Brownian Motion Effects Research Articles

Numerical Investigation of Nanofluids Mixed Convection in a Lid-Driven Cavity with Two Heat Sources

Heat transfer enhancement through using nanofluids improves energy efficiency and enables energy savings. In this paper, a nanofluids flow and heat transfer are numerically investigated in a cavity. Four nanoparticle types (CuO, Al2O3, ZnO and SiO2) dispersed in the base liquid (water) are considered. The cavity is partially heated by two identical sources placed on the vertical walls. Partial differential equations (PDEs) are solved using (ANSYS R2 (2020) software). The Maxwell physical model and the Brownian motion effect are used to calculate the thermal conductivity and dynamic viscosity considering the diameter of the nanoparticles. Numerical simulations are performed for various parameters including nanoparticle type, nanoparticle volume fraction (0 ≤ Φ ≤ 0.06), nanoparticle diameter (29 nm, 49 nm and 69 nm) and Richardson number (0.1 ≤ Ri ≤ 10). The streamlines, isotherms, and average Nusselt number are analyzed. The results of this study showed that the average Nusselt number increases with increasing the volume fraction of nanoparticles, and decreases with incrementing the nanoparticle diameter. The heat transfer increases as the Richardson number increases. The nanofluid SiO2-water is suggested as it showed the highest heat transfer rate among the investigated nanofluids. Using Φ = 6% nanoparticles with a diameter of 29 nm improves the average Nusselt number by 6.81%, 2.43% and 0.96% for SiO2, Al2O3, ZnO, respectively, when compared to CuO, for the right-wall (Nuaverage(1)), and 6.70%, 2.40% and 0.84% for the left wall (Nuaverage(2)).

Computational study on the effects of Brownian motion and thermophoresis on thermal performance of cross fluid with nanoparticles in the presence of Ohmic and viscous dissipation in chemically reacting regime

Computational study on the effects of Brownian motion and thermophoresis on thermal performance of cross fluid with nanoparticles in the presence of Ohmic and viscous dissipation in chemically reacting regime

Interplay between Brownian and hydrodynamic tracer diffusion in suspensions of swimming microorganisms

The general problem of tracer diffusion in non-equilibrium baths is important in a wide range of systems, from the cellular level to geographical length scales. In this paper, we revisit the archetypical example of such a system: a collection of small passive particles immersed in a dilute suspension of non-interacting dipolar microswimmers, representing bacteria or algae. In particular, we consider the interplay between thermal (Brownian) diffusion and hydrodynamic (active) diffusion due to the persistent advection of tracers by microswimmer flow fields. Previously, it has been argued that even a moderate amount of Brownian diffusion is sufficient to significantly reduce the persistence time of tracer advection, leading to a significantly reduced value of the effective active diffusion coefficient $D_A$ compared to the non-Brownian case. Here, we show by large-scale simulations and kinetic theory that this effect is in fact practically relevant only for microswimmers that effectively remain stationary while still stirring up the surrounding fluid – so-called shakers. In contrast, for moderate and high values of the swimming speed, relevant for biological microswimmer suspensions, the effect of Brownian motion on $D_A$ is negligible, leading to the effects of advection by microswimmers and Brownian motion being additive. This conclusion contrasts with previous results from the literature, and encourages a reinterpretation of recent experimental measurements of $D_A$ for tracer particles of varying size in bacterial suspensions.

Brownian motions and thermophoresis effects in a vertically stretching sheet with micropolar nanofluid flow

This work is about the investigation of the flow of a micropolar nanoliquid over a stretching surface, taking into account the effects of thermal radiation, thermophoresis, and Brownian motion. The study focuses on the impact of these factors on heat and mass transfer rates, with the assumption that the Newtonian heat impact dominates. The homotropy approach is used to generate non-dimensional transformational parameters, which are then used to create a system of nonlinear differential equations. The study includes charts and tables that define transfer rates based on various parameters, and the results suggest that increased radiance levels and Nb parameters lead to improvements in heat and mass convection. The graphics used in the study are accurate and consistent with previous research in the field. Overall, this research provides insights into the complex dynamics of micropolar nanoliquid flow and the factors that impact heat and mass transfer in this system.

MHD nanofluid flow through Darcy medium with thermal radiation and heat source

In this analysis, we have considered heat transmission in two-dimensional steady laminar nanofluid flow past a wedge. Magnetohydrodynamic (MHD), Brownian motion, viscous dissipation and thermophoresis effects are considered over the porous surface. Similarity transformations have been used to change the governing partial differential equations (PDEs) into nonlinear higher-order ordinary differential equations (ODEs). Governing ODEs with boundary conditions are then converted to the system of first-order initial value problem. After that the modeled system is solved numerically by RK4 technique. Impact of the magnetic number, Eckert number, Prandtl number, Lewis number, Brownian motion, thermophoresis and permeability parameters on the flow domain is analyzed graphically as well as in tabular form. It is noted that magnitude of Nusselt number for the flow regime increases with the increase of nondimensional parameter [Formula: see text] while opposite behavior is observed in case of R.

The Investigation of Thermoacoustic Methods for Nanofluid Stability on Heat Exchanger

Due to various engineering applications, nanofluids have gained much attention in the last decade. A Nanofluid is a nanometer-sized particle such as metal, oxide, carbide, etc., dispersed into a base heat transfer fluid. The heat exchanger is a device to transfer heat between fluids. Heat exchanger plays a very important role in modern industry. The new innovative fluid called nanofluid is introduced to improve the overall heat transfer and heat transfer rate. Thermoacoustic is a system which uses sound waves and a non-flammable mixture of inert gases to generate an effect. This paper investigates the enhancement of the heat transfer coefficient of a nanofluid containing alumina (Al2O3) nanoparticle with a volume fraction of 0.4% and sonification at 100 Hz, 500 Hz and 1000 Hz. The addition of Al2O3 nanoparticles will affect the characteristics of the nanofluids, which affect the values of density, specific heat, thermal conductivity, and dynamic viscosity. And the addition of the thermoacoustic method with the sonification of acoustic waves can stabilise the effect of Brownian motion in the nanofluid flow. The maximum results are obtained using acoustic waves at 1000 Hz at high temperatures.

Forced convective flows of Casson hybrid nanofluid and entropy production over diverging channel with variable thermophysical properties

The heat transfer occurring on boundary layer flows during dilute suspension of Cu–Al2O3 nanoparticles-based non-Newtonian Casson hybrid nanofluid over diverging channel is to be characterized in this model. The governing equations comprise continuity, momentum, energy and concentration equations which incorporated variable viscosity and magnetic effects in the momentum equation, variable thermal conductivity, chemical reaction, thermal radiative heat flux, uniform magnetic field, Joule heating and viscous dissipative effects in the energy equation and Brownian motion and thermophoretic effects in the concentration equation. The modeled equations are nondimensionalized using nonsimilar variables and linearized using quasilinearization technique. The system of linearized partial differential equations is solved numerically using implicit finite difference and successively iterated with the help of Varga’s algorithm. The physical impacts of viscous dissipation parameter (Ec), Brownian motion ([Formula: see text]) on velocity, temperature, concentration and Schmidt number (Sc) influences on skin friction, Nusselt number, Sherwood number profiles, Bejan lines and total entropy production profiles are simulated graphically. The velocity profiles are enhanced and the temperature profile declines for augmented values of Eckert number. Moreover, for augmented values of Schmidt number the heat and mass transfer rates are enhanced and the Bejan lines dropped a decreasing trend whereas total entropy production is augmented near the wall region. The improved values of the Schmidt number physically increased Sc in the heat transfer rate. The ascending profile of the mass transfer rate with increased values of the viscous dissipation parameter Ec demonstrated that the graph is raised for larger values of the viscous dissipating parameter (Ec). The physical behavior of incremental mass transfer rate led to the conclusion that the relative diffusivity of nanoparticles is characterized by both nondimensional numbers Ec and Sc which are directly proportional to the viscous forces.

Numerical Computation of Radiative MHD Micropolar Nanofluid Flow over a Stretching Sheet with First Order Chemical Reaction and Soret Effects

The outcomes of the current study may have broad applications in contemporary industrial technologies, including those involved in blood transportation, lubrication, rigid and random cooling particles of metallic sheets, etc. New studies have shown that the thermal conductivity of a nanofluid is triggered by Brownian motion and thermophoretic collisions. Primary research interests include the effects of chemical reaction, radiation, and the Soret effect on micropolar nanofluids along an inclined stretched sheet. Effects of thermophoresis and Brownian motion is considered and the Buongiorno's model is taken into account. To get the nonlinear ordinary differential equation from the PDEs, compatible transformations are used. Mathematica's NDSolve technique is implemented to do a numerical treatment of the dimensionless equations once they have been translated. The upsides of this strategy lie in its ability to automatically track errors and select the best algorithm. Graphical and numerical treatments of the physical quantities of interest are provided. The tabulated magnitudes of the numerical outputs compare well with those that currently exist. Graphs showing the energy transfer rate as a function of the many contributing factors. As the Brownian motion factor increases, the skin friction and the mass transfer rate upsurge and the rate at which energy may be transported climbs. As the angle of incidence increases, skin friction rises while the Nusselt number and Sherwood number fall. Velocity profile rises with the material parameter. Radiation parameter tends to rise the temperature.

Dual solutions for nanofluid flow past a moving plate embedded in a Darcy porous medium in attendance of heat source/sink

The aim of this study is to present forced convective nanofluid flow over a moving plate embedded in an absorbent medium. Following Darcy law’s for porous medium, the flow analysis is explored in attendance of warmth basis/drop. The main objective of this study is to explore the effects of Brownian motion and thermophoresis. The plate is considered to move in both directions: in the way of movement of fluid and in the opposite route of fluid movement. Similarity alterations have been applied to alter the leading partial differential equations (PDEs) to ordinary differential equations (ODEs). Numerical solutions have been obtained with the help of MATHEMATICA software. Dual solutions have been obtained when the plate and liquid go in reverse ways. Wall shear stress, Nusselt and Sherwood numbers all are found to rise with the rising permeability parameter of absorbent medium. For Nusselt and Sherwood numbers, ranges of dual solutions diminish by the mounting values of permeability parameter K. The critical values for porosity parameter [Formula: see text], 0.02, 0.03 are [Formula: see text], [Formula: see text], [Formula: see text], respectively. For decreasing values of s, range of dual solutions decreases. For [Formula: see text], dual solutions exist in the range [Formula: see text].

Computation of inclined magnetic field, thermophoresis and Brownian motion effects on mixed convective electroconductive nanofluid flow in a rectangular porous enclosure with adiabatic walls and hot slits

This analysis theoretically investigates the transport phenomena of mixed convection flows in an enclosure of rectangular geometry saturated with a permeable medium filled with an electrically conducting nanofluid. An inclined magnetic field is taken into consideration. Buongiorno’s model is utilized to characterize the nanoliquid. The enclosure has adiabatic walls and hot slits. A uniform cold temperature is maintained at the enclosure’s lower and upper walls. The enclosure’s vertical walls are thermally insulated with hot slits at the center of the walls. This kind of analysis on mixed convective, electrically conducting nanofluid flows in enclosures finds applications in smart nanomaterial processing systems and hybrid electromagnetic nanoliquid fuel cells. The Marker-And-Cell (MAC) method is utilized to solve the transformed nondimension system of governing equations subject to the fitted boundary conditions. The effects of key physical parameters on streamlines, isotherms, iso-concentration contour plots and the heat transmission rate are examined. The simulations demonstrate that the Richardson number has a predominant impact on the thermo-solutal features of nanofluid flow in the rectangular enclosure. Variations in magnetic field and buoyancy ratio parameters exert a notable influence on the iso-concentrations and isotherms. An increase in the Darcy number values exhibits a tendency to magnify the local heat transfer rate. Higher Grashof number values reduce the local Nusselt number profiles. The effect of porous parameter is significant in the streamlines, isotherms and iso-concentrations. Thus, the porous medium can significantly control the transport phenomena in the enclosure. The concentration, temperature and velocity contours are strongly modified by the variations in the Grashof number.

Analysis of Entropy Generation on MHD Radiative Viscous-Ohmic Dissipative Heat Transfer Over a Stretching Sheet in a Chemically Reactive Jeffrey Nanofluid with Non-Uniform Heat Source/Sink Based on SQLM

We have examined the effect of entropy generation and nonlinear thermal radiation on magnetohydrodynamic (MHD) in Jeffrey nanofluid over a permeable stretching sheet with viscous-Ohmic dissipation and non-uniform heat source/sink. Brownian motion and thermophoresis effects have also been taken into account. The basic governing equations of the boundary layer flow are then solved numerically by the Spectral Quasilinearization method (SQLM). Various controlling physical parameters effects on velocity, temperature, concentration, entropy generation and Bejan number profiles are presented graphically. Results show that increasing the magnetic parameter, Brownian motion parameter, and thermophoresis parameter enhance the temperature profiles. Furthermore, the entropy generation profiles increase with space-dependent and temperature-dependent parameters, wall mass flux parameter, and chemical reaction parameter near to the sheet. In contrast, reverse trends are observed away from the sheet. Novelty of entropy generation is also provided to reflect the effects of several relevant physical parameters on the entropy generation rate and Bejan number.

Chemically reactive MHD convective flow and heat transfer performance of ternary hybrid nanofluid past a curved stretching sheet

One of the topmost challenges of today’s industry age is to find an efficient heat transfer fluid because heat transfer rate in common fluids is unable to provide an efficient heating and cooling process in the industries. Ternary hybrid nanofluids are considered as next generation heat transfer fluids, which are prepared by suspension of three different type of nanoparticles in the base fluids. This novel class of nanofluids, due to its unique and dynamic thermophysical properties, has diverse applications in numerous arenas of nanotechnology and heat transfer appliances. This research article examines an electrically conducting and magnetically influenced 2D flow of modified hybrid nanofluid past a curved stretching sheet. The considered trihybrid nanofluid contains nanometer sized particles of three different materials (CuO, Al2O3, TiO2) suspended in the water. The preliminary assumptions in this numerical investigation include the exponential heating, Brownian motion, chemical factor, and thermophoresis effects. At boundary, convective mass and heat flux constraints are employed. This pragmatic investigation with the aforementioned presumption is conducted for the first time to evaluate heat and mass transference properties of ternary nanofluid past a curved stretchable surface. The problem is mathematically modelled by using the fundamental momentum and energy equations and modified to cater the solid additives concentration in the base fluid. The modelled Partial Differential Equations (PDEs) are subsequently transformed into Ordinary Differential Equations (ODEs) by employing suitable similarity transformation and subsequently solved by the MATLAB software bvp4c to demonstrate role of important controlling parameters in tabular and graphical form. The research concludes that the enhancement of curvature factor enhances the velocity profile while the impact is opposite for magnetic factor. The most important and an interesting aspect of this innovative study is that the rate of heat transfer increases for all embedding parameters (ie M,K,Nb,Nt,Ec,Δt,β,BiT,BiCandQe), which is the basic purpose of using nanofluids for their promising use in nanotechnology. The study reveals that frictional force at the stretching surface decreases by reducing curvature of surface. However, converse trend is observed for increasing magnetic factor. Moreover, said impact of curvature is more prominent for ternary hybrid nanofluid whereas M has greater impact for unitary nanofluid. The greater heat source factor, activation energy, concentration and thermal Biot numbers, temperature difference and thermophoresis factors increase the concentration boundary layer while decreasing trend is observed for Brownian motion, Schmidt number and chemical reaction factor. The Nusselt number increases for higher values of thermal Biot number, thermophoresis parameter and the heat source factor.

Optimizing geometrical structure of a residential parabolic solar collector relying on hydrothermal assessment and second law analysis

Researchers are interested in the optimization of thermal systems due to the rising demand towards renewable and green energy to reduce greenhouse gasses and expenses. To achieve this, the present work aims to conduct the numerical modeling on the residential scale trough solar collector. For this purpose, the lattice Boltzmann method is employed with special treatment for the curved physical boundaries. To enhance the thermal capability of the solar collector, the CuO-water nanofluid is utilized, which its thermal conductivity is estimated using Koo–Kleinstreuer and Li (KKL) model. Furthermore, the Brownian motion effect on the dynamic viscosity is taken into account. In addition, the local and volumetric second law analysis is performed. Besides, the heat line visualization is done to capture the path-line of heat energy within the solar collector. The thermal distribution, flow field, local entropy production (i.e. fluid friction irreversibility and heat transfer irreversibility maps), volumetric entropy generation, Bejan number, and average Nusselt number are the studied items in terms of the governing parameters. The Rayleigh number (103 ≤ Ra ≤ 106), CuO nanoparticle concentration (φ = 0, 0.01, 0.02, 0.03, 0.04) and four structural design of the solar collector (Single-pipe, Double-pipe, Triple-pipe, Quadruple-pipe) are assumed as the governing parameters.

Computational Assessment of Unsteady Flow Effects on Magnetic Nanoparticle Targeting Efficiency in a Magnetic Stented Carotid Bifurcation Artery.

Worldwide, cardiovascular disease is the leading cause of hospitalization and death. Recently, the use of magnetizable nanoparticles for medical drug delivery has received much attention for potential treatment of both cancer and cardiovascular disease. However, proper understanding of the interacting magnetic field forces and the hydrodynamics of blood flow is needed for effective implementation. This paper presents the computational results of simulated implant assisted medical drug targeting (IA-MDT) via induced magnetism intended for administering patient specific doses of therapeutic agents to specific sites in the cardiovascular system. The drug delivery scheme presented in this paper functions via placement of a faintly magnetizable stent at a diseased location in the carotid artery, followed by delivery of magnetically susceptible drug carriers guided by the local magnetic field. Using this method, the magnetic stent can apply high localized magnetic field gradients within the diseased artery, while only exposing the neighboring tissues, arteries, and organs to a modest magnetic field. The localized field gradients also produce the forces needed to attract and hold drug-containing magnetic nanoparticles at the implant site for delivering therapeutic agents to treat in-stent restenosis. The multi-physics computational model used in this work is from our previous work and has been slightly modified for the case scenario presented in this paper. The computational model is used to analyze pulsatile blood flow, particle motion, and particle capture efficiency in a magnetic stented region using the magnetic properties of magnetite (Fe3O4) and equations describing the magnetic forces acting on particles produced by an external cylindrical electromagnetic coil. The electromagnetic coil produces a uniform magnetic field in the computational arterial flow model domain, while both the particles and the implanted stent are paramagnetic. A Eulerian-Lagrangian technique is adopted to resolve the hemodynamic flow and the motion of particles under the influence of a range of magnetic field strengths (Br = 2T, 4T, 6T, and 8T). Particle diameter sizes of 10nm-4µm in diameter were evaluated. Two dimensionless numbers were evaluated in this work to characterize relative effects of Brownian motion (BM), magnetic force induced particle motion, and convective blood flow on particle motion. The computational simulations demonstrate that the greatest particle capture efficiency results for particle diameters within the micron range of 0.7-4µm, specifically in regions where flow separation and vortices are at a minimum. Similar to our previous work (which did not involve the use of a magnetic stent), it was also observed that the capture efficiency of particles decreases substantially with particle diameter, especially in the superparamagnetic regime. Contrary to our previous work, using a magnetic stent tripled the capture efficiency of superparamagnetic particles. The highest capture efficiency observed for superparamagnetic particles was 78% with an 8T magnetic field strength and 65% with a 2T magnetic field strength when analyzing 100nm particles. For 10nm particles and an 8T magnetic field strength, the particle capture efficiency was 55% and for a 2T magnetic field strength the particle capture efficiency was observed to be 43%. Furthermore, it was found that larger magnetic field strengths, large particle diameter sizes (1µm and above), and slower blood flow velocity improves the particle capture efficiency. The distribution of captured particles on the vessel wall along the axial and azimuthal directions is also discussed. Results for captured particles on the vessel wall along the axial flow direction showed that the particle density decreased along the axial direction, especially after the stented region. For the entrance section of the stented region, the captured particle density distribution along the axial direction is large, corresponding to the center-symmetrical distribution of the magnetic force in that section. The simulation results presented in this work have shown to yield favorable capture efficiencies for micron range particles and superparamagnetic particles using magnetized implants such as the stent discussed in this work. The results presented in this work justify further investigation of MDT as a treatment technique for cardiovascular disease.

The Role of Quadratic-Linearly Radiating Heat Source with Carreau Nanofluid and Exponential Space-Dependent Past a Cone and a Wedge: A Medical Engineering Application and Renewable Energy

A mathematical analysis for a steady, incompressible, laminar Carreau nanofluid flow over a porous cone and wedge is considered. The novelty of this research work is to scrutinize an exponential space-dependent Cattaneo–Christov heat flux and quadratic Rosseland approximation effects. Two-phase nanofluid model, i.e., Brownian motion, and thermophoretic effects are included. This study also employs non-linear thermal radiation and convective surface boundary conditions to investigate heat transport phenomena. The Carreau nanofluid boundary layer equations are derived using the standard boundary layer approximations. By applying the similarity transformations, the managing set of partial differential equations (PDEs) becomes a system of connected non-linear ordinary differential equations (ODEs). The resultant non-linear ODEs are solved numerically utilizing the numerical method, particularly the bvp4c function in MATLAB. The significances of the fluid motion are visualized by sketching several Carreau nanofluid flow’s relevant parameters using graphic outputs. The effects of a wide range of thermophysical variables on liquid properties including velocity, temperature, concentration, skin-friction, Nusselt number, and Sherwood number are investigated and discussed. This study’s findings are compared to previously announced results within a limited range, where strong validation was seen. The results demonstrate that the opposite mechanism is observed with repercussion of Weissenberg number (We) on velocity profile and concentration, the enhancement of We increases the momentum boundary layer while it reduces the concentration boundary layer. The outcomes could be applied to the cooling of equipment, electronics, and various industrial units.

Investigating the Effect of Gravity Modulation on Weakly Nonlinear Magnetoconvection in a Nonuniformly Rotating Nanofluid Layer

This paper investigates the impact of gravity modulation on weakly nonlinear magnetoconvection in a nanofluid layer that is nonuniformly rotating. The fundamental equations are obtained for the Cartesian approximation of the Couette flow using the Boussinesq approximation and gravitational modulation. The weakly nonlinear regime is analyzed using the method of perturbations with respect to the small supercritical parameter of the Rayleigh number, considering the effects of Brownian motion and thermophoresis in the nanofluid layer. Heat and mass transfer are evaluated in terms of finite amplitudes and calculated from the Nusselt numbers for the fluid and the volume concentration of nanoparticles. The findings demonstrate that gravitational modulation, nonuniform rotation, and differences in the volume concentration of nanoparticles at the layer boundaries can effectively control heat and mass transfer. Additionally, the negative rotation profile has a destabilizing effect. The study shows that the modulated system conveys more heat and mass than the unmodulated system.

Falkner-Skan aspects of a radiating (50% ethylene glycol + 50% water)-based hybrid nanofluid when Joule heating as well as Darcy-Forchheimer and Lorentz forces affect significantly

Falkner-Skan aspects are revealed numerically for a non-homogeneous hybrid mixture of 50% ethylene glycol-50% water, silver nanomaterials Ag, and molybdenum disulfide nanoparticles MoS2 during its motion over a static wedge surface in a Darcy-Forchheimer porous medium by employing the modified Buongiorno model. The Brownian and thermophoresis mechanisms are included implicitly along with the thermophysical properties of each phase via the mixture theory and some efficient phenomenological laws. The present simulation also accounts for the impacts of nonlinear radiative heat flux, magnetic forces, and Joule heating. Technically, the generalized differential quadrature method and Newton-Raphson technique are applied successfully for solving the resulting nonlinear boundary layer equations. In a limiting case, the obtained findings are validated accurately with the existing literature outcomes. The behaviors of velocity, temperature, and nanoparticles volume fraction are discussed comprehensively against various governing parameters. As crucial results, it is revealed that the temperature is enhanced due to magnetic field, linear porosity, radiative heat flux, Brownian motion, thermophoresis, and Joule heating effects. Also, it is depicted that the hybrid nanoliquids present a higher heat flux rate than the monotype nanoliquids and liquids cases. Moreover, the surface frictional impact is minimized via the linear porosity factor. Furthermore, the surface heat transfer rate receives a prominent improvement due to the radiative heat flux inclusion.

Numerical Solution of Natural Convection Nanofluid Flow over aNon-Isothermal Vertical Plate

The natural convection nanofluidflow over a non-isothermal vertical plate is studied numerically. The effects of Brownian motion and thermophoresis parameters are incorporated into models used for nanofluids. The non-linear partial differential equations and boundary conditions are transformed into a set of nonlinear ordinally differential equations using the similarity transformations. The resulting system of equations are solved numerically by using shooting techniques. This solution depends on the Prandtl number (Pr), Buoyancy ratio (Nr), Brownian-motion (Nb), thermophoresis parameter (Nt), Lewis number (Le), and power-law exponent (λ). For different values of λ, Le and Pr, the influence of reduced Nusselt number with Nr, Nb and Nt is represented by correlation formulas and compared with previously published results and found to be in better agreement.

Computational method for energy transport of MHD nanofluids flow near non-aligned stagnation point with non-linear thermal radiation and interface slip

Haemodialysis, nuclear reactors, cooling and heating systems, and heat exchangers are glimpses of applications where thermal problems are considered as a fundamental for flow over aligned stagnation points with heat and mass transfer components. The purpose of this study is to present steady dual solutions for non-aligned stagnation point flow of nanofluid over a linearly contracting/expanding surface under temperature and velocity slips. The mathematical model is established using boundary layer assumption. The authors acknowledge from prior investigations and studies that the non-aligned stagnation point flow across a contracting/expanding surface is highly rare in the field of engineering and fluid dynamics research. In the backdrop of non-linear thermal radiation, the problem of oblique hydromagnetic stagnation point flow of an electrically conducting optically dense viscous incompressible nanofluid across a convectively heated stretching sheet is formulated. The effects of Brownian motion and thermophoresis are incorporated into the nanofluid model. With the use of appropriate similarity transformations, the governing nonlinear partial differential equations for momentum, energy, and nanoparticle concentration are converted into a set of nonlinear ordinary differential equations. Using the BVP4c approach, the modified equations are numerically solved. It is discovered that when the strength of the magnetic field increases, the non-alignment of the re-attachment point on the sheet surface becomes less pronounced. The thickness of the thermal boundary layer grows as the magnetic and Biot parameters expand. The extent of the skin friction factor ascends with increasing magnetic field and suction variable inputs. The heat transfer rate detract with radiative parameter.

Radiative heat transfer on the peristaltic flow of an electrically conducting nanofluid through wavy walls of a tapered channel

Present analysis deals with the characteristics of radiative heat on the peristaltic flow of nanofluid through wavy walls of a tapered channel. Peristaltic flows within the pumping process arise in the region having lower to higher pressure region. Assumption of velocity slip along with the convective boundary condition energizes the thermal system as well as the flow phenomena. However, the combined effect of Brownian motion and thermophorsis due to the cross-diffusion effect affects the flow properties. One of the significant applications of the flow is that the blood pumping in the human body. It acts as a vehicle through the liquid that past through the wavy channels walls contacting liquids expands in its length due to the dynamical rush. However, solution of the transformed governing flow phenomena is obtained by employing approximate analytical technique known as Variation Parameter Method (VPM). The characteristics of the parameters involved in the system are presented via graphs. Present outcome warrants that, the significance of magnetic strength and flow through the permeable medium may favours to enhance the pumping procedure as the pressure gradient lower down in the non-Darcy medium found to be one of the important observations. Further, significant enhancement in the fluid temperature and concentration profile is exhibited due to the consideration of the convective conditions i.e. the augmentation in the thermal and solutalBiot numbers respectively.