scholarly journals Numerical Investigation of Mixed Convective Williamson Fluid Flow Over an Exponentially Stretching Permeable Curved Surface

Fluids ◽  
2021 ◽  
Vol 6 (7) ◽  
pp. 260
Author(s):  
Kamran Ahmed ◽  
Waqar A. Khan ◽  
Tanvir Akbar ◽  
Ghulam Rasool ◽  
Sayer O. Alharbi ◽  
...  
Keyword(s):  
Thermal Conductivity ◽  
Differential Equations ◽  
Variable Parameter ◽  
Pressure Profile ◽  
Curved Surface ◽  
Navier Stokes ◽  
Williamson Fluid ◽  
Exponential Stretching ◽  
Non Linear ◽  
Mixed Convective Flow

The present investigation aims to examine the heat flux mechanism in the hagnetohydrodynamic (MHD) mixed convective flow of Williamson-type fluid across an exponential stretching porous curved surface. The significant role of thermal conductivity (variable), non-linear thermal radiation, unequal source-sink, and Joules heating is considered. The governing problems are obtained using the Navier–Stokes theory, and the appropriate similarity transformation is applied to write the partial differential equations in the form of single-variable differential equations. The solutions are obtained by using a MATLAB-based built-in bvp4c package. The vital aspect of this analysis is to observe the effects of the curvature parameter, magnetic number, suction/injection parameter, permeability parameter, Prandtl factor, Eckert factor, non-linear radiation parameter, buoyancy parameter, temperature ratio parameter, Williamson fluid parameter, and thermal conductivity (variable) parameter on the velocity field, thermal distribution, and pressure profile which are discussed in detail using a graphical approach. The correlation with the literature reveals a satisfactory improvement in the existing results on permeability factors in Williamson fluids.

scholarly journals Application of the Poor Man’s Navier–Stokes Equations to Real-Time Control of Fluid Flow

2011 ◽  
Author(s):  
James B. Polly ◽  
J. M. McDonough
Keyword(s):  
Fluid Flow ◽  
Differential Equations ◽  
Real Time ◽  
Stokes Equations ◽  
Discrete Dynamical System ◽  
Navier Stokes ◽  
Control Force ◽  
The Poor ◽  
Non Linear ◽  
Non Linear System

Control of fluid flow is an important, and quite underutilized process possessing significant potential benefits ranging from avoidance of separation and stall on aircraft wings and reduction of friction factors in oil and gas pipelines to mitigation of noise from wind turbines. But the Navier–Stokes (N.–S.) equations governing fluid flow consist of a system of time-dependent, multi-dimensional, non-linear partial differential equations (PDEs) which cannot be solved in real time using current, or near-term foreseeable, computing hardware. The poor man’s Navier–Stokes (PMNS) equations comprise a discrete dynamical system that is algebraic—hence, easily (and rapidly) solved—and yet which retains many (possibly all) of the temporal behaviors of the full (PDE) N.–S. system at specific spatial locations. In this paper we outline derivation of these equations and present a short discussion of their basic properties. We then consider application of these equations to the problem of control by adding a control force. We examine the range of PMNS equation behaviors that can be achieved by changing values of this control force, and, in particular, consider controllability of this (non-linear) system via numerical experiments. Moreover, we observe that the derivation leading to the PMNS equations is very general, and, at least in principle, it can be applied to a wide variety of problems governed by PDEs and (possibly) time-delay ordinary differential equations such as, for example, models of machining processes.

Flow and Heat Transfer of Powell–Eyring Fluid due to an Exponential Stretching Sheet with Heat Flux and Variable Thermal Conductivity

2015 ◽  
Vol 70 (3) ◽  
pp. 163-169 ◽  
Author(s):  
Ahmed M. Megahed
Keyword(s):  
Heat Transfer ◽  
Thermal Conductivity ◽  
Heat Flux ◽  
Differential Equations ◽  
Variable Thermal Conductivity ◽  
Physical Parameters ◽  
Flow And Heat Transfer ◽  
Non Linear ◽  
Thermal Conductivity Parameter ◽  
Conductivity Parameter

AbstractAn analysis was carried out to describe the problem of flow and heat transfer of Powell–Eyring fluid in boundary layers on an exponentially stretching continuous permeable surface with an exponential temperature distribution in the presence of heat flux and variable thermal conductivity. The governing partial differential equations describing the problem were transformed into a set of coupled non-linear ordinary differential equations and then solved with a numerical technique using appropriate boundary conditions for various physical parameters. The numerical solution for the governing non-linear boundary value problem is based on applying the shooting method over the entire range of physical parameters. The effects of various parameters like the thermal conductivity parameter, suction parameter, dimensionless Powell–Eyring parameters and the Prandtl number on the flow and temperature profiles as well as on the local skin-friction coefficient and the local Nusselt number are presented and discussed. In this work, special attention was given to investigate the effect of the thermal conductivity parameter on the velocity and temperature fields above the sheet in the presence of heat flux. The numerical results were also validated with results from a previously published work on various special cases of the problem, and good agreements were seen.

scholarly journals Numerical Study of Thermal-Diffusion and Diffusion-Thermo Effects on Mixed Convective Flow and Mass Transfer in the Presence of MHD over an Accelerating Surface

2020 ◽  
Vol 11 (4) ◽  
pp. 11487``-11498
Keyword(s):  
Mass Transfer ◽  
Differential Equations ◽  
Thermal Diffusion ◽  
Variable Viscosity ◽  
Numerical Study ◽  
Linear Ordinary Differential Equations ◽  
Non Linear ◽  
Mixed Convective Flow ◽  
The Impact ◽  
And Diffusion

This study investigates the impact of MHD, variable viscosity, thermal-diffusion, and diffusion-thermo effects with the heat source on mixed convection of heat and mass transfer over an accelerating surface. The physical problem's governing equations involve a coupled non-linear partial differential equations, which are transformed to a coupled non-linear ordinary differential equations using a suitable similarity transformation. Numerical computation using shooting technique is adopted to study the physical characteristics of velocity, temperature, and concentration for various values of non-dimensional parameters like thermal diffusion parameter, diffusion-thermo parameter, viscosity parameter, Prandtl number, and strength of the magnetic field are involved in the problem. The obtained numerical results are found to be a good agreement with the earlier works.

Numerical simulation for transient flow of Williamson fluid with multiple slip model in the presence of chemically reacting species

2019 ◽  
Vol 29 (11) ◽  
pp. 4445-4461
Author(s):  
Aamir Hamid ◽  
Masood Khan ◽  
Metib Alghamdi
Keyword(s):  
Thermal Conductivity ◽  
Differential Equations ◽  
Transient Flow ◽  
Mathematical Formulation ◽  
Variable Thermal Conductivity ◽  
Integration Scheme ◽  
Fluid Temperature ◽  
Content Type ◽  
Williamson Fluid ◽  
Chemically Reacting

Purpose The purpose of this paper is to analyze a mathematical model for the time-dependent flow of non-Newtonian Williamson liquid because of a stretching surface. The mathematical formulation of the current model is accomplished from the momentum, energy and concentration balances by assuming a laminar, two-dimensional and incompressible flow subjected to a variable magnetic field. The study further aimed at discovering the possible effects of temperature-dependent thermal conductivity on the heat transfer characteristics. Design/methodology/approach In addition, a first-order chemical reaction is considered between the fluid and chemically reacting species. The governing transport model for Williamson fluid has been altered to ordinary differential equations via appropriate dimensionless parameters. These basic non-dimensional partially coupled differential equations of fluid motion are solved by an efficient Runge–Kutta–Fehlberg integration scheme along with the Nachtsheim–Swigert shooting technique. Findings It is found that the velocity slip parameter has a reducing impact on the skin friction coefficient. Moreover, we noticed that the Hartmann number and variable thermal conductivity parameters show prominent impacts on the velocity and temperature fields. It is also perceived that the fluid temperature shows an increasing trend with uplifting values of variable thermal conductivity. Originality/value No such work is yet published in the literature.

scholarly journals Impact of temperature dependent viscosity and thermal conductivity on MHD blood flow through a stretching surface with ohmic effect and chemical reaction

2021 ◽  
Vol 10 (1) ◽  
pp. 255-271
Author(s):  
Bhupendra K. Sharma ◽  
Chandan Kumawat
Keyword(s):  
Magnetic Field ◽  
Thermal Conductivity ◽  
Blood Flow ◽  
Differential Equations ◽  
Ordinary Differential Equations ◽  
Chemical Reaction ◽  
Stretching Surface ◽  
Temperature Dependent ◽  
Grashof Number ◽  
Non Linear

Abstract A study has been carried for a viscous, incompressible electrically conducting MHD blood flow with temperature-dependent thermal conductivity and viscosity through a stretching surface in the presence of thermal radiation, viscous dissipation, and chemical reaction. The flow is subjected to a uniform transverse magnetic field normal to the flow. The governing coupled partial differential equations are converted into a set of non-linear ordinary differential equations (ODE) using similarity analysis. The resultant non-linear coupled ordinary differential equations are solved numerically using the boundary value problem solver (bvp4c) in MATLAB with a convincible accuracy. The effects of the physical parameters such as viscosity parameter ( μ ( T ˜ b ) ) \left({\mu ({{\tilde T}_b})} \right) , permeability parameter (β), magnetic field parameter (M), Local Grashof number (Gr) for thermal diffusion, Local modified Grashof number for mass diffusion (Gm), the Eckert number (Ec), the thermal conductivity parameter ( K ( T ˜ b ) ) \left({K({{\tilde T}_b})} \right) on the velocity, temperature, concentration profiles, skin-friction coefficient, Nusselt number, and Sherwood number are presented graphically. The physical visualization of flow parameters that appeared in the problem is discussed with the help of various graphs to convey the real life application in industrial and engineering processes. A comparison has been made with previously published work and present study revels the good agreement with the published work. This study will be helpful in the clinical healing of pathological situations accompanied by accelerated circulation.

Magnetohydrodynamic flow of nano Williamson fluid generated by stretching plate with multiple slips

2019 ◽  
Vol 15 (5) ◽  
pp. 871-894 ◽  
Author(s):  
Jawad Raza ◽  
Fateh Mebarek-Oudina ◽  
B. Mahanthesh
Keyword(s):  
Thermal Conductivity ◽  
Differential Equations ◽  
Regression Line ◽  
Skin Friction Coefficient ◽  
Content Type ◽  
Williamson Fluid ◽  
Thermal Conductivity Parameter ◽  
Conductivity Parameter ◽  
Stretching Plate ◽  
Multiple Slips

Purpose The purpose of this paper is to present an exploration of multiple slips and temperature dependent thermal conductivity effects on the flow of nano Williamson fluid over a slendering stretching plate in the presence of Joule and viscous heating aspects. The effectiveness of nanoparticles is deliberated by considering Brownian moment and thermophoresis slip mechanisms. The effects of magnetism and radiative heat are also deployed. Design/methodology/approach The governing partial differential equations are non-dimensionalized and reduced to multi-degree ordinary differential equations via suitable similarity variables. The subsequent non-linear problem treated for numerical results. To measure the amount of increase/decrease in skin friction coefficient, Nusselt number and Sherwood number, the slope of linear regression line through the data points are calculated. Statistical approach is implemented to analyze the heat transfer rate. Findings The results show that temperature distribution across the flow decreases with thermal conductivity parameter. The maximum friction factor is ascertained at stronger magnetic field. Originality/value In the current paper, the magneto-nano Williamson fluid flow inspired by a stretching sheet of variable thickness is examined numerically. The rationale of the present study is to generalize the studies of Mebarek-Oudina and Makinde (2018) and Williamson (1929).

Variable viscosity and thermal conductivity effects on Williamson fluid flow over a slendering stretching sheet

2020 ◽  
Vol 17 (3) ◽  
pp. 357-371
Author(s):  
Moses Sunday Dada ◽  
Cletus Onwubuoya
Keyword(s):  
Thermal Conductivity ◽  
Boundary Layer ◽  
Mass Transfer ◽  
Fluid Flow ◽  
Differential Equations ◽  
Stretching Sheet ◽  
Analysis Method ◽  
Content Type ◽  
Williamson Fluid ◽  
Homotopy Analysis

Purpose The purpose of this paper is to consider heat and mass transfer on magnetohydrodynamics (MHD) Williamson fluid flow over a slendering stretching sheet with variable thickness in the presence of radiation and chemical reaction. All pertinent flow parameters are discussed and their influence on the hydrodynamics, thermal and concentration boundary layer are presented with the aid of the diagram. Design/methodology/approach The governing partial differential equations are reduced into a system of ordinary differential equations with the help of suitable similarity variables. A discrete version of the homotopy analysis method (HAM) called the spectral homotopy analysis method (SHAM) was used to solve the transformed equations. SHAM is efficient, and it converges faster than the HAM. The SHAM provides flexibility when solving linear ordinary differential equations with the use of the Chebyshev spectral collocation method. Findings The findings revealed that an increase in the variable thermal conductivity hike the temperature and the thermal boundary layer thickness, whereas the reverse is the case for velocity close to the wall. Originality/value The uniqueness of this paper is the exploration of combined effects of heat and mass transfer on MHD Williamson fluid flow over a slendering stretching sheet. The Williamson fluid term in the momentum equation is expressed as a linear function and the viscosity and thermal conductivity are considered to vary in the boundary layer.

scholarly journals Heat Transfer Exploration of MHD Flow Stream with Changing Viscosity and Thermal Conductivity due to Expandable Surface

2021 ◽  
Vol 8 (6) ◽  
pp. 955-960
Author(s):  
M.C. Kemparaju ◽  
Bommanna Lavanya ◽  
Mahantesh M. Nandeppanavar ◽  
N. Raveendra
Keyword(s):  
Heat Transfer ◽  
Thermal Conductivity ◽  
Partial Differential Equations ◽  
Differential Equations ◽  
Mhd Flow ◽  
Variable Thermal Conductivity ◽  
Partial Differential ◽  
Linear Ordinary Differential Equations ◽  
Linear Partial Differential Equations ◽  
Non Linear

In this paper an examination is completed to explore the influence of variable thickness and variable thermal conductivity on MHD stream. We have considered the governing stream and heat transfer conditions as partial differential equations. These non-linear partial differential equations are changed to non-linear ordinary differential equations at that point explained numerically utilizing fourth order RK strategy with shooting procedure. The influence of governing factors on velocity and temperature is concentrated through diagrams and numerical estimations of skin frictions and wall temperature inclination are determined, classified and examined.

Heat Transfer Phenomena in a Moving Nanofluid Over a Horizontal Surface

2012 ◽  
Vol 28 (3) ◽  
pp. 579-588 ◽  
Author(s):  
K. Vajravelu ◽  
K. V. Prasad
Keyword(s):  
Heat Transfer ◽  
Thermal Conductivity ◽  
Brownian Motion ◽  
Differential Equations ◽  
Volume Fraction ◽  
Numerical Study ◽  
Fluid Viscosity ◽  
Variable Fluid Properties ◽  
Non Linear ◽  
Fluid Properties

AbstractA numerical study is carried out to study the effects of variable fluid properties on the boundary layer flow and heat transfer of a nanofluid at a flat sheet. The effects of Brownian motion, thermophoresis and viscous dissipation due to frictional heating are also considered. The temperature-dependent variable fluid properties, namely, the fluid viscosity and the thermal conductivity are assumed to vary, respectively, as an inverse function and a linear function of temperature. Using a similarity transformation, the governing non-linear partial differential equations of the model problem are transformed into coupled non-linear ordinary differential equations and these equations are solved numerically by Keller-Box method. Velocity, temperature, and nanoparticles volume fraction profiles are presented and analyzed for several sets of values of the governing parameters; namely, variable fluid viscosity, variable thermal conductivity, Brownaian motion, thermophoresis and plate-velocity parameters with changes in the Prandtl and Schmidt numbers. It is observed that there is an increase in the skin friction in the upstream movement of the plate: But quite the opposite is true in the downstream movement of the plate. Also, the effect of the Schmidt number and the Brownian motion parameter is to reduce the Sherwood number, where as the effect of thermophoresis parameter is to enhance it.

scholarly journals Physical Aspects of Homogeneous-Heterogeneous Reactions on MHD Williamson Fluid Flow across a Nonlinear Stretching Curved Surface Together with Convective Boundary Conditions

2021 ◽  
Vol 2021 ◽  
pp. 1-13
Author(s):  
Kamran Ahmed ◽  
Tanvir Akbar ◽  
Taseer Muhammad
Keyword(s):  
Differential Equations ◽  
Boundary Conditions ◽  
Heterogeneous Reaction ◽  
Nonlinear Partial Differential Equations ◽  
Heterogeneous Reactions ◽  
Curved Surface ◽  
Convective Boundary Conditions ◽  
Convective Boundary ◽  
Williamson Fluid ◽  
Nonlinear Stretching

This article is concerned with the fluid mechanics of MHD steady 2D flow of Williamson fluid over a nonlinear stretching curved surface in conjunction with homogeneous-heterogeneous reactions with convective boundary conditions. An effective similarity transformation is considered that switches the nonlinear partial differential equations riveted to ordinary differential equations. The governing nonlinear coupled differential equations are solved by using MATLAB bvp4c code. The physical features of nondimensional Williamson fluid parameter λ , power-law stretching index m , curvature parameter K , Schmidt number Sc , magnetic field parameter M , Prandtl number Pr , homogeneous reaction strength k 1 , heterogeneous reaction strength k 2 , and Biot number γ are presented through the graphs. The tabulated form of results is obtained for the skin friction coefficient. It is noted that both the homogeneous and heterogeneous reaction strengths reduced the concentration profile.

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