer rate is boosted up to 37.40741% by using hybrid nanofluid compared to regular nanofluid. Moreover, the heat transfer rate was increased up to 11.149% by using different shapes of nanoparticles in the base fluid water. It is also observed that by using hybrid nanofluid skin fraction is boosted up at y = 0 and boosted down at y = 1. [ABSTRACT FROM AUTHOR]

In this paper, the mathematical models for flow and heat-transfer analysis of a non-Newtonian fluid with axisymmetric channels and porous walls are analyzed. The governing equations of the problem are derived by using the basic concepts of continuity and momentum equations. Furthermore, artificial intelligence-based feedforward neural networks (ANNs) are utilized with hybridization of a generalized normal-distribution optimization (GNDO) algorithm and sequential quadratic programming (SQP) to study the heat-transfer equations and calculate the approximate solutions for the momentum of a non-Newtonian fluid. Legendre polynomials based Legendre neural networks (LNN) are used to develop a mathematical model for the governing equations, which are further exploited by the global search ability of GNDO and SQP for rapid localization convergence. The proposed technique is applied to study the effect of variations in Reynolds number Re on the velocity profile (f ′) and the temperature profile (q) . The results obtained by the LeNN-GNDO-SQP algorithm are compared with the differential transformation method (DTM), which shows the stability of the results and the correctness of the technique. Extensive graphical and statistical analyses are conducted in terms of minimum, mean, and standard deviation based on fitness value, absolute errors, mean absolute deviation (MAD), error in the Nash–Sutcliffe efficiency (NSE), and root mean square error (RMSE). [ABSTRACT FROM AUTHOR]

Bioconvection has recently been the subject of dispute in a number of biotechnological fields that depend on fluids and their physical properties. When mixed nanofluids are subjected to heat and mass transmission, the process of bioconvection occurs. This attempt conveys the theoretical analysis of two-dimensional electrically conducting and magnetically susceptible binary fluid containing nanoparticles and gyrotactic microorganisms past a stratified stretching surface. Furthermore binary chemical reaction, thermal radiation, and activation energy are taken into assumptions. The analytical solution based on HAM has been performed. The convergence of HAM is presented with the help of figures. The present study is compared with previously published results and has established an excessive agreement which validate the present study. It is perceived that the presence and absence of an electric field influences the variations in fluid velocities due to presence of magnetic field. The micropolar constant heightens the velocity and microrotation of the fluid flow. The buoyancy parameter and bioconvection Rayleigh number diminish the velocity function while these parameters show dual impact on microrotation function. The skin friction and couple stress escalates with the increasing buoyancy ratio parameter and bioconvection Rayleigh number. [ABSTRACT FROM AUTHOR]

In this study, the effects of variable characteristics amalgamated with chemical reaction and Arrhenius activation energy are analyzed on a two-dimensional (2D) electrically conducting radiative Casson nanoliquid flow past a deformable cylinder embedded in a porous medium. The surface of the cylinder is deformable in the radial direction i.e., the z-axis. The impression of Soret and Dufour's effects boosts the transmission of heat and mass. The flow is analyzed numerically with the combined impacts of momentum slip, convective heat, and mass conditions. A numerical solution for the system of the differential equations is attained by employing the bvp4c function in MATLAB. The dimensionless protuberant parameters are graphically illustrated and discussed for the involved profiles. It is perceived that on escalating the velocity slip parameter and porosity parameter velocity field depreciates. Also, on escalating the radiation parameter and heat transfer Biot number a prominent difference is noticed in an upsurge of the thermal field. For growing values of Brownian motion and thermophoretic parameters, temperature field augments. On escalating the curvature parameter and porosity parameter, drag force coefficient upsurges. The outcome of the Soret number, mass transfer Biot number, and activation energy parameter is quite eminent on the concentration distribution for the sheet in comparison to the deformable cylinder. A comparative analysis of the present investigation with an already published work is also added to substantiate the envisioned problem. [ABSTRACT FROM AUTHOR]

The entropy generation for a reactive Williamson nanofluid flow past a vertical Riga system is the subject of this article. The effects of MHD, thermophoresis, nonlinear heat radiation and varying heat conductivity are modeled into the heat equation in the established model. Suitable similarity transformations are examined to bring down the partial differential equations into ordinary differential equations. The Homotopy analysis approach is used to solve the dimensionless transport equations analytically. The graphic information of the various parameters that emerged from the model is effectively collected and deliberated. The temperature field expands with thermophoresis, Brownian motion and temperature ratio parameters as the modified Hartmann number forces an increase in velocity, according to the findings of this analysis. With the increase in the fluid material terms, the entropy generation and Bejan number increase. Riga plate has numerous applications in improving the thermo-physics features of a fluid, the value of magnetic field embraces an important role in fluid mechanics. An external electric field can be used to control flow in weak electrically conductive fluids. The Riga plate is one of the devices used in this regard. It's a device that creates electromagnetic fields. They produce the Lorentz force which is a force that directs fluid flow. The authors have discussed the entropy optimization for a reactive Williamson nanofluid flow past a vertical Riga plate is addressed. This is the first investigation on mass and heat transfer flow that the authors are aware of, and no similar work has yet been published in the literature. A thorough mathematical examination is also required to demonstrate the model's regularity. The authors believe that the results acquired are novel and have not been plagiarized from any other sources. [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]

The numerical analysis of MHD boundary layer non-Newtonian micropolar fluid due to an exponentially curved stretching sheet is developed in this study. In the energy equation effects of viscous dissipation are included. For the mathematical description of the governing equations curvilinear coordinates are used. By utilizing exponential similarity variables, the modelled partial differential equations (PDEs) are reduced into ordinary ones. The resultant non-linear ODEs are numerically solved with two methods shooting and Keller box method. The study reveals that the governing parameters, namely, radius of curvature, material parameter, magnetic parameter, Prandtl number and Eckert number have major effects on the fluid velocity, micro-rotation velocity, surface friction, couple stress and heat transfer rate. The results indicate that the magnetic field diminishes the fluid velocity inside the hydrodynamics boundary layer whereas it enhances the temperature inside the thermal boundary layer. Microrotation profile decreases near the surface, as the magnetic parameter and radius of curvature increases but far away behavior is opposite. The material parameter enhances the velocity and microrotation profile whereas, opposite behaviors is noticed for the temperature distribution. Obtained outcomes are also compared with the existing literature and the comparison shows a good agreement with existing studies. [ABSTRACT FROM AUTHOR]

The first author Muhammad Arif appreciates the support provided by Petchra Pra Jom Klao Ph.D. Research Scholarship (Grant No. 14/2562 and Grant No. 25/2563)." The first author Muhammad Arif appreciate the support provided by Petchra Pra Jom Klao Ph.D. Research Scholarship (Grant No. 14/2562 and Grant No. 25/2563)." now reads: "The authors acknowledge the financial support provided by the Center of Excellence in Theoretical and Computational Science (TaCS-CoE), KMUTT. [Extracted from the article]