Maxwell Nanofluid Research Articles

Analysis of Entropy Optimization in MHD Flow of Non-Newtonian Nanofluids with Chemical Reaction and Thermal Energies

Investigation of nanofluid flows under various conditions is becoming fascinating research due to its numerous applications in many science and engineering fields such as solar energy, geothermal energy, water purification, glass blowing, enhanced oil recovery, petroleum production and food processing. For the present requirements in thermal energy applications, this mathematical model is considered to explore the diffusion and heat source effects on the flow of conductive Casson and Maxwell nanofluids in a porous medium on an elongating sheet with a chemical reaction. Further, the effects of viscous dissipation and thermal radiation are also examined. Moreover, the entropy generation is analyzed since this approach is employed in solar energy exchangers. The governing equations and the corresponding boundary conditions are constructed. This system of partial differential equations (PDEs) is changed into a system of nonlinear ordinary differential equations (ODEs) with the help of a suitable transformation and then solved numerically by the bvp5c MATLAB package. The influences of the physical parameters on the flow phenomena are discussed and presented through figures and tables. This analysis explains that the Casson fluid flow has a higher velocity field than the Maxwell fluid flow. The Nusselt number becomes higher as the Dufour numbers increase. It has also been noticed that increasing the Brinkmann number improves the entropy and, an increase in radiation enriches the temperature profile. The concentration of the fluid is decreased for the increasing values of the higher-order chemical reaction parameter. Furthermore, comparisons of the current results were conducted for limiting examples of the problem and found to be in good agreement with existing results in the literature.

The Upshots of Dufour and Soret in Stretching Porous Flow of Convective Maxwell Nanofluid with Nonlinear Thermal Emission

In this paper, the combined upshot of Soret and Dufoue of a convective Maxwell nanofluid on a porous perpendicular surface with nonlinear thermal emission was investigated. In the present work, the impact of permeable stretching sheet, nonlinear thermal emission, heat sour sink, Dufour and Soret effect, chemical reaction, Brownian motion and thermophoresis in a convective Maxwell nanofluid flow is widely discussed. The governing equations derived for the problem are highly nonlinear coupled partial differential equations. The governing equations were transformed into ordinary differential equations using Lie symmetry group alterations. The BVP4C MATLAB solver was employed to solve the ordinary differential equations numerically after validating the convergence of the method with existing results in the literature. The numerical results were established and discussed using tables and graphs. It was found that variations in porosity parameter (K), Dufour (Du) and Soret (Sr) improves velocity, temperature and concentration profiles respectively and the present of nonlinear thermal radiation and heat source emit more heat for the flow. Also, it is exciting to report that both porosity (K) and Dufour (Du) parameters has a strong impact on the flow of skin frictions, Nusselt number and Sherwood number. However, the current results may present applications in the areas of petroleum reservoir, heat exchangers, steel industries, cooling applications, nuclear waste disposal and so on.

Numerical study of Maxwell nanofluid flow with MWCNT and SWCNT considering quartic autocatalytic reactions and Thompson-Troian slip mechanism

The impact of the Thompson and Troian slip restrictions on continuous nanofluid flow, including CNTs near the stagnation point with constricting/enlarging surfaces, examined using a mathematical model. Engine oil is utilized as the base liquid, and both single-wall (SWCNTs) and multi-wall (MWCNTs) carbon nanotubes are taken into consideration. A Darcy-Forchheimer permeable medium and quartic autocatalysis, a chemical reaction for MHD stagnation point flow, are used to study the heat and flow characteristics of non-Newtonian flow. The original mathematical model is also expanded to include the impact of buoyancy forces. The numerical solution of non-dimensional velocity, temperature, and concentration profiles is obtained using the MATLAB-created bvp4c function, which employs the three-stage Lobatto IIIa formula. In the limited case, the validity of the recommended mathematical model is assessed by comparison with published work. A strong consensus is reached in this regard. Many dimensionless flow parameters, including the velocity slip parameter, the inertial coefficient, solid volume fraction, magnetic parameter, and the velocity parameter, have graphical representations that illustrate their behavior. Surface drag force estimates are presented to analyze the consequences on the extended surface. It has been demonstrated that increasing the slip velocity parameter boosts fluid flow speed while reducing surface drag. The efficiency of local thermal transmission decreases as the endothermic/exothermic coefficient rises. The altering viscosity factor for nanofluids causes an increase in axial velocity while a decrease in temperature distribution. Engine oil enriched with MWCNT and SWCNT can improve the thermal conductivity and viscosity of lubricants, leading to reduce wear and tear and better engine performance as well. Furthermore the incorporation of quartic autocatalytic reactions can enhance chemical processes that rely on catalysis, improving reaction rates. Also it has diverse applications in the system of cooling devices, manufacturing and material processing and heat transfer systems. It is revealed through this study that the system is shown to moderately cool off as measured by the solid volume ratio and heat generation. The velocity ratio parameter and the thermal expansion parameter had opposing outcomes on the system’s internal heat transfer mechanism.

Channel flow dynamics of fractional viscoelastic nanofluids in molybdenum disulphide grease: A case study

Nanoscopic fluids especially viscoelastic Nanofluids are very useful in engineering and industrial problems. This research is to determine the open channel flow of a viscoelastic nanofluid (namely Oldroyd-B (OBNF)). Oldroyd-B fluid (OBF) was used as the base fluid and molybdenum disulphide nanopatrials were added in the fluid to form desired OBNF. To convert the mathematical model to a fractional model from a classical order partial differential equation PDE, fractional type derivative named Caputo-Fabrizio (CF) was used. The main objective of this study is to find the exact mathematical solution for the temperature, concentration and velocity distributions by using integral transformation technique. Final results are discussed graphically for the influence of different parameters on calculated temperature, concentration and velocity. Skin friction of the said fluid and engineering related dimensionless numbers including Reynolds number (Re), Prandtl number (Pr), Grashof number (Gr) and Schmidt number (Sc) are also discussed. At the end a comparison is illustrated in graphical form between current studied fluid (i.e. OBNF), another non-Newtonian fluid (i.e. Maxwell Nanofluid (MWNF)) and Newtonian fluid. As we know speed of Newtonian fluid is greater than non-Newtonian fluid, the same statement is validated by our solution. It is also noted that adding molybdenum disulphide nanoparticles to grease, heat transmission increased to 19.11% and mass transmission decreased to 2.51%.

Radiative Maxwell Nanofluid Flow over a Stretching Sheet Undergoing a Chemical Reaction

Radiative Maxwell Nanofluid Flow over a Stretching Sheet Undergoing a Chemical Reaction

The electrokinetic energy conversion analysis of viscoelastic Maxwell nanofluids with couple stress in circular microchannels

The present study focuses on the unsteady flow of a viscoelastic Maxwell nanofluid with couple stress in a circular microchannel under the combined action of periodic pressure and magnetic field. The Green's function method is applied to the unsteady Cauchy momentum equation to derive the velocity field. We strive to check out the analytical solutions of the current model by validating them with existing results. In addition, the effects of several dimensionless parameters (such as the couple stress parameter γ, the Deborah number De, and the dimensionless frequency ω) on the streaming potential and the electrokinetic energy conversion (EKEC) efficiency of the three waveforms (cosine, square, and triangular) are portrayed via graphical illustrations. Within the range of parameters chosen in this study, the results demonstrate that increasing the value of the Deborah number or decreasing the dimensionless frequency can effectively enhance the streaming potential. The velocity field and EKEC efficiency are improved with increasing couple stress parameters. Furthermore, our investigation is extended to compare the EKEC efficiency for square and triangular waveforms when the couple stress parameters are set to 20 and 40, respectively. The results also indicate that increasing the couple stress parameter significantly improves the EKEC efficiency, particularly in the context of the square waveform. These findings will provide valuable assistance in the design of periodic pressure-driven microfluidic devices.

Impact of viscous dissipation on MHD flow of Maxwell nanofluid across a linear stretching sheet

The viscous dissipation of Maxwell nanofluid movement on a stretching sheet is examined in the present article. Constructed the modelling equalities with assumptions and emerging parameters such as Magnetic parameters, thermophoresis, Brownian motion, and Biot number etc. Convert those equation to simple third-order ODEs by applying stream functions, MATHEMATICA software used to solve ODE by applying the RK method approach with shooting technique. Presented our outcomes graphically by incorporating the parameters. The elasticity of the Maxwell fluid is directly proportional to temperature, resulting in a reduction in its velocity. The factors that affect fluid flow include viscous dissipation, Lewis number, Brownian motion, and the reversibility of temperature and velocity. Increasing the parameters of Brownian motion leads to significant movement of the nanofluid particles, which in turn increases their kinetic energy and enhances heat generation in the boundary layer. The Lorentz force, which hinders the movement of fluid, leads to a decrease in velocity profiles. This is determined by the magnetic parameter. The heat transfer rate, the velocity decay rate, and the occurrence of viscous dissipation are all occurring in close proximity to the sheet. Also, the model tabular validation presented and current results align well with previously published studies. Cancer treatment and the cooling process in industries, polymer processing, biotechnology and medicine, food industry, cosmetics, oil and gas, textiles, aerospace and automotive, and construction are just a few of the technical and biological uses for it. Industries may enhance material performance, process efficiency, and product quality in a variety of applications by using Maxwell fluid models.

Effect of chemical reactions and melting heat on the dynamics of maxwell nanofluid flow

AbstractThis study investigates the electrically conducting Maxwell fluid flow over a stretching sheet with the effects of homogeneous‐heterogeneous chemical reactions, thermal radiation, and melting heat. The nanomaterial characteristics are analyzed considering Brownian motion and thermophoresis (Buongiorno's model). Irreversibility analysis is conducted to assess entropy generation. The governing equations of the problem are transformed into dimensionless equations through appropriate similarity transformations. The graphical and tabular numerical solutions are attained through NDSolve via Mathematica. The study examines how various parameters affect the velocity, concentration, temperature, and entropy generation within the flow. This study provides insights into isothermal chemical processes which contribute to the optimization of industrial and engineering applications. It is seen that heterogeneous diffusion parameter increases molecular disorder and rate of irreversible processes, whereas homogeneous diffusion parameter shows opposite trend.

Significance of Cattaneo–Christov heat flux theory and convective heat transport on Maxwell nanofluid flow

AbstractRecently, nanofluids, which are solutions of fluids mixed with suspended nano‐particles, for instance, carbon nanotubes, metals, and metal oxides, have become a favorable alternative to conventional coolants. Caused by their outstanding thermal performance of conductivity, nanofluids are extensively used in battery‐operated drums, thermoelectric producers, and solar power. The suspension of minor solid components in energy dispersion fluids boosts their thermal enactment of conductivity and gives an economical and resourceful method to increase their transfer properties of heat significantly. Furthermore, additions of nanofluids to numerous engineering and mechanical matters, for instance, electrical kit conserving, heat exchangers, and chemical progressions, are uses of nanofluid. Here, the purpose of this work is to elaborate on the flow of Maxwell nanofluid by considering chemical reactions and heat sink/source. The mathematical structure is established with the presence of Brownian movement and thermophoresis effects. The remarkable aspects of non‐Fourier heat flux are also considered with the transport phenomenon of convective conditions. The similarity alterations change the partial differential equations (PDEs) into ordinary differential equations (ODEs). The obtained expressions of ODEs are solved numerically via the bvp4c approach. The graphical sketches display the declining behavior of Maxwell factor for velocity; however, the same impacts are examined for Brownian and thermophoresis factors. Furthermore, Schmidt and chemical reaction factors decline the concentration field of Maxwell nanofluid.

Diffusion-thermo and thermo-diffusion impacts on MHD natural convection flow of maxwell nanofluids over a stretching sheet

The present study carried out significant importance in its magnetic field and crosswise diffusion influenced the Maxwell nanofluid flow past a nonlinear stretching sheet. This investigation aimed to shed light on the behavior of critical parameters, particularly in the presence of thermophoresis and Brownian motion. The primary aim is to investigate the impact of thermal diffusion, diffusion-thermo, and various influencing factors on a Maxwell nanofluid near a stretching sheet in the magnetic field, and the impact of three distinct slip conditions (velocity, thermal, and solutal). The partial differential equations by the nonlinear coefficients are utilized in obtaining the most important equations. These equations are distorting to beneficial nonlinear ordinary differential equations making use of the appropriate transformations variables and transformation coefficients. To investigating the computational solutions for the reducing sets of the nonlinear ordinary differential equations, these were developing and utilized the Keller box methodology. The simulations are carried out the nanofluids velocity, temperature, concentration, skin friction coefficients, the rate of temperature transport, in addition to the rate of mass transportation, amongst previous variables. The validations of this methodology are displayed via the comparison of the present outputs through the preceding judgments into the literatures. The major conclusions drawn from this study are the concentration profiles exhibited opposing behaviours as concentration slip parameter increased. However, the temperature profile increases for Brownian motion parameter and thermophoresis parameter parameters. Secondly, concentration displayed an increasing behavior as the Soret number increased.

Entropy generation and Cattaneo–Christov heat flux analysis of binary and ternary hybrid Maxwell nanofluid flows with slip and convective conditions

Hybrid nanomaterials significantly enhance thermal systems through improved thermal conductivity, efficient energy storage, and customized thermomechanical properties. Due to their superior thermophysical characteristics, binary/ternary hybrid nanofluids are crucial in fields such as industry, biomedicine, transportation, and pharmaceuticals. This study examines the hydromagnetic flows and heat transfer properties of binary (CuO+Fe3O4/sodium alginate) and ternary (CuO+Fe3O4+MoS2/sodium alginate) hybrid Maxwell nanofluids over a radially stretching rotating disk. The governing flow equations incorporate Cattaneo–Christov heat flux, mixed convection, velocity and thermal slips, nonlinear radiation, viscous dissipation, and Joule heating in a Darcy–Forchheimer porous medium. These axisymmetric partial differential equations are transformed into ordinary differential equations using similarity variables, and the spectral quasilinearization method (SQLM) is applied for numerical solutions. Results reveal the effects of relevant parameters on velocity, temperature, skin friction, and heat transfer rates. Novelty lies in the comparative analysis of flow behaviors and entropy production rates between binary and ternary hybrid Maxwell nanofluids. When the heat source is included, the Nusselt number increases by 12.9% for ternary nanofluids and 16.07% for binary nanofluids as the thermal relaxation number increases from 0.5 to 1.5. Furthermore, the ternary hybrid nanofluid shows greater resistance to Lorentz and porous medium forces and exhibits a higher temperature distribution and better thermal management capabilities compared to the binary hybrid nanofluid.

Influence of Cattaneo-Christov Heat Flux Model Rotating Maxwell Nanofluid with MHD and Double Stratification Across a Bidirectional Stretching Surface

Influence of Cattaneo-Christov Heat Flux Model Rotating Maxwell Nanofluid with MHD and Double Stratification Across a Bidirectional Stretching Surface

The effects of bioconvection, non‐Fourier heat flux, and thermal radiations on Williamson nanofluids and Maxwell nanofluids transportation with prescribed thermal conditions

AbstractThe utilization of nanoentities in common fluids has opened new opportunities in the area of heat transportation. The rising requirements to enhance the efficiency of compact heat exchangers can be achieved by using various nanofluids. In this article, the thermal output of Maxwell and Williamson nanofluids transport over a prolonging sheet with bioconvection of self‐motivated organisms is scrutinized. A magnetic flux and the porous effects of a medium influence the flow of fluids. The fundamental principles for conservation of mass, concentration, momentum, and energy yield a nonlinear set of partial differential equations that can then be altered into ordinary differential form. A heat transfer flux is presented along with temperature boundary conditions, PST, and PHF (prescribed surface temperature and prescribed heat flux). The numerical results are acquired by executing the Runge–Kutta method with a shooting procedure in MATLAB coding. By fluctuating the inputs of influential variables of the dependent functions, a precise overview of the scheme is acquired. It can be seen that velocity decreases with the rising values of buoyancy ratio, magnetic force, Raleigh number, and porosity. Also, the temperature of the fluids begins to rise directly with the rising values of thermophoresis and Brownian motion parameters. The present study addresses bioconvection, non‐Fourier heat flow, and thermal radiations while combining the special properties of Williamson and Maxwell nanofluids. The field of biomedical engineering may benefit from this study, particularly with regard to therapies for hyperthermia and drug delivery systems. This study can be useful in cutting‐edge cooling systems, bioengineering, solar energy conversion and biotechnology.

Unsteady chemically reactive Maxwell nanofluid flow through a porous elastic surface with Cattaneo–Christov model

Unsteady chemically reactive Maxwell nanofluid flow through a porous elastic surface with Cattaneo–Christov model

3D-MHD mixed convection in a darcy-forchheimer maxwell fluid: Thermo diffusion, diffusion-thermo effects, and activation energy influence

In this article, the three-dimensional upper-convected Darcy-Forchheimer Maxwell (UCM) nanofluid flow over a stretching surface is analyzed to investigate the effects of activation energy, thermodiffusion, diffusion thermo, and magnetohydrodynamics (MHD) on heat and mass transfer. The energy equation incorporates a nonlinear radiative heat flux. Using similarity transformation, the nonlinear partial differential equations are reduced to ordinary differential equations, which are then solved using the well-known shooting technique via the fourth-order Runge-Kutta integration method. To validate our results, we also employ MATLAB's built-in function bvp4c. The impact of various parameters, such as activation energy, diffusion thermo, thermodiffusion, Brownian motion parameter, Prandtl number, thermophoresis parameter, and magnetic parameter, on velocity, temperature, and concentration is discussed both graphically and numerically. It is observed that the flow velocity decreases with an increasing magnetic field parameter. Additionally, higher values of the activation energy parameter reduce the nanoparticle concentration profile. The temperature and concentration exhibit opposite behaviors when thermodiffusion and diffusion thermo effects are enhanced.

Semi-analytical simulation of chemically reactive Maxwell nanofluid with Cattaneo–Christov heat and mass fluxes

The current study employs the Cattaneo–Christov diffusion law to analyze the thermal tendency of Maxwell nanomaterials flowing over an unsteady stretching sheet. Thermophoretic and Brownian diffusion aspects of nanosolids are incorporated to investigate thermal and nanoparticle’s concentration distribution. Through flow similarities, the governing PDEs (Partial Differential Equations) are articulated into a set of nonlinear ODEs (Ordinary Differential Equations). The homotopy analysis approach, a recognized semi-analytical technique, is implemented to solve these differential equations. Results are presented graphically, revealing that higher magnetic field strengths diminish the flowing field. Temperature and nanosolids concentration distributions escalate with increasing thermal and singular relaxation time phenomena. Furthermore, when nanoparticle concentration decreases and Brownian motion intensifies, the temperature field rises. It is also observed that heightened resistive heating enhances the fluid’s capability to carry thermal energy. Overall, this investigation sheds light on the intricate interplay between several factors influencing the thermal behavior of Maxwell nanomaterials over a stretching board, offering insights into their practical applications.

Analysis of the tri-hybrid Maxwell nanofluid flow with temperature-dependent thermophysical characteristics on static and dynamic surfaces employing Levenberg-Marquardt artificial neural networks

Using the Levenberg-Marquardt Artificial Neural Network (LM-ANN) model, this study applies computational neuroscience to the analysis of flow, heat, and mass transport characteristics. The novel characteristics of MHD Maxwell tri-hybrid nanofluid passing through static and moving wedge with temperature-dependent thermophysical properties (thermal conductivity, viscosity, diffusivity, and electrical field) in permeable, radiative, and mixed convection processes are investigated in this paper. Nonlinear PDEs are transformed into nonlinear ODEs using similarity variables. A dataset for the LM-ANN is generated across various scenarios by varying parameters such as the temperature-dependent viscosity parameter ( 0.07 − 0.1 ) , variable diffusivity parameter ( 0.4 − 2.5 ) , thermal buoyancy parameter ( 0.1 − 0.5 ) , nonlinear thermal buoyancy parameter ( 0.2 − 0.5 ) , thermal radiation ( 1 − 1.5 ) , buoyancy ratio parameter ( 0.2 − 0.5 ) , chemical reaction parameter ( 1 − 3 ) , and Schmidt number ( 1 − 3 ) using the Bvp5c numerical algorithm. The testing, training, and validation procedure of LM-ANN is utilized to examine the estimated solutions of specific situations, and the proposed algorithm is then validated. After that, the proposed LM-ANN is validated using regression analysis, MSE, and histogram analysis. The prescribed approach impeccably mirrors the recommended and cited findings, evincing a precision level within the realm of 10−9. Results indicate that increasing the permeability parameter from 1 to 1.2 and the temperature-dependent thermal conductivity parameter from 0.4 to 2.5 enhances the Nusselt number. Additionally, increasing the chemical reaction parameter from 1 to 3 leads to an increase in the Sherwood number. The significance of this study lies in its potential applications in industries such as aerospace, chemical processing, and energy systems, where efficient heat and mass transfer processes are crucial. For instance, the findings can be applied to enhance cooling techniques in high-performance aerospace components, optimize reactor designs in chemical plants, and improve thermal management in power generation systems.

Robin and zero‐mass diffusion analysis for radiated unsteady flow of Maxwell nanofluid due to porous stretched regime: Analytical simulations

AbstractOwing to the multidisciplinary applications of nanomaterials, a wide range of research has been conducted on this topic recently. The aim of current research is to analyze the enhancement of heat transfer due to the unsteady flow of Maxwell nanofluid associated with the zero mass thermal constraints. The applications of the radiated phenomenon and magnetic force are contributed to the current flow problem. The analysis is subject to the implementation of Robin and zero‐mass diffusion constraints. A bidirectional moving porous surface endorsed the flow. The appropriate variables are taken for simplifying the system. The homotopy analysis method (HAM) is used to compute the solution procedure. The obtained results are confirmed with already performed studies. It has been observed that the temperature and nanoparticle concentration distributions decrease for higher unsteady parameter values.

Exploring heat transfer in magnetized binary nanofluid flows with gyrotactic microorganisms through bioconvection analysis

Many industrial and thermal systems regard continuous thermal propagation as vital because it may improve the efficacy of thermal engineering machinery and engines. Consequently, this is a potential development for bettering power energy through employing magnetized nanomolecules within a heat-carrying non-Newtonian fluid. This study examines nanofluids with Casson and Maxwell nanofluids by considering nonlinear radiation and heat generation because of bioconvection over a stretchable surface with a porous material. Moreover, the interaction between gyrotactic microorganisms and activation energy has been discussed in detail. The flow model under consideration is formulated via Thermophoretic diffusion and Brownian motion. Using similarity conversions, the regulating partial differential equations (PDEs) are made dimensionless, thus reducing them to ordinary differential equations. A shooting technique was employed to solve the problem; MATLAB software used RK methods combined with the shooting method to solve this problem. Many diagrams have been depicted to describe the diverse flow factors; other interesting quantities, such as motile microbes’ density and Sherwood numbers, are computed and plotted. In addition, mixed convection, buoyancy ratio, bioconvection Rayleigh constant, and resistivity due to magnetized significantly affect velocity profile through Casson–Maxwell nanofluid. It is seen that both Casson and Maxwell fluids have nonuniform boundary layers of temperature and concentration fields. Maxwell fluids’ temperature and concentration fields are more sensitive than Casson fluids toward the same parameters.

Effects of Activation Energy and Diffusion Thermo an Unsteady MHD Maxwell Fluid Flow over a Porous Vertical Stretched Sheet in the Presence of Thermophoresis and Brownian Motion

This article discusses the effects of Activation energy and Diffusion thermo on an unsteady MHD flow of an electrically conducting Maxwell Nanofluid over a stretching sheet in a porous medium in the presence of thermophoresis and Brownian motion. Using the similarity transformations, the partial differential equations corresponding to the momentum, energy, and concentration equations are transformed into a system of nonlinear ordinary differential equations, which are solved numerically using a RungeKutta fourth-order method along with the shooting technique, and the results obtained for different governing flow parameters are drawn graphically, and their effects on velocity, temperature, and concentration profiles are discussed. The values of the skin friction coefficient, Nusselt number coefficient, and Sherwood number coefficient are presented in the table. A comparison with previously reported data is made, and an excellent agreement is noted. The objective of the present study is to use the Activation energy and Diffusion thermo parameters to increase the concentration of chemical species on the boundary layer and temperature, respectively. The temperature of the fluid increases as the radiation parameter, Brownian motion, thermophoresis, and magnetic parameters increase.