Brownian Motion Parameter Nb Research Articles

Buoyancy Effetcs On FalknerSkan Flow of a Maxwell Nanofluid Fluid With Activation Energy past a wedge: Finite Element Approach

A description of heat transportation in Maxwell fluids mixed with nanoparticles over a wedged wall is presented in this article. The porous and thermally convective boundary of the wedge undergoes a sudden movement. The physical mechanism is influenced by an invariant magnetic field. A transformed formulation is established in ordinary differential form by involving similarity functions. A robust coding based on finite element analysis is developed in Matlab script. The convergence and accuracy of the solution are tested against reliable criteria. The interest in computational effort centered on the formation of boundary layer patterns for fluid temperature, the volume fraction of nano-inclusions, and fluid velocity when influential parameters are varied. The larger Hartmann number Ha, unsteady parameter A, Deborah number β, and wedge parameter m made the flow along the wall faster and produced thinning of the boundary layer. The higher values of Hartmann number, mixed convection, buoyancy ratio parameter, thermophoresis parameter Nt, Brownian motion parameter Nb, wedge parameter m, and Biot number have raised the fluid temperature. The local heat transfer rate reduces against Nt and it is higher for stretching wedge and smaller for the shrinking wedge. An efficient heat transfer in macro-tech processes may utilize the procedure and findings of this study.

Finite element simulation of bioconvection Falkner–Skan flow of a Maxwell nanofluid fluid along with activation energy over a wedge

A description of heat transportation in Maxwell nano-fluids mixed with self-motile thermophile microorganisms over a wedged wall is presented in this article. The porous and thermally convective boundary of the wedge undergoes a sudden movement. The physical mechanism is influenced by an invariant magnetic field. A transformed formulation is established in ordinary differential form by involving similarity functions. A robust coding based on finite element analysis is developed in Matlab script. The convergence and accuracy of the solution are tested against reliable criteria. The interest in computational effort centered on the formation of boundary layer patterns for microorganism distribution, fluid temperature, the volume fraction of nano-inclusions, and fluid velocity when influential parameters are varied. The larger Hartmann number Ha, unsteady parameter A, Deborah number β, and wedge parameter m made the flow along the wall faster and produced thinning of the boundary layer. The higher values of Hartmann number, mixed convection, buoyancy ratio parameter, thermophoresis parameter Nt, Brownian motion parameter Nb, wedge parameter m, radiation parameter Rd, and Biot number have raised the fluid temperature. The local heat transfer rate reduces against Nt and it is higher for stretching wedge and smaller for the shrinking wedge. An efficient heat transfer in macro-tech processes may utilize the procedure and findings of this study.

Effect of heat source/sink on MHD free convection flow in a channel filled with nanofluid in the existence of induced magnetic field: an analytic approach

An attempt to examine the relevance of heat source/sink on magnetohydrodynamics free convection flow in a vertical channel with an induced magnetic field is achieved. The analytical solution to the set of the differential equation is obtained by perturbation method for small thermophoresis and Brownian diffusion parameters under the unified thermal boundary condition (isothermal and isoflux boundary condition) for the energy equation. Numerical solution to the flow equation is also obtained by incorporating RKF45 in Maple software. The influence of active parameters such as Hartman number (Ha), magnetic Prandtl number (Pm), heat source/sink parameter (± S), Buoyancy ratio (Br), Brownian motion (Nb) and thermophoretic parameter (Nt) on velocity, induced magnetic field, induced current density, nanoparticles concentration, temperature and skin friction are depicted and discussed in detail. Results reveal that the Brownian motion parameter (Nb) and Buoyancy ratio (Br) augment enhances the shear stress whereas the contrast is observed with Hartman number (Ha) and thermophoretic parameter (Nt). Results also reveal that Hartman number (Ha) and thermophoretic parameter (Nt) enhances the induced current density while the contrast is true for heat sink parameter (−S). Finally, the temperature of the nanofluid could be enhanced with increase in Brownian motion parameter (Nb) and heat source parameter (+ S).

Thin Film Flow of Couple Stress Magneto-Hydrodynamics Nanofluid with Convective Heat over an Inclined Exponentially Rotating Stretched Surface

In this article a couple stress magneto-hydrodynamic (MHD) nanofluid thin film flow over an exponential stretching sheet with joule heating and viscous dissipation is considered. Similarity transformations were used to obtain a non-linear coupled system of ordinary differential equations (ODEs) from a system of constitutive partial differential equations (PDEs). The system of ordinary differential equations of couple stress magneto-hydrodynamic (MHD) nanofluid flow was solved using the well-known Homotopy Analysis Method (HAM). Nusselt and Sherwood numbers were demonstrated in dimensionless forms. At zero Prandtl number the velocity profile was analytically described. Furthermore, the impact of different parameters over different state variables are presented with the help of graphs. Dimensionless numbers like magnetic parameter M, Brownian motion parameter Nb, Prandtl number Pr, thermophoretic parameter Nt, Schmidt number Sc, and rotation parameter S were analyzed over the velocity, temperature, and concentration profiles. It was observed that the magnetic parameter M increases the axial, radial, drainage, and induced profiles. It was also apparent that Nu reduces with greater values of Pr. On increasing values of the Brownian motion parameter the concentration profile declines, while the thermophoresis parameter increases.

Computational fluid dynamic simulation of two-fluid non-Newtonian nanohemodynamics through a diseased artery with a stenosis and aneurysm

This article presents a two-dimensional theoretical study of hemodynamics through a diseased permeable artery with a mild stenosis and an aneurysm present. The effect of metallic nanoparticles on the blood flow is considered, motivated by drug delivery (pharmacology) applications. Two different models are adopted to mimic non-Newtonian characteristics of the blood flow; the Casson (viscoplastic) fluid model is deployed in the core region and the Sisko (viscoelastic) fluid model employed in the peripheral (porous) region. The revised Buongiorno two-component nanofluid model is utilized for nanoscale effects. The blood is considered to contain a homogenous suspension of nanoparticles. The governing equations are derived by extending the Navier-Stokes equations with linear Boussinesq approximation (which simulates both heat and mass transfer). Natural (free) double-diffusive convection is considered to simulate the dual influence of thermal and solutal buoyancy forces. The conservation equations are normalised by employing appropriate non-dimensional variables. The transformed equations are solved numerically using the finite element method with the variational formulation scheme available in the FreeFEM++ code. A comprehensive mesh-independence study is included. The effect of selected parameters (thermophoresis, Brownian motion, Grashof number, thermo-solutal buoyancy ratio, Sisko parameter ratio, and permeability parameter) on velocity, temperature, nanoparticle concentration, and hemodynamic pressure have been calculated for two clinically important cases of arteries with stenosis and an aneurysm. Skin-friction coefficient, Nusselt number, volumetric flow rate, and resistance impedance of blood flow are also computed. Colour contours and graphs are employed to visualize the simulated blood flow characteristics. It is observed that by increasing the thermal buoyancy parameter, i.e. Grashof number (Gr), the nanoparticle concentration and temperature decrease, whereas velocity increases with an increment in the Brownian motion parameter (Nb). Furthermore, velocity decreases in the peripheral porous region with elevation in the Sisko material ratio (m) and permeability parameter (k’). The simulations are relevant to transport phenomena in pharmacology and nano-drug targeted delivery in haematology.

Peristaltic Flow of Dusty Nanofluids in Curved Channels

In this paper, numerical investigations for peristaltic motion of dusty nanofluids in a curved channel are performed. Two systems of partial differential equations are presented for the nanofluid and dusty phases and then the approximations of the long wave length and low Reynolds number are applied. The physical domain is transformed to a rectangular computational model using suitable grid transformations. The resulting systems are solved numerically using shooting method and mathematical forms for the pressure distributions are introduced. The controlling parameters in this study are the thermal buoyancy parameter Gr, the concentration buoyancy parameter Gc, the amplitude ratio ϵ, the Eckert number Ec, the thermophoresis parameter Nt and the Brownian motion parameter Nb and the dusty parameters Ds, αs. The obtained results revealed that an increase in the Eckert number enhances the temperature of the fluid and dusty particles while the nanoparticle volume fraction is reduced. Also, both of the temperature and nanoparticles volume fraction are supported by the growing of the Brownian motion parameter.

ZERO NANOPARTICLES FLUX EFFECT ON NATURAL CONVECTION ABOUT A CYLINDER OF ELLIPTIC CROSS SECTION IN POROUS MEDIA FILLED WITH A NANOFLUID

In this investigation, numerical analysis was performed on the zero nanoparticle flux (ZNF) effect on natural convection in a cylinder with an elliptical cross section embedded in Darcy porous media filled with a nanofluid. The boundary conditions of the cylinder with the elliptical cross section were maintained at uniform wall temperature and ZNF to ensure that the results obtained were realistic and useful. The model adopted for the nanofluid incorporated the effects of Brownian motion and thermophoresis. The non-similar governing equations were obtained by using an appropriate coordinate transformation, and then solved by the Keller box method. Comparisons with previously published work showed good agreement. Numerical data for the dimensionless temperature profiles and Nusselt numbers are presented in graphical and tabular forms for the eccentric angle (B), buoyancy ratio (Nr = 0.4), Brownian motion parameter (Nb = 0.3), thermophoresis parameter (Nt), and the Lewis number (Le). Increasing the thermophoresis parameter and the Lewis number decreased the Nusselt number. For blunt orientation, the Nusselt number first increased with increasing eccentric angle, reached a maximum, and then decreased to zero. For slender orientation, the Nusselt number decreased monotonically. The Nusselt number in the blunt configuration initially increased with an increase in the aspect ratio, attained a maximum, and then gradually decreased. For the slender configuration, the Nusselt number decreased. In this paper, the results of the investigated physical aspects of the problem are discussed in detail.

Theoretical analysis of non-Newtonian blood flow in a microchannel

Background: In this work the theoretical analysis is presented for a electroosmotic flow of Bingham nanofluid induced by applied electrostatic potential. The linearized Poisson-Boltzmann equation is considered in the presence of Electric double layer (EDL). A Bingham fluid model is employed to describe the rheological behavior of the non-Newtonian fluid. Mathematical formulation is presented under the assumption of long wavelength and small Reynolds number. Flow characteristics are investigated by employing Debye-Huckel linearization principle. Such preferences have not been reported previously for non-Newtonian Bingham nanofluid to the best of author’s knowledge.Method: The transformed equations for electroosmotic flow are solved to seek values for the nanofluid velocity, concentration and temperature along the channel length.Results: The effects of key parameters like Brinkmann number, Prandtl number, Debey Huckel parameter, thermophoresis parameter, Brownian motion parameter are plotted on velocity, temperature and concentration profiles. Graphical results for the flow phenomenon are discussed briefly.Conclusions: Non-uniformity in channel as well as yield stress τ0 cause velocity declaration for both positive and negative values of U. Nanofluid temperature is found an increasing function of electro osmotic parameter κ if U is positive while it is a decreasing function if U is negative. A completely reverse response is seen in case of concentration profile. The thermophoresis parameter Nt, the Brow nian motion parameter Nb and Brinkman number Br cause an enhancement in temperature. The results are new in case of U.

Scrutinization of 2D and mixed convection flow of generalized Newtonian fluid with nanoparticles and magnetic field

In this research paper we focus on presenting the local non-similar solutions for two-dimensional steady and mixed convective flow of electrically conducting Carreau nanofluid under the influence of Brownian motion and thermophoresis effects. This research paper also presents the new mass flux boundary condition of nanoparticles. The governing partial differential equations are converted into ordinary differential equations by using the local non-similar transformations called the Sparrow–Quack–Boerner local non-similar method. A numerical approach is used to investigate the local non-similar solutions of the entire problem. Outcomes for the skin friction and rate of heat and mass transfer have been obtained and discussed for parametric variations of the buoyancy parameter ξ, magnetic parameter M, Weissenberg number We, viscosity ratio parameter β*, Brownian motion parameter Nb, thermophoresis parameter Nt, Prandtl number Pr, and Schmidt number Sc. From the obtained results a considerable increase in the skin friction coefficient is observed with an increase in buoyancy parameter ξ. Also, ξ shows relative growth for the momentum and concentration profiles.

Multiple solutions for the modified Fourier and Fick’s theories for Carreau nanofluid

The present paper numerically investigated the dual solutions of Carreau nanofluids in the presence of Cattaneo–Christov double diffusion with focus on heat and mass transfer which contains the effects of Brownian motion and thermophoresis parameter. A nonlinearly shrinking sheet has been utilized to create the flow. The thermal and concentration diffusions are considered by introducing Cattaneo–Christov fluxes. This paper provides information about the energy and concentration equations which are constructed with the help of Cattaneo–Christov double-diffusion theory in the existence of Brownian motion parameter and thermophoresis parameter. The study showed the local similarity variables are used to renovate the governing equations into a set of nonlinear ordinary differential equations. The ascending differential system which is a collection of momentum, temperature and concentration equations is preserved through a numerical approach called the Runge–Kutta–Fehlberg integration technique. The study reveals that the multiple solutions occur for the different vital physical parameters, for example, suction parameter s, Weissenberg number We, Prandtl number Pr, velocity slip parameter $$\delta $$ , viscosity ratio parameter $$\beta ^{*}$$ , non-dimensional thermal relaxation time $$\delta _{e}$$ , Brownian motion parameter Nb and thermophoresis parameter Nt. Moreover, higher values of thermal relaxation time $$\delta _{e}$$ decrease the temperature profile.

Analytical solution for differential nonlinear and coupled equations in micropolar nanofluid flow between rotating parallel plates

This paper presents solution to micropolar nanofluid between two parallel plates in a rotating system via a new and innovative semi-analytical method called Akbari-Ganji’s method (AGM). The nanofluid flow between two parallel plates is taken under the influence of Hall current. The flow of micropolar nanofluid is in steady state. We get a set of differential nonlinear and coupled equations from suitable similarity variables and the elementary governing equations. Moreover, the physical discussion of the embedded parameters in the equations that is, viscosity parameter Re, rotating parameter Kr, magnetic parameter M, Prandtl number Pr, thermophoretic parameter Nt, Brownian motion parameter Nb, and Schmidt number Sc, by showing figures and tables, they have been analyzed. Our results show that the employed method is very efficient and practical for obtaining solutions to this category of coupled equations and the solutions are in excellent agreement for nonlinear higher order differential equations in engineering.

Mixed convection flow of Oldroyd-B nano fluid with Cattaneo-Christov heat and mass flux model with third order slip

This study reports the three-dimensional mixed convection flow of an Oldroyd-B nanofluid past a bidirectional stretching surface. Nonlinear partial differential equations obtained from the flow problem were converted into nonlinear ordinary differential equations using similarity transformation, and then, the numerical solutions of these ODEs with corresponding boundary conditions were obtained by employing a bvp4c solver. The effect of governing parameters on nondimensional velocity along x- and y-directions, temperature, particle concentration, local Nusselt number, and Sherwood number was presented through graphs and tables. It can be seen that the increasing values of the Brownian motion parameter Nb and thermophoresis parameter Nt lead to an increase in the temperature field and thermal boundary layer thickness, while the opposite behavior is observed for concentration field and concentration boundary layer thickness. As the Deborah number β1 increases, the concentration profile as well as concentration boundary layer thickness increase. However, the effects of β2 on the concentration profile are opposite to those of β1. An increase in δt, Pr, and α results in a decrease in temperature. It is reported that the local Nusselt number increases when β and Pr increase, whereas it decreases when λ, Nb, Nt, and Sc increase. An increase in Biot number Bi results in an increase in the Nusselt number, and an increase in Nt results in an increase in the Sherwood number. The results of the present analysis were compared with the available works in particular situations, and more agreement has been noted.

Magnetohydrodynamic Free Stream and Heat Transfer of Nanofluid Flow Over an Exponentially Radiating Stretching Sheet With Variable Fluid Properties

This paper deals with the MHD free stream nanofluid flow and heat transfer over an exponentially radiating stretching sheet accompanied with variable fluid properties. By integrating appropriate similarity transformations, the fundamental governing partial differential equations (PDEs) are transformed into nonlinear ordinary differential equations. The resulting equations are successfully solved by using shooting method and MATLAB built-in solver \emph{bvp4c}. The major effect of the skin friction coefficient, Nusselt number and Sherwood number on the flow field have been calculated. The alteration of fluid flow is governed by different parameters, magnetic parameter M, Prandtl number Pr, Lewis Number Le, thromophoresis paramter Nt, Brownian motion parameter Nb, radiation parameter Rd which are presented in tabulated format. Graphs are also plotted to observe the effects of different aforementioned parameters on velocity, temperature and concentration profiles.

Non-linear convection flow of micro polar nanofluid past an isothermal sphere

In this study, steady laminar two dimensional boundary layer flow of non-linear convection micropolar nanofluid over an isothermal sphere is examined. The mathematical developing for the flow problem has been made. By means of appropriate similarity transformation and dimensionless variable, the governing non-linear boundary value problems were reduced into combined high order non-linear ordinary differential equations. Then, solution for velocity, microrotation, temperature and concentration has been obtained numerically. The equations were calculated using method bvp4c from matlab software for various quantities of main parameters. The influences of diffident parameters on skin friction coefficient, wall duo stress coefficient the Nusselt number, Sherwood number as well as the velocities, temperature, and concentration are analyzed and discussed through the tables and plotted graphs. A comparison with previous paper obtainable in the literature has been performed and an excellent agreement is obtained. The finding results indicate the raise in either the values of thermal Grashof number Gr or Brownian motion parameter Nb or Schmidt number Sc allows to bringing down the kinematic viscosity of the fluid causes improve the temperature profile distribution within the boundary layer. On the other hand, it can be diminished by the growth in either the value of solutal Grashof number Gm or solutal non linear convection parameter s which agrees to enlarge fluid density.

Cattaneo–Christov double-diffusion model for viscoelastic nanofluid with activation energy and nonlinear thermal radiation

PurposeThe purpose of this paper is to explore the novel aspects of activation energy in the nonlinearly convective flow of Walter-B nanofluid in view of Cattaneo–Christov double-diffusion model over a permeable stretched sheet. Features of nonlinear thermal radiation, dual stratification, non-uniform heat generation/absorption, MHD and binary chemical reaction are also evaluated for present flow problem. Walter-B nanomaterial model is employed to describe the significant slip mechanism of Brownian and thermophoresis diffusions. Generalized Fourier’s and Fick’s laws are examined through Cattaneo–Christov double-diffusion model. Modified Arrhenius formula for activation energy is also implemented.Design/methodology/approachSeveral techniques are employed for solving nonlinear differential equations. The authors have used a homotopy technique (HAM) for our nonlinear problem to get convergent solutions. The homotopy analysis method (HAM) is a semi-analytical technique to solve nonlinear coupled ordinary/partial differential equations. The capability of the HAM to naturally display convergence of the series solution is unusual in analytical and semi-analytic approaches to nonlinear partial differential equations. This analytical method has the following great advantages over other techniques:It provides a series solution without depending upon small/large physical parameters and applicable for not only weakly but also strongly nonlinear problems.It guarantees the convergence of series solutions for nonlinear problems.It provides us a great choice to select the base function of the required solution and the corresponding auxiliary linear operator of the homotopy.Brief mathematical description of HAM technique (Liao, 2012; Mabood et al., 2016) is as follows. For a general nonlinear equation:(1)N[u(x)]=0,where N denotes a nonlinear operator, x the independent variables and u(x) is an unknown function, respectively. By means of generalizing the traditional homotopy method, Liao (1992) creates the so-called zero-order deformation equation:(2)(1−q)L[uˆ(x;q)−uo(x)]=qhH(x)N[uˆ(x;q)],here q∈[0, 1] is the embedding parameter, H(x) ≠ 0 is an auxiliary function, h(≠ 0) is a nonzero parameter, L is an auxiliary linear operator, uo(x) is an initial guess of u(x) and is an unknown function, respectively. It is significant that one has great freedom to choose auxiliary things in HAM. Noticeably, when q=0 and q=1, following holds:(3)uˆ(x;0)=uo(x)anduˆ(x;1)=u(x),Expanding in Taylor series with respect to (q), we have:(4)uˆ(x;q)=uo(x)+∑m=1∞um(x)qm,whereum(x)=1m!∂muˆ(x;q)∂qm|q=0.If the initial guess, the auxiliary linear operator, the auxiliary h and the auxiliary function are selected properly, then the series (4) converges at q=1, then we have:(5)u(x)=uo(x)+∑m=1+∞um(x).By defining a vector and differentiating Equation (2) m-times with respect to (q) and then setting q=0, we obtain the mth-order deformation equation:(6)L[uˆm(x)−χmum−1(x)]=hH(x)Rm[u→m−1],where:(7)Rm[u→m−1]=1(m−1)!∂m−1N[u(x;q)]∂qm−1|q=0andχm=|0m⩽11m>1.Applying L−1 on both sides of Equation (6), we get:(8)um(x)=χmum−1(x)+hL−1[H(x)Rm[u→m−1]].In this way, we obtain um for m ⩾ 1, at mth-order, we have:(9)u(x)=∑m=1Mum(x).FindingsIt is evident from obtained results that the nanoparticle concentration field is directly proportional to the chemical reaction with activation energy. Additionally, both temperature and concentration distributions are declining functions of thermal and solutal stratification parameters (P1) and (P2), respectively. Moreover, temperature Θ(Ω1) enhances for greater values of Brownian motion parameter (Nb), non-uniform heat source/sink parameter (B1) and thermophoresis factor (Nt). Reverse behavior of concentration ϒ(Ω1) field is remarked in view of (Nb) and (Nt). Graphs and tables are also constructed to analyze the effect of different flow parameters on skin friction coefficient, local Nusselt number, Sherwood numbers, velocity, temperature and concentration fields.Originality/valueThe novelty of the present problem is to inspect the Arrhenius activation energy phenomena for viscoelastic Walter-B nanofluid model with additional features of nonlinear thermal radiation, non-uniform heat generation/absorption, nonlinear mixed convection, thermal and solutal stratification. The novel aspect of binary chemical reaction is analyzed to characterize the impact of activation energy in the presence of Cattaneo–Christov double-diffusion model. The mathematical model of Buongiorno is employed to incorporate Brownian motion and thermophoresis effects due to nanoparticles.

Numerical and Analytical Investigation of an Unsteady Thin Film Nanofluid Flow over an Angular Surface

In the present study, we examine three-dimensional thin film flow over an angular rotating disk plane in the presence of nanoparticles. The governing basic equations are transformed into ordinary differential equations by using similarity variables. The series solution has been obtained by the homotopy asymptotic method (HAM) for axial velocity, radial velocity, darning flow, induced flow, and temperature and concentration profiles. For the sake of accuracy, the results are also clarified numerically with the help of the BVPh2- midpoint method. The effect of embedded parameters such as the Brownian motion parameter Nb, Schmidt number Sc, thermophoretic parameter and Prandtl number Pr are explored on velocity, temperature and concentration profiles. It is observed that with the increase in the unsteadiness factor S, the thickness of the momentum boundary layer increases, while the Sherwood number Sc, with the association of heat flow from sheet to fluid, reduces with the rise in S and results in a cooling effect. It is also remarkable to note that the thermal boundary layer increases with the increase of the Brownian motion parameter Nb and Prandtl number Pr, hindering the cooling process resulting from heat transfer.

Two-phase nanofluid over rotating disk with exponential variable thickness

PurposeThe purpose of this paper is to investigate the effect of nanofluid over rotating disk with the exponential variable thickness (c > 0, b > 0) and to analyze Brownian motion and thermophoresis of Buongiorno model on the disk embedded in nanofluid-saturated porous media.Design/methodology/approachUsing the generalized von Karman transformation, the boundary layer governing equations are transformed into semi-similar forms solved by bvp4c in MATLAB.FindingsThe effects of the thickness parameter a, the shape parameter b, the Brownian motion parameter Nb and thermophoresis parameter Nt on flow, heat and mass transfer are analyzed. With the increase of thickness parameter a, the radial velocity first decreases and then increases, showing the opposite trend on the two sides of the peak value. Moreover, temperature and concentration rise as the Brownian motion parameter Nb becomes larger.Originality/valueTo the best of the authors’ knowledge, this is the first work that has been done on rotating disk with exponential variable thickness in nanofluid. The impact of the two slip effects, namely, Brownian motion and thermophoresis, on the nanofluid boundary layer flow, heat and mass transfer because of rotating disk with exponential variable thickness (c > 0, b > 0) has been addressed in this study.

MHD Stagnation-Point Flow of a Nanofluid Past a Stretching Sheet with a Convective Boundary Condition and Radiation Effects

In this paper, the investigation of magnetohydrodynamic (MHD) stagnation point flow of a nanofluid past a stretching sheet with a convective boundary condition and radiation effects is carried out numerically. Similarity transformation is used to reduce the governing partial differential equations into third and second order non-linear ordinary differential equations. These equations are then being solved numerically using a problem solver built in the MATLAB software. The numerical solutions for the skin friction coefficient, local Nusselt number, velocity and temperature profiles for different values of the physical parameters are presented graphically and discussed further. The results indicate that the velocity and the temperature are influenced by the magnetic parameter M, Brownian motion parameter Nb and radiation parameter Nr. The local Nusselt number and the skin friction coefficient are affected significantly in the presence of suction at the boundary.

Activation energy and dual stratification effects for Walter-B fluid flow in view of Cattaneo-Christov double diffusionon

The purpose of the present article is to explore the novel aspects of activation energy in nonlinearly convective flow of Walter-B nanofluid in view of Cattaneo-Christov double diffusion model over a permeable stretched sheet. Generalized forms of Fourier's and Fick's law are utilized through Cattaneo-Christov double diffusion. Walter-B nanomaterial model is used that describes the significant slip mechanism namely Brownian and thermophoresis diffusions. Double stratification, heat generation/absorption and chemical reaction are considered. Modified Arrhenius formula for activation energy is implemented. The acquired nonlinear system is cracked through homotopic analysis method. Effects of emanating variables are examined through graphs and tables. It is evident that temperature distribution and thermal boundary layer thickness is monotonically dwindling function of thermal stratification parameter(P1), thermal relaxation time (δ2) and upsurge for the thermophoresis parameter (Nt), heat generation/absorption parameter (B₁), Brownian motion parameter (Nb). Nanoparticle concentration is directly comparable to the activation energy of reaction and impact of thermal relaxation time is qualitatively opposite to that of thermophoretic force.

Biomedical study of effects nanoparticles on unsteady blood (non-Newtonian) flow through a catheterized stenotic vessel

The purpose of this article is to theoretically discuss the unsteady hemo-dynamics of blood through a catheterized overlapping stenotic vessel with nanoparticles. The nature of the blood is characterized by the constitutive Cross model equation. This study is conducted under the assumption of mild stenotic conditions and the equations of momentum and temperature are simplified after making this assumption. Explicit finite difference method is employed to obtain the numerical results of the governing equations. Results for different values of emerging parameters, such as Weissenberg number, Lewis number, thermophoresis parameter, and Brownian motion parameter are shown at different locations of an arterial cross section. These results demonstrate a pictorial way to comprehend the theoretical biomedical problem. These results reveal that Lewis number (Le) and visco-elastic parameter Weissenberg number (We) both are decreasing functions of velocity profiles at each arterial cross section. Furthermore, it is also noted that the thermophoresis parameter (Nt) quantitatively decreases the flow of blood inside the vessel while the Brownian motion parameter (Nb) shows the opposite effects on blood flow; it increases the magnitude of velocity.