Numerical Simulation of Williamson Nanofluid Flow over an Inclined Surface: Keller Box Analysis

The study of nanofluids has become a key research area in mathematics, physics, engineering, and materials science. Nowadays, nanofluids are widely used in many industrial applications to improve thermophysical properties such as thermal conductivity, thermal diffusivity, convective heat transfer, and viscosity. This article discusses the effects of heat generation/absorption and chemical reaction on magnetohydrodynamics (MHD) flow of Williamson nanofluid over an inclined stretching surface. The impact of Williamson factor on velocity field is investigated numerically using Keller box analysis (KBA). Suitable similarity transformations are used to recover ordinary differential equations (ODEs) from the boundary flow equations. These ordinary differential equations are addressed numerically. The numerical computations revealed that energy and species exchange decrease with rising values of magnetic field. Moreover, it is found that increasing the chemical reaction parameter increases the Nusselt number and decreases skin friction. Further, the effect of Lewis parameter diminishes energy transport rate. In the same vein, it is also observed that increasing the inclination can enhance skin friction, while the opposite occurred for the energy and species transport rate. As given numerical computations demonstrate, our results are in reasonable agreement with the reported earlier studies.

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Convective conditions and dissipation on Tangent Hyperbolic fluid over a chemically heating exponentially porous sheet

Nonlinear Engineering ◽

10.1515/nleng-2018-0003 ◽

2019 ◽

Vol 8 (1) ◽

pp. 407-418 ◽

Cited By ~ 4

Author(s):

Mamata Patil ◽

Mahesha ◽

C.S.K. Raju

Keyword(s):

Boundary Layer ◽

Differential Equations ◽

Heat Source ◽

Ordinary Differential Equations ◽

Skin Friction ◽

Chemical Reaction ◽

Transfer Rate ◽

Manufacturing Systems ◽

Mass Transfer Rate ◽

Tangent Hyperbolic Fluid

Abstract In this present analysis we investigated the steady-state magnetohydrodynamic boundary layer flow of tangent hyperbolic fluid over an exponentially stretching surface in the presence of heat source and chemical reaction. The chemical reaction with combination of exponential surface has significance in many industrial and manufacturing systems. The partial nonlinear differential equations are transformed into ordinary differential equations by using the similarity conversion and the accomplished boundary layer ordinary differential equations are elucidated numerically by using Shooting technique. The effects of numerous non-dimensional governing factors on velocity, temperature and concentration profiles were depicted graphically and analyzed in detail. The numerically computed results of Skin friction factor, Nusselt and Sherwood numbers are presented in tabular form for suction and injection cases separately.Heat transfer rate at the surface increases with increasing values of power law of index and whereas it declines with the magnetic field, heat source and chemical reaction parameters. It observed that Biot number enhances the skin friction, Nusselt number and decrease the Sherwood number.Heat transfer rate and mass transfer rate increases and skin friction decreases with increasing Eckert number.

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MHD STAGNATION POINT FLOW OF HYPERBOLIC TANGENT FLUID WITH VISCOUS DISSIPATION AND CHEMICAL REACTION

Journal of Science and Arts ◽

10.46939/j.sci.arts-21.2-c01 ◽

2021 ◽

Vol 21 (2) ◽

pp. 569-588

Author(s):

KINZA ARSHAD ◽

MUHAMMAD ASHRAF

Keyword(s):

Magnetic Field ◽

Differential Equations ◽

Ordinary Differential Equations ◽

Stagnation Point ◽

Viscous Dissipation ◽

Chemical Reaction ◽

Normal Velocity ◽

Hyperbolic Tangent ◽

Linear Ordinary Differential Equations ◽

Non Linear

In the present work, two dimensional flow of a hyperbolic tangent fluid with chemical reaction and viscous dissipation near a stagnation point is discussed numerically. The analysis is performed in the presence of magnetic field. The governing partial differential equations are converted into non-linear ordinary differential equations by using appropriate transformation. The resulting higher order non-linear ordinary differential equations are discretized by finite difference method and then solved by SOR (Successive over Relaxation parameter) method. The impact of the relevant parameters is scrutinized by plotting graphs and discussed in details. The main conclusion is that the large value of magnetic field parameter and wiessenberg numbers decrease the streamwise and normal velocity while increase the temperature distribution. Also higher value of the Eckert number Ec results in increases in temperature profile.

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Hyperasymptotics

Proceedings of the Royal Society of London. Series A: Mathematical and Physical Sciences ◽

10.1098/rspa.1990.0111 ◽

1990 ◽

Vol 430 (1880) ◽

pp. 653-668 ◽

Cited By ~ 99

Keyword(s):

Asymptotic Expansion ◽

Differential Equations ◽

Ordinary Differential Equations ◽

Transition Point ◽

Asymptotic Series ◽

Stokes Phenomenon ◽

Numerical Computations ◽

Borel Summation ◽

Nested Sequence ◽

Exponentially Small

We develop a technique for systematically reducing the exponentially small (‘superasymptotic’) remainder of an asymptotic expansion truncated near its least term, for solutions of ordinary differential equations of Schrödinger type where one transition point dominates. This is achieved by repeatedly applying Borel summation to a resurgence formula discovered by Dingle, relating the late to the early terms of the original expansion. The improvements form a nested sequence of asymptotic series truncated at their least terms. Each such ‘hyperseries’ involves the terms of the original asymptotic series for the particular function being approximated, together with terminating integrals that are universal in form, and is half the length of its predecessor. The hyperasymptotic sequence is therefore finite, and leads to an ultimate approximation whose error is less than the square of the original superasymptotic remainder. The Stokes phenomenon is automatically and exactly incorporated into the scheme. Numerical computations confirm the efficacy of the technique.

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EFFECT OF HEAT AND MASS TRANSFER AND THERMAL RADIATION ON A STEADY MHD CONVECTIVE FLOW WITH VISCOUS DISSIPATION AND SUCTION/INJECTION

Latin American Applied Research - An international journal ◽

10.52292/j.laar.2022.754 ◽

2022 ◽

Vol 52 (1) ◽

pp. 35-41

Author(s):

Silpisikha Goswami ◽

Kamalesh Kumar Pandit ◽

Dipak Sarma

Keyword(s):

Nusselt Number ◽

Thermal Radiation ◽

Temperature Profile ◽

Skin Friction ◽

Viscous Dissipation ◽

Sherwood Number ◽

Fluid Velocity ◽

Physical Parameters ◽

Flow Equations ◽

The Impact

Our motive is to examine the impact of thermal radiation and suction or injection with viscous dissipation on an MHD boundary layer flow past a vertical porous stretched sheet immersed in a porous medium. The set of the flow equations is converted into a set of non-linear ordinary differential equations by using similarity transformation. We use Runge Kutta method and shooting technique in MATLAB Package to solve the set of equations. The impact of non-dimensional physical parameters on flow profiles is analysed and depicted in graphs. We observe the influence of non-dimensional physical quantities on the Nusselt number, the Sherwood number, and skin friction and presented in tables. A comparison of the obtained numerical results with existing results in a limiting sense is also presented. We enhance radiation to observe the deceleration of fluid velocity and temperature profile for both suction and injection. While enhancing porosity parameter accelerates velocity whereas decelerates temperature profile. As the heat source parameter increases, the temperature of the fluid decreases for both suction and injection, it has been found. With the increasing values of the radiation parameter, the skin friction and heat transfer rate decreases. Increasing magnetic parameter decelerates the skin friction, Nusselt number, and Sherwood number.

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Nonlinear translational symmetric equilibria relevant to the L–H transition

Journal of Plasma Physics ◽

10.1017/s0022377812000918 ◽

2012 ◽

Vol 79 (3) ◽

pp. 257-265 ◽

Cited By ~ 7

Author(s):

Ap. KUIROUKIDIS ◽

G. N. THROUMOULOPOULOS

Keyword(s):

Magnetic Field ◽

Differential Equations ◽

Ordinary Differential Equations ◽

Plasma Flow ◽

Sufficient Condition ◽

Sheared Flow ◽

Equilibrium Configurations ◽

Shafranov Equation ◽

The Impact ◽

The Magnetic Field

AbstractNonlinear z-independent solutions to a generalized Grad–Shafranov equation (GSE) with up to quartic flux terms in the free functions and incompressible plasma flow non-parallel to the magnetic field are constructed quasi-analytically. Through an ansatz, the GSE is transformed to a set of three ordinary differential equations and a constraint for three functions of the coordinate x, in Cartesian coordinates (x,y), which then are solved numerically. Equilibrium configurations for certain values of the integration constants are displayed. Examination of their characteristics in connection with the impact of nonlinearity and sheared flow indicates that these equilibria are consistent with the L–H transition phenomenology. For flows parallel to the magnetic field, one equilibrium corresponding to the H state is potentially stable in the sense that a sufficient condition for linear stability is satisfied in an appreciable part of the plasma while another solution corresponding to the L state does not satisfy the condition. The results indicate that the sheared flow in conjunction with the equilibrium nonlinearity plays a stabilizing role.

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Effects of chemical reaction and activation energy on a Carreau nanoliquid past a permeable surface under zero mass flux conditions

Proceedings of the Institution of Mechanical Engineers Part N Journal of Nanomaterials Nanoengineering and Nanosystems ◽

10.1177/2397791419881090 ◽

2019 ◽

Vol 234 (1-2) ◽

pp. 47-57

Author(s):

GK Ramesh ◽

K Ganesh Kumar ◽

Ali J Chamkha ◽

Rama Subba Reddy Gorla

Keyword(s):

Activation Energy ◽

Differential Equations ◽

Ordinary Differential Equations ◽

Chemical Reaction ◽

Permeable Surface ◽

Concentration Gradients ◽

Zero Mass ◽

Temperature Impact ◽

Fifth Order ◽

Physical Quantities

Arrhenius condition has been broadly utilized as a model of the temperature impact on the rate compound responses and organic procedure. Hence, our aim of this article is to examine the effects of chemical reaction and activation energy on a Carreau nanoliquid in a permeable surface. For thermal and mass transport curiosities, the cumulative upgrade of convective type condition and zero mass transition have been considered. The overseeing sets of partial differential equations are rendered into coupled nonlinear ordinary differential equations. The arrangement of the subsequent ordinary differential equations is acquired with the assistance of the Runge-Kutta-Fehlberg-fourth-fifth order (RKF-45) procedure. The influence of relevant parameters and physical quantities is investigated. The results show that the presence of reaction rate and energy activation term decelerates the temperature and concentration gradients.

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MHD Slip Flow of Newtonian Fluid past a Stretching Sheet with Thermal Convective Boundary Condition, Radiation, and Chemical Reaction

Mathematical Problems in Engineering ◽

10.1155/2013/359817 ◽

2013 ◽

Vol 2013 ◽

pp. 1-12 ◽

Cited By ~ 1

Author(s):

Reda G. Abdel-Rahman

Keyword(s):

Mass Transfer ◽

Boundary Condition ◽

Differential Equations ◽

Ordinary Differential Equations ◽

Heat And Mass Transfer ◽

Chemical Reaction ◽

Stretching Sheet ◽

Convective Boundary Condition ◽

Nonlinear Ordinary Differential Equations ◽

Convective Boundary

An analysis is carried out to study the problem of heat and mass transfer flow over a moving permeable flat stretching sheet in the presence of convective boundary condition, slip, radiation, heat generation/absorption, and first-order chemical reaction. The viscosity of fluid is assumed to vary linearly with temperature. Also the diffusivity is assumed to vary linearly with concentration. The governing partial differential equations have been reduced to the coupled nonlinear ordinary differential equations by using Lie group point of transformations. The system of transformed nonlinear ordinary differential equations is solved numerically using shooting techniques with fourth-order Runge-Kutta integration scheme. Comparison between the existing literature and the present study was carried out and found to be in excellent agreement. The effects of the various interesting parameters on the flow, heat, and mass transfer are analyzed and discussed through graphs in detail. The values of the local Nusselt number, the local skin friction, and the local Sherwood number for different physical parameters are also tabulated.

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On deterministic approximation of Markov processes by ordinary differential equations

Mathematical Problems in Engineering ◽

10.1155/s1024123x9800074x ◽

1998 ◽

Vol 4 (2) ◽

pp. 99-114 ◽

Cited By ~ 1

Author(s):

L. I. Rozonoer

Keyword(s):

Differential Equations ◽

Markov Model ◽

Ordinary Differential Equations ◽

Chemical Reaction ◽

Markov Processes ◽

Random Variables ◽

Mean Values ◽

Multidimensional Lattice ◽

The Mean

For a class of Markov processes on the integer multidimensional lattice, it is shown that the evolution of the mean values of some random variables can be approximated by ordinary differential equations. To illustrate the approach, a Markov model of a chemical reaction is considered

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The Effects of Chemical Reaction, Hall, and Ion-Slip Currents on MHD Micropolar Fluid Flow with Thermal Diffusivity Using a Novel Numerical Technique

Journal of Applied Mathematics ◽

10.1155/2012/689015 ◽

2012 ◽

Vol 2012 ◽

pp. 1-30 ◽

Cited By ~ 11

Author(s):

S. S. Motsa ◽

S. Shateyi

Keyword(s):

Fluid Flow ◽

Thermal Diffusivity ◽

Differential Equations ◽

Ordinary Differential Equations ◽

Chemical Reaction ◽

Numerical Technique ◽

Linearization Method ◽

Nonlinear Ordinary Differential Equations ◽

Successive Linearization Method ◽

Ion Slip

The problem of magnetomicropolar fluid flow, heat, and mass transfer with suction through a porous medium is numerically analyzed. The problem was studied under the effects of chemical reaction, Hall, ion-slip currents, and variable thermal diffusivity. The governing fundamental conservation equations of mass, momentum, angular momentum, energy, and concentration are converted into a system of nonlinear ordinary differential equations by means of similarity transformation. The resulting system of coupled nonlinear ordinary differential equations is the then solved using a fairly new technique known as the successive linearization method together with the Chebyshev collocation method. A parametric study illustrating the influence of the magnetic strength, Hall and ion-slip currents, Eckert number, chemical reaction and permeability on the Nusselt and Sherwood numbers, skin friction coefficients, velocities, temperature, and concentration was carried out.

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The Consequences of Thermal Radiation and Chemical Reactions on Magneto-hydrodynamics in Two Dimensions Over a Stretching Sheet with Jeffrey Fluid.

10.22541/au.163903063.31692115/v1 ◽

2021 ◽

Author(s):

Vijay Patel ◽

Jigisha Pandya

Keyword(s):

Differential Equations ◽

Thermal Radiation ◽

Ordinary Differential Equations ◽

Homotopy Analysis Method ◽

Stretching Sheet ◽

Fluid Velocity ◽

Jeffrey Fluid ◽

Analysis Method ◽

Homotopy Analysis ◽

The Impact

In this research paper, the Homotopy Analysis Method is used to investigate the twodimensional electrical conduction of a magneto-hydrodynamic (MHD) Jeffrey Fluid across a stretching sheet under various conditions, such as when electrical current and temperature are both present, and when heat is added in the presence of a chemical reaction or thermal radiation. Applying similarity transformation, the governing partial differential equation is transformed into terms of nonlinear coupled ordinary differential equations. The Homotopy Analysis Method is used to solve a system of ordinary differential equations. The impact of different numerical values on velocity, concentration, and temperature is examined and presented in tables and graphs. The fluid velocity reduces as the retardation time parameter(2) grows, while the fluid velocity inside the boundary layer increases as the Deborah number () increases. The velocity profiles decrease when the magnetic parameter M is increased. The results of this study are entirely compatible with those of a viscous fluid. The Homotopy Analysis Method calculations have been carried out on the PARAM Shavak high-performance computing (HPC) machine using the BVPh2.0 Mathematica tool.

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