scholarly journals On Numerical Analysis of Carreau–Yasuda Nanofluid Flow over a Non-Linearly Stretching Sheet under Viscous Dissipation and Chemical Reaction Effects

Mathematics ◽  
2020 ◽  
Vol 8 (7) ◽  
pp. 1148
Author(s):  
Stanford Shateyi ◽  
Hillary Muzara
Keyword(s):  
Differential Equations ◽  
Skin Friction ◽  
Viscous Dissipation ◽  
Chemical Reaction ◽  
Stretching Sheet ◽  
Fluid Velocity ◽  
Coupled System ◽  
Linear Differential Equations ◽  
Nanofluid Flow ◽  
Linear Differential

This work reports the Carreau–Yasuda nanofluid flow over a non-linearly stretching sheet viscous dissipation and chemical reaction effects. The coupled system of non-linear partial differential equations are changed into a system of linear differential equations employing similarity equations. The spectral quasi-linearization method was used to solve the linear differential equations numerically. Error norms were used to authenticate the accuracy and convergence of the numerical method. The effects of some thermophysical parameters of interest in this current study on the non-dimensional fluid velocity, concentration and temperature, the skin friction, local Nusselt and Sherwood numbers are presented graphically. Tables were used to depict the effects of selected parameters on the skin friction and the Nusselt number.

A reliable treatment of the homotopy analysis method for viscous flow over a non-linearly stretching sheet in presence of a chemical reaction and under influence of a magnetic field

Open Physics ◽  
2009 ◽  
Vol 7 (1) ◽  
Author(s):  
Saeed Dinarvand
Keyword(s):  
Magnetic Field ◽  
Differential Equations ◽  
Chemical Reaction ◽  
Homotopy Analysis Method ◽  
Stretching Sheet ◽  
Linear Differential Equations ◽  
Analysis Method ◽  
Non Linear ◽  
Homotopy Analysis ◽  
Linear Differential

AbstractThe similarity solution for the steady two-dimensional flow of an incompressible viscous and electrically conducting fluid over a non-linearly semi-infinite stretching sheet in the presence of a chemical reaction and under the influence of a magnetic field gives a system of non-linear ordinary differential equations. These non-linear differential equations are analytically solved by applying a newly developed method, namely the Homotopy Analysis Method (HAM). The analytic solutions of the system of non-linear differential equations are constructed in the series form. The convergence of the obtained series solutions is carefully analyzed. Graphical results are presented to investigate the influence of the Schmidt number, magnetic parameter and chemical reaction parameter on the velocity and concentration fields. It is noted that the behavior of the HAM solution for concentration profiles is in good agreement with the numerical solution given in reference [A. Raptis, C. Perdikis, Int. J. Nonlinear Mech. 41, 527 (2006)].

scholarly journals MHD free convection flow of Casson fluid over a permeable nonlinearly stretching sheet with chemical reaction

2017 ◽  
Vol 13 (3) ◽  
Author(s):  
Imran Ullah ◽  
Sharidan Shafie ◽  
Ilyas Khan
Keyword(s):  
Differential Equations ◽  
Free Convection ◽  
Chemical Reaction ◽  
Stretching Sheet ◽  
Fluid Velocity ◽  
Casson Fluid ◽  
Convection Flow ◽  
Free Convection Flow ◽  
Grashof Number ◽  
Keller Box Method

The problem of heat and mass transfer free convection flow of Casson fluid over a porous nonlinear stretching sheet in the presence of chemical reaction is investigated. Moreover the effect of magnetic field is also considered. The governing partial differential equations are transformed into ordinary differential equations by making use of suitable transformations and then solved numerically via Keller-box method. The results for skin friction are compared with previous results of the existing literature. The results are also reflected in good agreement. It is noted that concentration of Casson fluid reduces rapidly by increasing Schmidt number and chemical parameter. Also, thermal Grashof number and mass Grashof number enhance the momentum boundary layer thickness, whereas increment in chemical reaction parameter reduces the heat transfer rate. Moreover, both the fluid velocity and wall shear stress are observed to be decreased with increment in suction/blowing parameter.

scholarly journals Some remarks on moments for stochastic chemical kinetics

2015 ◽  
Author(s):  
Eduardo Sontag ◽  
Abhyudai Singh
Keyword(s):  
Differential Equations ◽  
Conservation Laws ◽  
Chemical Kinetics ◽  
Chemical Reaction ◽  
Higher Order ◽  
Linear Differential Equations ◽  
Reaction Networks ◽  
Stochastic Chemical Kinetics ◽  
Finite Dimensional ◽  
Linear Differential

We analyze a class of chemical reaction networks for which all moments can be computed by finite-dimensional linear differential equations. This class allows second and higher order reactions, but only under special assumptions on structure and/or conservation laws.

scholarly journals Analyzing the impact of induced magnetic flux and Fourier’s and Fick’s theories on the Carreau-Yasuda nanofluid flow

2021 ◽  
Vol 11 (1) ◽  
Author(s):  
Seemab Bashir ◽  
Muhammad Ramzan ◽  
Jae Dong Chung ◽  
Yu-Ming Chu ◽  
Seifedine Kadry
Keyword(s):  
Activation Energy ◽  
Nusselt Number ◽  
Brownian Motion ◽  
Friction Coefficient ◽  
Differential Equations ◽  
Skin Friction ◽  
Chemical Reaction ◽  
Skin Friction Coefficient ◽  
Nanofluid Flow ◽  
Stretching Ratio

AbstractThe current study analyzes the effects of modified Fourier and Fick's theories on the Carreau-Yasuda nanofluid flow over a stretched surface accompanying activation energy with binary chemical reaction. Mechanism of heat transfer is observed in the occurrence of heat source/sink and Newtonian heating. The induced magnetic field is incorporated to boost the electric conductivity of nanofluid. The formulation of the model consists of nonlinear coupled partial differential equations that are transmuted into coupled ordinary differential equations with high nonlinearity by applying boundary layer approximation. The numerical solution of this coupled system is carried out by implementing the MATLAB solver bvp4c package. Also, to verify the accuracy of the numerical scheme grid-free analysis for the Nusselt number is presented. The influence of different parameters, for example, reciprocal magnetic Prandtl number, stretching ratio parameter, Brownian motion, thermophoresis, and Schmidt number on the physical quantities like velocity, temperature distribution, and concentration distribution are addressed with graphs. The Skin friction coefficient and local Nusselt number for different parameters are estimated through Tables. The analysis shows that the concentration of nanoparticles increases on increasing the chemical reaction with activation energy and also Brownian motion efficiency and thermophoresis parameter increases the nanoparticle concentration. Opposite behavior of velocity profile and the Skin friction coefficient is observed for increasing the stretching ratio parameter. In order to validate the present results, a comparison with previously published results is presented. Also, Factors of thermal and solutal relaxation time effectively contribute to optimizing the process of stretchable surface chilling, which is important in many industrial applications.

scholarly journals Unsteady MHD Flow of Nanofluid with Variable Properties over a Stretching Sheet in the Presence of Thermal Radiation and Chemical Reaction

2019 ◽  
Vol 2019 ◽  
pp. 1-14 ◽  
Author(s):  
Musa Antidius Mjankwi ◽  
Verdiana Grace Masanja ◽  
Eunice W. Mureithi ◽  
Makungu Ng’oga James
Keyword(s):  
Thermal Conductivity ◽  
Mass Transfer ◽  
Differential Equations ◽  
Thermal Radiation ◽  
Skin Friction ◽  
Chemical Reaction ◽  
Stretching Sheet ◽  
Mhd Flow ◽  
Transfer Rates ◽  
Fluid Properties

The unsteady magnetohydrodynamics (MHD) flow of nanofluid with variable fluid properties over an inclined stretching sheet in the presence of thermal radiation and chemical reaction is studied taking into account the effect of variable fluid properties in thermal conductivity and diffusion coefficient. The governing partial differential equations are transformed into ordinary differential equations by using similarity transformation. The numerical solutions of the problem are obtained by using the fourth order Runge-Kutta method in line with the shooting technique. It is found that the increase in both thermal conductivity and radiative heat flux decreases the heat transfer rate but increases the skin friction and mass transfer rates. It is further observed that the increase in porosity parameter and magnetic field reduces the skin friction, heat, and mass transfer rates.

scholarly journals Finite Element Simulation of Multiple Slip Effects on MHD Unsteady Maxwell Nanofluid Flow over a Permeable Stretching Sheet with Radiation and Thermo-Diffusion in the Presence of Chemical Reaction

Processes ◽  
2019 ◽  
Vol 7 (9) ◽  
pp. 628 ◽  
Author(s):  
Bagh Ali ◽  
Yufeng Nie ◽  
Shahid Ali Khan ◽  
Muhammad Tariq Sadiq ◽  
Momina Tariq
Keyword(s):  
Finite Element ◽  
Friction Coefficient ◽  
Differential Equations ◽  
Numerical Solution ◽  
Skin Friction ◽  
Stretching Sheet ◽  
Skin Friction Coefficient ◽  
Nanofluid Flow ◽  
Maxwell Nanofluid ◽  
Slip Effects

The aim of the present study is to investigate the multiple slip effects on magnetohydrodynamic unsteady Maxwell nanofluid flow over a permeable stretching sheet with thermal radiation and thermo-diffusion in the presence of chemical reaction. The governing nonlinear partial differential equations are transformed into a system of coupled nonlinear ordinary differential equations with the aid of appropriate similarity variables, and the transformed equations are then solved numerically by using a variational finite element method. The effects of various physical parameters on the velocity, temperature, solutal concentration, and nanoparticle concentration profiles as well as on the skin friction coefficient, rate of heat transfer, and Sherwood number for solutal concentration are discussed by the aid of graphs and tables. An exact solution of flow velocity, skin friction coefficient, and Nusselt number is compared with the numerical solution obtained by FEM and also with numerical results available in the literature. A good agreement between the exact and numerical solution is observed. Also, to justify the convergence of the finite element numerical solution, the calculations are carried out by reducing the mesh size. The present investigation is relevant to high-temperature nanomaterial processing technology.

scholarly journals Radiative Heat and Mass Transfer of an MHD Free Convection Flow Along a Stretching Sheet with Chemical Reaction, Heat Generation and Viscous Dissipation

2013 ◽  
Vol 61 (1) ◽  
pp. 27-34 ◽  
Author(s):  
Ishrat Zahan ◽  
MA Samad
Keyword(s):  
Mass Transfer ◽  
Differential Equations ◽  
Free Convection ◽  
Heat And Mass Transfer ◽  
Viscous Dissipation ◽  
Chemical Reaction ◽  
Heat Generation ◽  
Stretching Sheet ◽  
Convection Flow ◽  
Free Convection Flow

In the present study, an analysis is carried out to investigate the effect of chemical reaction and radiation on a steady two-dimensional magneto-hydrodynamics (MHD) heat and mass transfer free convection flow of a viscous incompressible fluid along a stretching sheet with heat generation along with the effect of viscous dissipation. The basic non-linear partial differential equations governing the flow field are reduced to a system of coupled non-linear ordinary differential equations by similarity transformations and the equations are solved numerically by applying Nachtsheim-Swigert shooting iteration technique along with sixth order Runge-Kutta integration scheme. The numerical results with respect to embedded parameters are displayed graphically for the non-dimensional velocity, temperature and concentration profiles. Finally the effects of the pertinent parameters which are of physical and engineering interest are presented in tabular form. Dhaka Univ. J. Sci. 61(1): 27-34, 2013 (January) DOI: http://dx.doi.org/10.3329/dujs.v61i1.15092

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