The Effect of Suction on the Swirling Flow of Non-Newtonian Fluid

2014 ◽  
Vol 501-504 ◽  
pp. 2081-2084
Author(s):  
Chun Ying Ming ◽  
Lian Cun Zheng ◽  
Xin Xin Zhang
Keyword(s):  
Differential Equations ◽  
Power Law ◽  
Shooting Method ◽  
Numerical Solutions ◽  
Swirling Flow ◽  
Similarity Transformation ◽  
Rotating Disk ◽  
Shear Thinning Fluids ◽  
Suction Or Injection ◽  
Power Law Index

The flow of an incompressible viscous power-law fluid over an infinite rotating disk with uniform suction or injection is studied. The governing differential equations, which are partial and coupled, are simplified to a set of ordinary differential equations by generalized Karman similarity transformation. Numerical solutions of the non-linear two point boundary value problem are obtained by multi-shooting method. The effects of the power-law index and the porous parameter on the velocity fields are discussed for shear thinning fluids.

MHD Flow of Shear-Thinning Fluid over a Rotating Disk with Heat Transfer

2011 ◽  
Vol 130-134 ◽  
pp. 3599-3602
Author(s):  
Chun Ying Ming ◽  
Lian Cun Zheng ◽  
Xin Xin Zhang
Keyword(s):  
Heat Transfer ◽  
Differential Equations ◽  
Power Law ◽  
Swirling Flow ◽  
Mhd Flow ◽  
Rotating Disk ◽  
Electrically Conducting ◽  
Flow And Heat Transfer ◽  
Power Law Index ◽  
Shear Thinning Fluid

This paper studied the Magneto hydrodynamic (MHD) flow and heat transfer of an electrically conducting non-Newtonian fluid over a rotating disk in the presence of a uniform magnetic field. The steady, laminar and axial-symmetric flow is driven solely by the rotating disk, and the incompressible fluid obeys the inelastic Ostwald de-Waele power-law model. The governing differential equations were reduced to a set of ordinary differential equations by utilizing the generalized Karman similarity transformation. The nonlinear two-point boundary value problem is solved by multi-shooting method. Numerical results show that the magnetic parameter and the power-law index have significant effects on the swirling flow and heat transfer.

scholarly journals Impact of autocatalytic chemical reaction in an Ostwald-de-Waele nanofluid flow past a rotating disk with heterogeneous catalysis

2021 ◽  
Vol 11 (1) ◽  
Author(s):  
Bai Yu ◽  
Muhammad Ramzan ◽  
Saima Riasat ◽  
Seifedine Kadry ◽  
Yu-Ming Chu ◽  
...  
Keyword(s):  
Heat Transfer ◽  
Thermal Conductivity ◽  
Differential Equations ◽  
Chemical Reaction ◽  
Power Law ◽  
Variable Thickness ◽  
Rotating Disk ◽  
Thermal Profile ◽  
Nanofluid Flow ◽  
Power Law Index

AbstractThe nanofluids owing to their alluring attributes like enhanced thermal conductivity and better heat transfer characteristics have a vast variety of applications ranging from space technology to nuclear reactors etc. The present study highlights the Ostwald-de-Waele nanofluid flow past a rotating disk of variable thickness in a porous medium with a melting heat transfer phenomenon. The surface catalyzed reaction is added to the homogeneous-heterogeneous reaction that triggers the rate of the chemical reaction. The added feature of the variable thermal conductivity and the viscosity instead of their constant values also boosts the novelty of the undertaken problem. The modeled problem is erected in the form of a system of partial differential equations. Engaging similarity transformation, the set of ordinary differential equations are obtained. The coupled equations are numerically solved by using the bvp4c built-in MATLAB function. The drag coefficient and Nusselt number are plotted for arising parameters. The results revealed that increasing surface catalyzed parameter causes a decline in thermal profile more efficiently. Further, the power-law index is more influential than the variable thickness disk index. The numerical results show that variations in dimensionless thickness coefficient do not make any effect. However, increasing power-law index causing an upsurge in radial, axial, tangential, velocities, and thermal profile.

Inflow Conditions and Suddenly Expanding Annular Shear-Thinning Flows

2017 ◽  
Author(s):  
Khaled J. Hammad
Keyword(s):  
Power Law ◽  
Numerical Solutions ◽  
Shear Thinning ◽  
Diameter Ratio ◽  
Inflow Velocity ◽  
Flow Recirculation ◽  
Shear Thinning Fluids ◽  
Power Law Index ◽  
The Impact ◽  
Inflow Conditions

The impact of inflow conditions on the flow structure and evolution characteristics of annular flows of Newtonian and shear-thinning fluids through a sudden pipe expansion are studied. Numerical solutions to the elliptic form of the governing equations along with the power-law constitutive equation were obtained using a finite-difference scheme. A parametric study is performed to reveal the influence of inflow velocity profiles, annular diameter ratio, k, and power-law index, n, over the following range of parameters: inflow velocity profile = {fully-developed, uniform}, k = {0, 0.5, 0.7} and n = {1, 0.8, 0.6}. Flow separation and entrainment, downstream of the expansion plane, creates central and a much larger outer recirculation regions. The results demonstrate the influence of inflow conditions, annular diameter ratio, and rheology on the extent and intensity of both flow recirculation regions, the wall shear stress distribution, and the evolution and redevelopment characteristics of the flow downstream the expansion plane. Fully-developed inflows result in larger reattachment and redevelopment lengths as well as more intense recirculation, within the central and corner regions, in comparison with uniform inflow conditions.

scholarly journals Flow and Heat Transfer at a Nonlinearly Shrinking Porous Sheet:The Case of Asymptotically Large Powerlaw Shrinking Rates

2013 ◽  
Vol 18 (3) ◽  
pp. 779-791 ◽  
Author(s):  
K.V. Prasad ◽  
K. Vajravelu ◽  
I. Pop
Keyword(s):  
Heat Transfer ◽  
Differential Equations ◽  
Power Law ◽  
Numerical Solutions ◽  
Skin Friction Coefficient ◽  
Temperature Fields ◽  
Shrinking Sheet ◽  
Arbitrary Power ◽  
Keller Box Method ◽  
Flow And Heat Transfer

Abstract The boundary layer flow and heat transfer of a viscous fluid over a nonlinear permeable shrinking sheet in a thermally stratified environment is considered. The sheet is assumed to shrink in its own plane with an arbitrary power-law velocity proportional to the distance from the stagnation point. The governing differential equations are first transformed into ordinary differential equations by introducing a new similarity transformation. This is different from the transform commonly used in the literature in that it permits numerical solutions even for asymptotically large values of the power-law index, m. The coupled non-linear boundary value problem is solved numerically by an implicit finite difference scheme known as the Keller- Box method. Numerical computations are performed for a wide variety of power-law parameters (1 < m < 100,000) so as to capture the effects of the thermally stratified environment on the velocity and temperature fields. The numerical solutions are presented through a number of graphs and tables. Numerical results for the skin-friction coefficient and the Nusselt number are tabulated for various values of the pertinent parameters.

scholarly journals A note on the non-inertial similarity solution for von Kármán swirling flow

2020 ◽  
pp. 2150030
Author(s):  
Madeleine L. Combrinck
Keyword(s):  
Boundary Layer ◽  
Partial Differential Equations ◽  
Differential Equations ◽  
Ordinary Differential Equations ◽  
Similarity Solution ◽  
Shooting Method ◽  
Swirling Flow ◽  
Boundary Layer Equations ◽  
Von Karman ◽  
Von Kármán

This note proposes a non-inertial similarity solution for the classic von Kármán swirling flow as perceived from the rotational frame. The solution is obtained by implementing non-inertial similarity parameters in the non-inertial boundary layer equations. This reduces the partial differential equations to a set of ordinary differential equations that is solved through an integration routine and shooting method.

scholarly journals Finite-Energy Dressed String-Inspired Dirac-Like Monopoles

Universe ◽  
2018 ◽  
Vol 5 (1) ◽  
pp. 8 ◽  
Author(s):  
Nikolaos E. Mavromatos ◽  
Sarben Sarkar
Keyword(s):  
Differential Equations ◽  
Shooting Method ◽  
Numerical Solutions ◽  
Nonlinear Differential Equations ◽  
Finite Energy ◽  
Spherically Symmetric ◽  
New Class ◽  
The Standard Model ◽  
Monopole Solution ◽  
Asymptotic Analyses

On extending the Standard Model (SM) Lagrangian, through a non-linear Born–Infeld (BI) hypercharge term with a parameter β (of dimensions of [mass] 2 ), a finite energy monopole solution was claimed by Arunasalam and Kobakhidze. We report on a new class of solutions within this framework that was missed in the earlier analysis. This new class was discovered on performing consistent analytic asymptotic analyses of the nonlinear differential equations describing the model; the shooting method used in numerical solutions to boundary value problems for ordinary differential equations is replaced in our approach by a method that uses diagonal Padé approximants. Our work uses the ansatz proposed by Cho and Maison to generate a static and spherically-symmetric monopole with finite energy and differs from that used in the solution of Arunasalam and Kobakhidze. Estimates of the total energy of the monopole are given, and detection prospects at colliders are briefly discussed.

Coupled flow and heat transfer of power-law Nanofluids on a non-isothermal rough rotary disk subject to magnetic field

2021 ◽  
Author(s):  
Yunxian Pei ◽  
Xuelan Zhang ◽  
Liancun Zheng ◽  
Xinzi Wang
Keyword(s):  
Magnetic Field ◽  
Heat Transfer ◽  
Power Law ◽  
Numerical Solutions ◽  
Volume Fraction ◽  
Rotating Disk ◽  
Coupled Flow ◽  
Friction Coefficients ◽  
Nanoparticle Shape ◽  
Flow And Heat Transfer

Abstract In this paper, we study coupled flow and heat transfer of power-law nanofluids on a non-isothermal rough rotating disk subject to a magnetic field. The problem is formulated in terms of specified curvilinear orthogonal coordinate system. An improved BVP4C algorithm is proposed and numerical solutions are obtained. The influence of volume fraction, types and shapes of nanoparticles, magnetic field and power-law index on the flow and heat transfer behavior are discussed.<br/>Results show that the power-law exponents (PLE), nanoparticle volume fraction (NVF) and magnetic field inclination angle (MFIA) are almost no effects on velocities in wave surface direction, but have small or significant effects on azimuth direction. NVF have remarkable influence on local Nusselt number (LNN) and friction coefficients (FC) in radial and azimuth directions (AD). LNN increases with NVF while FC in AD decrease. The types of nanoparticles, magnetic field strength and inclination have small effects on LNN, but they have remarkable effects on the friction coefficients with positively correlated while the inclination is negatively correlated with heat transfer rate. The size of the nanoparticle shape factor is positively correlated with LNN.

Magnetohydrodynamics Thermocapillary Marangoni Convection Heat Transfer of Power-Law Fluids Driven by Temperature Gradient

2013 ◽  
Vol 135 (5) ◽  
Author(s):  
Yanhai Lin ◽  
Liancun Zheng ◽  
Xinxin Zhang
Keyword(s):  
Heat Transfer ◽  
Temperature Gradient ◽  
Differential Equations ◽  
Power Law ◽  
Numerical Solutions ◽  
Marangoni Convection ◽  
Convection Heat Transfer ◽  
Temperature Fields ◽  
Convection Heat ◽  
Power Law Fluids

This paper presents an investigation for magnetohydrodynamics (MHD) thermocapillary Marangoni convection heat transfer of an electrically conducting power-law fluid driven by temperature gradient. The surface tension is assumed to vary linearly with temperature and the effects of power-law viscosity on temperature fields are taken into account by modified Fourier law for power-law fluids (proposed by Pop). The governing partial differential equations are converted into ordinary differential equations and numerical solutions are presented. The effects of the Hartmann number, the power-law index and the Marangoni number on the velocity and temperature fields are discussed and analyzed in detail.

scholarly journals Serious Solutions for Unsteady Axisymmetric Flow over a Rotating Stretchable Disk with Deceleration

Symmetry ◽  
2020 ◽  
Vol 12 (1) ◽  
pp. 96 ◽  
Author(s):  
Sadiq
Keyword(s):  
Differential Equations ◽  
Numerical Solutions ◽  
Similarity Transformation ◽  
Nonlinear Partial Differential Equations ◽  
Axisymmetric Flow ◽  
Analysis Method ◽  
Highly Nonlinear ◽  
Homotopy Analysis ◽  
Rotating Stretchable Disk ◽  
Comparison Table

In this article, the author has examined the unsteady flow over a rotating stretchable disk with deceleration. The highly nonlinear partial differential equations of viscous fluid are simplified by existing similarity transformation. Reduced nonlinear ordinary differential equations are solved by homotopy analysis method (HAM). The convergence of HAM solutions is also obtained. A comparison table between analytical solutions and numerical solutions is also presented. Finally, the results for useful parameters, i.e., disk stretching parameters and unsteadiness parameters, are found.

Study of micropolar nanofluids with power-law spin gradient viscosity model by the Keller box method

2020 ◽  
Vol 98 (1) ◽  
pp. 16-27
Author(s):  
N. Akmal ◽  
M. Sagheer ◽  
S. Hussain ◽  
A. Kamran
Keyword(s):  
Brownian Motion ◽  
Differential Equations ◽  
Prandtl Number ◽  
Power Law ◽  
Nonlinear Partial Differential Equations ◽  
Shear Thickening ◽  
Lewis Number ◽  
Keller Box Method ◽  
Box Method ◽  
Power Law Index

The spin gradient viscosity with power-law model and its representation of the heat transfer capabilities of nanofluids have been examined. The theoretical analysis provides an insight into the heat conduction properties of shear-thinning and the shear-thickening fluids. Boundary-layer-approximation-based nonlinear partial differential equations are transformed into nonlinear ordinary differential equations before their solution is approximated by the finite-difference-based Keller box method. The results demonstrate that the heat exchange in nanofluids is affected substantially by the index exponent and the modified material parameter. In addition, the physical quantities of interest from the engineering perspective, the Nusselt and the Sherwood numbers, are calculated to examine the heat and mass transport efficiency of the nanofluids. It is discovered that the temperature profile augments with an increase in the Brownian motion and thermophoresis parameters and decreases with an increase in the Prandtl number and power-law index. However, the concentration deceases with a rise in the Brownian motion parameter and Lewis number, but increases with an increase in the thermophoresis parameter, Prandtl number, and the power-law index.

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