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.

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.

MHD Flow of Non-Newtonian Molybdenum Disulfide Nanofluid in a Converging/Diverging Channel with Rosseland Radiation

2020 ◽  
Vol 401 ◽  
pp. 92-106 ◽  
Author(s):  
J. Raza ◽  
Fateh Mebarek-Oudina ◽  
Paras Ram ◽  
S. Sharma
Keyword(s):  
Differential Equations ◽  
Thermal Radiation ◽  
Molybdenum Disulfide ◽  
Hartmann Number ◽  
Volume Fraction ◽  
Solid Volume Fraction ◽  
Mhd Flow ◽  
Opening Angle ◽  
Physical Parameters ◽  
Two Dimensional Flow

The steady two-dimensional flow of an incompressible non-Newtonian Molybdenum Disulfide nanofluid in the presence of source or sink between two stretchable or shrinkable walls under the influence of thermal radiation is investigated numerically. A generalized transformation is applied to convert the constructed set of partial differential equations (PDEs) into the system of non-linear coupled ordinary differential equations (ODEs). The obtained system of ODEs are solved by using Runge-Kutta 4th and 5th order. The influence of physical parameters, shrinking/ stretching parameter, Casson parameter, Hartmann number, Reynolds number, solid volume fraction, opening angle of the channel and radiation parameter on the velocity and temperature distribution are observed for converging and diverging channels. It is noticed that thermal boundary layer thickness is diminished for increased thermal radiation resulting in gradual temperature fall. The results also reveal that velocity and temperature profile both are elevated on raising the stretching parameter and Hartmann number. A comparative analysis is made out to validate the present results.

scholarly journals Numerical Simulation of Heat Transfer Flow Subject to MHD of Williamson Nanofluid with Thermal Radiation

Symmetry ◽  
2020 ◽  
Vol 13 (1) ◽  
pp. 10
Author(s):  
Muhammad Amer Qureshi
Keyword(s):  
Heat Transfer ◽  
Differential Equations ◽  
Thermal Radiation ◽  
Single Phase ◽  
Physical Parameters ◽  
Fundamental Symmetry ◽  
Box Scheme ◽  
Mhd Boundary Layer ◽  
Slippery Surface ◽  
Transfer Flow

In this paper, heat transfer and entropy of steady Williamson nanofluid flow based on the fundamental symmetry is studied. The fluid is positioned over a stretched flat surface moving non-uniformly. Nanofluid is analyzed for its flow and thermal transport properties by consigning it to a convectively heated slippery surface. Thermal conductivity is assumed to be varied with temperature impacted by thermal radiation along with axisymmetric magnetohydrodynamics (MHD). Boundary layer approximations lead to partial differential equations, which are transformed into ordinary differential equations in light of a single phase model accounting for Cu-water and TiO2-water nanofluids. The resulting ODEs are solved via a finite difference based Keller box scheme. Various formidable physical parameters affecting fluid movement, difference in temperature, system entropy, skin friction and Nusselt number around the boundary are presented graphically and numerically discussed. It has also been observed that the nanofluid based on Cu-water is identified as a superior thermal conductor rather than TiO2-water based nanofluid.

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.

Similarity solution of second grade fluid flow over a moving cylinder

2021 ◽  
Author(s):  
Nadeem Abbas ◽  
M. Y. Malik ◽  
Sohail Nadeem ◽  
Shafiq Hussain ◽  
A. S. El-Shafa
Keyword(s):  
Boundary Layer ◽  
Fluid Flow ◽  
Differential Equations ◽  
Material Parameter ◽  
Second Grade ◽  
Physical Parameters ◽  
Stretching Cylinder ◽  
Second Grade Fluid ◽  
Moving Cylinder ◽  
Grade Fluid

Stagnation point flow of viscoelastic second grade fluid over a stretching cylinder under the thermal slip and magnetic hydrodynamics effects are studied. The mathematical model has been developed under the assumption of non-Newtonian viscoelastic fluid flow over a stretching cylinder by means of the boundary layer approximations. The developed model further reduced through the similarity transformations and constructs the model of nonlinear ordinary differential equations. The system of nonlinear differential equations is dimensionless and solved through the numerical technique bvp5c methods. The results of the physical parameters are found and interpreted in the form of tables and graphs. The velocity shows that the graph of curves enhances away from the surface when the values material parameter [Formula: see text] increase, which means the momentum boundary layer increases for enhancing the material parameter [Formula: see text]. The temperature gradient reduced due enhancing the values of material parameter [Formula: see text] because thermal boundary layer reduced for higher values of material parameter [Formula: see text].

scholarly journals Unsteady flow over an expanding cylinder in a nanofluid containing gyrotactic microorganisms

2016 ◽  
Vol 94 (5) ◽  
pp. 466-473 ◽  
Author(s):  
Hui Chen ◽  
Hongxing Liang ◽  
Tianli Xiao ◽  
Heng Du ◽  
Ming Shen
Keyword(s):  
Differential Equations ◽  
Unsteady Flow ◽  
Shooting Method ◽  
Schmidt Number ◽  
Volume Fraction ◽  
Dual Solutions ◽  
Physical Parameters ◽  
Gyrotactic Microorganisms ◽  
Similarity Transformations ◽  
Fifth Order

In this paper, an analysis is made for the unsteady flow due to an expanding cylinder in a nanofluid that contains both nanoparticles and gyrotactic microoganisms with suction. The nonlinear system of partial differential equations is transformed into high-order nonlinear ordinary differential equations using similarity transformations, and then solved numerically using a shooting method with fourth-fifth-order Runge–Kutta integration technique. The influences of significant physical parameters on the distributions of the velocity, temperature, nanoparticle volume fraction, as well as the density of motile microorganisms are graphically presented and discussed in detail. It is found that dual solutions exist for both stretching and shrinking cases and the range of dual solutions increases with the strength of the expansion. The results also indicate that larger bioconvection Peclet number and smaller Schmidt number lead to an increased concentration of microorganisms and thicker boundary layer thickness.

scholarly journals Analytical Modelling of Three-Dimensional Squeezing Nanofluid Flow in a Rotating Channel on a Lower Stretching Porous Wall

2014 ◽  
Vol 2014 ◽  
pp. 1-14 ◽  
Author(s):  
Navid Freidoonimehr ◽  
Behnam Rostami ◽  
Mohammad Mehdi Rashidi ◽  
Ebrahim Momoniat
Keyword(s):  
Differential Equations ◽  
Ordinary Differential Equations ◽  
Volume Fraction ◽  
Three Dimensional ◽  
Porous Wall ◽  
Coupled System ◽  
Physical Parameters ◽  
Nonlinear Ordinary Differential Equations ◽  
Suction Parameter ◽  
Rotating Channel

A coupled system of nonlinear ordinary differential equations that models the three-dimensional flow of a nanofluid in a rotating channel on a lower permeable stretching porous wall is derived. The mathematical equations are derived from the Navier-Stokes equations where the governing equations are normalized by suitable similarity transformations. The fluid in the rotating channel is water that contains different nanoparticles: silver, copper, copper oxide, titanium oxide, and aluminum oxide. The differential transform method (DTM) is employed to solve the coupled system of nonlinear ordinary differential equations. The effects of the following physical parameters on the flow are investigated: characteristic parameter of the flow, rotation parameter, the magnetic parameter, nanoparticle volume fraction, the suction parameter, and different types of nanoparticles. Results are illustrated graphically and discussed in detail.

scholarly journals An MHD Fluid Flow over a Porous Stretching/Shrinking Sheet with Slips and Mass Transpiration

Micromachines ◽  
2022 ◽  
Vol 13 (1) ◽  
pp. 116
Author(s):  
A. B. Vishalakshi ◽  
U. S. Mahabaleshwar ◽  
Ioannis E. Sarris
Keyword(s):  
Fluid Flow ◽  
Prandtl Number ◽  
Thermal Radiation ◽  
Biot Number ◽  
Volume Fraction ◽  
Heat Transfer Analysis ◽  
Shrinking Sheet ◽  
Physical Parameters ◽  
Graphical Representations ◽  
Analytical Results

In the present paper, an MHD three-dimensional non-Newtonian fluid flow over a porous stretching/shrinking sheet in the presence of mass transpiration and thermal radiation is examined. This problem mainly focusses on an analytical solution; graphene water is immersed in the flow of a fluid to enhance the thermal efficiency. The given non-linear PDEs are mapped into ODEs via suitable transformations, then the solution is obtained in terms of incomplete gamma function. The momentum equation is analyzed, and to derive the mass transpiration analytically, this mass transpiration is used in the heat transfer analysis and to find the analytical results with a Biot number. Physical significance parameters, including volume fraction, skin friction, mass transpiration, and thermal radiation, can be analyzed with the help of graphical representations. We indicate the unique solution at stretching sheet and multiple solution at shrinking sheet. The physical scenario can be understood with the help of different physical parameters, namely a Biot number, magnetic parameter, inverse Darcy number, Prandtl number, and thermal radiation; these physical parameters control the analytical results. Graphene nanoparticles are used to analyze the present study, and the value of the Prandtl number is fixed to 6.2. The graphical representations help to discuss the results of the present work. This problem is used in many industrial applications such as Polymer extrusion, paper production, metal cooling, glass blowing, etc. At the end of this work, we found that the velocity and temperature profile increases with the increasing values of the viscoelastic parameter and solid volume fraction; additionally, efficiency is increased for higher values of thermal radiation.

scholarly journals Dual Solutions in the Boundary Layer Flow and Heat Transfer in the Presence of Thermal Radiation with Suction Effect

2018 ◽  
Vol 7 (4.33) ◽  
pp. 17
Author(s):  
Siti Nur Aisyah Azeman ◽  
. .
Keyword(s):  
Heat Transfer ◽  
Boundary Layer ◽  
Differential Equations ◽  
Thermal Radiation ◽  
Boundary Layer Flow ◽  
Numerical Solutions ◽  
Dual Solutions ◽  
Shooting Technique ◽  
Flow And Heat Transfer ◽  
Layer Flow

The dual solutions in the boundary layer flow and heat transfer in the presence of thermal radiation is quantitatively studied. The governing partial differential equations are derived into a system of ordinary differential equations using a similarity transformation, and afterward numerical solution obtained by a shooting technique. Dual solutions execute within a certain range of opposing and assisting flow which related to these numerical solutions. The similarity equations have two branches, upper or lower branch solutions, within a certain range of the mixed convection parameters. Further numerical results exist in our observations which enable to discuss the features of the respective solutions.  

scholarly journals Mixed Convection of a Radiating Magnetic Nanofluid past a Heated Permeable Stretching/Shrinking Sheet in a Porous Medium

2021 ◽  
Vol 2021 ◽  
pp. 1-21
Author(s):  
Feleke Buta Tadesse ◽  
Oluwole Daniel Makinde ◽  
Lemi Guta Enyadene
Keyword(s):  
Magnetic Field ◽  
Porous Medium ◽  
Differential Equations ◽  
Thermal Radiation ◽  
Skin Friction ◽  
Volume Fraction ◽  
Flow Stability ◽  
Collective Effects ◽  
Shrinking Sheet ◽  
Convective Heating

This paper analyzes the collective effects of buoyancy force, thermal radiation, convective heating, and magnetic field on stagnation point flow of an electrically conducting nanofluid past a permeable stretching/shrinking sheet in a porous medium. Similarity transformations are used on the resulting nonlinear partial differential equations to transfer into a system of coupled nonlinear ordinary differential equations. The fourth-fifth-order Runge–Kutta–Fehlberg method with shooting technique is applied to solve numerically. Results are obtained for dimensionless velocity, temperature, and nanoparticle volume fraction as well as the skin friction and local Nusselt and Sherwood numbers. The results indicate the existence of two real solutions for the shrinking sheet in the range of λ c < λ < 0 . The fluid flow stability is maintained by increasing the magnetic field effect, whereas the porous medium parameter inflates the flow stability. It is also noted that both the skin friction coefficient and the local Sherwood number approximately decline with the intensification of thermal radiation within the range from 9.83% to 14% and the range from 48.86% to 78.66%, respectively. It is also evident in the present work that the local Nusselt number upsurges with the porous and suction/injection parameters.

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