MHD FLOW OF AN EYRING-POWELL FLUID WITH THE EFFECT OF THERMAL RADIATION, JOULE HEATING AND VISCOUS DISSIPATION

2020 ◽  
Vol 9 (11) ◽  
pp. 9259-9271
Author(s):  
K.R. Babu ◽  
G. Narender ◽  
K. Govardhan
Keyword(s):  
Differential Equations ◽  
Thermal Radiation ◽  
Ordinary Differential Equations ◽  
Viscous Dissipation ◽  
Joule Heating ◽  
Mhd Flow ◽  
Physical Parameters ◽  
Shooting Technique ◽  
Similarity Transformations ◽  
The Magnetic Field

A two-dimensional stream of an magnetohydrodynamics (MHD) Eyring-Powell fluid on a stretching surface in the presence of thermal radiation, viscous dissipation and the Joule heating is analyzed. The flow model in the form of the Partial Differential Equations (PDEs) is transformed into a system of non-linear and coupled Ordinary Differential Equations (ODEs) by implementing appropriate similarity transformations. The resulting ordinary differential equations are solved numerically by the shooting technique with Adams-Moulton Method of fourth order. The numerical solution obtained for the velocity and temperature profiles has been presented through graphs for different choice of the physical parameters. The magnetic field is found to have a direct relation with the temperature profile and an inverse with the velocity profile. Increasing the thermal radiation, the temperature tends to rise.

Influence of nonlinear thermal radiation and viscous dissipation on three-dimensional flow of Jeffrey nano fluid over a stretching sheet in the presence of Joule heating

2017 ◽  
Vol 6 (3) ◽  
Author(s):  
K. Ganesh Kumar ◽  
N.G. Rudraswamy ◽  
B.J. Gireesha ◽  
M.R. Krishnamurthy
Keyword(s):  
Differential Equations ◽  
Thermal Radiation ◽  
Ordinary Differential Equations ◽  
Viscous Dissipation ◽  
Joule Heating ◽  
Stretching Sheet ◽  
Three Dimensional ◽  
Nonlinear Thermal Radiation ◽  
Nonlinear Ordinary Differential Equations ◽  
Three Dimensional Flow

AbstractPresent exploration discusses the combined effect of viscous dissipation and Joule heating on three dimensional flow and heat transfer of a Jeffrey nanofluid in the presence of nonlinear thermal radiation. Here the flow is generated over bidirectional stretching sheet in the presence of applied magnetic field by accounting thermophoresis and Brownian motion of nanoparticles. Suitable similarity transformations are employed to reduce the governing partial differential equations into coupled nonlinear ordinary differential equations. These nonlinear ordinary differential equations are solved numerically by using the Runge–Kutta–Fehlberg fourth–fifth order method with shooting technique. Graphically results are presented and discussed for various parameters. Validation of the current method is proved by comparing our results with the existing results under limiting situations. It can be concluded that combined effect of Joule and viscous heating increases the temperature profile and thermal boundary layer thickness.

scholarly journals Numerical Solution of Boundary Layer MHD Flow with Viscous Dissipation

2014 ◽  
Vol 2014 ◽  
pp. 1-5 ◽  
Author(s):  
S. R. Mishra ◽  
S. Jena
Keyword(s):  
Differential Equations ◽  
Viscous Dissipation ◽  
Graphical Representation ◽  
Mhd Flow ◽  
Transverse Magnetic ◽  
Shrinking Sheet ◽  
Shooting Technique ◽  
Electrically Conducting ◽  
Similarity Transformations ◽  
Runge Kutta Method

The present paper deals with a steady two-dimensional laminar flow of a viscous incompressible electrically conducting fluid over a shrinking sheet in the presence of uniform transverse magnetic field with viscous dissipation. Using suitable similarity transformations the governing partial differential equations are transformed into ordinary differential equations and then solved numerically by fourth-order Runge-Kutta method with shooting technique. Results for velocity and temperature profiles for different values of the governing parameters have been discussed in detail with graphical representation. The numerical evaluation of skin friction and Nusselt number are also given in this paper.

scholarly journals Effect of Convective Heat and Mass Conditions in Magnetohydrodynamic Boundary Layer Flow with Joule Heating and Thermal Radiation

2020 ◽  
Vol 25 (3) ◽  
pp. 103-116
Author(s):  
R.P. Sharma ◽  
Seema Tinker ◽  
B.J. Gireesha ◽  
B. Nagaraja
Keyword(s):  
Differential Equations ◽  
Thermal Radiation ◽  
Convective Heat ◽  
Joule Heating ◽  
Numerical Solutions ◽  
Nonlinear Partial Differential Equations ◽  
Mhd Flow ◽  
Radiation Chemical ◽  
Similarity Transformations ◽  
Layer Flow

AbstractA free convection viscous MHD flow over a semi-infinite vertical sheet with convective heat and mass conditions has been considered. The effects of thermal radiation, chemical reaction and Joule heating on flow are also accounted. The governing nonlinear partial differential equations have been transformed into a set of highly non-linear coupled ordinary differential equations (ODEs) using appropriate similarity transformations. Numerical solutions of transformed equations are obtained by employing the 5th order Runge-Kutta Fehlberg technique followed by the shooting technique. The influences of different flow parameters on the momentum, energy and mass field are discussed and shown graphically. Results reveal that temperature and concentration profiles enhance due to increasing heat and mass Biot number parameters.

scholarly journals Effects of ohmic heating and viscous dissipation on steady MHD flow near a stagnation point on an isothermal stretching sheet

2009 ◽  
Vol 13 (1) ◽  
pp. 5-12 ◽  
Author(s):  
Pushkar Sharma ◽  
Gurminder Singh
Keyword(s):  
Stagnation Point ◽  
Viscous Dissipation ◽  
Ohmic Heating ◽  
Mhd Flow ◽  
Transverse Magnetic ◽  
Skin Friction Coefficient ◽  
Physical Parameters ◽  
Governing Equations ◽  
Shooting Technique ◽  
Electrically Conducting

Aim of the paper is to investigate effects of ohmic heating and viscous dissipation on steady flow of a viscous incompressible electrically conducting fluid in the presence of uniform transverse magnetic field and variable free stream near a stagnation point on a stretching non-conducting isothermal sheet. The governing equations of continuity, momentum, and energy are transformed into ordinary differential equations and solved numerically using Runge-Kutta fourth order with shooting technique. The velocity and temperature distributions are discussed numerically and presented through graphs. Skin-friction coefficient and the Nusselt number at the sheet are derived, discussed numerically, and their numerical values for various values of physical parameters are compared with earlier results and presented through tables.

MHD flow, under the kinetic postulate, of fluids that are initially liquid under thermal radiation effects

2019 ◽  
Vol 97 (6) ◽  
pp. 579-587
Author(s):  
Azad Hussain ◽  
Zainia Muneer ◽  
M.Y. Malik ◽  
Saadia Ghafoor
Keyword(s):  
Nusselt Number ◽  
Differential Equations ◽  
Thermal Radiation ◽  
Skin Friction ◽  
Radiation Effects ◽  
Shooting Method ◽  
Porous Plate ◽  
Mhd Flow ◽  
Physical Parameters ◽  
Runge Kutta Method

The present study focuses on the non-Newtonian magnetohydrodynamic flow, under the kinetic postulate, of fluids that are initially liquid past a porous plate in the appearance of thermal radiation effects. Resemblance transfigurations are used to metamorphose the governing equations for temperature and velocity into a system of ordinary differential equations. We then solved these differential equations subject to convenient boundary conditions by using the shooting method along with the Runge–Kutta method. Heat transfer and characteristic flow results are acquired for different compositions of physical parameters. These results are extended graphically to demonstrate interesting attributes of the physics of the problem. Nusselt number and skin friction coefficients are also discussed via graphs and tables for different values of dimensionless parameters. Decline occurs in velocity profile due to escalating values of M. Temperature profile depicts growing behavior due to acceleration in the values of λ and M. Nusselt number and skin friction curves represent rising behavior according to their parameters.

Numerical exploration of the combined effects of non-linear thermal radiation and variable thermo-physical properties on the flow of Casson nanofluid over a wedge

2017 ◽  
Vol 13 (4) ◽  
pp. 628-647 ◽  
Author(s):  
Archana M. ◽  
Gireesha B.J. ◽  
Prasannakumara B.C. ◽  
Rama Subba Reddy Gorla
Keyword(s):  
Differential Equations ◽  
Thermal Radiation ◽  
Physical Properties ◽  
Physical Parameters ◽  
Content Type ◽  
Casson Nanofluid ◽  
Linear Ordinary Differential Equations ◽  
Similarity Transformations ◽  
Non Linear ◽  
Thermo Physical Properties

Purpose The effect of non-linear thermal radiation and variable thermo-physical properties are investigated in the Falkner-Skan flow of a Casson nanofluid in the presence of magnetic field. The paper aims to discuss this issue. Design/methodology/approach Selected bunch of similarity transformations are used to reduce the governing partial differential equations into a set of non-linear ordinary differential equations. The resultant equations are numerically solved using Runge-Kutta-Fehlberg fourth-fifth-order method along with shooting technique. Findings The velocity, temperature and concentration profiles are evaluated for several emerging physical parameters and are analyzed through graphs and tables in detail. Research limitations/implications This study only begins to reveal the research potential and pitfalls of research and publishing on boundary-layer flow, heat and mass transfer of Casson nanofluid past and the moving and static wedge-shaped bodies. Originality/value It is found that the presence of non-linear thermal radiation and variable properties has more influence in heat transfer. Furthermore, temperature profile increases as the radiation parameter increases.

Viscous Dissipation and Thermal Radiation effects in MHD flow of Jeffrey Nanofluid through Impermeable Surface with Heat Generation/Absorption

2017 ◽  
Vol 6 (2) ◽  
Author(s):  
Kalpna Sharma ◽  
Sumit Gupta
Keyword(s):  
Thermal Radiation ◽  
Viscous Dissipation ◽  
Radiation Effects ◽  
Mhd Flow ◽  
Physical Parameters ◽  
Homotopy Analysis ◽  
Two Dimensional Flow ◽  
Jeffrey Nanofluid ◽  
Layer Flow ◽  
Mhd Boundary Layer Flow

AbstractThis paper investigates steady two dimensional flow of an incompressible magnetohydrodynamic (MHD) boundary layer flow and heat transfer of nanofluid over an impermeable surface in presence of thermal radiation and viscous dissipation. By using similarity transformation, the arising governing equations of momentum, energy and nanoparticle concentration are transformed into coupled nonlinear ordinary differential equations, which are than solved by homotopy analysis method (HAM). The effect of different physical parameters, namely, Prandtl number Pr, Eckert number

scholarly journals Magneto-Bioconvection Flow of Williamson Nanofluid over an Inclined Plate with Gyrotactic Microorganisms and Entropy Generation

Fluids ◽  
2021 ◽  
Vol 6 (3) ◽  
pp. 109
Author(s):  
Tunde A. Yusuf ◽  
Fazle Mabood ◽  
B. C. Prasannakumara ◽  
Ioannis E. Sarris
Keyword(s):  
Differential Equations ◽  
Thermal Radiation ◽  
Physical Parameters ◽  
Bejan Number ◽  
Inclined Plate ◽  
Similarity Transformations ◽  
Schmidt Numbers ◽  
Flow Through ◽  
Inclined Plates ◽  
Limit Approximation

The fluid flow through inclined plates has several applications in magneto-aerodynamics, materials processing and magnetohydrodynamic propulsion thermo-fluid dynamics. Inspired by these applications, the rate of entropy production in a bio-convective flow of a magnetohydrodynamic Williamson nanoliquid over an inclined convectively heated stretchy plate with the influence of thermal radiation, porous materials and chemical reaction has been deliberated in this paper. The presence of microorganisms aids in stabilizing the suspended nanoparticles through a bioconvection process. Also, the thermal radiation assumed an optically thick limit approximation. With the help of similarity transformations, the coupled partial differential equations are converted to nonlinear ordinary differential equations and the resulting model is numerically tackled using the shooting method. The influences of the determining thermo-physical parameters on the flow field are incorporated and extensively discussed. The major relevant outcomes of the present analysis are that the upsurge in values of Schmidt number decays the mass transfer characteristics, but the converse trend is depicted for boost up values of the thermophoresis parameter. Enhancement in bioconvection Peclet and Schmidt numbers deteriorates the microorganism density characteristics. Further, the upsurge in the Williamson parameter declines the Bejan number and irreversibility ratio.

scholarly journals Effects of Stefan Blowing and Slip Conditions on Unsteady MHD Casson Nanofluid Flow Over an Unsteady Shrinking Sheet: Dual Solutions

Symmetry ◽  
2020 ◽  
Vol 12 (3) ◽  
pp. 487 ◽  
Author(s):  
Liaquat Ali Lund ◽  
Zurni Omar ◽  
Jawad Raza ◽  
Ilyas Khan ◽  
El-Sayed M. Sherif
Keyword(s):  
Boundary Layer ◽  
Differential Equations ◽  
Mhd Flow ◽  
Dual Solutions ◽  
Partial Slip ◽  
Shrinking Sheet ◽  
Physical Parameters ◽  
Casson Nanofluid ◽  
Slip Conditions ◽  
Similarity Transformations

In this article, the magnetohydrodynamic (MHD) flow of Casson nanofluid with thermal radiation over an unsteady shrinking surface is investigated. The equation of momentum is derived from the Navier–Stokes model for non-Newtonian fluid where components of the viscous terms are symmetric. The effect of Stefan blowing with partial slip conditions of velocity, concentration, and temperature on the velocity, concentration, and temperature distributions is also taken into account. The modeled equations of partial differential equations (PDEs) are transformed into the equivalent boundary value problems (BVPs) of ordinary differential equations (ODEs) by employing similarity transformations. These similarity transformations can be obtained by using symmetry analysis. The resultant BVPs are reduced into initial value problems (IVPs) by using the shooting method and then solved by using the fourth-order Runge–Kutta (RK) technique. The numerical results reveal that dual solutions exist in some ranges of different physical parameters such as unsteadiness and suction/injection parameters. The thickness of the velocity boundary layer is enhanced in the second solution by increasing the magnetic and velocity slip factor effect in the boundary layer. Increment in the Prandtl number and Brownian motion parameter is caused by a reduction of the thickness of the thermal boundary layer and temperature. Moreover, stability analysis performed by employing the three-stage Lobatto IIIA formula in the BVP4C solver with the help of MATLAB software reveals that only the first solution is stable and physically realizable.

scholarly journals A Numerical Exploration of Modified Second-Grade Nanofluid with Motile Microorganisms, Thermal Radiation, and Wu’s Slip

Symmetry ◽  
2020 ◽  
Vol 12 (3) ◽  
pp. 393 ◽  
Author(s):  
Yurong Li ◽  
Hassan Waqas ◽  
Muhammad Imran ◽  
Umar Farooq ◽  
Fouad Mallawi ◽  
...  
Keyword(s):  
Differential Equations ◽  
Thermal Radiation ◽  
Volume Fraction ◽  
Thermal Characteristics ◽  
Second Grade ◽  
Physical Parameters ◽  
Flux Boundary Condition ◽  
Shooting Technique ◽  
Automobile Engines ◽  
Nanoparticles Concentration

This study is carried out to scrutinize the gyrotactic bioconvection effects on modified second-grade nanofluid with motile microorganisms and Wu’s slip (second-order slip) features. The activation energy and thermal radiation are also incorporated. The suspended nanoparticles in a host fluid are practically utilized in numerous technological and industrial products such as metallic strips, energy enhancement, production processes, automobile engines, laptops, and accessories. Nanoparticles with high thermal characteristics and low volume fraction may improve the thermal performance of the base fluid. By employing the appropriate self-similar transformations, the governing set of partial differential equations (PDEs) are reduced into the ordinary differential equations (ODEs). A zero mass flux boundary condition is proposed for nanoparticle diffusion. Then, the transmuted set of ODEs is solved numerically with the help of the well-known shooting technique. The numerical and graphical illustrations are developed by using a collocation finite difference scheme and three-stage Lobatto III as the built-in function of the bvp4c solver via MATLAB. Behaviors of the different proficient physical parameters on the velocity field, temperature distribution, volumetric nanoparticles concentration profile, and the density of motile microorganism field are deliberated numerically as well as graphically.

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