Mixed Convection Boundary Layer Flow of Williamson Fluid with Slip Conditions Over a Stretching Cylinder by Using Keller Box Method

2017 ◽  
Vol 18 (1) ◽  
pp. 9-17 ◽  
Author(s):  
T. Salahuddin ◽  
M. Y. Malik ◽  
Arif Hussain ◽  
M. Awais ◽  
S. Bilal
Keyword(s):  
Boundary Layer ◽  
Differential Equations ◽  
Mixed Convection ◽  
Ordinary Differential Equations ◽  
Convection Flow ◽  
Physical Parameters ◽  
Stretching Cylinder ◽  
Williamson Fluid ◽  
Keller Box Method ◽  
Box Method

AbstractThe aim of the present analysis is to examine the effects of slip boundary conditions and mixed convection flow of Williamson fluid over a stretching cylinder. The boundary layer partial differential equations are transformed into ordinary differential equations by using group theory transformations. The required ordinary differential equations are solved numerically by using implicit finite difference method known as Keller box method. The influence of dimensionless physical parameters on velocity and temperature profile as well as skin friction coefficient and local Nusselt number are presented graphically. Comparison has been made to the previous literature in order to check the accuracy of the method.

scholarly journals Separation time analysis of transient magnetohydrodynamic mixed convection flow of nanofluid at lower stagnation point past a sphere

2017 ◽  
Vol 13 (3) ◽  
Author(s):  
Mohamad Alif Ismail ◽  
Nurul Farahain Mohammad ◽  
Sharidan Shafie
Keyword(s):  
Boundary Layer ◽  
Differential Equations ◽  
Mixed Convection ◽  
Stagnation Point ◽  
Magnetic Particles ◽  
Volume Fraction ◽  
Convection Flow ◽  
Mixed Convection Flow ◽  
Boundary Layer Equations ◽  
Keller Box Method

In this paper, the unsteady magnetohydrodynamics (MHD) mixed convection flow of nanofluid at lower stagnation point past a sphere is studied. Nanoparticles Cu and TiO2 with water as a base fluid are considered. The separation times of the flow as the boundary layer start to separate at the surface of the sphere are given attention. The governing boundary layer equations in the form of partial differential equations are transformed into nonlinear coupled ordinary differential equations and solved numerically using an implicit finite-difference scheme known as Keller-box method. Results of the separation times of boundary layer flow for viscous and nanofluid influenced by magnetic parameter and volume fraction are shown in tabular form and analysed. This study concluded that the separation times can be delayed by added more magnetic particles and small amount the volume fraction.

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].

g-Jitter Induced Mixed Convection Flow of Heat and Mass Transfer Past an Inclined Stretching Sheet

2014 ◽  
Vol 71 (1) ◽  
Author(s):  
Noraihan Afiqah Rawi ◽  
Abdul Rahman Mohd Kasim ◽  
Mukheta Isa ◽  
Sharidan Shafie
Keyword(s):  
Mass Transfer ◽  
Differential Equations ◽  
Mixed Convection ◽  
Heat And Mass Transfer ◽  
Stretching Sheet ◽  
Convection Flow ◽  
Convection Boundary Layer ◽  
Keller Box Method ◽  
Unsteady Mixed Convection ◽  
Layer Flow

This paper studies unsteady mixed convection boundary layer flow of heat and mass transfer past an inclined stretching sheet associated with the effect of periodical gravity modulation or g-jitter. The temperature and concentration are assumed to vary linearly with x, where x is the distance along the plate. The governing partial differential equations are transformed to a set of coupled ordinary differential equations using non-similarity transformation and solved numerically by Keller-box method. Numerical results for velocity, temperature and concentration profiles as well as skin friction, Nusselt number and Sherwood number are presented and analyzed for different values of inclination angle parameter.

scholarly journals Numerical investigation of mixed convection boundary layer flow for nanofluids under quasilinearization technique

2021 ◽  
Vol 3 (11) ◽  
Author(s):  
Srimanta Maji ◽  
Akshaya K. Sahu
Keyword(s):  
Heat Transfer ◽  
Boundary Layer ◽  
Differential Equations ◽  
Mixed Convection ◽  
Boundary Layer Flow ◽  
Dual Solutions ◽  
Nonlinear Pdes ◽  
Convection Boundary Layer ◽  
Physical Parameters ◽  
Layer Flow

AbstractThe study of boundary layer flow under mixed convection has been investigated numerically for various nanofluids over a semi-infinite flat plate which has been placed vertically upward for both buoyancy-induced assisting and buoyancy-induced opposing flow cases. To facilitate numerical calculations, a suitable transformation has been made for the governing partial differential equations (PDEs). Then, similarity method has been applied locally to approximate the nonlinear PDEs into a coupled nonlinear ordinary differential equations (ODEs). Then, quasilinearization method has been taken for linearizing the nonlinear terms which are present in the governing equations. Thereafter, implicit trapezoidal rule has been taken for integration numerically along with principle of superposition. The effect of physical parameters which are involved in the study are analyzed on the flow and heat transfer characteristics. This study reveals the presence of dual solutions in case of opposing flow. Further, this study shows that with increasing $$\phi$$ ϕ and Pr, the range of existence of dual solutions becomes wider. Also, it has been noted that nanofluids enhance the process of heat transfer for buoyancy assisting flow and it delays the separation point in case of opposing flow.

scholarly journals Mixed convection flow of Jeffrey fluid along an inclined stretching cylinder with double stratification effect

2017 ◽  
Vol 21 (2) ◽  
pp. 849-862 ◽  
Author(s):  
Tasawar Hayat ◽  
Sajid Qayyum ◽  
Muhammad Farooq ◽  
Ahmad Alsaedi ◽  
Muhammad Ayub
Keyword(s):  
Differential Equations ◽  
Mixed Convection ◽  
Variable Temperature ◽  
Heat Transfer Analysis ◽  
Convection Flow ◽  
Jeffrey Fluid ◽  
Convection Boundary Layer ◽  
Stretching Cylinder ◽  
Double Stratification ◽  
Non Linear

This paper addresses double stratified mixed convection boundary layer flow of Jeffrey fluid due to an impermeable inclined stretching cylinder. Heat transfer analysis is carried out with heat generation/absorption. Variable temperature and concentration are assumed at the surface of cylinder and ambient fluid. Non-linear partial differential equations are reduced into the non-linear ordinary differential equations after using the suitable transformations. Convergent series solutions are computed. Effects of various pertinent parameters on the velocity, temperature, and concentration distributions are analyzed graphically. Numerical values of skin friction coefficient, Nusselt, and Sherwood numbers are also computed and discussed.

scholarly journals On Mixed Convection Squeezing Flow of Nanofluids

Energies ◽  
2020 ◽  
Vol 13 (12) ◽  
pp. 3138 ◽  
Author(s):  
Sheikh Irfan Ullah Khan ◽  
Ebraheem Alzahrani ◽  
Umar Khan ◽  
Noreena Zeb ◽  
Anwar Zeb
Keyword(s):  
Nonlinear System ◽  
Differential Equations ◽  
Mixed Convection ◽  
Ordinary Differential Equations ◽  
Volume Fraction ◽  
Squeezing Flow ◽  
Physical Parameters ◽  
Gamma Alumina ◽  
Highly Nonlinear ◽  
The Impact

In this article, the impact of effective Prandtl number model on 3D incompressible flow in a rotating channel is proposed under the influence of mixed convection. The coupled nonlinear system of partial differential equations is decomposed into a highly nonlinear system of ordinary differential equations with aid of suitable similarity transforms. Then, the solution of a nonlinear system of ordinary differential equations is obtained numerically by using Runge–Kutta–Fehlberg (RKF) method. Furthermore, the surface drag force C f and the rate of heat transfer N u are portrayed numerically. The effects of different emerging physical parameters such as Hartmann number (M), Reynold’s number (Re), squeezing parameter ( β ), mixed convection parameter λ , and volume fraction ( φ ) are also incorporated graphically for γ — alumina. Due to the higher viscosity and thermal conductivity ethylene-based nanofluids, it is observed to be an effective common base fluid as compared to water. These observations portrayed the temperature of gamma-alumina ethylene-based nanofluids rising on gamma-alumina water based nanofluids.

scholarly journals Thermal radiation and magnetic field effects on unsteady mixed convection flow and mass transfer over a porous stretching surface with heat generation

2013 ◽  
Vol 18 (4) ◽  
pp. 1151-1164 ◽  
Author(s):  
G.V.R. Reddy ◽  
B.A. Reddy ◽  
N.B. Reddy
Keyword(s):  
Mass Transfer ◽  
Differential Equations ◽  
Mixed Convection ◽  
Thermal Radiation ◽  
Heat Generation ◽  
Convection Flow ◽  
Physical Parameters ◽  
Mixed Convection Flow ◽  
Stretching Surface ◽  
Porous Stretching Surface

Abstract The effects of thermal radiation and mass transfer on an unsteady hydromagnetic boundary layer mixed convection flow along a vertical porous stretching surface with heat generation are studied. The fluid is assumed to be viscous and incompressible. The governing partial differential equations are transformed into a system of ordinary differential equations using similarity variables. Numerical solutions of these equations are obtained by using the Runge-Kutta fourth order method along with the shooting technique. Velocity, temperature, concentration, the skin-friction coefficient, Nusselt number and Sherwood number for variations in the governing thermo physical parameters are computed, analyzed and discussed.

scholarly journals Homogeneous-heterogeneous reactions in Williamson fluid model over a stretching cylinder by using Keller box method

AIP Advances ◽  
2015 ◽  
Vol 5 (10) ◽  
pp. 107227 ◽  
Author(s):  
M. Y. Malik ◽  
T. Salahuddin ◽  
Arif Hussain ◽  
S. Bilal ◽  
M. Awais
Keyword(s):  
Fluid Model ◽  
Heterogeneous Reactions ◽  
Stretching Cylinder ◽  
Williamson Fluid ◽  
Keller Box Method ◽  
Box Method

scholarly journals BOUNDARY LAYER FLOW AND HEAT TRANSFER WITH VARIABLE VISCOSITY IN THE PRESENCE OF MAGNETIC FIELD

2016 ◽  
Vol 12 (7) ◽  
pp. 6412-6421
Author(s):  
Ajala O.A ◽  
Aseelebe L. O ◽  
Ogunwobi Z. O
Keyword(s):  
Heat Transfer ◽  
Boundary Layer ◽  
Differential Equations ◽  
Ordinary Differential Equations ◽  
Boundary Layer Flow ◽  
Variable Viscosity ◽  
Physical Parameters ◽  
Flow And Heat Transfer ◽  
Dimensional Boundary ◽  
Layer Flow

A steady two dimensional boundary layer flow and heat transfer with variable viscosity electrically conducting fluid at T in the presence of magnetic fields and thermal radiation was considered. The governing equations which are partial differential equations were transformed into ordinary differential equations using similarity variables, and the resulting coupled ordinary differential equations were solved using collocation method in MAPLE 18. The velocity and temperature profiles were studied graphically for different physical parameters. The effects of the parameters on velocity and temperature profile were showed.

scholarly journals HYDROMAGNETIC MIXED CONVECTION FLOW OF AN EXOTHERMIC FLUID IN A VERTICAL CHANNEL

2019 ◽  
Vol 1 (1) ◽  
pp. 19-37
Author(s):  
Abdulazeez Sheriff ◽  
Murtala Sani
Keyword(s):  
Nusselt Number ◽  
Differential Equations ◽  
Mixed Convection ◽  
Ordinary Differential Equations ◽  
Skin Friction ◽  
Sherwood Number ◽  
Vertical Channel ◽  
Transformation Method ◽  
Convection Flow ◽  
Mixed Convection Flow

In this paper, Hydromagnetic mixed convection flow of an exothermic fluid in a vertical channel is considered. The dimensionless ordinary differential equations were solved using differential transformation method (DTM) to obtain the expression of velocity, temperature and concentration. From momentum, energy and mass equations.  The effect of Skin friction, Nusselt number and Sherwood number with various parameters on velocity, temperature and concentration are presented and discussed. The result indicated that the effect of t, is to increase the Skin friction while K increases it at upper plate and suppresses it at lower plate.

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