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Brownian motion, often known as BM, is an inherent characteristic of minute particles suspended in a fluid. It plays an important role in several physical and chemical processes. Thermophoresis refers to the process where particles in a fluid are carried along with a gradient in temperature (Temp). This feature has significant importance in several applications, including microfluidics, thermal control, and energy conversion. Through the examination of the thermophoresis phenomenon in water/graphene nanofluid (NF), researchers might get valuable knowledge on the potential uses of these materials. The current study examined the effect of various sizes of graphene nanoparticles (NPs) (5, 6, 9, and 10 Å) on the thermal behavior (TB), BM, and thermophoresis of water/graphene NF using molecular dynamics (MD) simulation. This study reported the changes in heat flux (HF), thermal conductivity (TC), average Brownian displacement (BD), and thermophoresis. It is concluded that by increasing the size of graphene NPs from 5 to 10 Å, the average BD and thermophoresis increased from 3.06 Å and 23.88 Å to 4.16 Å and 31.46 Å, respectively. Due to their higher kinetic energy (KE) and momentum, larger graphene NPs experienced more BM, enabling them to withstand random thermal fluctuations more effectively than smaller particles. In addition, as the size of graphene NPs increased, the HF and TC values ​​increased from 39.54 W/m2 and 0.36 W/(m.K) to 47.19 W/m2 and 0.51 W/(m.K) after 10 ns. Therefore, the size-dependent changes in BD and thermophoretic effects led to a simultaneous increase in HF and TC of the NF, which was attributed to the larger heat transfer (HT) surface area, improved HT properties, and synergistic effects of larger graphene NPs. The maximum (Max) temperature increases from 1415 K to 1504 K. These findings were useful in a variety of industries, particularly for improving TB in different NFs.

Nanofluids have significant industrial applications and motivating heat transfer characteristics for various factors that contribute to the movement of nanofluids are essential significance. The aim of the present study focused on importance of heat transfer analysis on engine oil conveying copper nano particles embedded in a porous rotating disk with potential application in aerospace technology. In this model we considered magnetohydrodynamics, non-linear thermal radiation, thermophoresis and Brownian motion. The present investigation utilized copper nanoparticle and engine oil as a base fluid. The mathematical flow equations are transformed into ordinary differential equations (ODEs) by employing suitable self-similarity variables. The resultant ordinary differential equations are solved numerically by using the Midrich technique in the Maple software. The results are calculated to measure the impact of active parameters on velocity, temperature, concentration equations are presented graphically and in tabular form. Higher values of the magnetic field parameter the velocity profile decreased while the opposite tendency we noticed on energy profile. When increasing the radiation parameter values the energy profile increased. In both cases when increasing the magnetic field and radiation parameter values the Nusselt number profile increased. The research has important implications in a number of real-world situations. In particularly, the advancement of aircraft technology has presented manufacturers with new criteria and problems for the functioning of their devices. It is essential that, in order to guarantee the secure operation of aerospace machinery, the failure mechanisms be identified and the operational durability of critical structural components be improved as quickly as possible.

In this work, a comparative analysis on magnetohydrodynamic nanofluid flow containing spherical and cylindrical-shaped alumina nanoparticles over a stretching curved surface is mainly focused. The effects of Brownian motion, Joule heating, thermophoresis, chemical reaction and activation energy are taken into consideration in this work. It is important to mention that this analysis considers a 4 % volume fraction of the alumina nanoparticles. A thermal convective and zero-mass flux conditions are imposed to scrutinize the heat transfer analysis. The leading equations are transformed into dimensionless form by using suitable similarity variables. A numerical solution is obtained using the shooting technique. The acquired outcomes depict that greater magnetic factor enhances the skin friction coefficient. The greater magnetic factor, thermal Biot number, Eckert number, and interfacial layer thickness augment the heat transfer rate, while a greater nanoparticle diameter diminishes the thermal transfer rate. A higher magnetic factor has an increasing impact on thermal distribution and a reducing impact on velocity distribution. A greater curvature factor enhances both the velocity and thermal distributions. The concentration distribution is enhanced by the higher interfacial layer thickness and activation energy factor, while it is reduced by a higher nanoparticle diameter, Brownian motion factor, and chemical reaction factor. From the comparative analysis, it is found that the velocity, thermal, and concentration distributions are higher for the cylindrical-shaped nanoparticles compared to spherical-shaped nanoparticles.

This study investigates the heat and mass transfer characteristics of MHD rotating Fe₃O₄-Al₂O₃/H₂O hybrid nanofluid flow over a three-dimensional stretching surface. Comparative analysis was conducted among the base fluid H₂O, Al₂O₃-H₂O nanofluid, and Fe₃O₄-Al₂O₃/H₂O hybrid nanofluid, focusing on velocity, temperature, and concentration distributions influenced by thermophoresis, Brownian motion, Hall current, temperature ratio, magnetic parameter, rotation, and thermal radiation. The governing nonlinear partial differential equations were transformed into ordinary differential equations using similarity adaptations and solved numerically with the BVP-5C method in MATLAB. Results indicate that increasing the thermophoresis and Brownian motion parameters elevates the temperature profile while affecting the concentration distribution differently. The hybrid nanofluid exhibited a higher temperature distribution compared to the nanofluid and base fluid, whereas the base fluid showed a greater concentration gradient.

In this paper, studied the impact of heat generation of Nanofluid movement over a stretching sheet by the consideration of Thermophoresis, Brownian motion & first order chemical react parameters etc. Constructed the modelling equations with based on assumptions and by introducing emerging parameters. The equations converted to third order ODE through stream functions. FDM with collocation polynomial technique (bvp4c) employed to solve those equations through MATLAB software. The results are presented through graphical form with the influence of emerging parameters. Thickness of thermal boundary stratum decreased as enhancing of Prandtl number. Influence of Brownian motion parameter, fluid temperature raised and fall down the concentration. Temperature of fluid and concentration raised as enhancement of thermophoresis. A decrease in the heat transfer rate and an increase in the mass transfer rate are observed as thermophoresis, Brownian motion, and heat generation parameter values increasing. The enhancement of chemical reaction parameters intensifies the driving forces of temperature and concentration gradients, which govern heat and mass transfer, leading to increased rates of both heat and mass transfer. Validation of the model presented and the present results align well by past reported studies. This model can extent to analyse the hybrid nanofluid in the manufacturing process of detergent, painting and lubricants, analysis of blood flow in artery etc.

The current study deeply investigates nanofluid's heat and mass transport in a staggered-shaped enclosure with wavy walls. A nonhomogeneous mathematical model with thermophoresis and Brownian diffusion is considered in our study. The finite element method is implemented to solve the set of governing equations. Impacts of magnetic field (B0) and its orientation (γ), undulation number (N), amplitude (A) and nanoparticle types are examined for heat and mass flow. Investigations show that the most demoting trend is obtained when the inclination of B0 is either vertical or horizontal. It is concluded that mean Nusselt (Nuavg) and Sherwood number (Shavg) are increasing functions of Ra. When Ra is changed from 103 to 107, the Shavg value is increased up to six times. The impacts of wall shape show that as we increase A, the Nuavg decreases while the maximum can be obtained for the flat boundary. For small N, Shavg is an increasing function. Shape optimization revealed that there exists a critical point between Shavg and N after which it declines. Investigations further show that this point can be changed. Some critical points have been calculated that can be counted as novel results.

This study analyzes the unsteady nanofluid flow phenomenon adjacent to an accelerating vertical plate under the influence of magnetic fields, chemical reactions,viscous dissipation and solid volume fraction factors. The analysis motivates the understanding of the behavior of complex fluids to improve existing processes and develop new technologies. The finite difference technique, with the help of the boundary and initial conditions, was employed for the numerical result. The numerical solutions were graphically analyzed through MATLAB software. The results reveal intricate flow behaviors, including the influence of magnetic fields and solid volume fraction in reducing the velocity of the nanofluid. Interestingly, a magnetic field drops the temperature of the nanofluid, which can be observed in a particular case. The chemical reaction is found to absorb the heat, leading to a decline in the velocity and concentration due to temperature drop and solute destruction factors. The viscous dissipation raises the temperature of the nanofluid, but the heat sink affects the temperature oppositely. The Soret number essentially quantifies the phenomenon known as thermophoresis, where solutes concentrate more in cooler regions. This analysis provides valuable insights into the design and optimization of systems involving nanofluids subjected to external magnetic fields, with implications for various engineering applications such as thermal management systems and nanofluid-based heat exchangers.

This study observes the numerical analysis of Powell-Eyring hybrid nanofluid along a stretching sheet. The movement of sheet in x-direction is taken to be the source of motion in the fluid. Nanoparticles are considered as agents for increasing thermal properties of fluids. This research emphasizes the amalgamation of copper oxide and carbon nanotubes with engine oil as a base fluid. A significant increase is observed by adding these agents. Porous medium is considered using Darcy law. Magnetics field is also taken for studying mass transfer analysis. For heat transfer mechanisms, thermophoresis and Brownian diffusions are taken into account. The whole procedure is shown through nonlinear differential equations. Appropriate transformations are used for simplification purposes. After transformations, partial differential equations are converted into ordinary differential equations and handled through numerical technique. Shooting numerical technique has been used to solve the governing system of equations, and the obtained results are thoroughly examined and discussed graphically. The thermal characteristics of the hybrid nanofluid are analyzed, in the presence of thermal radiation and thermophoresis effects. To validate our results, a comparison analysis is drawn with existing literature in some specific scenarios.

The current work examines the significant impact of Carreau hybrid nanofluid, particularly in enhancing thermal conductivity and heat transfer efficiency, which is discussed through the integration of aluminium oxide (Al2O3) and titanium dioxide (TiO2) nanoparticles into a base fluid made of 50 % water and 50 % ethylene glycol solution. The study is concentrated on thermal radiation, chemical reactions, thermophoresis, Brownian motion, and viscous dissipation over an exponentially curved Riga surface. The governing partial differential equations are formulated in light of all of these factors. Subsequently, the original partial differential equations are transformed using boundary layer approximations and similarity variables to produce a dimensionless ordinary differential equation. The above equations are solved numerically using the shooting method and the MATLAB function bvp4c. The behaviour of heat and mass transfer in both shear thinning (pseudoplastic) fluids and shear thickening (dilatant) fluids is discussed in detail, and efforts are made to highlight some important parameters such as the Weissenberg number, the curvature radius, the modified Hartmann number, Thermophoresis, Brownian motion, and chemical reaction. The fundamental observation is that a rise in the Weissenberg number results in a reduction of skin friction and Nusselt number in shear thickening scenarios, whereas it leads to an increase in shear thinning scenarios. Increasing the modified Hartmann number results in elevated skin friction and a reduction in the Nusselt number for both shear thickening and shear thinning scenarios. These findings are advantageous for developing strategies applicable to heat control across many industries and biological sectors to enhance energy efficiency and system performance.

This research paper has inspected the phenomena related to heat and mass transfer within a balanced, stable nanofluid flow confined between two parallel sheets. Our investigation focuses on a uniform magnetic field as a contributing factor. The nanofluid model incorporates the significance of thermophoresis and Brownian motion. We have opted for the Akbari Ganji Method)AGM(Python and Homotopy Perturbation Method)HPM(Python to solve the ruling equations because of their significant accuracy, high speed, and lower input volume. Utilizing these two approaches also requires activating the SymPy library. We have juxtaposed the obtained findings with those derived from a numerical approach, specifically the 4th-order Runge-Kutta, to validate the precision and accuracy of AGM and HPM. The analysis comprehensively evaluates various critical parameters, including the magnetic parameter, viscosity coefficient, thermophoretic parameter, and Brownian parameter. The findings reveal as the thermophoretic and Brownian parameters increase, there is a decline in the Nusselt number, while conversely, a contrasting current is exhibited in the viscosity coefficient. Furthermore, as the Brownian motion rises, the nanofluid concentration and Nusselt number decline. Any increase in magnetic parameters reduces the viscosity and concentration profile while heat transfer increases. An increase in the Schmidt number results in a decline in both concentration and the Nusstlet number.

Many external factors influence the properties of nanoparticles in the working fluid, which subsequently determines the efficacy attributes of the ensuing nanofluid. Incorporating these factors is essential for studying heat and mass transfer in hybrid nanofluids, as it provides a detailed representation of the mechanism. Such factors are porous medium, heat source, Thermophoresis, and Brownian motion. The rotation of a cylinder can alter the flow field and boundary layer around it, which could be used for flow management scenarios such as drag reduction or separation of boundary layers control, and the complex flow patterns generated through a rotating cylinder could be utilized for improved mixing and heat transfer in processes in industry. Thus, the current novel aspect of the study examines the impacts of thermophoresis and Brownian motion over a rotating cylinder in the presence of a porous media comprised of water-based TiO2 and Fe2O4. The physical circumstances are primarily represented as PDEs based on the considered flow conditions, which then get transformed into a system of ODEs using the relevant similarity variables. The numerical solution is obtained by using RKF-45th and the shooting procedure. The flow symmetry and the effects of the specific variables associated with the problem are examined and delivered graphically. The findings confirm that the drag coefficient improves with porous material, altering fluid dynamics. Heat transmission steadily drops as the thermophoretic parameter gets larger, but mass transfer displays a contrary trend for evolving Brownian motion parameters. Also, the current results are validated with existing past studies.

Controlling the translational and rotational motion of microparticles is a topic of current interest in soft matter and statistical mechanics. Roll rotation of a microparticle in a hydro-thermophoretic trap – which is a device that uses the flow of fluids and thermophoresis to trap and manipulate microparticles – was recently reported (Nalupurackal et al., 2023). Here, we study the coupled translational and rotational motion of a microparticle in a hydro-thermophoretic trap. We demonstrate, using experiments and theory, that the dynamical system describing the motion of the microparticle undergoes bifurcations when the power of lasers used in a hydro-thermophoretic trap is changed. We show that the advective fluid flow from laser heating and thermophoresis depend on the power of the laser through two distinct exponents. We obtain these exponents from experimental data. Using these exponents and a linear stability analysis of the equations of motion, we show that locations at which a microparticle can be trapped (stable fixed points of the dynamical system) can be tuned by changing the power of the lasers at the two hotspots. At higher power values, we find that there are no stable fixed points; hence, the microparticle can no longer be trapped. Our experimental findings support these theoretical results.

This research explores how nanoparticle shapes affect the thermal behavior of nanofluid film boiling along a vertical cylinder, utilizing a Continuous-Species-Transfer method embedded in a Computational Multi-Fluid Dynamics framework. By modeling the behavior of nanoparticles in both liquid and vapor phases, with considerations for Brownian motion and thermophoresis, a comprehensive 2D axisymmetric analysis is conducted. The analysis focuses on the effects of various Al2O3 nanoparticle shapes – spheres, bricks, blades, cylinders, and platelets – on boiling heat transfer performance. Results demonstrate that while nanoparticle shape has a minimal impact on deposition dynamics, it significantly affects kinematic viscosity, particularly for platelet-shaped nanoparticles. Blade-shaped nanoparticles stand out for their substantial enhancement of thermal transport, as demonstrated by pronounced temperature gradients and elevated thermal conductivity. Furthermore, these nanoparticles contribute to a notable improvement in the Nusselt Number, suggesting enhanced efficiency in boiling heat transfer. This improvement is particularly significant at higher nanoparticle concentrations, where the effects are more pronounced, though not strictly linear when compared to the effects at lower concentrations. Future work will explore different nanoparticle materials, boiling scenarios, and experimental validation.

This investigation aims to study the behavior of a Jeffery fluid on a stretching surface while considering thermophoresis and Brownian motion effects through Buongiorno's model. The governing equations include thermal and mass transport effects, heat source-sink interactions and chemical reaction rates. Similarity transformations are utilized to solve partial differential equations, transforming them into ordinary differential equations. The bvp5c built-in program in MATLAB is then used to obtain a numerical solution for the ODEs. The study generates graphs to examine how different physical flow parameters affect fluid flow, temperature, and concentration distributions. The graphical analysis shows that mass diffusion decreases as the Brownian parameter and Schmidt number increase, while an increase in thermophoresis and heat source-sink improves thermal transport. The study also explores the influence of various emerging variables on velocity, thermal, and solutal distributions, providing valuable insights into the complex interplay of these factors and contributing to advancing our understanding of fluid dynamics.

The influence of Thermophoresis and Brownian motion on the pulsing flow of nano-fluid (blood) through a curved artery with stenosis and post-stenotic dilatation in its interior is investigated numerically. The Herschel-Bulkley model of fluid dynamics accurately represents the fluid's rheology. By applying the mild stenosis condition, the highly coupled momentum, energy, and mass concentration equations can be modelled and reduced. Explicit finite differences methods are used to discretize and solve the non-dimensionalized governing equations associated with the boundary condition. Entropy creation in blood flow due to loss and magnetohydrodynamic processes is also investigated. Graphs and discussions of the effects of changing pertinent geometric and rheological factors on key flow characteristics, such as temperature, velocity, and mass concentration, are provided. Because of the small changes in blood temperature and mass concentration caused by the artery's curvature, it is observed that the radius of the curved channel has a significant impact on blood velocity. An increase in Brownian motion also resulted in a drop in the nano-temperature, a fluid's but the thermophoresis parameter exhibited the reverse behavior.

In this study, the computational analysis of entropy generation optimization for synthetic cilia regulated ternary hybrid Jeffery nanofluid (Ag–Au–TiO2/PVA) flow through a peristaltic vertical channel with swimming motile Gyrotactic microorganisms is investigated. Understanding the intricate interaction of multiple physical phenomena in biomedical applications is essential for optimizing entropy generation and advancing microfluidic systems. The characteristics of nanofluid are explored for the electroosmotic MHD fluid flow in the presence of thermophoresis and Brownian motion, viscous dissipation, Ohmic heating and chemical reaction. Using the appropriate transformations, a set of ordinary differential equations are created from the governing partial differential equations. The resulting ODEs are numerically solved using the shooting technique using BVP5C in MATLAB after applying the long-wavelength and low Reynolds number approximation. The velocity, temperature, concentration, electroosmosis, and microorganism density profiles are analyzed graphically for different emerging parameters. Graphical investigation of engineering interest quantities like heat transfer rate, mass transfer rate, skin friction coefficient, and entropy generation optimization are also presented. It is observed that the rate of mass transfer increases for increasing thermophoretic parameter, while reverse effect is noted for Brownian motion parameter, Schmidt number, and chemical reaction number. The outcomes of present study can be pertinent in studying Cilia properties of respiratory tract, reproductive system, and brain ventricles.

Nanofluids (NFs) are nanoscale colloidal suspensions containing dense nanomaterials. They are two-phase systems with solid in liquid phase. Due to their high thermal conductivity, nanoparticles increase the thermal conductivity (TC) of base fluids, one of the basic heat transfer parameters, when distributed in the base fluids. The present research investigates the thermal behavior, Brownian motion, and thermophoresis of water/graphene NF affected by different numbers of atomic wall layers (4, 5, 6 and 7) by molecular dynamics (MD) simulation. This investigation reports changes in heat flux (HF), TC, average Brownian displacement, and thermophoresis displacement. By raising the number of atomic wall layers from 4 to 7, the average Brownian displacement and thermophoresis displacement increase from 3.06 Å and 23.88 Å to 3.62 and 25.05 Å, respectively. Increasing the number of layers due to the decrease in temperature increases the temperature difference between the hot and cold points along the channel. It increases the Brownian motion and the maximum temperature. Additionally, by raising the atomic layers of the channel wall, the values of HF and TC increase from 39.54 W/m2 and 0.36 W/mK to 41.18 W/m2 and 0.42 W/mK after 10 ns, respectively. The temperature rose from 1415 to 1538 K. These results are useful in different industries, especially for improving the thermal properties of different NFs.

Objective: This paper provides a rudimentary insight into the influence of heat and mass transfer on the magneto-hydrodynamic (MHD) Jeffrey fluid peristaltic flow filling porous space in a symmetric inclined channel using a rotating frame with chemical reaction. In contrast to previous attempts, the flow formulation is based on the impact of a modified Darcy's law porous media on the Jeffrey fluid condition. Methodology: The derived equations were solved analytically via the standard long wavelength and low Reynolds number assumptions to determine the pressure gradient, temperature, dimensionless velocity, pressure rise, and friction force. Otherwise, the concentration was numerically processed using the ND-Solve built-in command of Mathematica. Such a numerical technique is beneficial in minimizing error and reducing CPU time per evaluation. It chooses an appropriate algorithm for solving the problem. Results: The graph is used to physically interpret the numerical answers for the base flow profiles. For numerous parameters of interest that enter into the issues, graphical findings are developed and tested. The impacts of various involved parameters appearing in the solutions are carefully analyzed. The trapping phenomena are discussed for several parameters. Electromagnetic peristaltic micropumps, for example, are one application of the current study in biomedical engineering. It was claimed that our systematic approach may constitute a basis for accurately examining the impact of heat and mass transfer on the magneto-hydrodynamic (MHD) Jeffrey fluid peristaltic flow filling porous space in a symmetric inclined channel using a rotating frame with chemical reaction, useful for diverse medical applications such as gastric fluid flow through the small intestine.

Nanomaterials have attracted extensive relevance from researchers and scientists around the globe because of their unique thermo-physical features and ample potential advantages and utilizations in crucial areas, for illustration, biomedicine, electronics, energy, vehicles and aerospace. This attempt accounts magnetohydrodynamics and chemical reaction consideration in couple-stress nanomaterial confined by convectively heated vertical surface. Flow is mixed convective and thermally radiative. Brownian motion, heat generation, thermophoresis, Robin conditions and transpiration are considered for formulation. Boundary-layer expressions representing couple-stress liquid are implied utilizing transformation procedure. The obtained nonlinear expressions are tackled analytically by implementing series solution methodology (known as homotopy analysis method (HAM)). Convergence of analytical solutions is authenticated arithmetically (i.e., via table) and by drawing ℏ− curves. In addition, the significant parameters occurring in dimensionless expressions are addressed graphically. Our findings indicate retardation in flow when suction variable is augmented. Transfer of heat is higher for radiation and heat source parameters. Nanoparticles concentration decays for larger estimations of destructive reaction factor while it upsurges for generative reaction factor.

For the accurate modeling and simulation of the flame spray pyrolysis (FSP) process, all the essential phenomena need to be taken into account. A validated model could then be used for process optimization and design with reasonably reduced costs. In that sense, this work uses a combination of computational fluid dynamics (CFD) and a population balance model (PBM) to investigate the influence of thermophoresis and other parameters (related to sintering and turbulent particle diffusion) in the final produced particle size. This work simulates the flame spray using CFD under an Eulerian–Lagrangian framework. Furthermore, a monodisperse solver for a bivariate PBM is implemented into ANSYS Fluent to simulate the formation and evolution of nanoparticles inside the reactor. We investigate the production of zirconium dioxide (ZrO2) nanoparticles and use experimental data from the literature for model validation. The model produces accurate results for some of the investigated cases.

In the presence of a uniform magnetic field, the heat and mass transmission mechanisms of steady magnetohydrodynamic nanofluid flows between two parallel plates are presented in this paper. Ethylene glycol and water are mixed in equal proportions in the fluid. The hybrid nanoparticle is analyzed in this work, utilizing MWCNT and Ag as the particles. As a novelty, the nonlinear equations were solved using the Radial Basis Function methodology for the first time, and the numerical fourth-order Runge–Kutta method was used to compare the results, which were then illustrated in figures. The end result demonstrates that the numerical method and the Radial Basis Function approach are in excellent accord. Furthermore, the impact of various shape factors was investigated. The impact of a variety of active parameters, such as the magnetic parameter, viscosity coefficient, thermophoretic parameter, Brownian parameter, and nanofluid shape factor, on non-dimensional velocity, temperature, and concentration profiles has been shown. The Nusselt number drops as the thermophoretic and Brownian parameters are increased, but the viscosity coefficient has the reverse tendency.

Owing to enhanced thermal impact of nanomaterials, different applications are suggested in engineering and industrial systems like heat transfer devices, energy generation, extrusion processes, engine cooling, thermal systems, heat exchanger, chemical processes, manufacturing systems, hybrid-powered plants etc. The current communication concerns the optimized flow of Sutterby nanofluid due to stretched surface in view of different thermal sources. The investigation is supported with the applications of external heat source, magnetic force and radiative phenomenon. The irreversibility investigation is deliberated with implementation of thermodynamics second law. The thermophoresis and random movement characteristics are also studied. Additionally, first order binary reaction is also examined. The nonlinear system of the governing problem is obtained which are numerically computed by s method. The physical aspects of prominent flow parameters are attributed graphically. Further, the analysis for entropy generation and Bejan number is focused. It is observed that the velocity profile increases due to Reynolds number and Deborah number. Larger Schmidt number reduces the concentration distribution. Further, the entropy generation is improved against Reynolds number and Brinkman parameter.

Blood flow analysis through arterial walls depicts unsteady non-Newtonian fluid flow behavior. Arterial walls are impacted by various chemical reactions and magnetohydrodynamic effects during treatment of malign and tumors, cancers, drug targeting and endoscopy. In this regard, current manuscript focuses on modeling and analysis of unsteady non-Newtonian Carreau-Yasuda fluid with chemical reaction, Brownian motion and thermophoresis under variable magnetic field. The main objective is to simulate the effect of different fluid parameters, especially variable magnetic field, chemical reaction and viscous dissipation on the blood flow to help medical practitioners in predicting the changes in blood to make diagnosis and treatment more efficient. Suitable similarity transformations are used for the conversion of partial differential equations into a coupled system of ordinary differential equations. Homotopy analysis method is used to solve the system and convergent results are drawn. Effect of different dimensionless parameters on the velocity, temperature and concentration profiles of blood flow are analyzed in shear thinning and thickening cases graphically. Analysis reveals that chemical reaction increases blood concentration which enhance the drug transportation. It is also observed that magnetic field elevates the blood flow in shear thinning and thickening scenarios. Furthermore, Brownian motion and thermophoresis increases temperature profile.

The idea of activation energy appearing in a chemical reaction has been widely applied to the production of biodiesel, hydrogen, oil storage, geothermal manufacturing, base liquid mechanics, oil emulsified, food manufacturing, a significant renewable energy source, as well as sewage systems. This study aims to investigate the resultant repercussions of double diffusion, activation energy, Brownian motion, thermal radiation, thermophoresis, viscous dissipation, magnetic field, and Joule heating on bioconvection of a tangent hyperbolic nanofluid flow over a vertical stretching porous surface containing microbe (gyrotactic microorganisms). The fluid transport equations are converted into ordinary differential equations using appropriate self-similarity variables after being solved using the finite difference method. The impacts of key parameters on the fluid's transport properties are depicted in graphs and tables. When the dimensionless activation energy is higher, the mass transfer rate at the stretched nanomaterial sheet drops. The nanofluid concentration near the sheet minimizes by increasing the porosity parameter value, but the opposite behavior happens far from the sheet.

The theme of this article is to address the irreversibility in an incompressible Reiner-Rivlin nanofluid subject to stretchable rotating disk. Dissipation and radiation in heat expression are incorporated. Random diffusion and thermophoresis impacts are addressed. Physical feature of entropy rate is also accounted. Furthermore, first order reaction rate is scrutinized. Ordinary system (ODEs) is obtained through implementation of suitable variables. To construct convergent solution, we employed numerical method (ND-solve method). Outcomes for flow variables on velocity profile, thermal field, concentration and entropy optimization are discussed. Computational outcomes of moment coefficient, skin friction coefficient, entrainment velocity (disk pumping efficiency), Sherwood number and gradient of temperature versus sundry variables are studied. An expansion in radial velocity is observed for Reiner-Rivlin fluid variable. An augmentation in stretching parameter leads to opposite behavior of radial and tangential velocity components. An amplification in temperature distribution and entropy rate are observed for radiation variable. An improvement in thermophoresis parameter augments concentration and temperature distribution. Higher approximation of Brinkman number rises entropy generation rate.

The heat and mass transfer of carbon nanotubes based-water nanofluids flowing through a moving plate was thoroughly investigated in this numerical work. The Tiwari and Das nanofluid model, as well as the Buongiorno nanofluid model, are formulated to characterise the problem. In transforming the governing partial differential equations into a dimensionless ordinary differential equation, similarity transformations are introduced. The numerical solver bvp4c was then deployed to investigate the dimensionless differential equations. The impact of main parameters on the skin friction, Nusselt and Sherwood numbers are elucidated and thoroughly explained. Results are then compared with published works, and the outcomes are genuinely in close alliance. With the occurrence of thermophoresis Nt, Brownian motion Nb and nanoparticle volume fraction φ, the heat and mass transfer performance are outlined. The local number Nusselt seems to be decreased by higher parameters φ, Nb and Nt. Besides, the local Sherwood number is augmenting with an increase in the φ and Nb parameters and, inversely, a decreasing function with a lower Nt parameter. The results obtained from this study may lead to new knowledge and indirectly contribute to the fluid engineering industry.

To achieve efficient heat dissipation using polymer composites, it is important to optimize the heat conduction pathway. Therefore, manipulating the orientation of thermally conductive and anisotropic fillers in composites represents a judicious strategy. So far, external fields have been applied to align fillers within the matrix. However, these processes are energy-intensive and require stimuli-responsive fillers through surface modification, further complicating the process and deteriorating filler thermal conductivity. Herein, to these ends, a facile method for manufacturing composite with an orientation-controlled model anisotropic filler, hexagonal boron nitride (h-BN), was proposed by harnessing thermophoresis. Thermophoresis causes movement and/or rotation of solid particles in a fluid with a steady temperature gradient. A suspension of UV-curable monomer with well-dispersed h-BN was subjected to a temperature gradient, inducing filler rotation via thermophoresis. A subsequent photo-curing yielded a solid composite with the frozen h-BN aligned in a direction agreed with expected for thermophoresis, as indicated by the anisotropic thermal conductivity measurement and cross-sectional scanning electron microscopy (SEM) observation. Additionally, the theoretically estimated Peclet number, induced by thermophoresis, was higher than the experimentally determined value required to align suspended h-BN. To our best knowledge, the current study is the first experimental demonstration of controlling anisotropic filler orientation using thermophoresis.

This experiment has studied the exploration of tangent hyperbolic nanofluid (THNF) unsteady magneto-hydrodynamic (MHD) flow with Dufour and Soret effects. The governing partial differential equations (PDE) in terms of continuity, temperature, concentration, and momentum are reformed into ordinary differential equation (ODE) form and then explained numerically by employing the explicit finite difference (EFDM) technique using Fortran programming with the help of Compaq Visual Fortran 6.6a. The behavior of the engaged physical constraints (Weissenberg number, chemical reaction parameter, Lewis number, Eckert number, Prandtl number, thermophoresis number, and Brownian parameter) on temperature, velocity, and concentration are deciphered meticulously. The outcomes indicate that adding the Soret number into the THNF generates an increment in the concentration outline. The same incident happens to Dufour’s number and temperature profile. Assessment of the current findings with earlier distributed literature is identified and observed in a good contract. Consequences of distinctive physical factors on dimensionless velocity, temperature, and concentration are particularized through graphs and tables.

This study focuses on an incompressible non-Newtonian nanofluid in a 2-dimensional transient boundary layer through a cone. The Arrhenius activation energy and radiation absorption are both accounted for the non-Newtonian nanofluid model. The Runge-Kutta integration method via ODE45 MATLAB bvp4c is used and the converted coupled nonlinear equations are solved numerically. The numerical results are obtained for the nanoparticle concentration temperature, velocity distributions and also Sherwood number, Nusselt number, and skin friction for different values of the parameters, specifically the convection parameter, Prandtl number, nanofluid parameters and Lewis number. Also there are some discussions over the dependence of the thermophysical characteristics on these factors. Analyzing the impacts of activation energy and radiation absorption is a new approach which is the main novelty of this study. As results when the activation energy parameter has higher values, the skin friction decreases, but the Nusselt value and the Sherwood value exhibits reverse tendency. Skin-friction and the Sherwood value both are increasing as the values of the radiation absorption parameter go up, but the Nusselt number exhibits the reverse pattern. We compared the outcomes of our study with previous works to show the efficiency of this research.

The aim of present study is to investigate the convective heat and mass transfer in steady MHD boundary layer flow of an electrically conducting micropolar fluid over an inclined surface. Partial differential equations resulting from the mathematical modeling of the phenomenon are reduce to nonlinear ODEs, and a finite difference based scheme has been adopted to iteratively find the numerical solution by employing the successive over-relaxation (SOR) method. A self-developed computer code has been used in the MATLAB environment. Influence of chemical reaction, Brownian motion, thermophoresis, and viscous dissipation on the relevant features of the flow are discussed and analyzed through graphs and tables. Temperature dependent thermal conductivity and viscosity enhances the flow velocity. Wall suction slows down the flow in the boundary layer and brings the optimum value of the velocity very nearer to the inclined plane. The magnetic field affects the shear stress and viscous dissipation that is parallel due to suction. A decrease in the fluid temperature is noticed throughout the boundary layer for Prandtl number, Schmidt number, and suction parameter whereas an opposite trend is seen for temperature-dependent thermal conductivity, injection parameter, magnetic field, Brownian motion, and thermophoresis.

The effects of magnetic field and heat generation/absorption are investigated along a permeable stretching/shrinking wedge on unsteady MHD forced convective flow with thermophoresis and variable fluid properties. The obtained results are found to be in excellent harmony with previously published work. For various parameter values ​​entered into the problem, the non-dimensional velocity curve, temperature fields, and concentration curves and the numerical results for variable Prandtl and variable Schmidt numbers are graphically depicted. Since the Prandtl and Schmidt numbers vary greatly inside the boundary layer for flows with temperature-dependent variable thermal conductivity and variable viscosity, therefore, in the physical system- we must consider the Prandtl and Schmidt number as variables rather than constant when the fluid properties are the function of temperature.

The current research explores the problem of steady laminar flow of nanofluid on a two dimensional boundary layer using heat transfer of Cassona cross the linearly stretching sheet. The governing equations are partial differential equations which are transformed into non-linear ordinary differential equations by using some similarity transformation. The converted form of the combined non-linear higher-order ODEswith a set of boundary conditions are solved by means of Runge-Kutta 4th-order approach along with the shooting method. The nanoparticle concentration profiles, velocity, and temperature are examined by taking account of their influence of Prandtl number, “Brownian motion parameter”, Lewis number, thermophoresis, and Casson fluid parameter. It is reported that the temperature increase as Nt and Nb increases which causes thickening of the thermal boundary layer. Also it is observed that, there is increment in temperature profile for increasing values of Brownian motion parameter and the energy distribution grows with increment in the values of Thermophoresis parameter. The comparison for the local Nusselt & local Sherwood number has been tabulated with respect to variation of the Brownian Motion Parameter and Thermophoresis parameter. All the findings of the results are graphically represented and discussed.

In this report, the hydromagnetic dissipative Newtonian/non-Newtonian fluid flow over a stretched surface is examined numerically. Brownian moment, Joule heating, thermophoresis effects are considered. Similarity variables are employed to transform the non-linear PDEs into ODEs. The eminent shooting scheme is employed to determine the solution of the nonlinear equations. Solutions are achieved for different benefits of parameters of the model and the consequences are predicted in plots and tables. The Brownian moment imposed to accelerate the energy field and the dissipation influences to expand both the thermal and momentum fields. Also, simultaneous solutions are exhibited and found that the heat transport in Casson fluids has superior properties than the regular fluid.

Here we scrutinize magnetohydrodynamic mixed convection flow of viscous nanoliquid by a stretching cylinder. Heat flux, Joule heating and dissipation effect are examined in heat equation. Thermophoresis and Brownian diffusion behaviors are accounted. Entropy generation investigation is addressed. A first order chemical reaction is also accounted. Nonlinear PDEs are converted to ordinary differential system employing similarity variables. To develop a convergent solution we implemented ND-solve method. Variation of various sundry variables on Bejan number, velocity, entropy rate, concentration and temperature are graphically deliberated. Variation of various influential variables on Nusselt and Sherwood numbers are graphically examined. Larger slip parameter reduces the velocity field. Temperature is improved against the larger radiation variable. Concentration has a reverse trend against thermophoresis and Brownian motion variables. Radiation and magnetic variables have similar behavior on entropy optimization. Bejan number is reduced versus larger Brinkman number.

This investigation aims to scrutinize the flow phenomenon, thermal and concentration variations of two different hybrid nanofluids flow induced by a curved surface. The novelty of the work is to examine the heat and mass transport phenomena of Ag–MgO/water hybrid nanofluid and Fe3O4 –CoFe 2O4/water–ethylene glycol hybrid nanofluid under the influences of viscous dissipation, heat generation/absorption and chemical reaction using Buongiorno model. Suitable similarity transformations are implemented to convert the set of partial differential equation (PDEs) into non-linear ordinary differential equations (ODEs), and then shooting based Runge–Kutta–Fehlberg method of fourth fifth order (RKF45) via MATLAB is executed to achieve the numerical solution. The solution is discussed through graphs which provide a detailed physical clarification of each profile in terms of involved parameters effects. Also, the comparison of heat and mass transfer rates in both hybrid nanofluids is deliberated with the assistance of tables. It is noticed that the temperature profiles for both hybrid nanofluids grow high with a boost in the values of the viscous dissipation, heat generation/absorption and thermophoresis parameters. Moreover, the increasing values of thermophoresis parameter and chemical reaction parameter improve the mass transfer rate of both Ag–MgO/water hybrid nanofluid and Fe3O4 –CoFe 2O4/water–ethylene glycol hybrid nanofluid. The proposed investigation shows the importance of these hybrid nanofluids in chemical, manufacturing and nuclear plants, solar technologies, etc.

Thermophoresis is of common interest due to its influence on the deposition of particles. Present research on thermophoretic deposition mainly focused on the sub-micron particles, whereas the particle size during the radioactive aerosol monitoring process usually exceeds the range. In order to study the effect of thermophoresis on the deposition characteristics of aerosols ranging from 1 to 10 µm, direct numerical simulation (DNS) and experiments of particle deposition are performed in this paper aiming at still and turbulent flow respectively. The results obtained by DNS coupled with Lagrangian particle tracking (LPT) are validated by the experimental data and the theoretical values. The results indicate that thermophoresis has an influence on the deposition of micron-sized particles, and the effect of thermophoresis on deposition velocity depends on particle size. In the still air, when the temperature gradient is 3000 K/m, the deposition velocity of 1 and 10 µm particles will be increased by 87% and 4.8% respectively when compared with gravitational deposition velocity. In the turbulent flow, the motion of particles is dominated by turbulent motion. In the region near the wall, thermophoresis can increase the deposition rate on the cold wall.

In this study, we investigate steady-state convective boundary layer fluid flow of heat and mass transfer features of a nanofluid moving over a nonlinearly stretching sheet in detail. The nanofluid physical model of the problem comprises with effects of thermophoresis and Brownian motion. The mathematical model scrutinizes mass, momentum and heat transfer equations are reduced to ordinary differential equations over infinite domain using suitable similarity variables. Haar wavelet collocation method is used to solve the resulting coupled nonlinear ordinary differential equations with an infinite domain. The obtained results are validated with available numerical findings and the solutions are more efficient which confirm and verify the wavelet method. The impact of several interesting physical aspects viz. thermophoresis parameter, stretching parameter, Brownian motion and Schmidt number on nanoparticle volume fraction and temperature profile curves are graphically demonstrated. The derived quantities of various parameters on the rate of heat and mass transfer are depicted in tabular forms. It predicts that the increase in Brownian motion and thermophoresis parameter reduces the local Nusselt number. The local Sherwood number increases with an increase in the parameters of Brownian motion and thermophoresis. For both temperature and volume fraction profiles decreases due to an increase in the Schmidt number.

Deposition of micron particles in heat exchange duct is commonly encountered in many thermal and HVAC engineering applications. Previous studies on this important issue always considered turbulent air flow regime without conjugate heat transfer (CHT). However, the flow regimes and the CHT may have significant influences on particle deposition behaviors. Therefore, this paper aims to study particle deposition characteristics in laminar flow (LF), developing turbulent flow (DTF) and fully developed turbulent flow (FDTF) regimes with and without CHT. The v′2‾−fturbulence model and discrete particle model (DPM) were used to predict gas phase and solid phase, respectively. Moreover, a modified discrete random walk method was adopted to model turbulent particle dispersion. The results showed that particle deposition velocities greatly increase for small particles (dp20μm) due to thermophoretic deposition. WhenΔT=100Kanddp=1μm, the peak deposition velocity enhancement ratio reaches 3.8, 9.7 and 7.5 for LF, DTF and FDTF regimes respectively. Different flow regimes have obvious effects on the deposition characteristics. Particle deposition velocity for DTF regime is the highest, followed by FDTF case and LF case. Thermophoresis effect is reduced by the CHT, as the temperature difference decreases due to thermal conduction in solid domain. The CHT in DTF or FDTF regime has obviously larger effect on deposition characteristics, compared with the LF regime.

In this study, Galerkin weighted residual Finite Element Method is used to find the thermophoresis and Brownian diffusion motion of two phase nanofluid flow around a vertical cone in porous media. Gravity, Drag, Thermophoresis and Brownian forces are confided on the nanoparticles to find their motion during the time. The problem is solved in both transient and steady conditions. The effect of Nc and Nv parameters on the temperature and velocity profiles are investigated. Also, the effect of boundary conditions on the temperature and nanoparticles concentrations are investigated through the graphical contours. As a main result, variable thermal conductivity parameter (Nc) increament from zero to unity increased the velocity and temperature profile values, while had not significant effect on the nanoparticles concentration. Also, results revealed that increasing the Nv (from 2 to 200) and Nc (from 0 to 1), increased the (−θ′(0)) and (−f′(0)) to 1.36% and 0.15%, respectively.

The main objective of current study is investigation on thermo-hydraulic behavior of nanofluids in a sinusoidal wavy channel as a novel geometry under influences of thermophoresis and Brownian motion. Differential quadrature method and optimal homotopy asymptotic scheme have been employed to solve the momentum, continuity, energy and nanoparticle fraction equations. The validity of the proposed approaches is evaluated by comparing with previously published results. The impacts of some other physical parameters on temperature, nanoparticle concentration and velocity profiles will be analyzed in details. For instance, the results indicate that increment of the thermophoresis leads to enhance in values of temperature distribution. Also, the volume fraction of nanoparticle enhances by decreasing the parameter of thermophoresis.

The thermal convection in a horizontal layer of a porous medium saturated with a viscoelastic nanofluid was studied analytically. A Kuvshiniski-type constitutive equation is used to describe the behavior of viscoelastic nanofluids. The model used for the viscoelastic nanofluid incorporates the effects of Brownian motion and thermophoresis. A physically more realistic boundary condition than the previous ones on the nanoparticle volume fraction is considered i.e. the nanoparticle flux is assumed to be zero rather than prescribing the nanoparticle volume fraction on the boundaries. Using linear stability theory, the exact analytical expression for the Darcy–Rayleigh number is obtained in terms of various non-dimensional parameters. Results indicate that the coefficient of viscosity, porous medium and nanoparticles significantly influences the stability characteristics of the system. The effect of various parameters on the thermal instability is also presented graphically.

Heat and mass flux conditions on magnetohydrodynamic unsteady Eyring-Powell dusty nanofluid over a sheet is addressed. The combined effect of Brownian motion and thermophoresis in nanofluid modeling are retained. The Cattaneo-Christov heat flux model is imposed. A set of similarity variables are utilized to form ordinary differential system from the prevailing partial differential equations. The problem of ordinary differential system (ODS) is analyzed numerically through Runge-Kutta based shooting method. Graphical results of pertinent parameters on the velocity, temperature and nanoparticle concentration are studied. Skin friction coefficient, local Nusselt and Sherwood number are also addressed with help of graphs and also validated the present solutions with already existing solutions in the form of table. It is found that the thermal relaxation parameter improves the heat transfer rate and minimizes the mass transfer rate. The heat transfer rate is higher in prescribed heat flux (PHF) case when compared with prescribed wall temperature (PWT) case.

In this article, heat and mass transfer behavior of steady nanofluid flow between parallel plates in the presence of uniform magnetic field is studied. The important effect of Brownian motion and thermophoresis has been included in the model of nanofluid. The governing equations are solved via the Differential Transformation Method. The validity of this method was verified by comparison of previous work which is done for viscous fluid. The analysis is carried out for different parameters namely: viscosity parameter, Magnetic parameter, thermophoretic parameter and Brownian parameter. Results reveal that skin friction coefficient enhances with rise of viscosity and Magnetic parameters. Also it can be found that Nusselt number augments with an increase of viscosity parameters but it decreases with augment of Magnetic parameter, thermophoretic parameter and Brownian parameter.

This communication addresses the thermophoresis and Brownian motion effects on magnetohydrodynamic radiative Falkner-Skan flow of Casson fluid over a wedge with convective condition. In most of the existing studies thermal radiation is linear. Due to the noticeable significance of the numerous industrial as well as engineering applications, in this study we measured the thermal radiation is nonlinear. Numerical results are presented graphically as well as in tabular form with aid of Runge-Kutta and Newton’s methods. Effects of pertinent parameters on velocity, temperature and concentration distributions are presented and discussed for three wedge positions (i.e. static wedge, forward and backward movements of wedge). For engineering interest we also computed friction factor, heat and mass transfer rates. It is observed that thermal, concentration and momentum boundary layers are not uniform at different wedge positions. It is also observed that the heat and mass transfer rate is high when the wedge is moving in forward direction.

The problem of boundary layer of nanofluid flow which results from the stretching of a flat surface has been investigated numerically. The model includes the effects of Brownian motion, magnetic effect, non-linear velocity, variable thickness, thermophoresis, chemical reaction, porous medium, shape, thickness and heat source. The Partial differential equations are converted to ordinary deferential equations to solve analytically using shooting technique. The velocity, temperature and concentration profiles are discussed in detail for all parameters.

The problem of unsteady convective with thermophoresis, chemical reaction and radiative heat transfer in a micropolar fluid flow past a vertical porous surface moving through binary mixture considering temperature dependent dynamic viscosity and constant vortex viscosity has been investigated theoretically. For proper and correct analysis of fluid flow along vertical surface with a temperature lesser than that of the free stream, Boussinesq approximation and temperature dependent viscosity model were modified and incorporated into the governing equations. The governing equations are converted to systems of ordinary differential equations by applying suitable similarity transformations and solved numerically using fourth-order Runge–Kutta method along with shooting technique. The results of the numerical solution are presented graphically and in tabular forms for different values of parameters. Velocity profile increases with temperature dependent variable fluid viscosity parameter. Increase of suction parameter corresponds to an increase in both temperature and concentration within the thin boundary layer.

This paper investigates the influence of thermophoresis on mixed convection heat and mass transfer flow over a vertical wavy surface in a porous medium with variable properties, namely variable viscosity and variable thermal conductivity. The effect of wavy surface is incorporated into non-dimensional equations by using suitable transformations and then transformed into non-linear ordinary differential equations by employing the similarity transformations and then solved numerically. The transport process of flow, heat and mass transfer in the boundary layer for aiding and opposing flow cases is discussed. The structure of flow, temperature and concentration fields in the Darcy porous media are more pronounced by complex interactions among variable viscosity, variable thermal conductivity, mixed convective parameter, thermophoresis and amplitude of the wavy surface. Increasing thermophoresis parameter enhances velocity profile, concentration distribution and Sherwood number while reduces Nusselt number. As increase in variable viscosity, temperature and concentration distributions are enhanced while velocity profile, Nusselt number and Sherwood numbers are reduced. This study finds applications in aerosol Technology, space technology and processes involving high temperatures.