Spectral computation of reactive bi-directional hydromagnetic non-Newtonian convection flow from a stretching upper parabolic surface in non-Darcyporous medium

2021 ◽  
Author(s):  
A. Shahid ◽  
M. M. Bhatti ◽  
O. Anwar Bég ◽  
I. L. Animasaun ◽  
Khurram Javid
Keyword(s):  
Activation Energy ◽  
Boundary Layer ◽  
Brownian Motion ◽  
Boundary Layer Thickness ◽  
Index Formula ◽  
Rate Parameter ◽  
Nanoparticle Concentration ◽  
Parabolic Surface ◽  
Thickness Parameter ◽  
Momentum Boundary Layer

This paper presents a mathematical model for bi-directional convection magnetohydrodynamic (MHD) tangent hyperbolic nanofluid flow from the upper horizontal subsurface of a stretching parabolic surface to a non-Darcian porous medium, as a simulation of nanocoating. Chemical reaction, activation energy and thermo solutal buoyancy effects are included. The Darcy–Brinkman–Forchheimer model is deployed which permits the analysis of inertial (second order) porous drag effects. The Buongiorno nanoscale model is deployed which includes Brownian motion and thermophoresis effects. The dimensionless, transformed, nonlinear, coupled ordinary differential equations are solved by implementing the spectral relaxation method (SRM). Validation with previous studies is included. The numerical influence of key parameters on transport characteristics is evaluated and visualized graphically. Velocity is elevated (and momentum boundary layer thickness is reduced) with increasing wall thickness parameter, permeability parameter, Forchheimer parameter, Weissenberg (rheological) parameter and modified Hartmann (magnetic body force) number. Velocity enhancement is also computed with increment in stretching rate parameter, rheological power-law index, thermal Grashof number, and species (solutal) Grashof number, and momentum boundary layer thickness diminishes. Temperature is suppressed with increasing stretching rate index and Prandtl number whereas it is substantially elevated with increasing Brownian motion and thermophoresis parameters. Velocity and temperature profiles are reduced adjacent to the parabolic surface with larger wall thickness parameter for stretching rate index [Formula: see text]1, whereas the reverse behavior is observed for stretching rate index [Formula: see text]1. Nanoparticle concentration magnitude is depleted with larger numeric of Lewis number and the Brownian motion parameter, whereas it is enhanced with greater values of the stretching index and thermophoresis parameter. The nanoparticle concentration magnitude is reduced with an increase in chemical reaction rate parameter whereas it is boosted with activation energy parameter. Skin friction, Nusselt number and Sherwood number are also computed. The study is relevant to electromagnetic nanomaterials coating processes with complex chemical reactions.

Flow of nanofluid towards a Riga surface with heat and mass transfer under the effects of activation energy and thermal radiation

2021 ◽  
pp. 2150266
Author(s):  
A. Al-Zubaidi ◽  
Mubbashar Nazeer ◽  
S. Saleem ◽  
Farooq Hussain ◽  
Fayyaz Ahmad
Keyword(s):  
Activation Energy ◽  
Boundary Layer ◽  
Mass Transfer ◽  
Porous Medium ◽  
Shooting Technique ◽  
Highly Nonlinear ◽  
Riga Plate ◽  
Buongiorno Model ◽  
Momentum Boundary Layer

This paper numerically simulates the nanofluid flow over a thermally expanding Riga plate. Buongiorno model for nanofluid is employed to investigate the contribution of Brownian motion and thermophoretic force on the nanoflow. Magnetohydrodynamics (MHD) of viscous nanofluid through a porous medium is characterized with the help of Darcy–Forchheimer’s model. In addition, the simultaneous effects of activation energy and chemical reaction have been incorporated. Moreover, highly nonlinear coupled differential equations are formulated which highlight the influence of viscous dissipation and heat generation. A numerical solution is achieved with the help of the Range–Kutta fourth-order (RK4) method combined with the shooting technique. Finally, the role of emerging parameters is studied via performing the numerical simulation which reveals that the momentum boundary layer of nanofluid shrinks due to the porous medium. Whereas, thermal boundary layer expands for all variables, except for the Prandtl number. Finally, mass transfer rated suffers due to Schmidt number.

scholarly journals Magnetohydrodynamic (MHD) Boundary Layer Flow Past a Wedge with Heat Transfer and Viscous Effects of Nanofluid Embedded in Porous Media

2019 ◽  
Vol 2019 ◽  
pp. 1-12 ◽  
Author(s):  
Wubshet Ibrahim ◽  
Ayele Tulu
Keyword(s):  
Boundary Layer ◽  
Porous Media ◽  
Brownian Motion ◽  
Prandtl Number ◽  
Boundary Layer Flow ◽  
Boundary Layer Thickness ◽  
Lewis Number ◽  
Mhd Boundary Layer ◽  
Layer Flow ◽  
Mhd Boundary Layer Flow

The problem of two-dimensional steady laminar MHD boundary layer flow past a wedge with heat and mass transfer of nanofluid embedded in porous media with viscous dissipation, Brownian motion, and thermophoresis effect is considered. Using suitable similarity transformations, the governing partial differential equations have been transformed to nonlinear higher-order ordinary differential equations. The transmuted model is shown to be controlled by a number of thermophysical parameters, viz. the pressure gradient, magnetic, permeability, Prandtl number, Lewis number, Brownian motion, thermophoresis, and Eckert number. The problem is then solved numerically using spectral quasilinearization method (SQLM). The accuracy of the method is checked against the previously published results and an excellent agreement has been obtained. The velocity boundary layer thickness reduces with an increase in pressure gradient, permeability, and magnetic parameters, whereas thermal boundary layer thickness increases with an increase in Eckert number, Brownian motion, and thermophoresis parameters. Greater values of Prandtl number, Lewis number, Brownian motion, and magnetic parameter reduce the nanoparticles concentration boundary layer.

A Study of Boundary-Layer Characteristics of Turbomachine Blade Rows and Their Relation to Over-All Blade Loss

1960 ◽  
Vol 82 (3) ◽  
pp. 588-592 ◽  
Author(s):  
Warner L. Stewart ◽  
Warren J. Whitney ◽  
Robert Y. Wong
Keyword(s):  
Boundary Layer ◽  
Layer Thickness ◽  
Surface Diffusion ◽  
Boundary Layer Thickness ◽  
Blade Surface ◽  
Loss Analysis ◽  
Blade Row ◽  
Momentum Boundary Layer ◽  
Turbomachine Blade ◽  
Blade Loss

This paper presents the results of a number of investigations concerned with the boundary-layer characteristics of turbomachine blade rows and their relation to the over-all blade loss. It is demonstrated how the over-all blade loss can be obtained from the momentum boundary-layer thickness. The momentum boundary-layer thickness is in turn shown to be correlated by flow Reynolds number and total blade surface diffusion. By assuming Zweifel’s form of blade-loading diagram the total blade surface diffusion parameter can be determined as a function of blade solidity and reaction across the blade row. Thus, this type of loss analysis enables an approximate predetermination of the over-all blade row loss as derived from fundamental boundary-layer concepts. In addition, it shows the effect on over-all blade loss of varying such design features as solidity and reaction.

scholarly journals Two-phase nanofluid over rotating disk with exponential variable thickness

2019 ◽  
Vol 29 (10) ◽  
pp. 3781-3794 ◽  
Author(s):  
Chunyan Liu ◽  
Yiming Ding ◽  
Liancun Zheng ◽  
Ping Lin ◽  
Ruilin Li
Keyword(s):  
Boundary Layer ◽  
Mass Transfer ◽  
Brownian Motion ◽  
Variable Thickness ◽  
Rotating Disk ◽  
Content Type ◽  
Flow Heat ◽  
Exponential Variable ◽  
Thickness Parameter ◽  
Brownian Motion Parameter

Purpose The purpose of this paper is to investigate the effect of nanofluid over rotating disk with the exponential variable thickness Z=ce−bRR0 (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/approach Using the generalized von Karman transformation, the boundary layer governing equations are transformed into semi-similar forms solved by bvp4c in MATLAB. Findings The 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/value To 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 Z=ce−bRR0 (c > 0, b > 0) has been addressed in this study.

scholarly journals Mathematical Modelling of Hydromagnetic Casson non-Newtonian Nanofluid Convection Slip Flow from an Isothermal Sphere

2019 ◽  
Vol 8 (1) ◽  
pp. 645-660 ◽  
Author(s):  
A. Subba Rao ◽  
Seela Sainath ◽  
P. Rajendra ◽  
G. Ramu
Keyword(s):  
Boundary Layer ◽  
Brownian Motion ◽  
Partial Differential Equations ◽  
Differential Equations ◽  
Layer Thickness ◽  
Boundary Layer Thickness ◽  
Particle Concentration ◽  
External Boundary ◽  
Nano Particle ◽  
Partial Differential

Abstract In this article, the combined magnetohydrodynamic heat, momentum and mass (species) transfer in external boundary layer flow of Casson nanofluid from an isothermal sphere surface with convective condition under an applied magnetic field is studied theoretically. The effects of Brownian motion and thermophoresis are incorporated in the model in the presence of both heat and nanoparticle mass transfer convective conditions. The governing partial differential equations (PDEs) are transformed into highly nonlinear, coupled, multi-degree non-similar partial differential equations consisting of the momentum, energy and concentration equations via appropriate non-similarity transformations. These transformed conservation equations are solved subject to appropriate boundary conditions with a second order accurate finite difference method of the implicit type. The influences of the emerging parameters i.e. magnetic parameter (M), Buoyancy ratio parameter (N), Casson fluid parameter (β), Brownian motion parameter (Nb) and thermophoresis parameter (Nt), Lewis number (Le), Prandtl number (Pr) and thermal slip (ST) on velocity, temperature and nano-particle concentration distributions is illustrated graphically and interpreted at length. Increasing viscoplastic (Casson) parameter decelerates the flow and also decreases thermal and nano-particle concentration. Increasing Brownian motion accelerates the flow and enhances temperatures whereas it reduces nanoparticle concentration boundary layer thickness. Increasing thermophoretic parameter increasing momentum (hydrodynamic) boundary layer thickness and nanoparticle boundary layer thickness whereas it reduces thermal boundary layer thickness. Increasing magnetohydrodynamic body force parameter decelerates the flow whereas it enhances temperature and nano-particle (species) concentrations. The study is relevant to enrobing processes for electric-conductive nano-materials, of potential use in aerospace and other industries.

Multiple slip effects on MHD non-Newtonian nanofluid flow over a nonlinear permeable elongated sheet

2019 ◽  
Vol 15 (5) ◽  
pp. 913-931 ◽  
Author(s):  
Jawad Raza ◽  
Mushayydha Farooq ◽  
Fateh Mebarek-Oudina ◽  
B. Mahanthesh
Keyword(s):  
Boundary Layer ◽  
Brownian Motion ◽  
Differential Equations ◽  
Layer Thickness ◽  
Boundary Layer Thickness ◽  
Stretching Surface ◽  
Nanofluid Flow ◽  
Content Type ◽  
Slip Effects ◽  
Nonlinear Stretching

Purpose The purpose of this paper is to examine the interaction effects of a transverse magnetic field and slip effects of Casson fluid with suspended nanoparticles over a nonlinear stretching surface. Mathematical modeling for the law of conservation of mass, momentum, heat and concentration of nanoparticles is executed. Design/methodology/approach Governing nonlinear partial differential equations are reduced into nonlinear ordinary differential equations and then shooting method is employed for its solution. The slope of the linear regression line of the data points is calculated to measure the rate of increase/decrease in the reduced Nusselt number. Findings The effects of magnetic parameter (0=M=4), Casson parameter (0.1=β<8), nonlinear stretching parameter (0=n=3) and porosity parameter (0=P=6) on axial velocity are shown graphically. Numerical results were compared with another numerical approach and an excellent agreement was observed. This study reveals the fact that the Brownian motion parameter and boundary layer thickness have a direct relationship with temperature. Also, Brownian motion and thermophoresis contribute to an increase in the thermal boundary layer thickness. Originality/value Despite the immense significance and repeated employment of non-Newtonian fluids in industry and science, no attempt has been made up till now to inspect the Casson nanofluid flow with a permeable nonlinear stretching surface.

scholarly journals Activation energy and binary chemical reaction effects in mixed convective nanofluid flow with convective boundary conditions

2018 ◽  
Vol 6 (2) ◽  
pp. 149-158 ◽  
Author(s):  
Mlamuli Dhlamini ◽  
Peri K. Kameswaran ◽  
Precious Sibanda ◽  
Sandile Motsa ◽  
Hiranmoy Mondal
Keyword(s):  
Activation Energy ◽  
Boundary Layer ◽  
Brownian Motion ◽  
Chemical Reaction ◽  
Chemical Species ◽  
Main Process ◽  
Heated Plate ◽  
Infinite Length ◽  
Fluid Temperature ◽  
Combined Effects

Abstract In this paper, we present a theoretical study of the combined effects of activation energy and binary chemical reaction in an unsteady mixed convective flow over a boundary of infinite length. The current study incorporates the influence of the Brownian motion, thermophoresis and viscous dissipation on the velocity of the fluid, temperature of the fluid and concentration of chemical species. The equations are solved numerically to a high degree of accuracy using the spectral quasilinearization method. Brownian motion was noted as the main process by which the mass is transported out of the boundary layer. The effect of thermophoretic parameter seems to be contrary to the expected norm. We expect the thermophoretic force to ‘push’ the mass away from the surface thereby reducing the concentration in the boundary layer, however, concentration of chemical species is seen to increase in the boundary layer with an increase in the thermophoretic parameter. The use of a heated plate of infinite length increased the concentration of chemical species in the boundary layer. The Biot number which increases and exceeds a value of one for large heated solids immersed in fluids increases the concentration of chemical species for its increasing values. Highlights Combined effects of activation energy and binary chemical reaction are proposed. Spectral quasi-linearization method (SQLM) is used for computer simulations. Use Arrhenius activation energy in the chemical species concentration. Validate the accuracy and convergence using residual error analysis.

Effects of temperature-dependent viscosity and thermal conductivity on mixed convection flow along a magnetized vertical surface

2016 ◽  
Vol 26 (5) ◽  
pp. 1580-1592 ◽  
Author(s):  
Ashraf Muhammad ◽  
Ali J Chamkha ◽  
S Iqbal ◽  
Masud Ahmad
Keyword(s):  
Magnetic Field ◽  
Thermal Conductivity ◽  
Boundary Layer ◽  
Prandtl Number ◽  
Layer Thickness ◽  
Boundary Layer Thickness ◽  
Thermal Boundary Layer ◽  
Content Type ◽  
Variation Parameter ◽  
Momentum Boundary Layer

Purpose – The purpose of this paper is to report a numerical solution for the problem of steady, two dimensional boundary layer buoyant flow on a vertical magnetized surface, when both the viscosity and thermal conductivity are assumed to be temperature-dependent. In this case, the motion is governed by a coupled set of three nonlinear partial differential equations, which are solved numerically by using the finite difference method (FDM) by introducing the primitive variable formulation. Calculations of the coupled equations are performed to investigate the effects of the different governing parameters on the profiles of velocity, temperature and the transverse component of magnetic field. The effects of the thermal conductivity variation parameter, viscosity variation parameter, magnetic Prandtl number Pmr, magnetic force parameter S, mixed convection parameter Ri and the Prandtl number Pr on the flow structure and heat transfer characteristics are also examined. Design/methodology/approach – FDM. Findings – It is noted that when the Prandtl number Pr is sufficiently large, i.e. Pr=100, the buoyancy force that driven the fluid motion is decreased that decrease the momentum boundary layer and there is no change in thermal boundary layer is noticed. It is also noted that due to slow motion of the fluid the magnetic current generates which increase the magnetic boundary layer thickness at the surface. It is observed that the momentum boundary layer thickness is increased, thermal and magnetic field boundary layers are decreased with the increase of thermal conductivity variation parameter =100. The maximum boundary layer thickness is increased for =100 and there is no change seen in the case of thermal boundary layer thickness but magnetic field boundary layer is deceased. The momentum boundary layer thickness shoot quickly for =40 but is very smooth for =50.There is no change is seen for the case of thermal boundary layer and very clear decay for =40 is noted. Originality/value – This work is original research work.

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