The current paper explores the flow of dusty nanoliquid over a rotating and stretchable disk with non-uniform heat sink/source. Further, we have done a comparative study on Single wall carbon ...nanotubes (SWCNT)-water and multi wall carbon nanotubes (MWCNT)-water based dusty fluid flows. By means of apt similarity variables, the governing equations are converted to set of nonlinear ordinary differential equations and then they are numerically tackled using Runge-Kutta-Fehlberg's fourth fifth order (RKF45) method by adopting shooting technique. The influence of non-dimensional parameters on the heat transfer fields are incorporated and extensively discussed by means of appropriate graphs. Further, the reduced shear stresses at the disk in the tangential direction, in the radial direction and the heat transference rates of the fluid and particles are deliberated graphically. Results reveal that, the escalating values of space and temperature dependent heat source/sink parameters improves the heat transference of both liquids. The SWCNT-water based fluid shows improved shear stress in tangential and radial direction when compared to MWCNT-water based fluid for both the phases. The SWCNT-water based fluid shows enhanced heat transfer rate than MWCNT-water based fluid for both fluid and dust phases.
Boundary conditions for fractional diffusion Baeumer, Boris; Kovács, Mihály; Meerschaert, Mark M. ...
Journal of computational and applied mathematics,
07/2018, Volume:
336
Journal Article
Peer reviewed
Open access
This paper derives physically meaningful boundary conditions for fractional diffusion equations, using a mass balance approach. Numerical solutions are presented, and theoretical properties are ...reviewed, including well-posedness and steady state solutions. Absorbing and reflecting boundary conditions are considered, and illustrated through several examples. Reflecting boundary conditions involve fractional derivatives. The Caputo fractional derivative is shown to be unsuitable for modeling fractional diffusion, since the resulting boundary value problem is not positivity preserving.
This topic addresses the influence of binary chemical reaction and activation energy in hydromagnetic flow of third grade nanofluid associated with convective conditions. Flow is developed through ...nonlinearly stretched surface. Nanoparticles concentration and temperature profiles are considered in the presence of Brownian dispersion and thermophoresis effects. Third grade liquid is electrically conducted via uniform applied magnetic field. Assumption of boundary layer has been used in the problem development. Governing differential systems have been computed in frame of NDsolve. The graphical illustrations explore influences of various sundry variables. Further surface drag force, heat and mass transfer rate are sketched and analyzed. Temperature and concentration distributions are declared increasing functions of Hartman number while reverse trend is seen for velocity distribution. Furthermore an enhancement is observed in temperature and concentration distributions for the higher values of thermal and concentration Biot numbers respectively.
•Magnetohydrodynamic flow of third grade nanofluid is modeled.•Binary chemical reaction and Arrhenius activation energy aspects are utilized.•Heat and mass transfer attributes are analyzed through Brownian motion and thermophoresis effects.•Convective heat and mass conditions are also implemented at the surface.•Numerical solutions are developed by shooting technique.
We introduce a new generalized Caputo-type fractional derivative which generalizes Caputo fractional derivative. Some characteristics were derived to display the new generalized derivative features. ...Then, we present an adaptive predictor corrector method for the numerical solution of generalized Caputo-type initial value problems. The proposed algorithm can be considered as a fractional extension of the classical Adams-Bashforth-Moulton method. Dynamic behaviors of some fractional derivative models are numerically discussed. We believe that the presented generalized Caputo-type fractional derivative and the proposed algorithm are expected to be further used to formulate and simulate many generalized Caputo type fractional models.
•The stagnation point flow of hybrid nano fluid over a stretching cylinder is the key highlight.•Effects of inclined magnetic field are useful for the boundary layer control in hybrid nano ...fluid.•Numerical solutions are computed for the complicated problem.•The extended versions of Xue model and Yamada Ota model for hybrid nanofluid is taken into account.
Focus of the present analysis is on the stagnation point flow of hybrid nanofluid with inclined magnetic field over a moving cylinder. The extended version of two models (e.g. Xue model and Yamada-Ota model for hybrid nanofluids) are considered in this study). A mathematical model of hybrid nanofluid flow is developed under certain flow assumptions. Boundary layer approximations are also utilized to model a system of partial differential equations. The systems of partial differential equations are further converted to dimensionless systems of ordinary differential equations by means of suitable similarity transformations. A numerical solution is obtained by applying bv4c technique. Effects of variation in physical parameters involved are depicted through graphs. Skin friction coefficient and Nusselt number are highlighted through tables. Our main objective is to investigate the heat transfer rate on the surface of the nonlinear stretching cylinder. The results of Xue model and Yamada-Ota model for the hybrid nanofluid due to nonlinear stretching cylinder are computed for comparison. In both cases, velocity and temperature profiles are best compared to the decay results.
•Numerical computation of SDEs in high dimension is approached via Gaussian analysis.•We make use of the Kolmogorov equation associated to the SDE to compute probabilities.•A novel strategy that ...allow to reuse samples from a Gaussian process is applied to study nonlinear problems.
Stochastic Differential Equations (SDEs) in high dimension, having the structure of finite dimensional approximation of Stochastic Partial Differential Equations (SPDEs), are considered. The aim is to numerically compute the expected values and probabilities associated to their solutions, by solving the corresponding Kolmogorov equations, with a partial use of Monte Carlo strategy - precisely, using Monte Carlo only for the linear part of the SDE. The basic idea was presented in 16, but here we strongly improve the numerical results by means of a shift of the auxiliary Gaussian process. For relatively simple nonlinearities, we have good results in dimension of the order of 100.
This article discussed the flow characteristics of human blood under stenoses assumptions. The human blood is considered as Newtonian fluid. The problem governing equations along with the boundary ...conditions are reduced to dimensionless form by using appropriate similarity transformation to obtain the numerical solution of velocity and temperature of blood flow through stenosed artery. The flow quantities are calculated at cylindrical surface and results are also shown through graphs and tables. Gold nanoparticles can improve the flow of blood and could be a promising therapeutic approach against arterial diseases as compared to Cu and Al2O3-NPs. Results shows that velocity and temperature of blood decreases by increasing the size of gold nanoparticles. Additionally, the skin friction and heat transfer analysis for the blood flow dynamics is also examined. It is noticed that by increasing the values of flow parameter, heat transfer rate and skin friction coefficient decreases. To predict the reason of the atherosclerosis, the modeling and numerical solution plays an incredible role.
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•Maxwell fluid in the presence of nanoparticle is presented first time.•Governing nonlinear partial differential equations are transformed into system ordinary differential equations.•Obtaining ...coupled ordinary differential equations are investigated numerically.•Comparative study with the previous literature is presented.
In the present article, two dimensional boundary-layer flows and the heat transfer of a Maxwell fluid past a stretching sheet are studied numerically. The effects of magnetohydrodynamics (MHD) and elasticity on the flow are considered. Moreover, the effects of nanoparticles are also investigated. Similarity transformations are presented to convert the governing nonlinear partial differential equation into coupled ordinary differential equations. The reduced boundary layer equations of the Maxwell nanofluid model are solved numerically. The effects of the emerging parameters, namely, the magnetic parameter M, the elastic parameter K, the Prandtl parameter Pr, the Brownian motion Nb, the thermophoresis parameter Nt and the Lewis number Le on the temperature and the concentration profile are discussed. Interesting results are shown graphically. The skin friction coefficient, the dimensionless heat transfer rate and the concentration rate are also plotted against the flow control parameters.
An analysis has been carried out to study a problem of the boundary-layer flow of Carreau nanofluid over a non-linearly stretched sheet with chemical reaction and the heat generation/absorption in a ...porous medium. A power-law model includes a two-phase model for Carreau nanofluid with a convective condition. The governing PDEs with the corresponding boundary conditions are modified to a system of non-linear ODEs with the appropriate boundary conditions by picking local similarity conversions and solved numerically by using Runge–Kutta–Fehlberg 4th–5th order numerical method (RKF45) on based shooting technique. This investigation discusses the effects of study parameters like the porosity parameter K1, the heat source λ>0 or sink λ<0 parameter, the chemical reaction parameter γ1 and the Biot number Bi on flow velocity, temperature and nanofluid volume fraction in addition to the heat and mass transfer rates tabular and graphically. A comparative study is likewise revealed showing the comparison of current results with previously published data.
•Boundary-layer flow of Carreau nanofluid is modeled.•Flow is caused by a convectively heated nonlinear stretching surface.•Brownian motion and thermophoresis effects are considered.•Numerical solutions are obtained by Runge–Kutta–Fehlberg method.
A metal extrusion was process that extrusion puncture perforate surface of material to throw and flow across outlet of die. This operation was a complex process in extrusion while penetration ...occurred at same time. This process can be seen in many production operations, like in forming of making portion of metal strip, and forming of extruded portion in a complex fineblanking with extrusion operation. Also exhibit the operation properties and give the method of numerical solution. So increasing load to 610KN with increased friction factor to 0.7 and increased with increasing the reduction ratio and stroke of operation. For the results and mesh distortion, with allocations of strains may be predicted. Analyzing results was submitted of metal extruded may be classified into two zones for the different lineaments deformation. moreover, energy in the zones of deformation may be classified into two parts for their different lineaments of internal zone and contact zone with the die . Fracture location has been found from simulations. Keyword Load, Extrusion, upper bound, numerical solution
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