Nanoparticle Volume Fraction Parameter Research Articles

Unsteady Magneto-radiative Flow of Copper-water Nanofluid Over an Exponentially Stretching Surface

Understanding the complex behavior of fluid flows under various physical influences is crucial for advancing engineering and industrial applications. This paper presents the investigation of the unsteady, incompressible, single-phase magneto-radiative flow of a copper-water nanofluid over an exponentially stretching surface, considering the effects of viscous dissipation and temperature-dependent heat sources. This model, proposed in the present analysis, is based on fundamentals of the continuity and Navier–Stokesequations with mass conservation. Further, use of a similarity transformation will reduce the equations to dimensionless form and provide a numerical solution using the Runge–Kutta–Fehlberg method. In physics, engineering, and industrial applications, the most interesting parameters are the velocity, temperature, skin friction, and the Nusselt number (Nu). The results of this study are compared with previous works, showing significant agreement with findings under similar conditions. The analysis reveals that both temperature and velocity boundary layer increase when all very specific effects of radiation (R), heat source (Q), copper nanoparticle volume fraction, and magnetic field strength parameter are present. On the other hand, it is found that skin friction increases when considering both copper nanoparticle volume fraction and magnetic field strength parameter, but the Nu decreases if R, Q, copper nanoparticle volume fraction, and magnetic field strength parameter are the factors responsible for that. These outcomes will be further delineated through graphics and be elaborated in engineering and industrial context.

The significance of magnetized thermal radiation on the magnetohydrodynamic (MHD) behavior of Williamson hybrid ferrofluids over a stretching sheet

The goal of this study is to investigate the fluid dynamics of a pseudoplastic Williamson nanofluid model, explicitly focusing on blood infused with magnetite (Fe2O3) and (Cu) copper nanoparticles, with the aim of enhancing its physiological and industrial applications. This research offers a novel approach by integrating the Williamson fluid model with magnetic nanoparticles, which has not been widely explored in biomedical applications like antitumor therapy and magnetic hyperthermia. The study is mathematically modeled using partial differential equations (PDEs) accounting for the deformation vortices of a stretching surface. These governing equations are transformed into ordinary differential equations (ODEs) via similarity transformations and solved numerically using the Runge-Kutta (R-K) 4th-order method coupled with the shooting technique. The velocity and temperature fields are then analyzed through MATLAB simulations. Results indicate that increasing the Williamson, radiation, and nanoparticle volume fraction parameters elevates the fluid temperature, whereas higher magnetic field strength, Prandtl number, and stretching parameter values reduce it. The novelty of this work lies in its application of the Williamson nanofluid model to real-time medical applications, such as cancer treatment through magnetic hyperthermia, and its potential use in advanced biomedical devices.

Analyzing thermal performance and entropy generation in time-dependent buoyancy flow of water-based over rotating sphere with ternary nanoparticle shape factor

Abstract The heat transfer augmentation, solar power systems, medical equipment, semiconductor cooling, aerospace, and automotive industries all use ternary hybrid nanofluids (Thnf). The current study is mainly about a magnetized Thnf flow that can't be squished around a spinning sphere that has different viscosity, thermal conductivity, and shape (brick, platelets, cylinder, blade). The heat transport simulation incorporates the principles of viscous dissipation and joule heating. Water is mixed with silver, magnesium oxide, and iron trioxide to make the ternary hybrid nanofluid. Similarity substitution converts model equations to ordinary differential equations (ODEs). Runge-Kutta fourth order numerically estimates the non-dimensional set of ODEs. For certain emergent parameters, velocity, temperature, entropy generation, Nusselt number, and skin friction are computed and analyzed. The research shows that entropy generation increases with brinkman number, nanoparticle volume fraction and magnetic parameters and reduces with temperature difference parameter. Increasing the unsteadiness parameter upsurges velocity in the x-direction, but decreases it in the z-direction and temperature curve. Skin friction upsurges in the x-direction and declines in the z-direction with rotation. Platelet-shaped nanoparticles usually outperform blade, brick, and cylinder shapes. When mass suction $( S )$ is elevated from 1.0 to 2.0, the heat transfer rate increases by 47.25% for the Brick form, 47.26% for the Platelets shape, 35.08% for the Cylinders shape, and 37.65% for the Blades shape. Comparing the results to prior literature shows excellent agreement.

EMHD flow and heat transport in cross ternary nanofluid with gyrotactic microorganisms: A case study on thermophoretic particle deposition

The study of ternary nanofluids has gained significant interest in engineering and biomedical applications due to their enhanced thermal conductivity and heat transfer properties. This research specifically focuses on electromagnetic hydrodynamic (EMHD) flow and heat transport in cross-flow ternary nanofluids containing gyrotactic microorganisms, where thermophoretic particle deposition plays a key role. Efficient thermal management and targeted particle deposition are crucial in advanced applications, including solar collectors and biomedical devices. This research presents a comprehensive investigation into the Marangoni convective flow of kerosene oil containing ternary nanoparticles Gra,MgO,andSiO2 over a sheet with significant impact of thermal conductivity varies linearly with temperature. Also, the work utilized the Cross model to capture the shear-thinning features of TNFs, describing their non-Newtonian performance. System of PDEs are achieved and reduced to ODEs using appropriate variables. The spectral collocation method based on Appell-Changhee polynomials was utilized to solve ODEs. The results show that the thermal distribution improves for growing values of exponential heat source and thermal radiation parameter. An increase in the nanoparticle volume fraction parameter reduces the velocity distribution, while the temperature distribution displays an opposite effect. These findings support applications in bioengineering and medical technologies, where precise control of flow and thermal properties is essential.

Dual characteristics of mixed convection flow of three-particle aqueous nanofluid upon a shrinking porous plate

PurposeThis study aims to analyze the thermo-hydrodynamic characteristics for the mixed convection boundary layer flow of three-particle aqueous nanofluid on a shrinking porous plate with the influences of thermal radiation and magnetic field.Design/methodology/approachThe basic equations have been normalized with the help of similarity transformations. The obtained equations have been solved numerically using the shooting method in conjunction with the sixth-order Runge–Kutta technique. Numerical results for the velocity and temperature are illustrated with varying relevant parameters.FindingsThe results reveal that the local drag coefficient increases with higher values of the magnetic field parameter, nanoparticle volume fraction and suction parameter. On the other hand, boosting the radiation parameter and nanoparticle concentration notably enhances heat transfer. Furthermore, it is noted that the suction parameter and magnetic field parameter both lead to an increase in velocity and promote the occurrence of dual solutions within the problem conditions.Research limitations/implicationsThe limitations are that the model is appropriate for thermal equilibrium of base fluid and nanoparticles, and constant thermo-physical properties.Originality/valueTo the best of the authors' knowledge, no study has taken an attempt to predict the flow and heat transfer characteristics of unsteady mixed convection ternary hybrid nanofluid flow over a shrinking sheet, particularly under the influence of magnetic field and radiation. The findings obtained here may hold particular significance for those interested in the underlying theoretical and practical implications.

Characterizing magnetohydrodynamic effects on developed nanofluid flow in an obstructed vertical duct under constant pressure gradient

Abstract This research endeavors to conduct an examination of the thermal characteristics within the duct filled with the copper nanoparticles and water as base fluid. In exhaust systems, like car exhausts, chimneys, and kitchen hoods, duct flows are crucial. These systems safely discharge odors, smoke, and contaminants into the atmosphere after removing them from enclosed places. The study focuses on a laminar flow regime that is both hydrodynamically and thermally developed, with a specified constraints at any cross-sectional plane. To address this, we employ the finite volume method as it stands as a judicious choice, offering a balance between computational efficiency and solution accuracy. Notably, we have observed that the deceleration of flow induced by elevated Rayleigh numbers can be effectively regulated by the application of an appropriately calibrated external magnetic field. The prime parameters of the problem with ranges are: pressure gradient ( 1 ≤ p 0 ≤ 100 ) (1\le {p}_{0}\le 100) , Hartmann number ( 0 ≤ Ha ≤ 50 ) (0\le \text{Ha}\le 50) , Rayleigh number ( 1 , 000 ≤ Ra ≤ 40 , 000 ) (1,000\le \text{Ra}\le 40,000) , and magnetic parameter ( 0 ≤ M ≤ 50 ) (0\le M\le 50) . Furthermore, our analysis reveals that the Nusselt number exhibits a nearly linear correlation with the nanoparticle volume fraction parameter, a trend observed across a range of Rayleigh numbers and magnetic parameter values. We have noted that a mere 20% nanoparticle volume fraction can result in up to 62% rise in the Nusselt number while causing an almost 50% decrease in the factor f Re. This research framework serves as a robust foundation for understanding the intricate interplay between magnetic influences and thermal-hydraulic behavior within the delineated system.

Comparative approach of Darcy–Forchheimer flow on water based hybrid nanofluid ([formula omitted]) and mono nanofluid ([formula omitted]) over a stretched surface with injection/suction

The hybrid nanofluids are crucial for enhancing heat transfer efficiency in different technological and industrial operations like nuclear reactor cooling, fuel cells, drug delivery systems, etc. Taking this factor into account, the current investigation focused on the MHD Darcy–Forchheimer flow of water-based hybrid nanofluid (Cu-Al2O3) and mono nanofluid (Cu) past a stretched surface with injection/suction. Additionally, the investigation focuses on analyzing the consequences of nonlinear thermal radiation and heat consumption/generation. The governing higher-order PDEs are rehabilitated into ODEs through a suitable transformation process. Finally, we solve these equations using the quantitative approach of the Bvp4c algorithm in MATLAB and visualize the results in tables and graphs. Our study revealed that the intensified magnetic field, porosity, and injection/suction parameters suppress the fluid velocity. The fluid heat is enhanced when intensifying the radiation, and nanoparticles volume fraction parameters. Augmenting the magnetic field parameter results in a reduction in the skin friction coefficient. It is also found that the highest dwindling percentage of the skin friction coefficient is 24% (HNF), 33.38% (NF), and 25.70% (VF) when the magnetic field parameter changes from 0 to 1. The largest growing percentage of the local Nusselt number is 34.02% (HNF), 36.75% (NF) and 39.52 (VF), which occurs when the suction/injection parameter is modified from −0.3 to 0.

The Effect of a Riga Plate On Casson Hybrid Nanofluid Flow Along a Stretching Cylinder with an Exponential Heat Source and Thermal Radiation

This study investigates the effect of a Riga plate on the flow characteristics of a Casson hybrid nanofluid through a stretching cylinder embedded in a porous medium in the presence of an exponential heat source and thermal radiation. This model is used toexplore the potential applications of this analysis in the fields of cancer treatment and wound healing. The governing partial differential equations are converted into a system of nonlinear ordinary differential equations using suitable similarity transformations. The governing partial differential equations (PDEs) were reduced to ordinary differential equations (ODEs) using similarity variables, and the heat transfer phenomena, fluid flow dynamics, and nanoparticle behavior in the base fluid were captured through numerical analysis. The Casson fluid model was used to capture the non-Newtonian characteristics of blood-like fluids in the circulatory system, and stretching was employed to mimic the blood vessel. The modeling involved incorporating thermal radiation (Ra) and an exponential heat source, which are encountered in cancer treatment. The Runge-Kutta order 4 with shooting technique was used to obtain numerical solutions of the governing equations, and the effects of the Casson fluid parameter, curvature parameter, nanoparticle volume fraction, Eckert number, and radiation parameter were analyzed. The results showed that the Riga plate affected the flow patterns by increasing the temperature, and the temperature distribution was improved by increasing the radiation parameter and nanoparticle concentration. The insights from this study could be used to optimize heat-based treatments for cancer and wound healing, where control of fluid dynamics and heat transfer processes is critical.

Hybrid carbon nanotubes flow and heat transfer over a vertical thin needle with suction effect: A numerical and optimisation analysis

The present study aims to provide a numerical and optimisation analysis of the hybrid carbon nanotubes flow over a vertical thin needle under the suction effect. The thin needle is suspended in water-based hybrid nanofluids containing a combination of single- and multi-walled carbon nanotubes. The heat is transported using the mixed convection flow. A mathematical model of partial differential equations (PDEs) is developed subject to boundary conditions. The PDEs system is converted to non-dimensional ordinal differential equations (ODEs) by using the similarity solution method. Then, the first order of the ODEs system is solved in a MATLAB bvp4c function. We innovatively carry out an optimisation process using response surface methodology (RSM) to enhance the efficiency of the numerical experiment data and fill a gap in the optimised analysis. To observe the variation solutions for the reduced skin friction and heat transfer coefficients, several parameters, such as the mixed convection and suction parameters, are altered into several values. The solutions are essential for accurately forecasting the occurrence of boundary layer separation, particularly in the case of dual solutions. Our analysis reveals that the model generates multiple solutions for the opposing flow, and the boundary layer separates slowly due to the suction effect. To complete the research, RSM reveals that the highest value of the nanoparticle volume fraction and suction parameters, as well as the smallest value of the needle size, generate the maximum transmitting heat through the slender needle. Furthermore, both the numerical and RSM results show that hybrid carbon nanotubes perform better than mono‑carbon nanotubes for better practical reference.

Time-Depending Flow of Ternary Hybrid Nanofluid Past a Stretching Sheet with Suction and Magnetohydrodynamic (MHD) Effects

This research examines the laminar magnetohydrodynamic (MHD) flow of a mixture of three different nanoparticles, known as a ternary hybrid nanofluid, over a permeable stretching sheet. In this analysis, we are considering a permeable stretching sheet that is decelerating, with unsteadiness parameter . The governing equations are turned into similarity equations by utilizing appropriate similarity transformations. The MATLAB software is then employed to program the code, utilizing the bvp4c function. The skin friction and heat transfer coefficients plots, along with velocity and temperature profiles, are delivered for various values of the suction, unsteadiness, magnet, and nanoparticle volume fraction parameters. According to the numerical findings, both unsteadiness and suction parameters play roles in boosting the heat transfer rate. Nevertheless, the heat transfer rate is reduced by the augmentation of magnetic parameter.

Effect of slip boundary conditions on unsteady pulsatile nanofluid flow through a sinusoidal channel: an analytical study

A novel analysis of the pulsatile nano-blood flow through a sinusoidal wavy channel, emphasizing the significance of diverse influences in the modelling, is investigated in this paper. This study examines the collective effects of slip boundary conditions, magnetic field, porosity, channel waviness, nanoparticle concentration, and heat source on nano-blood flow in a two-dimensional wavy channel. In contrast to prior research that assumed a constant pulsatile pressure gradient during channel waviness, this innovative study introduces a variable pressure gradient that significantly influences several associated parameters. The mathematical model characterising nano-blood flow in a horizontally wavy channel is solved using the perturbation technique. Analytical solutions for fundamental variables such as stream function, velocity, wall shear stress, pressure gradient, and temperature are visually depicted across different physical parameter values. The findings obtained for various parameter values in the given problem demonstrate a significant influence of the amplitude ratio parameter of channel waviness, Hartmann number of the magnetic field, permeability parameter of the porous medium, Knudsen number due to the slip boundary, volume fraction of nanoparticles, radiation parameter, Prandtl number, and heat source parameters on the flow dynamics. The simulations provide valuable insights into the decrease in velocity with increasing magnetic field and its increase with increasing permeability and slip parameters. Additionally, the temperature increases with increasing nanoparticle volume fraction and radiation parameter, while it decreases with increasing Prandtl number.

Entropy analysis of Hall effect with variable viscosity and slip conditions on rotating hybrid nanofluid flow over nonlinear radiative surface

PurposeWith possible uses in engineering and industrial processes, this work aims to further our knowledge of fluid dynamics and heat transfer in complicated flow configurations. This study looks at how Al2O3−Cu/H2O hybrid nanofluids move across a nonlinear radiative 3D unsteady surface. It tries to figure out what happens when the Hall current, variable viscosity, viscous dissipation, velocity and thermal slip conditions work together. The goal of this analysis is to provide insight into the system's thermodynamic behavior and the ways in which these elements affect the flow's entropy generation. MethodologyThe controlling system is converted into nonlinear nondimensional partial differential equations (PDEs) by applying suitable non-similar transformations. In this work, the governing equations are simulated using the local non-similarity (LNS) approach up to the second truncation level using the numerical technique bvp4c in MATLAB. FindingsThe temperature, velocity, entropy production, skin friction in both directions, and Nusselt number profiles of the nanofluid and hybrid nanofluid are detailed in many figures. The tabular form contains the results of computing the local Nusselt number for linear, nonlinear, and radiation-free scenarios. The velocity profiles in both directions and the temperature profile grow as the rotation parameter and nanoparticle volume fraction parameter increase. Conversely, the velocity profiles drop when the variable viscosity parameter falls, while the temperature profile increases. When the unsteadiness parameter A is set to 0.5 and the nanoparticle volume fraction is 1%, hybrid nanofluid has 4.26% lower x-direction skin friction than nanofluid and 3.62% greater y-direction friction. When the unsteadiness parameter A = 0.5 and the nanoparticle volume percentage is 1%, a hybrid nanofluid has a 2.77% higher Nusselt number than a nanofluid. The generation of entropy was also enhanced by an increase in the volume fraction of nanoparticles, radiation, temperature ratio, and Brinkman number. We evaluate and contrast the results of this study with those of earlier research.

Numerical analysis of non-linear radiative Casson fluids containing CNTs having length and radius over permeable moving plate

Abstract Casson fluids containing carbon nanotubes of various lengths and radii on a moving permeable plate reduce friction and improve equipment efficiency. They improve plate flow dynamics to improve heat transfer, particularly in electronic cooling and heat exchangers. The core objective of this study is to investigate the heat transmission mechanism and identify the prerequisites for achieving high cooling speeds within a two-dimensional, stable, axisymmetric boundary layer. This study considers a sodium alginate-based nanofluid containing single/multi-wall carbon nanotubes (SWCNTs/MWCNTs) and Casson nanofluid flow on a permeable moving plate with varying length, radius, and nonlinear thermal radiation effects. The plate has the capacity to move either parallel to or perpendicular to the free stream. The governing partial differential equations for the boundary layer, which are interconnected, are transformed into standard differential equations. These equations are then numerically solved using the Runge–Kutta fourth-order scheme incorporated in the shooting method. This research analyses and graphically displays the effects of factors including mass suction, nanoparticle volume fraction, Casson parameter, thermal radiation, and temperature ratio. Additionally, a comparison is made between the present result and the previous finding, which presented in a tabular format. The coefficient of skin friction decreases in correlation with an increase in Casson fluid parameters and Prandtl number. Heat transfer rate decreases with a variation in viscosity parameter, while it is increasing with an increase in Prandtl number. In addition, this study demonstrates that heat transfer rate for MWCNT is significantly higher than that of SWCNT nanoparticles. Thermal radiation and temperature ratio reduce the heat transfer rate, whereas nanoparticle volume fraction and Casson parameter enhance it over a shrinking surface.

Pulsatile nanofluid flow with variable pressure gradient and heat transfer in wavy channel

This research contributes to the comprehension of nanofluid behaviour through a wavy channel, emphasizing the significance of considering diverse influences in the modelling process. The study explores the collective influence of pressure gradient variation, magnetic field, porosity, channel waviness, nanoparticle concentration, and heat transfer on nano-blood flow in a two-dimensional wavy channel. In contrast to prior research assuming a constant pulsatile pressure gradient during channel waviness, this innovative study introduces a variable pressure gradient, significantly influencing several associated parameters. The mathematical model characterizing nano-blood flow in a horizontally wavy channel is solved using the perturbation technique. Analytical solutions for fundamental variables such as stream function, velocity, wall shear stress, pressure gradient, and temperature are visually depicted across different physical parameters values. The findings obtained for differing parameter values in the given problem demonstrate a significant influence of the amplitude ratio parameter of channel waviness, Hartmann number of the magnetic field, permeability parameter of the porous medium, volume fraction of nanoparticles, radiation parameter, Prandtl number, and the suction/injection parameter on the flow dynamics. The simulations provide valuable insights into the decrease in velocity with increasing magnetic field and its increase with higher permeability. Additionally, the temperature is observed to escalate with a rising nanoparticle volume fraction and radiation parameter, while it declines with increasing Prandtl number.

Newtonian Heating on Casson Mixed Convection Transport by Ternary Hybrid Nanofluids over Vertical Stretching Sheet: Numerical Study

Numerous physical characteristics occurring from the structure and micro-motions of fluid nanoparticles can be examined using the governing models of nanofluids. Also, It can describe the demeanor of a vast field of actual fluids. This achieved a significant turn in the enhancement of heat transfer that improves manufacturing and engineering modernization. Depending on that, the assumptions that form our aims are numerically examining energy transport and heat transfer via Casson ternary hybrid nanofluids that contain the states of combined convection flow over a vertical stretching sheet. Also, Newtonian heating boundary conditions and magnetohydrodynamics (MHD) effects are investigated. Mathematical models (governing equations) that emulate and construct the conduct of these boosted ternary hybrid nanofluids are formed by developing the Tiwari and Das models. These governing equations are converted to partial differential equations (PDEs) employing appropriate substitutions. An accurate and efficient method called the Keller box numerical method is executed to get outcomes to the physical model. These numerical calculations are found and presented by employing MATLAB codes, to acquire tables of numerical outcomes, and graphic exhibits, which provide the impacts of important parameters on the physical quantities supporting heat transfer. Furthermore, the new results, in the Newtonian fluid case, were compared with prior literature, which were in excellent agreement. The studied problem parameters are examined at a Casson parameter domain of 1 to 5, a mixed convection parameter domain of -1 to 3, a conjugate parameter of 0.2 to 1, a magnetic parameter domain of 0.1 to 5, and a nanoparticle volume fraction parameter of 0.001 to 0.008. The numerical consequences deduced that the local skin friction rises when the conjugate and mixed convection parameters are increased. But the opposite case happens when the effects are obtained for the nanoparticle volume fraction, magnetic, and Casson parameters. Also, the Nusselt number rises with growing nanoparticle volume fraction and Casson parameters.

Numerical Investigation of Three-Dimensional Magnetohydrodynamic Flow of Ag 􀀀 H2O Nanofluid Over an Oscillating Surface in a Rotating Porous Medium

Objective: To investigate the three-dimensional flow of a nanofluid (Ag-water) over a stretchable vertical oscillatory sheet. This study involves considering fluctuating temperatures on the sheet and comparing them to the free stream temperature. The formulation of the unsteady boundary layer equations leading to the flow of nanofluid also takes into consideration the occurrence of the heterogeneous-homogeneous chemical reaction and thermal radiation. Method: The governing equations and the boundary conditions have been derived in a dimensionless form by using the appropriate transformations, and they are then solved using an EFDS (Explicit Finite Difference Scheme) in Matlab software. The Von-Neumann stability analysis is used to determine the method’s stability requirements for constant sizes of the grid. Findings: The physical factors impact on the concentration fields, temperature distribution, and velocity distribution were obtained and are studied by graphs and described in extensive detail. Convergence and stability requirements are attained in order to achieve accurate solutions. Novelty: In this study fluctuations in the temperature and stretching velocity of sheet on three-dimensional magnetohydrodynamic flow of Ag − H2O nanofluid over an oscillating surface through rotating porous are taken into account. Impacts of porous media permeability, velocity slip, magnetic fields, nanoparticle volume fraction, heat radiation, rotation, and homogeneous and heterogeneous chemical reaction parameters had all been attempted to be determined. Keywords: Oscillatory Surface, Heat transmission, Nonlinear PDE, Explicit Finite Difference Scheme, Nanoparticle

Analysis of mixed convective stagnation point flow of hybrid nanofluid over sheet with variable thermal conductivity and slip Conditions: A Model-Based study

This research looks at the stagnation point flow of MHD Al2O3-Cu/H2O hybrid nanofluid against a permeable, vertically extending surface that uses thermal radiation and how different models of thermal conductivity affect it. This study is unique because it looks at how changes in thermal conductivity, mixed convection, and the slip velocity of hybrid nanofluids affect the stretching surface. It also looks at how changes in temperature, skin-friction coefficient, Nusselt number, and velocity affect convective thermal boundary conditions. With the use of boundary layer approximations, the complicated system of PDEs is simplified. The dimensionality of these PDEs and the boundary conditions they include are eliminated by applying certain modifications. Combining a local non-similarity approach up to the second truncation level with MATLAB's built-in finite difference code (bvp4c), one can obtain the results of the updated model. The research demonstrates and analyzes the impact of different factors on fluid flow and heat transfer characteristics in the studied flow situations. This is done by comparing the computed data with available literature and presenting the findings in graphical form. Tables are generated to present the numerical fluctuations of the drag coefficient and Nusselt number. This study shows how important thermal conductivity is in the mixed convection of hybrid nanofluids and looks into what happens when the thermal conductivity parameter is changed. Significantly, an augmentation in this parameter results in an elevation in the temperature distribution of the hybrid nanofluid while simultaneously reducing the rate of heat transfer across various models. Furthermore, increasing the nanoparticle volume fraction parameter leads to higher temperature and Nusselt number profiles while reducing skin friction. The mixed convection parameter has a notable impact on increasing the friction coefficient on the stretched vertical surface. However, because these elements function as regulating variables, it decreases when the magnetic, mass suction, and velocity slip parameters are present. The results also demonstrate notable discrepancies in the mean Nusselt values generated by various thermal conductivity models. According to the analysis, the Hamilton-Crosser model has the lowest average Nusselt numbers, followed by the Yamada-Ota model and the Xue model, in that order.

The lie group analysis method for heat transfer in steady boundary layer flow field of nanofluid

In order to reveal the mechanism of the abnormal movement (Brownian motion enhances thermal scattering) of nanoparticles on the fluid enhanced heat transfer, the two-phase model was used to study the abnormal convection and diffusion of viscous nanofluids in the flat boundary layer of porous medium. Firstly, for the two-dimensional steady boundary layer stagnation point flow of incompressible Newtonian-nanofluids, the nonlinear governing equations of the flow field and temperature field of nanofluids are established from the Oberbeck-Boussinesq approximate equations. Secondly, the modern Lie group analysis method is introduced, we give the Lie symmetry determining equation of the flow field partial differential equations and the characteristics of the solutions. Further, using the relationship between the Lie symmetries and the conserved quantities, the conservation vector form of the flow field and the group invariant solution are derived in detail, and the reduced order model of the nanofluid flat boundary layer is obtained. Finally, the correctness of the analytical results obtained by the Lie group method was verified for different values of the flow parameter Prandtl. Research has shown that the Lie group method can be used to analytically solve the velocity and temperature distribution functions of abnormal motion of nanoparticles. The fluid temperature increases with the increase of the volume fraction parameter of nanoparticles, but decreases with the increase of the Prandtl value of the base fluid, and decreases with the increase of the plate stretching speed. The Lie group analysis method in this paper provides reference value for numerical simulation solutions of various heat and mass transfer in nanofluids.

Numerical Solution of Falkner-Skan Equation for a Moving Wedge in Hybrid Nanofluids

The flow and heat transfer past a moving wedge in a hybrid nanofluid is studied. A set of governing equations is transformed into ordinary differential equations using the similarity transformation. The resulting equations are then solved using bvp4c solver in MATLAB. The effects of the wedge angle parameter and nanoparticle volume fraction parameter of Al2O3-Cu/water on the skin friction coefficient and heat transfer characteristics are investigated. It is found that increasing the wedge angle parameter and Cu nanoparticles volume fraction gives rise to the skin friction coefficient and heat transfer on the surface. Further, dual solutions exist when the wedge moves in the opposite direction with the free stream.

Effect of interface layer on the enhancement of thermal conductivity of SiC-Water nanofluids: Molecular dynamics simulation

To investigate the impact of interfacial layer effects on the thermal conductivity of nanofluids and the microscopic mechanisms of enhanced thermal conductivity, this study employed non-equilibrium molecular dynamics to compute the thermal conductivity, number density, radial distribution function, and mean square displacement distribution of SiC nanofluids. The impact of nanoparticle volume fraction and particle size parameters on the thermal conductivity of nanofluids and the structure of interfacial adsorption layers was discussed. The simulation calculation results show that the coefficient of thermal conductivity of nanofluid is positively related to the volume fraction of nanoparticles, increasing from 0.6529 W/(m·K) to 0.8159 W/(m·K), and the enhancement of thermal conductivity by the volume fraction can be up to 33.97 %. The thermal conductivity is inversely correlated with the change in particle size, and the maximum improvement in thermal conductivity by particle size can reach up to 12.05 %. The simulated results of the thermal conductivity of nanofluid are almost consistent with the predicted results of the Yu&Choi model, and the error is controlled within 5 %. Simultaneously, the thickness of the interfacial adsorption layer decreases with an increase in particle size. This reduction arises due to larger particles having a smaller specific surface area, resulting in fewer particle surfaces covered by the interface layer. Moreover, the impact of particle size on the arrangement and affinity of molecules within the interface layer contributes to this decrease. Overall, interface layer effects exhibit a dual impact on the thermal conduction of nanofluids. The structured formation and high-density distribution of the adsorption layer contribute to enhanced heat transfer, while thermal resistance between nanoparticle surfaces and the fluid restricts heat transmission.